%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP038^1 : 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 : n019.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 08:55:03 AM UTC 2026
% Result : Theorem 4.15s 2.03s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 64 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 133 ( 10 ~; 5 |; 0 &; 114 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 45 ( 44 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 171 ( 168 usr; 15 con; 0-10 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
denota610675952t_unit: $tType ).
thf(type_def_7,type,
trm_a_c: $tType ).
thf(type_def_8,type,
trm_sf_sz: $tType ).
thf(type_def_9,type,
set_a: $tType ).
thf(type_def_10,type,
a: $tType ).
thf(type_def_11,type,
produc866628903_sc_sz: $tType ).
thf(type_def_12,type,
set_Pr1169339874_sc_sz: $tType ).
thf(type_def_13,type,
finite824932053eal_sz: $tType ).
thf(type_def_14,type,
real: $tType ).
thf(type_def_15,type,
bounde472938360z_real: $tType ).
thf(type_def_16,type,
denota231621370t_unit: $tType ).
thf(type_def_17,type,
set_Su1783761653um_b_c: $tType ).
thf(type_def_18,type,
produc190496183real_c: $tType ).
thf(type_def_19,type,
set_Sum_sum_c_c: $tType ).
thf(type_def_20,type,
produc1149990247eal_sz: $tType ).
thf(type_def_21,type,
set_Sum_sum_sz_sz: $tType ).
thf(type_def_22,type,
finite1398487019real_c: $tType ).
thf(type_def_23,type,
freche2095075217_sc_sz: $tType ).
thf(type_def_24,type,
frechet_strm_sf_sz: $tType ).
thf(type_def_25,type,
frechet_strm_a_c: $tType ).
thf(type_def_26,type,
freche914690577_a_b_c: $tType ).
thf(type_def_27,type,
sz: $tType ).
thf(type_def_28,type,
sf: $tType ).
thf(type_def_29,type,
sc: $tType ).
thf(type_def_30,type,
produc1065634396_o_a_o: $tType ).
thf(type_def_31,type,
produc903182423_set_a: $tType ).
thf(type_def_32,type,
produc1553439972f_sz_o: $tType ).
thf(type_def_33,type,
product_prod_a_o_a_o: $tType ).
thf(type_def_34,type,
produc1561113620_set_a: $tType ).
thf(type_def_35,type,
produc1241881959eal_sz: $tType ).
thf(type_def_36,type,
produc1144880887f_sz_o: $tType ).
thf(type_def_37,type,
produc1989635468_a_a_o: $tType ).
thf(type_def_38,type,
produc1691597095_set_a: $tType ).
thf(type_def_39,type,
set_Fi291318197eal_sz: $tType ).
thf(type_def_40,type,
set_trm_a_c: $tType ).
thf(type_def_41,type,
set_trm_sf_sz: $tType ).
thf(type_def_42,type,
sum_su737395349um_b_c: $tType ).
thf(type_def_43,type,
produc1892666919z_real: $tType ).
thf(type_def_44,type,
produc1821101996_sc_sz: $tType ).
thf(type_def_45,type,
list_f1238882004_sc_sz: $tType ).
thf(type_def_46,type,
set_De455519194t_unit: $tType ).
thf(type_def_47,type,
set_De208295462t_unit: $tType ).
thf(type_def_48,type,
formula_sf_sc_sz: $tType ).
thf(type_def_49,type,
c: $tType ).
thf(func_def_0,type,
set_Pr1169339874_sc_sz: $tType ).
thf(func_def_1,type,
produc1821101996_sc_sz: $tType ).
thf(func_def_2,type,
produc1892666919z_real: $tType ).
thf(func_def_3,type,
produc1241881959eal_sz: $tType ).
thf(func_def_4,type,
produc1149990247eal_sz: $tType ).
thf(func_def_5,type,
produc190496183real_c: $tType ).
thf(func_def_6,type,
produc866628903_sc_sz: $tType ).
thf(func_def_7,type,
produc1144880887f_sz_o: $tType ).
thf(func_def_8,type,
produc903182423_set_a: $tType ).
thf(func_def_9,type,
produc1553439972f_sz_o: $tType ).
thf(func_def_10,type,
produc1065634396_o_a_o: $tType ).
thf(func_def_11,type,
bounde472938360z_real: $tType ).
thf(func_def_12,type,
set_De208295462t_unit: $tType ).
thf(func_def_13,type,
set_De455519194t_unit: $tType ).
thf(func_def_14,type,
denota610675952t_unit: $tType ).
thf(func_def_15,type,
denota231621370t_unit: $tType ).
thf(func_def_16,type,
set_Su1783761653um_b_c: $tType ).
thf(func_def_17,type,
set_Fi291318197eal_sz: $tType ).
thf(func_def_18,type,
freche2095075217_sc_sz: $tType ).
thf(func_def_19,type,
produc1691597095_set_a: $tType ).
thf(func_def_20,type,
freche914690577_a_b_c: $tType ).
thf(func_def_21,type,
produc1989635468_a_a_o: $tType ).
thf(func_def_22,type,
produc1561113620_set_a: $tType ).
thf(func_def_23,type,
sum_su737395349um_b_c: $tType ).
thf(func_def_24,type,
product_prod_a_o_a_o: $tType ).
thf(func_def_25,type,
finite824932053eal_sz: $tType ).
thf(func_def_26,type,
finite1398487019real_c: $tType ).
thf(func_def_27,type,
list_f1238882004_sc_sz: $tType ).
thf(func_def_28,type,
frechet_strm_sf_sz: $tType ).
thf(func_def_29,type,
set_Sum_sum_sz_sz: $tType ).
thf(func_def_30,type,
frechet_strm_a_c: $tType ).
thf(func_def_31,type,
set_Sum_sum_c_c: $tType ).
thf(func_def_32,type,
set_trm_sf_sz: $tType ).
thf(func_def_33,type,
set_trm_a_c: $tType ).
thf(func_def_34,type,
formula_sf_sc_sz: $tType ).
thf(func_def_35,type,
trm_sf_sz: $tType ).
thf(func_def_36,type,
trm_a_c: $tType ).
thf(func_def_37,type,
set_a: $tType ).
thf(func_def_38,type,
real: $tType ).
thf(func_def_39,type,
sz: $tType ).
thf(func_def_40,type,
sf: $tType ).
thf(func_def_41,type,
sc: $tType ).
thf(func_def_42,type,
c: $tType ).
thf(func_def_43,type,
a: $tType ).
thf(func_def_44,type,
bNF_eq1660582207t_unit: ( denota610675952t_unit > $o ) > denota610675952t_unit > denota610675952t_unit > $o ).
thf(func_def_45,type,
bNF_eq_onp_trm_a_c: ( trm_a_c > $o ) > trm_a_c > trm_a_c > $o ).
thf(func_def_46,type,
bNF_eq_onp_trm_sf_sz: ( trm_sf_sz > $o ) > trm_sf_sz > trm_sf_sz > $o ).
thf(func_def_47,type,
bNF_Gr1775200401_sc_sz: set_a > ( a > denota610675952t_unit ) > ( a > produc866628903_sc_sz ) > set_Pr1169339874_sc_sz ).
thf(func_def_48,type,
bounde397081123z_real: ( finite824932053eal_sz > real ) > bounde472938360z_real ).
thf(func_def_49,type,
denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o ).
thf(func_def_50,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(func_def_51,type,
denota102713844ree_sz: produc1149990247eal_sz > produc1149990247eal_sz > set_Sum_sum_sz_sz > $o ).
thf(func_def_52,type,
denota2112424896_a_b_c: denota231621370t_unit > trm_a_c > produc190496183real_c > real ).
thf(func_def_53,type,
denota453121236_sc_sz: denota610675952t_unit > trm_sf_sz > produc1149990247eal_sz > real ).
thf(func_def_54,type,
denota229585092_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > finite1398487019real_c > real ).
thf(func_def_55,type,
denota1979904720_sc_sz: denota610675952t_unit > trm_sf_sz > finite824932053eal_sz > finite824932053eal_sz > real ).
thf(func_def_56,type,
denota258389581_a_b_c: denota231621370t_unit > $o ).
thf(func_def_57,type,
denota1579475975_sc_sz: denota610675952t_unit > $o ).
thf(func_def_58,type,
denota2042094639_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > real ).
thf(func_def_59,type,
denota1179238309_sc_sz: denota610675952t_unit > trm_sf_sz > finite824932053eal_sz > real ).
thf(func_def_60,type,
freche585307148_sc_sz: freche2095075217_sc_sz > frechet_strm_sf_sz > finite824932053eal_sz > bounde472938360z_real ).
thf(func_def_61,type,
freche58918398_sc_sz: denota610675952t_unit > freche2095075217_sc_sz > $o ).
thf(func_def_62,type,
frechet_cr_strm_a_c: trm_a_c > frechet_strm_a_c > $o ).
thf(func_def_63,type,
freche1244000341_sf_sz: trm_sf_sz > frechet_strm_sf_sz > $o ).
thf(func_def_64,type,
freche1473475332_a_b_c: denota231621370t_unit > freche914690577_a_b_c ).
thf(func_def_65,type,
freche1784963216_sc_sz: denota610675952t_unit > freche2095075217_sc_sz ).
thf(func_def_66,type,
freche1608036107_a_b_c: freche914690577_a_b_c > denota231621370t_unit ).
thf(func_def_67,type,
freche1421597129_sc_sz: freche2095075217_sc_sz > denota610675952t_unit ).
thf(func_def_68,type,
frechet_raw_term_a_c: frechet_strm_a_c > trm_a_c ).
thf(func_def_69,type,
freche782854530_sf_sz: frechet_strm_sf_sz > trm_sf_sz ).
thf(func_def_70,type,
freche665377492rm_a_c: trm_a_c > frechet_strm_a_c ).
thf(func_def_71,type,
freche1046279700_sf_sz: trm_sf_sz > frechet_strm_sf_sz ).
thf(func_def_72,type,
ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o ).
thf(func_def_73,type,
if_Bou1785791806z_real: $o > bounde472938360z_real > bounde472938360z_real > bounde472938360z_real ).
thf(func_def_74,type,
quotie842200089_sc_sz: ( denota610675952t_unit > denota610675952t_unit > $o ) > ( denota610675952t_unit > freche2095075217_sc_sz ) > ( freche2095075217_sc_sz > denota610675952t_unit ) > ( denota610675952t_unit > freche2095075217_sc_sz > $o ) > $o ).
thf(func_def_75,type,
quotie1467858509rm_a_c: ( trm_a_c > trm_a_c > $o ) > ( trm_a_c > frechet_strm_a_c ) > ( frechet_strm_a_c > trm_a_c ) > ( trm_a_c > frechet_strm_a_c > $o ) > $o ).
thf(func_def_76,type,
quotie1549861309_sf_sz: ( trm_sf_sz > trm_sf_sz > $o ) > ( trm_sf_sz > frechet_strm_sf_sz ) > ( frechet_strm_sf_sz > trm_sf_sz ) > ( trm_sf_sz > frechet_strm_sf_sz > $o ) > $o ).
thf(func_def_77,type,
ord_le2003534918unit_o: ( denota610675952t_unit > denota610675952t_unit > $o ) > ( denota610675952t_unit > denota610675952t_unit > $o ) > $o ).
thf(func_def_78,type,
ord_le108471557c_sz_o: ( denota610675952t_unit > produc866628903_sc_sz > $o ) > ( denota610675952t_unit > produc866628903_sc_sz > $o ) > $o ).
thf(func_def_79,type,
ord_le8515534f_sz_o: ( trm_sf_sz > trm_sf_sz > $o ) > ( trm_sf_sz > trm_sf_sz > $o ) > $o ).
thf(func_def_80,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_81,type,
ord_le775706699real_c: finite1398487019real_c > finite1398487019real_c > $o ).
thf(func_def_82,type,
ord_le787639925eal_sz: finite824932053eal_sz > finite824932053eal_sz > $o ).
thf(func_def_83,type,
ord_le2132572860_o_a_o: produc1065634396_o_a_o > produc1065634396_o_a_o > $o ).
thf(func_def_84,type,
ord_le1643089911_set_a: produc903182423_set_a > produc903182423_set_a > $o ).
thf(func_def_85,type,
ord_le472894788f_sz_o: produc1553439972f_sz_o > produc1553439972f_sz_o > $o ).
thf(func_def_86,type,
ord_le1883211903_o_a_o: product_prod_a_o_a_o > product_prod_a_o_a_o > $o ).
thf(func_def_87,type,
ord_le72828020_set_a: produc1561113620_set_a > produc1561113620_set_a > $o ).
thf(func_def_88,type,
ord_le850691415real_c: produc190496183real_c > produc190496183real_c > $o ).
thf(func_def_89,type,
ord_le473656583eal_sz: produc1149990247eal_sz > produc1149990247eal_sz > $o ).
thf(func_def_90,type,
ord_le978883847eal_sz: produc1241881959eal_sz > produc1241881959eal_sz > $o ).
thf(func_def_91,type,
ord_le1884788375f_sz_o: produc1144880887f_sz_o > produc1144880887f_sz_o > $o ).
thf(func_def_92,type,
ord_le501349868_a_a_o: produc1989635468_a_a_o > produc1989635468_a_a_o > $o ).
thf(func_def_93,type,
ord_le486764743_set_a: produc1691597095_set_a > produc1691597095_set_a > $o ).
thf(func_def_94,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_95,type,
ord_le41263445eal_sz: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o ).
thf(func_def_96,type,
ord_le1230423618_sc_sz: set_Pr1169339874_sc_sz > set_Pr1169339874_sc_sz > $o ).
thf(func_def_97,type,
ord_le929608341um_b_c: set_Su1783761653um_b_c > set_Su1783761653um_b_c > $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_le1110131657_sz_sz: set_Sum_sum_sz_sz > set_Sum_sum_sz_sz > $o ).
thf(func_def_100,type,
ord_le1369644495rm_a_c: set_trm_a_c > set_trm_a_c > $o ).
thf(func_def_101,type,
ord_le1697056455_sf_sz: set_trm_sf_sz > set_trm_sf_sz > $o ).
thf(func_def_102,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_103,type,
top_to1399053141c_sz_o: denota610675952t_unit > produc866628903_sc_sz > $o ).
thf(func_def_104,type,
top_to646513176l_sz_o: finite824932053eal_sz > $o ).
thf(func_def_105,type,
top_to1201357528_b_c_o: sum_su737395349um_b_c > $o ).
thf(func_def_106,type,
top_to1787697847eal_sz: produc1241881959eal_sz ).
thf(func_def_107,type,
top_to1873962757eal_sz: set_Fi291318197eal_sz ).
thf(func_def_108,type,
top_to1499569298_sc_sz: set_Pr1169339874_sc_sz ).
thf(func_def_109,type,
top_to524132421um_b_c: set_Su1783761653um_b_c ).
thf(func_def_110,type,
top_to1660572043um_c_c: set_Sum_sum_c_c ).
thf(func_def_111,type,
top_top_set_a: set_a ).
thf(func_def_112,type,
produc1152932438_o_a_o: ( trm_sf_sz > trm_sf_sz > $o ) > ( a > $o ) > produc1065634396_o_a_o ).
thf(func_def_113,type,
produc1543226183_set_a: ( trm_sf_sz > trm_sf_sz > $o ) > set_a > produc903182423_set_a ).
thf(func_def_114,type,
produc593159062f_sz_o: ( a > $o ) > ( trm_sf_sz > trm_sf_sz > $o ) > produc1553439972f_sz_o ).
thf(func_def_115,type,
product_Pair_a_o_a_o: ( a > $o ) > ( a > $o ) > product_prod_a_o_a_o ).
thf(func_def_116,type,
produc1916559302_set_a: ( a > $o ) > set_a > produc1561113620_set_a ).
thf(func_def_117,type,
produc784663575z_real: bounde472938360z_real > bounde472938360z_real > produc1892666919z_real ).
thf(func_def_118,type,
produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz ).
thf(func_def_119,type,
produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(func_def_120,type,
produc1308130519eal_sz: finite824932053eal_sz > finite824932053eal_sz > produc1149990247eal_sz ).
thf(func_def_121,type,
produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz ).
thf(func_def_122,type,
produc1235791063eal_sz: set_Fi291318197eal_sz > set_Fi291318197eal_sz > produc1241881959eal_sz ).
thf(func_def_123,type,
produc1174558183f_sz_o: set_a > ( trm_sf_sz > trm_sf_sz > $o ) > produc1144880887f_sz_o ).
thf(func_def_124,type,
produc634809990_a_a_o: set_a > ( a > $o ) > produc1989635468_a_a_o ).
thf(func_def_125,type,
produc1928581911_set_a: set_a > set_a > produc1691597095_set_a ).
thf(func_def_126,type,
produc2013638506_o_a_o: produc1065634396_o_a_o > trm_sf_sz > trm_sf_sz > $o ).
thf(func_def_127,type,
produc407272755_set_a: produc903182423_set_a > trm_sf_sz > trm_sf_sz > $o ).
thf(func_def_128,type,
produc1453865130f_sz_o: produc1553439972f_sz_o > a > $o ).
thf(func_def_129,type,
product_fst_a_o_a_o: product_prod_a_o_a_o > a > $o ).
thf(func_def_130,type,
produc1045727450_set_a: produc1561113620_set_a > a > $o ).
thf(func_def_131,type,
produc870616579z_real: produc1892666919z_real > bounde472938360z_real ).
thf(func_def_132,type,
produc1503602930_sc_sz: produc1821101996_sc_sz > denota610675952t_unit ).
thf(func_def_133,type,
produc2010422875real_c: produc190496183real_c > finite1398487019real_c ).
thf(func_def_134,type,
produc1111759555eal_sz: produc1149990247eal_sz > finite824932053eal_sz ).
thf(func_def_135,type,
produc548504323_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
thf(func_def_136,type,
produc286845635eal_sz: produc1241881959eal_sz > set_Fi291318197eal_sz ).
thf(func_def_137,type,
produc38604755f_sz_o: produc1144880887f_sz_o > set_a ).
thf(func_def_138,type,
produc1911461786_a_a_o: produc1989635468_a_a_o > set_a ).
thf(func_def_139,type,
produc1926412547_set_a: produc1691597095_set_a > set_a ).
thf(func_def_140,type,
produc1630531752_o_a_o: produc1065634396_o_a_o > a > $o ).
thf(func_def_141,type,
produc776178293_set_a: produc903182423_set_a > set_a ).
thf(func_def_142,type,
produc1070758376f_sz_o: produc1553439972f_sz_o > trm_sf_sz > trm_sf_sz > $o ).
thf(func_def_143,type,
product_snd_a_o_a_o: product_prod_a_o_a_o > a > $o ).
thf(func_def_144,type,
produc1305389080_set_a: produc1561113620_set_a > set_a ).
thf(func_def_145,type,
produc1422611269z_real: produc1892666919z_real > bounde472938360z_real ).
thf(func_def_146,type,
produc974239792_sc_sz: produc1821101996_sc_sz > produc866628903_sc_sz ).
thf(func_def_147,type,
produc314122909real_c: produc190496183real_c > finite1398487019real_c ).
thf(func_def_148,type,
produc1269210629eal_sz: produc1149990247eal_sz > finite824932053eal_sz ).
thf(func_def_149,type,
produc4753477_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
thf(func_def_150,type,
produc1746886149eal_sz: produc1241881959eal_sz > set_Fi291318197eal_sz ).
thf(func_def_151,type,
produc407510293f_sz_o: produc1144880887f_sz_o > trm_sf_sz > trm_sf_sz > $o ).
thf(func_def_152,type,
produc23639768_a_a_o: produc1989635468_a_a_o > a > $o ).
thf(func_def_153,type,
produc918972485_set_a: produc1691597095_set_a > set_a ).
thf(func_def_154,type,
collec451781861t_unit: ( denota231621370t_unit > $o ) > set_De455519194t_unit ).
thf(func_def_155,type,
collec1767975749t_unit: ( denota610675952t_unit > $o ) > set_De208295462t_unit ).
thf(func_def_156,type,
collec1002602816eal_sz: ( finite824932053eal_sz > $o ) > set_Fi291318197eal_sz ).
thf(func_def_157,type,
collec1199592193_sc_sz: ( produc1821101996_sc_sz > $o ) > set_Pr1169339874_sc_sz ).
thf(func_def_158,type,
collec2086029184um_b_c: ( sum_su737395349um_b_c > $o ) > set_Su1783761653um_b_c ).
thf(func_def_159,type,
collect_trm_a_c: ( trm_a_c > $o ) > set_trm_a_c ).
thf(func_def_160,type,
collect_trm_sf_sz: ( trm_sf_sz > $o ) > set_trm_sf_sz ).
thf(func_def_161,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_162,type,
static_FVDiff_a_c: trm_a_c > set_Sum_sum_c_c ).
thf(func_def_163,type,
static_FVDiff_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
thf(func_def_164,type,
static_FVT_a_c: trm_a_c > set_Sum_sum_c_c ).
thf(func_def_165,type,
static_FVT_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
thf(func_def_166,type,
static_SIGT_a_c: trm_a_c > set_a ).
thf(func_def_167,type,
sum_In2139678582um_b_c: a > sum_su737395349um_b_c ).
thf(func_def_168,type,
predic913887884_sf_sz: sc > formula_sf_sc_sz ).
thf(func_def_169,type,
dfree_a_c: trm_a_c > $o ).
thf(func_def_170,type,
dfree_sf_sz: trm_sf_sz > $o ).
thf(func_def_171,type,
p_sc_sf_sz: sc > formula_sf_sc_sz ).
thf(func_def_172,type,
empty_sz_sf: sz > trm_sf_sz ).
thf(func_def_173,type,
f0_sf_sz: sf > trm_sf_sz ).
thf(func_def_174,type,
function_a_c: a > ( c > trm_a_c ) > trm_a_c ).
thf(func_def_175,type,
function_sf_sz: sf > ( sz > trm_sf_sz ) > trm_sf_sz ).
thf(func_def_176,type,
plus_a_c: trm_a_c > trm_a_c > trm_a_c ).
thf(func_def_177,type,
plus_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
thf(func_def_178,type,
times_a_c: trm_a_c > trm_a_c > trm_a_c ).
thf(func_def_179,type,
times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
thf(func_def_180,type,
topolo885751137z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > bounde472938360z_real ) > $o ).
thf(func_def_181,type,
topolo1027477648z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > produc1892666919z_real ) > $o ).
thf(func_def_182,type,
topolo1348430467z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > real ) > $o ).
thf(func_def_183,type,
type_d1092523951t_unit: ( freche2095075217_sc_sz > denota610675952t_unit ) > ( denota610675952t_unit > freche2095075217_sc_sz ) > set_De208295462t_unit > $o ).
thf(func_def_184,type,
type_d1238563341rm_a_c: ( frechet_strm_a_c > trm_a_c ) > ( trm_a_c > frechet_strm_a_c ) > set_trm_a_c > $o ).
thf(func_def_185,type,
type_d46389773_sf_sz: ( frechet_strm_sf_sz > trm_sf_sz ) > ( trm_sf_sz > frechet_strm_sf_sz ) > set_trm_sf_sz > $o ).
thf(func_def_186,type,
member1777622435t_unit: denota231621370t_unit > set_De455519194t_unit > $o ).
thf(func_def_187,type,
member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o ).
thf(func_def_188,type,
member1693951742eal_sz: finite824932053eal_sz > set_Fi291318197eal_sz > $o ).
thf(func_def_189,type,
member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o ).
thf(func_def_190,type,
member1893232190um_b_c: sum_su737395349um_b_c > set_Su1783761653um_b_c > $o ).
thf(func_def_191,type,
member_trm_a_c: trm_a_c > set_trm_a_c > $o ).
thf(func_def_192,type,
member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
thf(func_def_193,type,
member_a: a > set_a > $o ).
thf(func_def_194,type,
i: denota231621370t_unit ).
thf(func_def_195,type,
j: denota231621370t_unit ).
thf(func_def_196,type,
nu: produc190496183real_c ).
thf(func_def_197,type,
nu2: produc190496183real_c ).
thf(func_def_198,type,
t1: trm_a_c ).
thf(func_def_199,type,
t2: trm_a_c ).
thf(func_def_214,type,
sK0: produc190496183real_c > finite1398487019real_c ).
thf(func_def_215,type,
sK1: produc190496183real_c > finite1398487019real_c ).
thf(func_def_216,type,
sK2: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_217,type,
sK3: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_218,type,
sK4: produc190496183real_c > finite1398487019real_c ).
thf(func_def_219,type,
sK5: produc190496183real_c > finite1398487019real_c ).
thf(func_def_220,type,
sK6: ( finite1398487019real_c > finite1398487019real_c > $o ) > finite1398487019real_c ).
thf(func_def_221,type,
sK7: ( finite1398487019real_c > finite1398487019real_c > $o ) > finite1398487019real_c ).
thf(func_def_222,type,
sK8: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_223,type,
sK9: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_226,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f1201,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1117,f1200]) ).
thf(f1200,plain,
spl10_7,
inference(avatar_contradiction_clause,[status(thm)],[f1199]) ).
thf(f1199,plain,
( $false
| spl10_7 ),
inference(subsumption_resolution,[status(thm)],[f1197,f1113]) ).
thf(f1113,plain,
( ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
!= $true )
| spl10_7 ),
inference(avatar_component_clause,[status(thm)],[f1111]) ).
thf(f1111,definition,
( spl10_7
<=> ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_7])],[avatar_definition]) ).
thf(f1197,plain,
( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1193]) ).
thf(f1193,plain,
( ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f987,f990]) ).
thf(f990,plain,
( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ t1 @ t2 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f484]) ).
thf(f484,plain,
( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ t1 @ t2 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f483]) ).
thf(f483,plain,
denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ t1 @ t2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ t1 @ t2 ) ),
file('/export/starexec/sandbox/tmp/tmp.VtE5UpiK52/DTF2THF_30300.p',fact_2_agree) ).
thf(f987,plain,
! [X2: trm_a_c,X3: produc190496183real_c,X0: produc190496183real_c,X1: trm_a_c] :
( ( ( denota1997846518gree_c @ X3 @ X0 @ ( static_FVDiff_a_c @ ( plus_a_c @ X1 @ X2 ) ) )
!= $true )
| ( ( denota1997846518gree_c @ X3 @ X0 @ ( static_FVDiff_a_c @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f922]) ).
thf(f922,plain,
! [X0: produc190496183real_c,X1: trm_a_c,X2: trm_a_c,X3: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X3 @ X0 @ ( static_FVDiff_a_c @ X2 ) )
= $true )
| ( ( denota1997846518gree_c @ X3 @ X0 @ ( static_FVDiff_a_c @ ( plus_a_c @ X1 @ X2 ) ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f492]) ).
thf(f492,plain,
! [X0: produc190496183real_c,X1: trm_a_c,X2: trm_a_c,X3: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X3 @ X0 @ ( static_FVDiff_a_c @ ( plus_a_c @ X1 @ X2 ) ) )
= $true )
=> ( ( denota1997846518gree_c @ X3 @ X0 @ ( static_FVDiff_a_c @ X2 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f491]) ).
thf(f491,plain,
! [X0: produc190496183real_c,X1: trm_a_c,X2: trm_a_c,X3: produc190496183real_c] :
( ( denota1997846518gree_c @ X3 @ X0 @ ( static_FVDiff_a_c @ ( plus_a_c @ X1 @ X2 ) ) )
=> ( denota1997846518gree_c @ X3 @ X0 @ ( static_FVDiff_a_c @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: produc190496183real_c,X2: trm_a_c,X3: trm_a_c,X0: produc190496183real_c] :
( ( denota1997846518gree_c @ X0 @ X1 @ ( static_FVDiff_a_c @ ( plus_a_c @ X2 @ X3 ) ) )
=> ( denota1997846518gree_c @ X0 @ X1 @ ( static_FVDiff_a_c @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VtE5UpiK52/DTF2THF_30300.p',fact_1_agree__plus2) ).
thf(f1117,plain,
~ spl10_7,
inference(avatar_split_clause,[status(thm)],[f964,f1111]) ).
thf(f964,plain,
( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f895]) ).
thf(f895,plain,
( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
!= $true ),
inference(flattening,[status(thm)],[f742]) ).
thf(f742,plain,
( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f741]) ).
thf(f741,plain,
~ ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) ),
inference(rectify,[status(thm)],[f359]) ).
thf(f359,negated_conjecture,
~ ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f358,conjecture,
denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ),
file('/export/starexec/sandbox/tmp/tmp.VtE5UpiK52/DTF2THF_30300.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP038^1 : 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
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:24:24 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : ITP038^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.46 % Domain : Interactive Theorem Proving
% 0.20/0.46 % Problem : Sledgehammer Coincidence problem prob_231__7211966_1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Des21]
% 0.20/0.46 % Names : Coincidence/prob_231__7211966_1 [Des21]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.20/0.46 % Syntax : Number of formulae : 558 ( 170 unt; 200 typ; 0 def)
% 0.20/0.46 % Number of atoms : 896 ( 365 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 12 ( 2 avg)
% 0.20/0.46 % Number of connectives : 2644 ( 54 ~; 1 |; 87 &;2190 @)
% 0.20/0.46 % ( 0 <=>; 312 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 25 ( 6 avg)
% 0.20/0.46 % Number of types : 45 ( 44 usr)
% 0.20/0.46 % Number of type conns : 550 ( 550 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 159 ( 156 usr; 14 con; 0-10 aty)
% 0.20/0.46 % Number of variables : 1070 ( 122 ^; 925 !; 23 ?;1070 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:01.725
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (44)
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_J,type,
% 0.20/0.46 set_Pr1169339874_sc_sz: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 0.20/0.46 produc1821101996_sc_sz: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_Mt__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_J,type,
% 0.20/0.46 produc1892666919z_real: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J_J,type,
% 0.20/0.46 produc1241881959eal_sz: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 0.20/0.46 produc1149990247eal_sz: $tType ).
% 0.20/0.46
% 0.20/0.46 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,
% 0.20/0.46 produc190496183real_c: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.20/0.46 produc866628903_sc_sz: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_Eo_J_J_J,type,
% 0.20/0.46 produc1144880887f_sz_o: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_Eo_J_J_Mt__Set__Oset_Itf__a_J_J,type,
% 0.20/0.46 produc903182423_set_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__a_M_Eo_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_Eo_J_J_J,type,
% 0.20/0.46 produc1553439972f_sz_o: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_Eo_J_J_M_062_Itf__a_M_Eo_J_J,type,
% 0.20/0.46 produc1065634396_o_a_o: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J,type,
% 0.20/0.46 bounde472938360z_real: $tType ).
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% 0.20/0.46 % dfree1
% 0.20/0.46 thf(fact_12_raw__interp__inject,axiom,
% 0.20/0.46 ! [X: freche2095075217_sc_sz,Y: freche2095075217_sc_sz] :
% 0.20/0.46 ( ( ( freche1421597129_sc_sz @ X )
% 0.20/0.46 = ( freche1421597129_sc_sz @ Y ) )
% 0.20/0.46 = ( X = Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % raw_interp_inject
% 0.20/0.46 thf(fact_13_raw__term__inject,axiom,
% 0.20/0.46 ! [X: frechet_strm_sf_sz,Y: frechet_strm_sf_sz] :
% 0.20/0.46 ( ( ( freche782854530_sf_sz @ X )
% 0.20/0.46 = ( freche782854530_sf_sz @ Y ) )
% 0.20/0.46 = ( X = Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % raw_term_inject
% 0.20/0.46 thf(fact_14_raw__term__inject,axiom,
% 0.20/0.46 ! [X: frechet_strm_a_c,Y: frechet_strm_a_c] :
% 0.20/0.46 ( ( ( frechet_raw_term_a_c @ X )
% 0.20/0.46 = ( frechet_raw_term_a_c @ Y ) )
% 0.20/0.46 = ( X = Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % raw_term_inject
% 0.20/0.46 thf(fact_15_agree__times1,axiom,
% 0.20/0.46 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.20/0.46 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 0.20/0.46 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % agree_times1
% 0.20/0.46 thf(fact_16_agree__times1,axiom,
% 0.20/0.46 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.20/0.46 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 0.20/0.46 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % agree_times1
% 0.20/0.46 thf(fact_17_agree__times2,axiom,
% 0.20/0.46 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.20/0.46 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 0.20/0.46 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % agree_times2
% 0.20/0.46 thf(fact_18_agree__times2,axiom,
% 0.20/0.46 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.20/0.46 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 0.20/0.46 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % agree_times2
% 0.20/0.46 thf(fact_19_agree__func,axiom,
% 0.20/0.46 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,Var: sf,Args: sz > trm_sf_sz,I: sz] :
% 0.20/0.46 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( function_sf_sz @ Var @ Args ) ) )
% 0.20/0.46 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( Args @ I ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % agree_func
% 0.20/0.46 thf(fact_20_agree__func,axiom,
% 0.20/0.46 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Var: a,Args: c > trm_a_c,I: c] :
% 0.20/0.46 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( function_a_c @ Var @ Args ) ) )
% 0.20/0.46 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( Args @ I ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % agree_func
% 0.20/0.46 thf(fact_21_P__def,axiom,
% 0.20/0.46 p_sc_sf_sz = predic913887884_sf_sz ).
% 0.20/0.46
% 0.20/0.46 % P_def
% 0.20/0.46 thf(fact_22_IH2,axiom,
% 0.20/0.46 ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
% 0.20/0.46 => ( ( denota69106024_a_b_c @ i @ j
% 0.20/0.46 @ ( collec2086029184um_b_c
% 0.20/0.46 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.20/0.46 ? [X2: a] :
% 0.20/0.46 ( ( Uu
% 0.20/0.46 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.20/0.46 & ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) ) )
% 0.20/0.46 => ( ( denota229585092_a_b_c @ i @ t2 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
% 0.20/0.46 = ( denota229585092_a_b_c @ j @ t2 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % IH2
% 0.20/0.46 thf(fact_23_seq__sem_Ocases,axiom,
% 0.20/0.46 ! [X: produc1821101996_sc_sz] :
% 0.20/0.46 ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( produc789536734_sc_sz @ I2 @ S ) ) ).
% 0.20/0.46
% 0.20/0.46 % seq_sem.cases
% 0.20/0.46 thf(fact_24_raw__term,axiom,
% 0.20/0.46 ! [X: frechet_strm_a_c] : ( member_trm_a_c @ ( frechet_raw_term_a_c @ X ) @ ( collect_trm_a_c @ dfree_a_c ) ) ).
% 0.20/0.46
% 0.20/0.46 % raw_term
% 0.20/0.46 thf(fact_25_raw__term,axiom,
% 0.20/0.46 ! [X: frechet_strm_sf_sz] : ( member_trm_sf_sz @ ( freche782854530_sf_sz @ X ) @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ).
% 0.20/0.46
% 0.20/0.46 % raw_term
% 0.20/0.46 thf(fact_26_raw__term__cases,axiom,
% 0.20/0.46 ! [Y: trm_a_c] :
% 0.20/0.46 ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.20/0.46 => ~ ! [X3: frechet_strm_a_c] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( frechet_raw_term_a_c @ X3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % raw_term_cases
% 0.20/0.46 thf(fact_27_raw__term__cases,axiom,
% 0.20/0.46 ! [Y: trm_sf_sz] :
% 0.20/0.46 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.20/0.46 => ~ ! [X3: frechet_strm_sf_sz] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( freche782854530_sf_sz @ X3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % raw_term_cases
% 0.20/0.46 thf(fact_28_raw__term__induct,axiom,
% 0.20/0.46 ! [Y: trm_a_c,P: trm_a_c > $o] :
% 0.20/0.46 ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.20/0.46 => ( ! [X3: frechet_strm_a_c] : ( P @ ( frechet_raw_term_a_c @ X3 ) )
% 0.20/0.46 => ( P @ Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % raw_term_induct
% 0.20/0.46 thf(fact_29_raw__term__induct,axiom,
% 0.20/0.46 ! [Y: trm_sf_sz,P: trm_sf_sz > $o] :
% 0.20/0.46 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.20/0.46 => ( ! [X3: frechet_strm_sf_sz] : ( P @ ( freche782854530_sf_sz @ X3 ) )
% 0.20/0.46 => ( P @ Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % raw_term_induct
% 0.20/0.46 thf(fact_30_coincidence__frechet,axiom,
% 0.20/0.46 ! [Theta: trm_a_c,Nu: produc190496183real_c,Nu2: produc190496183real_c,I3: denota231621370t_unit] :
% 0.20/0.46 ( ( dfree_a_c @ Theta )
% 0.20/0.46 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ Theta ) )
% 0.20/0.46 => ( ( denota229585092_a_b_c @ I3 @ Theta @ ( produc2010422875real_c @ Nu ) @ ( produc314122909real_c @ Nu ) )
% 0.20/0.46 = ( denota229585092_a_b_c @ I3 @ Theta @ ( produc2010422875real_c @ Nu2 ) @ ( produc314122909real_c @ Nu2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % coincidence_frechet
% 0.20/0.46 thf(fact_31_coincidence__frechet,axiom,
% 0.20/0.46 ! [Theta: trm_sf_sz,Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,I3: denota610675952t_unit] :
% 0.20/0.46 ( ( dfree_sf_sz @ Theta )
% 0.20/0.46 => ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ Theta ) )
% 0.20/0.46 => ( ( denota1979904720_sc_sz @ I3 @ Theta @ ( produc1111759555eal_sz @ Nu ) @ ( produc1269210629eal_sz @ Nu ) )
% 0.20/0.46 = ( denota1979904720_sc_sz @ I3 @ Theta @ ( produc1111759555eal_sz @ Nu2 ) @ ( produc1269210629eal_sz @ Nu2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % coincidence_frechet
% 0.20/0.46 thf(fact_32_IA,axiom,
% 0.20/0.46 ( denota69106024_a_b_c @ i @ j
% 0.20/0.46 @ ( collec2086029184um_b_c
% 0.20/0.46 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.20/0.46 ? [X2: a] :
% 0.20/0.46 ( ( Uu
% 0.20/0.46 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.20/0.46 & ( member_a @ X2 @ ( static_SIGT_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % IA
% 0.20/0.46 thf(fact_33_IA1,axiom,
% 0.20/0.46 ( denota69106024_a_b_c @ i @ j
% 0.20/0.46 @ ( collec2086029184um_b_c
% 0.20/0.46 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.20/0.46 ? [X2: a] :
% 0.20/0.46 ( ( Uu
% 0.20/0.46 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.20/0.46 & ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % IA1
% 0.20/0.46 thf(fact_34_IA2,axiom,
% 0.20/0.46 ( denota69106024_a_b_c @ i @ j
% 0.20/0.46 @ ( collec2086029184um_b_c
% 0.20/0.46 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.20/0.46 ? [X2: a] :
% 0.20/0.46 ( ( Uu
% 0.20/0.46 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.20/0.46 & ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % IA2
% 0.20/0.46 thf(fact_35_IH1,axiom,
% 0.20/0.46 ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t1 ) )
% 0.20/0.46 => ( ( denota69106024_a_b_c @ i @ j
% 0.20/0.46 @ ( collec2086029184um_b_c
% 0.20/0.46 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.20/0.46 ? [X2: a] :
% 0.20/0.46 ( ( Uu
% 0.20/0.46 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.20/0.46 & ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) ) )
% 0.20/0.46 => ( ( denota229585092_a_b_c @ i @ t1 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
% 0.20/0.46 = ( denota229585092_a_b_c @ j @ t1 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % IH1
% 0.20/0.46 thf(fact_36_Iagree__comm,axiom,
% 0.20/0.46 ! [A: denota231621370t_unit,B: denota231621370t_unit,V: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( denota69106024_a_b_c @ A @ B @ V )
% 0.20/0.46 => ( denota69106024_a_b_c @ B @ A @ V ) ) ).
% 0.20/0.46
% 0.20/0.46 % Iagree_comm
% 0.20/0.46 thf(fact_37_Iagree__refl,axiom,
% 0.20/0.46 ! [I3: denota231621370t_unit,A: set_Su1783761653um_b_c] : ( denota69106024_a_b_c @ I3 @ I3 @ A ) ).
% 0.20/0.46
% 0.20/0.46 % Iagree_refl
% 0.20/0.46 thf(fact_38_subs_I2_J,axiom,
% 0.20/0.46 ( ord_le929608341um_b_c
% 0.20/0.46 @ ( collec2086029184um_b_c
% 0.20/0.46 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.20/0.46 ? [X2: a] :
% 0.20/0.46 ( ( Uu
% 0.20/0.46 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.20/0.46 & ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) )
% 0.20/0.46 @ ( collec2086029184um_b_c
% 0.20/0.46 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.20/0.46 ? [X2: a] :
% 0.20/0.46 ( ( Uu
% 0.20/0.46 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.20/0.46 & ( member_a @ X2 @ ( static_SIGT_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subs(2)
% 0.20/0.46 thf(fact_39_subs_I1_J,axiom,
% 0.20/0.46 ( ord_le929608341um_b_c
% 0.20/0.46 @ ( collec2086029184um_b_c
% 0.20/0.46 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.20/0.46 ? [X2: a] :
% 0.20/0.46 ( ( Uu
% 0.20/0.46 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.20/0.46 & ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) )
% 0.20/0.46 @ ( collec2086029184um_b_c
% 0.20/0.46 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.20/0.46 ? [X2: a] :
% 0.20/0.46 ( ( Uu
% 0.20/0.46 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.20/0.47 & ( member_a @ X2 @ ( static_SIGT_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subs(1)
% 0.20/0.47 thf(fact_40_simple__term__inverse,axiom,
% 0.20/0.47 ! [Y: trm_a_c] :
% 0.20/0.47 ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.20/0.47 => ( ( frechet_raw_term_a_c @ ( freche665377492rm_a_c @ Y ) )
% 0.20/0.47 = Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % simple_term_inverse
% 0.20/0.47 thf(fact_41_simple__term__inverse,axiom,
% 0.20/0.47 ! [Y: trm_sf_sz] :
% 0.20/0.47 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.20/0.47 => ( ( freche782854530_sf_sz @ ( freche1046279700_sf_sz @ Y ) )
% 0.20/0.47 = Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % simple_term_inverse
% 0.20/0.47 thf(fact_42_prod_Ocollapse,axiom,
% 0.20/0.47 ! [Prod: produc866628903_sc_sz] :
% 0.20/0.47 ( ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) )
% 0.20/0.47 = Prod ) ).
% 0.20/0.47
% 0.20/0.47 % prod.collapse
% 0.20/0.47 thf(fact_43_prod_Ocollapse,axiom,
% 0.20/0.47 ! [Prod: produc1241881959eal_sz] :
% 0.20/0.47 ( ( produc1235791063eal_sz @ ( produc286845635eal_sz @ Prod ) @ ( produc1746886149eal_sz @ Prod ) )
% 0.20/0.47 = Prod ) ).
% 0.20/0.47
% 0.20/0.47 % prod.collapse
% 0.20/0.47 thf(fact_44_prod_Ocollapse,axiom,
% 0.20/0.47 ! [Prod: produc1892666919z_real] :
% 0.20/0.47 ( ( produc784663575z_real @ ( produc870616579z_real @ Prod ) @ ( produc1422611269z_real @ Prod ) )
% 0.20/0.47 = Prod ) ).
% 0.20/0.47
% 0.20/0.47 % prod.collapse
% 0.20/0.47 thf(fact_45_prod_Ocollapse,axiom,
% 0.20/0.47 ! [Prod: produc1149990247eal_sz] :
% 0.20/0.47 ( ( produc1308130519eal_sz @ ( produc1111759555eal_sz @ Prod ) @ ( produc1269210629eal_sz @ Prod ) )
% 0.20/0.47 = Prod ) ).
% 0.20/0.47
% 0.20/0.47 % prod.collapse
% 0.20/0.47 thf(fact_46_prod_Ocollapse,axiom,
% 0.20/0.47 ! [Prod: produc1821101996_sc_sz] :
% 0.20/0.47 ( ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) )
% 0.20/0.47 = Prod ) ).
% 0.20/0.47
% 0.20/0.47 % prod.collapse
% 0.20/0.47 thf(fact_47_prod_Ocollapse,axiom,
% 0.20/0.47 ! [Prod: produc190496183real_c] :
% 0.20/0.47 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 0.20/0.47 = Prod ) ).
% 0.20/0.47
% 0.20/0.47 % prod.collapse
% 0.20/0.47 thf(fact_48_cr__good__interp__def,axiom,
% 0.20/0.47 ( freche58918398_sc_sz
% 0.20/0.47 = ( ^ [X2: denota610675952t_unit,Y2: freche2095075217_sc_sz] :
% 0.20/0.47 ( X2
% 0.20/0.47 = ( freche1421597129_sc_sz @ Y2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % cr_good_interp_def
% 0.20/0.47 thf(fact_49_cr__strm__def,axiom,
% 0.20/0.47 ( freche1244000341_sf_sz
% 0.20/0.47 = ( ^ [X2: trm_sf_sz,Y2: frechet_strm_sf_sz] :
% 0.20/0.47 ( X2
% 0.20/0.47 = ( freche782854530_sf_sz @ Y2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % cr_strm_def
% 0.20/0.47 thf(fact_50_cr__strm__def,axiom,
% 0.20/0.47 ( frechet_cr_strm_a_c
% 0.20/0.47 = ( ^ [X2: trm_a_c,Y2: frechet_strm_a_c] :
% 0.20/0.47 ( X2
% 0.20/0.47 = ( frechet_raw_term_a_c @ Y2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % cr_strm_def
% 0.20/0.47 thf(fact_51_dfree__Times__simps,axiom,
% 0.20/0.47 ! [A2: trm_a_c,B2: trm_a_c] :
% 0.20/0.47 ( ( dfree_a_c @ ( times_a_c @ A2 @ B2 ) )
% 0.20/0.47 = ( ( dfree_a_c @ A2 )
% 0.20/0.47 & ( dfree_a_c @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Times_simps
% 0.20/0.47 thf(fact_52_dfree__Times__simps,axiom,
% 0.20/0.47 ! [A2: trm_sf_sz,B2: trm_sf_sz] :
% 0.20/0.47 ( ( dfree_sf_sz @ ( times_sf_sz @ A2 @ B2 ) )
% 0.20/0.47 = ( ( dfree_sf_sz @ A2 )
% 0.20/0.47 & ( dfree_sf_sz @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Times_simps
% 0.20/0.47 thf(fact_53_dfree__Plus__simps,axiom,
% 0.20/0.47 ! [A2: trm_sf_sz,B2: trm_sf_sz] :
% 0.20/0.47 ( ( dfree_sf_sz @ ( plus_sf_sz @ A2 @ B2 ) )
% 0.20/0.47 = ( ( dfree_sf_sz @ A2 )
% 0.20/0.47 & ( dfree_sf_sz @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Plus_simps
% 0.20/0.47 thf(fact_54_dfree__Plus__simps,axiom,
% 0.20/0.47 ! [A2: trm_a_c,B2: trm_a_c] :
% 0.20/0.47 ( ( dfree_a_c @ ( plus_a_c @ A2 @ B2 ) )
% 0.20/0.47 = ( ( dfree_a_c @ A2 )
% 0.20/0.47 & ( dfree_a_c @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Plus_simps
% 0.20/0.47 thf(fact_55_dfree__Fun__simps,axiom,
% 0.20/0.47 ! [I: a,Args: c > trm_a_c] :
% 0.20/0.47 ( ( dfree_a_c @ ( function_a_c @ I @ Args ) )
% 0.20/0.47 = ( ! [X2: c] : ( dfree_a_c @ ( Args @ X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Fun_simps
% 0.20/0.47 thf(fact_56_dfree__Fun__simps,axiom,
% 0.20/0.47 ! [I: sf,Args: sz > trm_sf_sz] :
% 0.20/0.47 ( ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) )
% 0.20/0.47 = ( ! [X2: sz] : ( dfree_sf_sz @ ( Args @ X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Fun_simps
% 0.20/0.47 thf(fact_57_simple__term__cases,axiom,
% 0.20/0.47 ! [X: frechet_strm_a_c] :
% 0.20/0.47 ~ ! [Y3: trm_a_c] :
% 0.20/0.47 ( ( X
% 0.20/0.47 = ( freche665377492rm_a_c @ Y3 ) )
% 0.20/0.47 => ~ ( member_trm_a_c @ Y3 @ ( collect_trm_a_c @ dfree_a_c ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % simple_term_cases
% 0.20/0.47 thf(fact_58_simple__term__cases,axiom,
% 0.20/0.47 ! [X: frechet_strm_sf_sz] :
% 0.20/0.47 ~ ! [Y3: trm_sf_sz] :
% 0.20/0.47 ( ( X
% 0.20/0.47 = ( freche1046279700_sf_sz @ Y3 ) )
% 0.20/0.47 => ~ ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % simple_term_cases
% 0.20/0.47 thf(fact_59_raw__term__inverse,axiom,
% 0.20/0.47 ! [X: frechet_strm_a_c] :
% 0.20/0.47 ( ( freche665377492rm_a_c @ ( frechet_raw_term_a_c @ X ) )
% 0.20/0.47 = X ) ).
% 0.20/0.47
% 0.20/0.47 % raw_term_inverse
% 0.20/0.47 thf(fact_60_raw__term__inverse,axiom,
% 0.20/0.47 ! [X: frechet_strm_sf_sz] :
% 0.20/0.47 ( ( freche1046279700_sf_sz @ ( freche782854530_sf_sz @ X ) )
% 0.20/0.47 = X ) ).
% 0.20/0.47
% 0.20/0.47 % raw_term_inverse
% 0.20/0.47 thf(fact_61_simple__term__inject,axiom,
% 0.20/0.47 ! [X: trm_a_c,Y: trm_a_c] :
% 0.20/0.47 ( ( member_trm_a_c @ X @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.20/0.47 => ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.20/0.47 => ( ( ( freche665377492rm_a_c @ X )
% 0.20/0.47 = ( freche665377492rm_a_c @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % simple_term_inject
% 0.20/0.47 thf(fact_62_simple__term__inject,axiom,
% 0.20/0.47 ! [X: trm_sf_sz,Y: trm_sf_sz] :
% 0.20/0.47 ( ( member_trm_sf_sz @ X @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.20/0.47 => ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.20/0.47 => ( ( ( freche1046279700_sf_sz @ X )
% 0.20/0.47 = ( freche1046279700_sf_sz @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % simple_term_inject
% 0.20/0.47 thf(fact_63_simple__term__induct,axiom,
% 0.20/0.47 ! [P: frechet_strm_a_c > $o,X: frechet_strm_a_c] :
% 0.20/0.47 ( ! [Y3: trm_a_c] :
% 0.20/0.47 ( ( member_trm_a_c @ Y3 @ ( collect_trm_a_c @ dfree_a_c ) )
% 0.20/0.47 => ( P @ ( freche665377492rm_a_c @ Y3 ) ) )
% 0.20/0.47 => ( P @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % simple_term_induct
% 0.20/0.47 thf(fact_64_simple__term__induct,axiom,
% 0.20/0.47 ! [P: frechet_strm_sf_sz > $o,X: frechet_strm_sf_sz] :
% 0.20/0.47 ( ! [Y3: trm_sf_sz] :
% 0.20/0.47 ( ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.20/0.47 => ( P @ ( freche1046279700_sf_sz @ Y3 ) ) )
% 0.20/0.47 => ( P @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % simple_term_induct
% 0.20/0.47 thf(fact_65_old_Oprod_Oinject,axiom,
% 0.20/0.47 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 0.20/0.47 ( ( ( produc394644079real_c @ A2 @ B2 )
% 0.20/0.47 = ( produc394644079real_c @ A3 @ B3 ) )
% 0.20/0.47 = ( ( A2 = A3 )
% 0.20/0.47 & ( B2 = B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inject
% 0.20/0.47 thf(fact_66_old_Oprod_Oinject,axiom,
% 0.20/0.47 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 0.20/0.47 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 0.20/0.47 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 0.20/0.47 = ( ( A2 = A3 )
% 0.20/0.47 & ( B2 = B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inject
% 0.20/0.47 thf(fact_67_old_Oprod_Oinject,axiom,
% 0.20/0.47 ! [A2: set_Fi291318197eal_sz,B2: set_Fi291318197eal_sz,A3: set_Fi291318197eal_sz,B3: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( ( produc1235791063eal_sz @ A2 @ B2 )
% 0.20/0.47 = ( produc1235791063eal_sz @ A3 @ B3 ) )
% 0.20/0.47 = ( ( A2 = A3 )
% 0.20/0.47 & ( B2 = B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inject
% 0.20/0.47 thf(fact_68_old_Oprod_Oinject,axiom,
% 0.20/0.47 ! [A2: bounde472938360z_real,B2: bounde472938360z_real,A3: bounde472938360z_real,B3: bounde472938360z_real] :
% 0.20/0.47 ( ( ( produc784663575z_real @ A2 @ B2 )
% 0.20/0.47 = ( produc784663575z_real @ A3 @ B3 ) )
% 0.20/0.47 = ( ( A2 = A3 )
% 0.20/0.47 & ( B2 = B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inject
% 0.20/0.47 thf(fact_69_old_Oprod_Oinject,axiom,
% 0.20/0.47 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 0.20/0.47 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 0.20/0.47 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 0.20/0.47 = ( ( A2 = A3 )
% 0.20/0.47 & ( B2 = B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inject
% 0.20/0.47 thf(fact_70_prod_Oinject,axiom,
% 0.20/0.47 ! [X1: finite1398487019real_c,X22: finite1398487019real_c,Y1: finite1398487019real_c,Y22: finite1398487019real_c] :
% 0.20/0.47 ( ( ( produc394644079real_c @ X1 @ X22 )
% 0.20/0.47 = ( produc394644079real_c @ Y1 @ Y22 ) )
% 0.20/0.47 = ( ( X1 = Y1 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inject
% 0.20/0.47 thf(fact_71_prod_Oinject,axiom,
% 0.20/0.47 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz,Y1: list_f1238882004_sc_sz,Y22: list_f1238882004_sc_sz] :
% 0.20/0.47 ( ( ( produc1822718231_sc_sz @ X1 @ X22 )
% 0.20/0.47 = ( produc1822718231_sc_sz @ Y1 @ Y22 ) )
% 0.20/0.47 = ( ( X1 = Y1 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inject
% 0.20/0.47 thf(fact_72_prod_Oinject,axiom,
% 0.20/0.47 ! [X1: set_Fi291318197eal_sz,X22: set_Fi291318197eal_sz,Y1: set_Fi291318197eal_sz,Y22: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( ( produc1235791063eal_sz @ X1 @ X22 )
% 0.20/0.47 = ( produc1235791063eal_sz @ Y1 @ Y22 ) )
% 0.20/0.47 = ( ( X1 = Y1 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inject
% 0.20/0.47 thf(fact_73_prod_Oinject,axiom,
% 0.20/0.47 ! [X1: bounde472938360z_real,X22: bounde472938360z_real,Y1: bounde472938360z_real,Y22: bounde472938360z_real] :
% 0.20/0.47 ( ( ( produc784663575z_real @ X1 @ X22 )
% 0.20/0.47 = ( produc784663575z_real @ Y1 @ Y22 ) )
% 0.20/0.47 = ( ( X1 = Y1 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inject
% 0.20/0.47 thf(fact_74_prod_Oinject,axiom,
% 0.20/0.47 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz,Y1: denota610675952t_unit,Y22: produc866628903_sc_sz] :
% 0.20/0.47 ( ( ( produc789536734_sc_sz @ X1 @ X22 )
% 0.20/0.47 = ( produc789536734_sc_sz @ Y1 @ Y22 ) )
% 0.20/0.47 = ( ( X1 = Y1 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inject
% 0.20/0.47 thf(fact_75_trm_Oinject_I3_J,axiom,
% 0.20/0.47 ! [X31: a,X32: c > trm_a_c,Y31: a,Y32: c > trm_a_c] :
% 0.20/0.47 ( ( ( function_a_c @ X31 @ X32 )
% 0.20/0.47 = ( function_a_c @ Y31 @ Y32 ) )
% 0.20/0.47 = ( ( X31 = Y31 )
% 0.20/0.47 & ( X32 = Y32 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(3)
% 0.20/0.47 thf(fact_76_trm_Oinject_I3_J,axiom,
% 0.20/0.47 ! [X31: sf,X32: sz > trm_sf_sz,Y31: sf,Y32: sz > trm_sf_sz] :
% 0.20/0.47 ( ( ( function_sf_sz @ X31 @ X32 )
% 0.20/0.47 = ( function_sf_sz @ Y31 @ Y32 ) )
% 0.20/0.47 = ( ( X31 = Y31 )
% 0.20/0.47 & ( X32 = Y32 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(3)
% 0.20/0.47 thf(fact_77_trm_Oinject_I4_J,axiom,
% 0.20/0.47 ! [X41: trm_sf_sz,X42: trm_sf_sz,Y41: trm_sf_sz,Y42: trm_sf_sz] :
% 0.20/0.47 ( ( ( plus_sf_sz @ X41 @ X42 )
% 0.20/0.47 = ( plus_sf_sz @ Y41 @ Y42 ) )
% 0.20/0.47 = ( ( X41 = Y41 )
% 0.20/0.47 & ( X42 = Y42 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(4)
% 0.20/0.47 thf(fact_78_trm_Oinject_I4_J,axiom,
% 0.20/0.47 ! [X41: trm_a_c,X42: trm_a_c,Y41: trm_a_c,Y42: trm_a_c] :
% 0.20/0.47 ( ( ( plus_a_c @ X41 @ X42 )
% 0.20/0.47 = ( plus_a_c @ Y41 @ Y42 ) )
% 0.20/0.47 = ( ( X41 = Y41 )
% 0.20/0.47 & ( X42 = Y42 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(4)
% 0.20/0.47 thf(fact_79_trm_Oinject_I5_J,axiom,
% 0.20/0.47 ! [X51: trm_a_c,X52: trm_a_c,Y51: trm_a_c,Y52: trm_a_c] :
% 0.20/0.47 ( ( ( times_a_c @ X51 @ X52 )
% 0.20/0.47 = ( times_a_c @ Y51 @ Y52 ) )
% 0.20/0.47 = ( ( X51 = Y51 )
% 0.20/0.47 & ( X52 = Y52 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(5)
% 0.20/0.47 thf(fact_80_trm_Oinject_I5_J,axiom,
% 0.20/0.47 ! [X51: trm_sf_sz,X52: trm_sf_sz,Y51: trm_sf_sz,Y52: trm_sf_sz] :
% 0.20/0.47 ( ( ( times_sf_sz @ X51 @ X52 )
% 0.20/0.47 = ( times_sf_sz @ Y51 @ Y52 ) )
% 0.20/0.47 = ( ( X51 = Y51 )
% 0.20/0.47 & ( X52 = Y52 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.inject(5)
% 0.20/0.47 thf(fact_81_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A2: finite824932053eal_sz,P: finite824932053eal_sz > $o] :
% 0.20/0.47 ( ( member1693951742eal_sz @ A2 @ ( collec1002602816eal_sz @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_82_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A2: produc1821101996_sc_sz,P: produc1821101996_sc_sz > $o] :
% 0.20/0.47 ( ( member1057565379_sc_sz @ A2 @ ( collec1199592193_sc_sz @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_83_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A2: trm_sf_sz,P: trm_sf_sz > $o] :
% 0.20/0.47 ( ( member_trm_sf_sz @ A2 @ ( collect_trm_sf_sz @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_84_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A2: trm_a_c,P: trm_a_c > $o] :
% 0.20/0.47 ( ( member_trm_a_c @ A2 @ ( collect_trm_a_c @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_85_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A2: a,P: a > $o] :
% 0.20/0.47 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_86_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A2: sum_su737395349um_b_c,P: sum_su737395349um_b_c > $o] :
% 0.20/0.47 ( ( member1893232190um_b_c @ A2 @ ( collec2086029184um_b_c @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_87_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( collec1002602816eal_sz
% 0.20/0.47 @ ^ [X2: finite824932053eal_sz] : ( member1693951742eal_sz @ X2 @ A ) )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_88_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: set_Pr1169339874_sc_sz] :
% 0.20/0.47 ( ( collec1199592193_sc_sz
% 0.20/0.47 @ ^ [X2: produc1821101996_sc_sz] : ( member1057565379_sc_sz @ X2 @ A ) )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_89_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: set_trm_sf_sz] :
% 0.20/0.47 ( ( collect_trm_sf_sz
% 0.20/0.47 @ ^ [X2: trm_sf_sz] : ( member_trm_sf_sz @ X2 @ A ) )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_90_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: set_trm_a_c] :
% 0.20/0.47 ( ( collect_trm_a_c
% 0.20/0.47 @ ^ [X2: trm_a_c] : ( member_trm_a_c @ X2 @ A ) )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_91_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: set_a] :
% 0.20/0.47 ( ( collect_a
% 0.20/0.47 @ ^ [X2: a] : ( member_a @ X2 @ A ) )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_92_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: set_Su1783761653um_b_c] :
% 0.20/0.47 ( ( collec2086029184um_b_c
% 0.20/0.47 @ ^ [X2: sum_su737395349um_b_c] : ( member1893232190um_b_c @ X2 @ A ) )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_93_Collect__cong,axiom,
% 0.20/0.47 ! [P: finite824932053eal_sz > $o,Q: finite824932053eal_sz > $o] :
% 0.20/0.47 ( ! [X3: finite824932053eal_sz] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( collec1002602816eal_sz @ P )
% 0.20/0.47 = ( collec1002602816eal_sz @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_94_Collect__cong,axiom,
% 0.20/0.47 ! [P: produc1821101996_sc_sz > $o,Q: produc1821101996_sc_sz > $o] :
% 0.20/0.47 ( ! [X3: produc1821101996_sc_sz] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( collec1199592193_sc_sz @ P )
% 0.20/0.47 = ( collec1199592193_sc_sz @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_95_Collect__cong,axiom,
% 0.20/0.47 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 0.20/0.47 ( ! [X3: trm_sf_sz] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( collect_trm_sf_sz @ P )
% 0.20/0.47 = ( collect_trm_sf_sz @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_96_Collect__cong,axiom,
% 0.20/0.47 ! [P: trm_a_c > $o,Q: trm_a_c > $o] :
% 0.20/0.47 ( ! [X3: trm_a_c] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( collect_trm_a_c @ P )
% 0.20/0.47 = ( collect_trm_a_c @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_97_Collect__cong,axiom,
% 0.20/0.47 ! [P: a > $o,Q: a > $o] :
% 0.20/0.47 ( ! [X3: a] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( collect_a @ P )
% 0.20/0.47 = ( collect_a @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_98_Collect__cong,axiom,
% 0.20/0.47 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.20/0.47 ( ! [X3: sum_su737395349um_b_c] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( collec2086029184um_b_c @ P )
% 0.20/0.47 = ( collec2086029184um_b_c @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_99_agree__sub,axiom,
% 0.20/0.47 ! [A: set_Sum_sum_sz_sz,B: set_Sum_sum_sz_sz,Nu: produc1149990247eal_sz,Omega: produc1149990247eal_sz] :
% 0.20/0.47 ( ( ord_le1110131657_sz_sz @ A @ B )
% 0.20/0.47 => ( ( denota102713844ree_sz @ Nu @ Omega @ B )
% 0.20/0.47 => ( denota102713844ree_sz @ Nu @ Omega @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % agree_sub
% 0.20/0.47 thf(fact_100_agree__sub,axiom,
% 0.20/0.47 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,Nu: produc190496183real_c,Omega: produc190496183real_c] :
% 0.20/0.47 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.47 => ( ( denota1997846518gree_c @ Nu @ Omega @ B )
% 0.20/0.47 => ( denota1997846518gree_c @ Nu @ Omega @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % agree_sub
% 0.20/0.47 thf(fact_101_agree__supset,axiom,
% 0.20/0.47 ! [B: set_Sum_sum_sz_sz,A: set_Sum_sum_sz_sz,Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz] :
% 0.20/0.47 ( ( ord_le1110131657_sz_sz @ B @ A )
% 0.20/0.47 => ( ( denota102713844ree_sz @ Nu @ Nu2 @ A )
% 0.20/0.47 => ( denota102713844ree_sz @ Nu @ Nu2 @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % agree_supset
% 0.20/0.47 thf(fact_102_agree__supset,axiom,
% 0.20/0.47 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,Nu: produc190496183real_c,Nu2: produc190496183real_c] :
% 0.20/0.47 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.20/0.47 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ A )
% 0.20/0.47 => ( denota1997846518gree_c @ Nu @ Nu2 @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % agree_supset
% 0.20/0.47 thf(fact_103_old_Oprod_Oinducts,axiom,
% 0.20/0.47 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 0.20/0.47 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inducts
% 0.20/0.47 thf(fact_104_old_Oprod_Oinducts,axiom,
% 0.20/0.47 ! [P: produc866628903_sc_sz > $o,Prod: produc866628903_sc_sz] :
% 0.20/0.47 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inducts
% 0.20/0.47 thf(fact_105_old_Oprod_Oinducts,axiom,
% 0.20/0.47 ! [P: produc1241881959eal_sz > $o,Prod: produc1241881959eal_sz] :
% 0.20/0.47 ( ! [A4: set_Fi291318197eal_sz,B4: set_Fi291318197eal_sz] : ( P @ ( produc1235791063eal_sz @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inducts
% 0.20/0.47 thf(fact_106_old_Oprod_Oinducts,axiom,
% 0.20/0.47 ! [P: produc1892666919z_real > $o,Prod: produc1892666919z_real] :
% 0.20/0.47 ( ! [A4: bounde472938360z_real,B4: bounde472938360z_real] : ( P @ ( produc784663575z_real @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inducts
% 0.20/0.47 thf(fact_107_old_Oprod_Oinducts,axiom,
% 0.20/0.47 ! [P: produc1821101996_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 0.20/0.47 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inducts
% 0.20/0.47 thf(fact_108_old_Oprod_Oexhaust,axiom,
% 0.20/0.47 ! [Y: produc190496183real_c] :
% 0.20/0.47 ~ ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( produc394644079real_c @ A4 @ B4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.exhaust
% 0.20/0.47 thf(fact_109_old_Oprod_Oexhaust,axiom,
% 0.20/0.47 ! [Y: produc866628903_sc_sz] :
% 0.20/0.47 ~ ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( produc1822718231_sc_sz @ A4 @ B4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.exhaust
% 0.20/0.47 thf(fact_110_old_Oprod_Oexhaust,axiom,
% 0.20/0.47 ! [Y: produc1241881959eal_sz] :
% 0.20/0.47 ~ ! [A4: set_Fi291318197eal_sz,B4: set_Fi291318197eal_sz] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( produc1235791063eal_sz @ A4 @ B4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.exhaust
% 0.20/0.47 thf(fact_111_old_Oprod_Oexhaust,axiom,
% 0.20/0.47 ! [Y: produc1892666919z_real] :
% 0.20/0.47 ~ ! [A4: bounde472938360z_real,B4: bounde472938360z_real] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( produc784663575z_real @ A4 @ B4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.exhaust
% 0.20/0.47 thf(fact_112_old_Oprod_Oexhaust,axiom,
% 0.20/0.47 ! [Y: produc1821101996_sc_sz] :
% 0.20/0.47 ~ ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( produc789536734_sc_sz @ A4 @ B4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.exhaust
% 0.20/0.47 thf(fact_113_Pair__inject,axiom,
% 0.20/0.47 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 0.20/0.47 ( ( ( produc394644079real_c @ A2 @ B2 )
% 0.20/0.47 = ( produc394644079real_c @ A3 @ B3 ) )
% 0.20/0.47 => ~ ( ( A2 = A3 )
% 0.20/0.47 => ( B2 != B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_inject
% 0.20/0.47 thf(fact_114_Pair__inject,axiom,
% 0.20/0.47 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 0.20/0.47 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 0.20/0.47 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 0.20/0.47 => ~ ( ( A2 = A3 )
% 0.20/0.47 => ( B2 != B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_inject
% 0.20/0.47 thf(fact_115_Pair__inject,axiom,
% 0.20/0.47 ! [A2: set_Fi291318197eal_sz,B2: set_Fi291318197eal_sz,A3: set_Fi291318197eal_sz,B3: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( ( produc1235791063eal_sz @ A2 @ B2 )
% 0.20/0.47 = ( produc1235791063eal_sz @ A3 @ B3 ) )
% 0.20/0.47 => ~ ( ( A2 = A3 )
% 0.20/0.47 => ( B2 != B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_inject
% 0.20/0.47 thf(fact_116_Pair__inject,axiom,
% 0.20/0.47 ! [A2: bounde472938360z_real,B2: bounde472938360z_real,A3: bounde472938360z_real,B3: bounde472938360z_real] :
% 0.20/0.47 ( ( ( produc784663575z_real @ A2 @ B2 )
% 0.20/0.47 = ( produc784663575z_real @ A3 @ B3 ) )
% 0.20/0.47 => ~ ( ( A2 = A3 )
% 0.20/0.47 => ( B2 != B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_inject
% 0.20/0.47 thf(fact_117_Pair__inject,axiom,
% 0.20/0.47 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 0.20/0.47 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 0.20/0.47 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 0.20/0.47 => ~ ( ( A2 = A3 )
% 0.20/0.47 => ( B2 != B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_inject
% 0.20/0.47 thf(fact_118_prod__cases,axiom,
% 0.20/0.47 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 0.20/0.47 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_cases
% 0.20/0.47 thf(fact_119_prod__cases,axiom,
% 0.20/0.47 ! [P: produc866628903_sc_sz > $o,P2: produc866628903_sc_sz] :
% 0.20/0.47 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_cases
% 0.20/0.47 thf(fact_120_prod__cases,axiom,
% 0.20/0.47 ! [P: produc1241881959eal_sz > $o,P2: produc1241881959eal_sz] :
% 0.20/0.47 ( ! [A4: set_Fi291318197eal_sz,B4: set_Fi291318197eal_sz] : ( P @ ( produc1235791063eal_sz @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_cases
% 0.20/0.47 thf(fact_121_prod__cases,axiom,
% 0.20/0.47 ! [P: produc1892666919z_real > $o,P2: produc1892666919z_real] :
% 0.20/0.47 ( ! [A4: bounde472938360z_real,B4: bounde472938360z_real] : ( P @ ( produc784663575z_real @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_cases
% 0.20/0.47 thf(fact_122_prod__cases,axiom,
% 0.20/0.47 ! [P: produc1821101996_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 0.20/0.47 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 0.20/0.47 => ( P @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_cases
% 0.20/0.47 thf(fact_123_surj__pair,axiom,
% 0.20/0.47 ! [P2: produc190496183real_c] :
% 0.20/0.47 ? [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.20/0.47 ( P2
% 0.20/0.47 = ( produc394644079real_c @ X3 @ Y3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_pair
% 0.20/0.47 thf(fact_124_surj__pair,axiom,
% 0.20/0.47 ! [P2: produc866628903_sc_sz] :
% 0.20/0.47 ? [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 0.20/0.47 ( P2
% 0.20/0.47 = ( produc1822718231_sc_sz @ X3 @ Y3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_pair
% 0.20/0.47 thf(fact_125_surj__pair,axiom,
% 0.20/0.47 ! [P2: produc1241881959eal_sz] :
% 0.20/0.47 ? [X3: set_Fi291318197eal_sz,Y3: set_Fi291318197eal_sz] :
% 0.20/0.47 ( P2
% 0.20/0.47 = ( produc1235791063eal_sz @ X3 @ Y3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_pair
% 0.20/0.47 thf(fact_126_surj__pair,axiom,
% 0.20/0.47 ! [P2: produc1892666919z_real] :
% 0.20/0.47 ? [X3: bounde472938360z_real,Y3: bounde472938360z_real] :
% 0.20/0.47 ( P2
% 0.20/0.47 = ( produc784663575z_real @ X3 @ Y3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_pair
% 0.20/0.47 thf(fact_127_surj__pair,axiom,
% 0.20/0.47 ! [P2: produc1821101996_sc_sz] :
% 0.20/0.47 ? [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.20/0.47 ( P2
% 0.20/0.47 = ( produc789536734_sc_sz @ X3 @ Y3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_pair
% 0.20/0.47 thf(fact_128_prod__induct3,axiom,
% 0.20/0.47 ! [P: produc1821101996_sc_sz > $o,X: produc1821101996_sc_sz] :
% 0.20/0.47 ( ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) )
% 0.20/0.47 => ( P @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_induct3
% 0.20/0.47 thf(fact_129_prod__cases3,axiom,
% 0.20/0.47 ! [Y: produc1821101996_sc_sz] :
% 0.20/0.47 ~ ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_cases3
% 0.20/0.47 thf(fact_130_fst__conv,axiom,
% 0.20/0.47 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 0.20/0.47 ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 0.20/0.47 = X1 ) ).
% 0.20/0.47
% 0.20/0.47 % fst_conv
% 0.20/0.47 thf(fact_131_fst__conv,axiom,
% 0.20/0.47 ! [X1: set_Fi291318197eal_sz,X22: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( produc286845635eal_sz @ ( produc1235791063eal_sz @ X1 @ X22 ) )
% 0.20/0.47 = X1 ) ).
% 0.20/0.47
% 0.20/0.47 % fst_conv
% 0.20/0.47 thf(fact_132_fst__conv,axiom,
% 0.20/0.47 ! [X1: bounde472938360z_real,X22: bounde472938360z_real] :
% 0.20/0.47 ( ( produc870616579z_real @ ( produc784663575z_real @ X1 @ X22 ) )
% 0.20/0.47 = X1 ) ).
% 0.20/0.47
% 0.20/0.47 % fst_conv
% 0.20/0.47 thf(fact_133_fst__conv,axiom,
% 0.20/0.47 ! [X1: finite824932053eal_sz,X22: finite824932053eal_sz] :
% 0.20/0.47 ( ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ X1 @ X22 ) )
% 0.20/0.47 = X1 ) ).
% 0.20/0.47
% 0.20/0.47 % fst_conv
% 0.20/0.47 thf(fact_134_fst__conv,axiom,
% 0.20/0.47 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 0.20/0.47 ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 0.20/0.47 = X1 ) ).
% 0.20/0.47
% 0.20/0.47 % fst_conv
% 0.20/0.47 thf(fact_135_fst__conv,axiom,
% 0.20/0.47 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.20/0.47 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.20/0.47 = X1 ) ).
% 0.20/0.47
% 0.20/0.47 % fst_conv
% 0.20/0.47 thf(fact_136_fst__eqD,axiom,
% 0.20/0.47 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A2: list_f1238882004_sc_sz] :
% 0.20/0.47 ( ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( X = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fst_eqD
% 0.20/0.47 thf(fact_137_fst__eqD,axiom,
% 0.20/0.47 ! [X: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,A2: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( ( produc286845635eal_sz @ ( produc1235791063eal_sz @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( X = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fst_eqD
% 0.20/0.47 thf(fact_138_fst__eqD,axiom,
% 0.20/0.47 ! [X: bounde472938360z_real,Y: bounde472938360z_real,A2: bounde472938360z_real] :
% 0.20/0.47 ( ( ( produc870616579z_real @ ( produc784663575z_real @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( X = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fst_eqD
% 0.20/0.47 thf(fact_139_fst__eqD,axiom,
% 0.20/0.47 ! [X: finite824932053eal_sz,Y: finite824932053eal_sz,A2: finite824932053eal_sz] :
% 0.20/0.47 ( ( ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( X = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fst_eqD
% 0.20/0.47 thf(fact_140_fst__eqD,axiom,
% 0.20/0.47 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: denota610675952t_unit] :
% 0.20/0.47 ( ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( X = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fst_eqD
% 0.20/0.47 thf(fact_141_fst__eqD,axiom,
% 0.20/0.47 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A2: finite1398487019real_c] :
% 0.20/0.47 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( X = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fst_eqD
% 0.20/0.47 thf(fact_142_snd__conv,axiom,
% 0.20/0.47 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 0.20/0.47 ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % snd_conv
% 0.20/0.47 thf(fact_143_snd__conv,axiom,
% 0.20/0.47 ! [X1: set_Fi291318197eal_sz,X22: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ X1 @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % snd_conv
% 0.20/0.47 thf(fact_144_snd__conv,axiom,
% 0.20/0.47 ! [X1: bounde472938360z_real,X22: bounde472938360z_real] :
% 0.20/0.47 ( ( produc1422611269z_real @ ( produc784663575z_real @ X1 @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % snd_conv
% 0.20/0.47 thf(fact_145_snd__conv,axiom,
% 0.20/0.47 ! [X1: finite824932053eal_sz,X22: finite824932053eal_sz] :
% 0.20/0.47 ( ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ X1 @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % snd_conv
% 0.20/0.47 thf(fact_146_snd__conv,axiom,
% 0.20/0.47 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 0.20/0.47 ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % snd_conv
% 0.20/0.47 thf(fact_147_snd__conv,axiom,
% 0.20/0.47 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.20/0.47 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % snd_conv
% 0.20/0.47 thf(fact_148_snd__eqD,axiom,
% 0.20/0.47 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A2: list_f1238882004_sc_sz] :
% 0.20/0.47 ( ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( Y = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % snd_eqD
% 0.20/0.47 thf(fact_149_snd__eqD,axiom,
% 0.20/0.47 ! [X: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,A2: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( Y = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % snd_eqD
% 0.20/0.47 thf(fact_150_snd__eqD,axiom,
% 0.20/0.47 ! [X: bounde472938360z_real,Y: bounde472938360z_real,A2: bounde472938360z_real] :
% 0.20/0.47 ( ( ( produc1422611269z_real @ ( produc784663575z_real @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( Y = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % snd_eqD
% 0.20/0.47 thf(fact_151_snd__eqD,axiom,
% 0.20/0.47 ! [X: finite824932053eal_sz,Y: finite824932053eal_sz,A2: finite824932053eal_sz] :
% 0.20/0.47 ( ( ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( Y = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % snd_eqD
% 0.20/0.47 thf(fact_152_snd__eqD,axiom,
% 0.20/0.47 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: produc866628903_sc_sz] :
% 0.20/0.47 ( ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( Y = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % snd_eqD
% 0.20/0.47 thf(fact_153_snd__eqD,axiom,
% 0.20/0.47 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A2: finite1398487019real_c] :
% 0.20/0.47 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( Y = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % snd_eqD
% 0.20/0.47 thf(fact_154_prod__eq__iff,axiom,
% 0.20/0.47 ( ( ^ [Y4: produc1149990247eal_sz,Z: produc1149990247eal_sz] : ( Y4 = Z ) )
% 0.20/0.47 = ( ^ [S2: produc1149990247eal_sz,T: produc1149990247eal_sz] :
% 0.20/0.47 ( ( ( produc1111759555eal_sz @ S2 )
% 0.20/0.47 = ( produc1111759555eal_sz @ T ) )
% 0.20/0.47 & ( ( produc1269210629eal_sz @ S2 )
% 0.20/0.47 = ( produc1269210629eal_sz @ T ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_eq_iff
% 0.20/0.47 thf(fact_155_prod__eq__iff,axiom,
% 0.20/0.47 ( ( ^ [Y4: produc1821101996_sc_sz,Z: produc1821101996_sc_sz] : ( Y4 = Z ) )
% 0.20/0.47 = ( ^ [S2: produc1821101996_sc_sz,T: produc1821101996_sc_sz] :
% 0.20/0.47 ( ( ( produc1503602930_sc_sz @ S2 )
% 0.20/0.47 = ( produc1503602930_sc_sz @ T ) )
% 0.20/0.47 & ( ( produc974239792_sc_sz @ S2 )
% 0.20/0.47 = ( produc974239792_sc_sz @ T ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_eq_iff
% 0.20/0.47 thf(fact_156_prod__eq__iff,axiom,
% 0.20/0.47 ( ( ^ [Y4: produc190496183real_c,Z: produc190496183real_c] : ( Y4 = Z ) )
% 0.20/0.47 = ( ^ [S2: produc190496183real_c,T: produc190496183real_c] :
% 0.20/0.47 ( ( ( produc2010422875real_c @ S2 )
% 0.20/0.47 = ( produc2010422875real_c @ T ) )
% 0.20/0.47 & ( ( produc314122909real_c @ S2 )
% 0.20/0.47 = ( produc314122909real_c @ T ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_eq_iff
% 0.20/0.47 thf(fact_157_prod_Oexpand,axiom,
% 0.20/0.47 ! [Prod: produc1149990247eal_sz,Prod2: produc1149990247eal_sz] :
% 0.20/0.47 ( ( ( ( produc1111759555eal_sz @ Prod )
% 0.20/0.47 = ( produc1111759555eal_sz @ Prod2 ) )
% 0.20/0.47 & ( ( produc1269210629eal_sz @ Prod )
% 0.20/0.47 = ( produc1269210629eal_sz @ Prod2 ) ) )
% 0.20/0.47 => ( Prod = Prod2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.expand
% 0.20/0.47 thf(fact_158_prod_Oexpand,axiom,
% 0.20/0.47 ! [Prod: produc1821101996_sc_sz,Prod2: produc1821101996_sc_sz] :
% 0.20/0.47 ( ( ( ( produc1503602930_sc_sz @ Prod )
% 0.20/0.47 = ( produc1503602930_sc_sz @ Prod2 ) )
% 0.20/0.47 & ( ( produc974239792_sc_sz @ Prod )
% 0.20/0.47 = ( produc974239792_sc_sz @ Prod2 ) ) )
% 0.20/0.47 => ( Prod = Prod2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.expand
% 0.20/0.47 thf(fact_159_prod_Oexpand,axiom,
% 0.20/0.47 ! [Prod: produc190496183real_c,Prod2: produc190496183real_c] :
% 0.20/0.47 ( ( ( ( produc2010422875real_c @ Prod )
% 0.20/0.47 = ( produc2010422875real_c @ Prod2 ) )
% 0.20/0.47 & ( ( produc314122909real_c @ Prod )
% 0.20/0.47 = ( produc314122909real_c @ Prod2 ) ) )
% 0.20/0.47 => ( Prod = Prod2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.expand
% 0.20/0.47 thf(fact_160_prod__eqI,axiom,
% 0.20/0.47 ! [P2: produc1149990247eal_sz,Q2: produc1149990247eal_sz] :
% 0.20/0.47 ( ( ( produc1111759555eal_sz @ P2 )
% 0.20/0.47 = ( produc1111759555eal_sz @ Q2 ) )
% 0.20/0.47 => ( ( ( produc1269210629eal_sz @ P2 )
% 0.20/0.47 = ( produc1269210629eal_sz @ Q2 ) )
% 0.20/0.47 => ( P2 = Q2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_eqI
% 0.20/0.47 thf(fact_161_prod__eqI,axiom,
% 0.20/0.47 ! [P2: produc1821101996_sc_sz,Q2: produc1821101996_sc_sz] :
% 0.20/0.47 ( ( ( produc1503602930_sc_sz @ P2 )
% 0.20/0.47 = ( produc1503602930_sc_sz @ Q2 ) )
% 0.20/0.47 => ( ( ( produc974239792_sc_sz @ P2 )
% 0.20/0.47 = ( produc974239792_sc_sz @ Q2 ) )
% 0.20/0.47 => ( P2 = Q2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_eqI
% 0.20/0.47 thf(fact_162_prod__eqI,axiom,
% 0.20/0.47 ! [P2: produc190496183real_c,Q2: produc190496183real_c] :
% 0.20/0.47 ( ( ( produc2010422875real_c @ P2 )
% 0.20/0.47 = ( produc2010422875real_c @ Q2 ) )
% 0.20/0.47 => ( ( ( produc314122909real_c @ P2 )
% 0.20/0.47 = ( produc314122909real_c @ Q2 ) )
% 0.20/0.47 => ( P2 = Q2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_eqI
% 0.20/0.47 thf(fact_163_dfree__Fun,axiom,
% 0.20/0.47 ! [Args: c > trm_a_c,I: a] :
% 0.20/0.47 ( ! [I4: c] : ( dfree_a_c @ ( Args @ I4 ) )
% 0.20/0.47 => ( dfree_a_c @ ( function_a_c @ I @ Args ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Fun
% 0.20/0.47 thf(fact_164_dfree__Fun,axiom,
% 0.20/0.47 ! [Args: sz > trm_sf_sz,I: sf] :
% 0.20/0.47 ( ! [I4: sz] : ( dfree_sf_sz @ ( Args @ I4 ) )
% 0.20/0.47 => ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Fun
% 0.20/0.47 thf(fact_165_dfree_Odfree__Plus,axiom,
% 0.20/0.47 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 0.20/0.47 ( ( dfree_sf_sz @ Theta_1 )
% 0.20/0.47 => ( ( dfree_sf_sz @ Theta_2 )
% 0.20/0.47 => ( dfree_sf_sz @ ( plus_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree.dfree_Plus
% 0.20/0.47 thf(fact_166_dfree_Odfree__Plus,axiom,
% 0.20/0.47 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 0.20/0.47 ( ( dfree_a_c @ Theta_1 )
% 0.20/0.47 => ( ( dfree_a_c @ Theta_2 )
% 0.20/0.47 => ( dfree_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree.dfree_Plus
% 0.20/0.47 thf(fact_167_dfree__Times,axiom,
% 0.20/0.47 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 0.20/0.47 ( ( dfree_a_c @ Theta_1 )
% 0.20/0.47 => ( ( dfree_a_c @ Theta_2 )
% 0.20/0.47 => ( dfree_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Times
% 0.20/0.47 thf(fact_168_dfree__Times,axiom,
% 0.20/0.47 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 0.20/0.47 ( ( dfree_sf_sz @ Theta_1 )
% 0.20/0.47 => ( ( dfree_sf_sz @ Theta_2 )
% 0.20/0.47 => ( dfree_sf_sz @ ( times_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dfree_Times
% 0.20/0.47 thf(fact_169_trm_Odistinct_I23_J,axiom,
% 0.20/0.47 ! [X31: a,X32: c > trm_a_c,X41: trm_a_c,X42: trm_a_c] :
% 0.20/0.47 ( ( function_a_c @ X31 @ X32 )
% 0.20/0.47 != ( plus_a_c @ X41 @ X42 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(23)
% 0.20/0.47 thf(fact_170_trm_Odistinct_I23_J,axiom,
% 0.20/0.47 ! [X31: sf,X32: sz > trm_sf_sz,X41: trm_sf_sz,X42: trm_sf_sz] :
% 0.20/0.47 ( ( function_sf_sz @ X31 @ X32 )
% 0.20/0.47 != ( plus_sf_sz @ X41 @ X42 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(23)
% 0.20/0.47 thf(fact_171_trm_Odistinct_I25_J,axiom,
% 0.20/0.47 ! [X31: a,X32: c > trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 0.20/0.47 ( ( function_a_c @ X31 @ X32 )
% 0.20/0.47 != ( times_a_c @ X51 @ X52 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(25)
% 0.20/0.47 thf(fact_172_trm_Odistinct_I25_J,axiom,
% 0.20/0.47 ! [X31: sf,X32: sz > trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 0.20/0.47 ( ( function_sf_sz @ X31 @ X32 )
% 0.20/0.47 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(25)
% 0.20/0.47 thf(fact_173_trm_Odistinct_I31_J,axiom,
% 0.20/0.47 ! [X41: trm_sf_sz,X42: trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 0.20/0.47 ( ( plus_sf_sz @ X41 @ X42 )
% 0.20/0.47 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(31)
% 0.20/0.47 thf(fact_174_trm_Odistinct_I31_J,axiom,
% 0.20/0.47 ! [X41: trm_a_c,X42: trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 0.20/0.47 ( ( plus_a_c @ X41 @ X42 )
% 0.20/0.47 != ( times_a_c @ X51 @ X52 ) ) ).
% 0.20/0.47
% 0.20/0.47 % trm.distinct(31)
% 0.20/0.47 thf(fact_175_surjective__pairing,axiom,
% 0.20/0.47 ! [T3: produc866628903_sc_sz] :
% 0.20/0.47 ( T3
% 0.20/0.47 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ T3 ) @ ( produc4753477_sc_sz @ T3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjective_pairing
% 0.20/0.47 thf(fact_176_surjective__pairing,axiom,
% 0.20/0.47 ! [T3: produc1241881959eal_sz] :
% 0.20/0.47 ( T3
% 0.20/0.47 = ( produc1235791063eal_sz @ ( produc286845635eal_sz @ T3 ) @ ( produc1746886149eal_sz @ T3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjective_pairing
% 0.20/0.47 thf(fact_177_surjective__pairing,axiom,
% 0.20/0.47 ! [T3: produc1892666919z_real] :
% 0.20/0.47 ( T3
% 0.20/0.47 = ( produc784663575z_real @ ( produc870616579z_real @ T3 ) @ ( produc1422611269z_real @ T3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjective_pairing
% 0.20/0.47 thf(fact_178_surjective__pairing,axiom,
% 0.20/0.47 ! [T3: produc1149990247eal_sz] :
% 0.20/0.47 ( T3
% 0.20/0.47 = ( produc1308130519eal_sz @ ( produc1111759555eal_sz @ T3 ) @ ( produc1269210629eal_sz @ T3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjective_pairing
% 0.20/0.47 thf(fact_179_surjective__pairing,axiom,
% 0.20/0.47 ! [T3: produc1821101996_sc_sz] :
% 0.20/0.47 ( T3
% 0.20/0.47 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ T3 ) @ ( produc974239792_sc_sz @ T3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjective_pairing
% 0.20/0.47 thf(fact_180_surjective__pairing,axiom,
% 0.20/0.47 ! [T3: produc190496183real_c] :
% 0.20/0.47 ( T3
% 0.20/0.47 = ( produc394644079real_c @ ( produc2010422875real_c @ T3 ) @ ( produc314122909real_c @ T3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjective_pairing
% 0.20/0.47 thf(fact_181_prod_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Prod: produc866628903_sc_sz] :
% 0.20/0.47 ( Prod
% 0.20/0.47 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.exhaust_sel
% 0.20/0.47 thf(fact_182_prod_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Prod: produc1241881959eal_sz] :
% 0.20/0.47 ( Prod
% 0.20/0.47 = ( produc1235791063eal_sz @ ( produc286845635eal_sz @ Prod ) @ ( produc1746886149eal_sz @ Prod ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.exhaust_sel
% 0.20/0.47 thf(fact_183_prod_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Prod: produc1892666919z_real] :
% 0.20/0.47 ( Prod
% 0.20/0.47 = ( produc784663575z_real @ ( produc870616579z_real @ Prod ) @ ( produc1422611269z_real @ Prod ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.exhaust_sel
% 0.20/0.47 thf(fact_184_prod_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Prod: produc1149990247eal_sz] :
% 0.20/0.47 ( Prod
% 0.20/0.47 = ( produc1308130519eal_sz @ ( produc1111759555eal_sz @ Prod ) @ ( produc1269210629eal_sz @ Prod ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.exhaust_sel
% 0.20/0.47 thf(fact_185_prod_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Prod: produc1821101996_sc_sz] :
% 0.20/0.47 ( Prod
% 0.20/0.47 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.exhaust_sel
% 0.20/0.47 thf(fact_186_prod_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Prod: produc190496183real_c] :
% 0.20/0.47 ( Prod
% 0.20/0.47 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.exhaust_sel
% 0.20/0.47 thf(fact_187_Pair__le,axiom,
% 0.20/0.47 ! [A2: set_a,B2: set_a,C2: set_a,D: set_a] :
% 0.20/0.47 ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A2 @ B2 ) @ ( produc1928581911_set_a @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_less_eq_set_a @ A2 @ C2 )
% 0.20/0.47 & ( ord_less_eq_set_a @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_188_Pair__le,axiom,
% 0.20/0.47 ! [A2: set_a,B2: a > $o,C2: set_a,D: a > $o] :
% 0.20/0.47 ( ( ord_le501349868_a_a_o @ ( produc634809990_a_a_o @ A2 @ B2 ) @ ( produc634809990_a_a_o @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_less_eq_set_a @ A2 @ C2 )
% 0.20/0.47 & ( ord_less_eq_a_o @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_189_Pair__le,axiom,
% 0.20/0.47 ! [A2: a > $o,B2: set_a,C2: a > $o,D: set_a] :
% 0.20/0.47 ( ( ord_le72828020_set_a @ ( produc1916559302_set_a @ A2 @ B2 ) @ ( produc1916559302_set_a @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_less_eq_a_o @ A2 @ C2 )
% 0.20/0.47 & ( ord_less_eq_set_a @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_190_Pair__le,axiom,
% 0.20/0.47 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 0.20/0.47 ( ( ord_le850691415real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc394644079real_c @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_le775706699real_c @ A2 @ C2 )
% 0.20/0.47 & ( ord_le775706699real_c @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_191_Pair__le,axiom,
% 0.20/0.47 ! [A2: a > $o,B2: a > $o,C2: a > $o,D: a > $o] :
% 0.20/0.47 ( ( ord_le1883211903_o_a_o @ ( product_Pair_a_o_a_o @ A2 @ B2 ) @ ( product_Pair_a_o_a_o @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_less_eq_a_o @ A2 @ C2 )
% 0.20/0.47 & ( ord_less_eq_a_o @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_192_Pair__le,axiom,
% 0.20/0.47 ! [A2: set_Fi291318197eal_sz,B2: set_Fi291318197eal_sz,C2: set_Fi291318197eal_sz,D: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( ord_le978883847eal_sz @ ( produc1235791063eal_sz @ A2 @ B2 ) @ ( produc1235791063eal_sz @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_le41263445eal_sz @ A2 @ C2 )
% 0.20/0.47 & ( ord_le41263445eal_sz @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_193_Pair__le,axiom,
% 0.20/0.47 ! [A2: set_a,B2: trm_sf_sz > trm_sf_sz > $o,C2: set_a,D: trm_sf_sz > trm_sf_sz > $o] :
% 0.20/0.47 ( ( ord_le1884788375f_sz_o @ ( produc1174558183f_sz_o @ A2 @ B2 ) @ ( produc1174558183f_sz_o @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_less_eq_set_a @ A2 @ C2 )
% 0.20/0.47 & ( ord_le8515534f_sz_o @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_194_Pair__le,axiom,
% 0.20/0.47 ! [A2: trm_sf_sz > trm_sf_sz > $o,B2: set_a,C2: trm_sf_sz > trm_sf_sz > $o,D: set_a] :
% 0.20/0.47 ( ( ord_le1643089911_set_a @ ( produc1543226183_set_a @ A2 @ B2 ) @ ( produc1543226183_set_a @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_le8515534f_sz_o @ A2 @ C2 )
% 0.20/0.47 & ( ord_less_eq_set_a @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_195_Pair__le,axiom,
% 0.20/0.47 ! [A2: trm_sf_sz > trm_sf_sz > $o,B2: a > $o,C2: trm_sf_sz > trm_sf_sz > $o,D: a > $o] :
% 0.20/0.47 ( ( ord_le2132572860_o_a_o @ ( produc1152932438_o_a_o @ A2 @ B2 ) @ ( produc1152932438_o_a_o @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_le8515534f_sz_o @ A2 @ C2 )
% 0.20/0.47 & ( ord_less_eq_a_o @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_196_Pair__le,axiom,
% 0.20/0.47 ! [A2: a > $o,B2: trm_sf_sz > trm_sf_sz > $o,C2: a > $o,D: trm_sf_sz > trm_sf_sz > $o] :
% 0.20/0.47 ( ( ord_le472894788f_sz_o @ ( produc593159062f_sz_o @ A2 @ B2 ) @ ( produc593159062f_sz_o @ C2 @ D ) )
% 0.20/0.47 = ( ( ord_less_eq_a_o @ A2 @ C2 )
% 0.20/0.47 & ( ord_le8515534f_sz_o @ B2 @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_le
% 0.20/0.47 thf(fact_197_directional__derivative__def,axiom,
% 0.20/0.47 ( denota2112424896_a_b_c
% 0.20/0.47 = ( ^ [I5: denota231621370t_unit,T: trm_a_c,V2: produc190496183real_c] : ( denota229585092_a_b_c @ I5 @ T @ ( produc2010422875real_c @ V2 ) @ ( produc314122909real_c @ V2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % directional_derivative_def
% 0.20/0.47 thf(fact_198_directional__derivative__def,axiom,
% 0.20/0.47 ( denota453121236_sc_sz
% 0.20/0.47 = ( ^ [I5: denota610675952t_unit,T: trm_sf_sz,V2: produc1149990247eal_sz] : ( denota1979904720_sc_sz @ I5 @ T @ ( produc1111759555eal_sz @ V2 ) @ ( produc1269210629eal_sz @ V2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % directional_derivative_def
% 0.20/0.47 thf(fact_199_raw__interp__inverse,axiom,
% 0.20/0.47 ! [X: freche2095075217_sc_sz] :
% 0.20/0.47 ( ( freche1784963216_sc_sz @ ( freche1421597129_sc_sz @ X ) )
% 0.20/0.47 = X ) ).
% 0.20/0.47
% 0.20/0.47 % raw_interp_inverse
% 0.20/0.47 thf(fact_200_type__definition__strm,axiom,
% 0.20/0.47 type_d1238563341rm_a_c @ frechet_raw_term_a_c @ freche665377492rm_a_c @ ( collect_trm_a_c @ dfree_a_c ) ).
% 0.20/0.47
% 0.20/0.47 % type_definition_strm
% 0.20/0.47 thf(fact_201_type__definition__strm,axiom,
% 0.20/0.47 type_d46389773_sf_sz @ freche782854530_sf_sz @ freche1046279700_sf_sz @ ( collect_trm_sf_sz @ dfree_sf_sz ) ).
% 0.20/0.47
% 0.20/0.47 % type_definition_strm
% 0.20/0.47 thf(fact_202_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.47 ! [P: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A2: produc866628903_sc_sz] :
% 0.20/0.47 ( ( P @ X @ Y )
% 0.20/0.47 => ( ( A2
% 0.20/0.47 = ( produc1822718231_sc_sz @ X @ Y ) )
% 0.20/0.47 => ( P @ ( produc548504323_sc_sz @ A2 ) @ ( produc4753477_sc_sz @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.47 thf(fact_203_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.47 ! [P: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o,X: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,A2: produc1241881959eal_sz] :
% 0.20/0.47 ( ( P @ X @ Y )
% 0.20/0.47 => ( ( A2
% 0.20/0.47 = ( produc1235791063eal_sz @ X @ Y ) )
% 0.20/0.47 => ( P @ ( produc286845635eal_sz @ A2 ) @ ( produc1746886149eal_sz @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.47 thf(fact_204_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.47 ! [P: bounde472938360z_real > bounde472938360z_real > $o,X: bounde472938360z_real,Y: bounde472938360z_real,A2: produc1892666919z_real] :
% 0.20/0.47 ( ( P @ X @ Y )
% 0.20/0.47 => ( ( A2
% 0.20/0.47 = ( produc784663575z_real @ X @ Y ) )
% 0.20/0.47 => ( P @ ( produc870616579z_real @ A2 ) @ ( produc1422611269z_real @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.47 thf(fact_205_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.47 ! [P: finite824932053eal_sz > finite824932053eal_sz > $o,X: finite824932053eal_sz,Y: finite824932053eal_sz,A2: produc1149990247eal_sz] :
% 0.20/0.47 ( ( P @ X @ Y )
% 0.20/0.47 => ( ( A2
% 0.20/0.47 = ( produc1308130519eal_sz @ X @ Y ) )
% 0.20/0.47 => ( P @ ( produc1111759555eal_sz @ A2 ) @ ( produc1269210629eal_sz @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.47 thf(fact_206_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.47 ! [P: denota610675952t_unit > produc866628903_sc_sz > $o,X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: produc1821101996_sc_sz] :
% 0.20/0.47 ( ( P @ X @ Y )
% 0.20/0.47 => ( ( A2
% 0.20/0.47 = ( produc789536734_sc_sz @ X @ Y ) )
% 0.20/0.47 => ( P @ ( produc1503602930_sc_sz @ A2 ) @ ( produc974239792_sc_sz @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.47 thf(fact_207_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.47 ! [P: finite1398487019real_c > finite1398487019real_c > $o,X: finite1398487019real_c,Y: finite1398487019real_c,A2: produc190496183real_c] :
% 0.20/0.47 ( ( P @ X @ Y )
% 0.20/0.47 => ( ( A2
% 0.20/0.47 = ( produc394644079real_c @ X @ Y ) )
% 0.20/0.47 => ( P @ ( produc2010422875real_c @ A2 ) @ ( produc314122909real_c @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.47 thf(fact_208_conjI__realizer,axiom,
% 0.20/0.47 ! [P: list_f1238882004_sc_sz > $o,P2: list_f1238882004_sc_sz,Q: list_f1238882004_sc_sz > $o,Q2: list_f1238882004_sc_sz] :
% 0.20/0.47 ( ( P @ P2 )
% 0.20/0.47 => ( ( Q @ Q2 )
% 0.20/0.47 => ( ( P @ ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ P2 @ Q2 ) ) )
% 0.20/0.47 & ( Q @ ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conjI_realizer
% 0.20/0.47 thf(fact_209_conjI__realizer,axiom,
% 0.20/0.47 ! [P: set_Fi291318197eal_sz > $o,P2: set_Fi291318197eal_sz,Q: set_Fi291318197eal_sz > $o,Q2: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( P @ P2 )
% 0.20/0.47 => ( ( Q @ Q2 )
% 0.20/0.47 => ( ( P @ ( produc286845635eal_sz @ ( produc1235791063eal_sz @ P2 @ Q2 ) ) )
% 0.20/0.47 & ( Q @ ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conjI_realizer
% 0.20/0.47 thf(fact_210_conjI__realizer,axiom,
% 0.20/0.47 ! [P: bounde472938360z_real > $o,P2: bounde472938360z_real,Q: bounde472938360z_real > $o,Q2: bounde472938360z_real] :
% 0.20/0.47 ( ( P @ P2 )
% 0.20/0.47 => ( ( Q @ Q2 )
% 0.20/0.47 => ( ( P @ ( produc870616579z_real @ ( produc784663575z_real @ P2 @ Q2 ) ) )
% 0.20/0.47 & ( Q @ ( produc1422611269z_real @ ( produc784663575z_real @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conjI_realizer
% 0.20/0.47 thf(fact_211_conjI__realizer,axiom,
% 0.20/0.47 ! [P: finite824932053eal_sz > $o,P2: finite824932053eal_sz,Q: finite824932053eal_sz > $o,Q2: finite824932053eal_sz] :
% 0.20/0.47 ( ( P @ P2 )
% 0.20/0.47 => ( ( Q @ Q2 )
% 0.20/0.47 => ( ( P @ ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ P2 @ Q2 ) ) )
% 0.20/0.47 & ( Q @ ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conjI_realizer
% 0.20/0.47 thf(fact_212_conjI__realizer,axiom,
% 0.20/0.47 ! [P: denota610675952t_unit > $o,P2: denota610675952t_unit,Q: produc866628903_sc_sz > $o,Q2: produc866628903_sc_sz] :
% 0.20/0.47 ( ( P @ P2 )
% 0.20/0.47 => ( ( Q @ Q2 )
% 0.20/0.47 => ( ( P @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q2 ) ) )
% 0.20/0.47 & ( Q @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conjI_realizer
% 0.20/0.47 thf(fact_213_conjI__realizer,axiom,
% 0.20/0.47 ! [P: finite1398487019real_c > $o,P2: finite1398487019real_c,Q: finite1398487019real_c > $o,Q2: finite1398487019real_c] :
% 0.20/0.47 ( ( P @ P2 )
% 0.20/0.47 => ( ( Q @ Q2 )
% 0.20/0.47 => ( ( P @ ( produc2010422875real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) )
% 0.20/0.47 & ( Q @ ( produc314122909real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conjI_realizer
% 0.20/0.47 thf(fact_214_exI__realizer,axiom,
% 0.20/0.47 ! [P: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,Y: list_f1238882004_sc_sz,X: list_f1238882004_sc_sz] :
% 0.20/0.47 ( ( P @ Y @ X )
% 0.20/0.47 => ( P @ ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) ) @ ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % exI_realizer
% 0.20/0.47 thf(fact_215_exI__realizer,axiom,
% 0.20/0.47 ! [P: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o,Y: set_Fi291318197eal_sz,X: set_Fi291318197eal_sz] :
% 0.20/0.47 ( ( P @ Y @ X )
% 0.20/0.47 => ( P @ ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ X @ Y ) ) @ ( produc286845635eal_sz @ ( produc1235791063eal_sz @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % exI_realizer
% 0.20/0.47 thf(fact_216_exI__realizer,axiom,
% 0.20/0.47 ! [P: bounde472938360z_real > bounde472938360z_real > $o,Y: bounde472938360z_real,X: bounde472938360z_real] :
% 0.20/0.47 ( ( P @ Y @ X )
% 0.20/0.47 => ( P @ ( produc1422611269z_real @ ( produc784663575z_real @ X @ Y ) ) @ ( produc870616579z_real @ ( produc784663575z_real @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % exI_realizer
% 0.20/0.47 thf(fact_217_exI__realizer,axiom,
% 0.20/0.47 ! [P: finite824932053eal_sz > finite824932053eal_sz > $o,Y: finite824932053eal_sz,X: finite824932053eal_sz] :
% 0.20/0.47 ( ( P @ Y @ X )
% 0.20/0.47 => ( P @ ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ X @ Y ) ) @ ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % exI_realizer
% 0.20/0.47 thf(fact_218_exI__realizer,axiom,
% 0.20/0.47 ! [P: produc866628903_sc_sz > denota610675952t_unit > $o,Y: produc866628903_sc_sz,X: denota610675952t_unit] :
% 0.20/0.47 ( ( P @ Y @ X )
% 0.20/0.47 => ( P @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % exI_realizer
% 0.20/0.47 thf(fact_219_exI__realizer,axiom,
% 0.20/0.47 ! [P: finite1398487019real_c > finite1398487019real_c > $o,Y: finite1398487019real_c,X: finite1398487019real_c] :
% 0.20/0.47 ( ( P @ Y @ X )
% 0.20/0.47 => ( P @ ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) ) @ ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % exI_realizer
% 0.20/0.47 thf(fact_220_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le850691415real_c
% 0.20/0.47 = ( ^ [X2: produc190496183real_c,Y2: produc190496183real_c] :
% 0.20/0.47 ( ( ord_le775706699real_c @ ( produc2010422875real_c @ X2 ) @ ( produc2010422875real_c @ Y2 ) )
% 0.20/0.47 & ( ord_le775706699real_c @ ( produc314122909real_c @ X2 ) @ ( produc314122909real_c @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_221_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le486764743_set_a
% 0.20/0.47 = ( ^ [X2: produc1691597095_set_a,Y2: produc1691597095_set_a] :
% 0.20/0.47 ( ( ord_less_eq_set_a @ ( produc1926412547_set_a @ X2 ) @ ( produc1926412547_set_a @ Y2 ) )
% 0.20/0.47 & ( ord_less_eq_set_a @ ( produc918972485_set_a @ X2 ) @ ( produc918972485_set_a @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_222_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le501349868_a_a_o
% 0.20/0.47 = ( ^ [X2: produc1989635468_a_a_o,Y2: produc1989635468_a_a_o] :
% 0.20/0.47 ( ( ord_less_eq_set_a @ ( produc1911461786_a_a_o @ X2 ) @ ( produc1911461786_a_a_o @ Y2 ) )
% 0.20/0.47 & ( ord_less_eq_a_o @ ( produc23639768_a_a_o @ X2 ) @ ( produc23639768_a_a_o @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_223_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le72828020_set_a
% 0.20/0.47 = ( ^ [X2: produc1561113620_set_a,Y2: produc1561113620_set_a] :
% 0.20/0.47 ( ( ord_less_eq_a_o @ ( produc1045727450_set_a @ X2 ) @ ( produc1045727450_set_a @ Y2 ) )
% 0.20/0.47 & ( ord_less_eq_set_a @ ( produc1305389080_set_a @ X2 ) @ ( produc1305389080_set_a @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_224_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le473656583eal_sz
% 0.20/0.47 = ( ^ [X2: produc1149990247eal_sz,Y2: produc1149990247eal_sz] :
% 0.20/0.47 ( ( ord_le787639925eal_sz @ ( produc1111759555eal_sz @ X2 ) @ ( produc1111759555eal_sz @ Y2 ) )
% 0.20/0.47 & ( ord_le787639925eal_sz @ ( produc1269210629eal_sz @ X2 ) @ ( produc1269210629eal_sz @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_225_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le1883211903_o_a_o
% 0.20/0.47 = ( ^ [X2: product_prod_a_o_a_o,Y2: product_prod_a_o_a_o] :
% 0.20/0.47 ( ( ord_less_eq_a_o @ ( product_fst_a_o_a_o @ X2 ) @ ( product_fst_a_o_a_o @ Y2 ) )
% 0.20/0.47 & ( ord_less_eq_a_o @ ( product_snd_a_o_a_o @ X2 ) @ ( product_snd_a_o_a_o @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_226_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le1884788375f_sz_o
% 0.20/0.47 = ( ^ [X2: produc1144880887f_sz_o,Y2: produc1144880887f_sz_o] :
% 0.20/0.47 ( ( ord_less_eq_set_a @ ( produc38604755f_sz_o @ X2 ) @ ( produc38604755f_sz_o @ Y2 ) )
% 0.20/0.47 & ( ord_le8515534f_sz_o @ ( produc407510293f_sz_o @ X2 ) @ ( produc407510293f_sz_o @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_227_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le1643089911_set_a
% 0.20/0.47 = ( ^ [X2: produc903182423_set_a,Y2: produc903182423_set_a] :
% 0.20/0.47 ( ( ord_le8515534f_sz_o @ ( produc407272755_set_a @ X2 ) @ ( produc407272755_set_a @ Y2 ) )
% 0.20/0.47 & ( ord_less_eq_set_a @ ( produc776178293_set_a @ X2 ) @ ( produc776178293_set_a @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_228_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le2132572860_o_a_o
% 0.20/0.47 = ( ^ [X2: produc1065634396_o_a_o,Y2: produc1065634396_o_a_o] :
% 0.20/0.47 ( ( ord_le8515534f_sz_o @ ( produc2013638506_o_a_o @ X2 ) @ ( produc2013638506_o_a_o @ Y2 ) )
% 0.20/0.47 & ( ord_less_eq_a_o @ ( produc1630531752_o_a_o @ X2 ) @ ( produc1630531752_o_a_o @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_229_less__eq__prod__def,axiom,
% 0.20/0.47 ( ord_le472894788f_sz_o
% 0.20/0.47 = ( ^ [X2: produc1553439972f_sz_o,Y2: produc1553439972f_sz_o] :
% 0.20/0.47 ( ( ord_less_eq_a_o @ ( produc1453865130f_sz_o @ X2 ) @ ( produc1453865130f_sz_o @ Y2 ) )
% 0.20/0.47 & ( ord_le8515534f_sz_o @ ( produc1070758376f_sz_o @ X2 ) @ ( produc1070758376f_sz_o @ Y2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_prod_def
% 0.20/0.47 thf(fact_230_Iagree__sub,axiom,
% 0.20/0.47 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,I3: denota231621370t_unit,J: denota231621370t_unit] :
% 0.20/0.47 ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.47 => ( ( denota69106024_a_b_c @ I3 @ J @ B )
% 0.20/0.47 => ( denota69106024_a_b_c @ I3 @ J @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Iagree_sub
% 0.20/0.47 thf(fact_231_subset__Collect__iff,axiom,
% 0.20/0.47 ! [B: set_Fi291318197eal_sz,A: set_Fi291318197eal_sz,P: finite824932053eal_sz > $o] :
% 0.20/0.47 ( ( ord_le41263445eal_sz @ B @ A )
% 0.20/0.47 => ( ( ord_le41263445eal_sz @ B
% 0.20/0.47 @ ( collec1002602816eal_sz
% 0.20/0.47 @ ^ [X2: finite824932053eal_sz] :
% 0.20/0.47 ( ( member1693951742eal_sz @ X2 @ A )
% 0.20/0.47 & ( P @ X2 ) ) ) )
% 0.20/0.47 = ( ! [X2: finite824932053eal_sz] :
% 0.20/0.47 ( ( member1693951742eal_sz @ X2 @ B )
% 0.20/0.47 => ( P @ X2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_Collect_iff
% 0.20/0.47 thf(fact_232_subset__Collect__iff,axiom,
% 0.20/0.47 ! [B: set_Pr1169339874_sc_sz,A: set_Pr1169339874_sc_sz,P: produc1821101996_sc_sz > $o] :
% 0.20/0.47 ( ( ord_le1230423618_sc_sz @ B @ A )
% 0.20/0.47 => ( ( ord_le1230423618_sc_sz @ B
% 0.20/0.47 @ ( collec1199592193_sc_sz
% 0.20/0.47 @ ^ [X2: produc1821101996_sc_sz] :
% 0.20/0.47 ( ( member1057565379_sc_sz @ X2 @ A )
% 0.20/0.47 & ( P @ X2 ) ) ) )
% 0.20/0.47 = ( ! [X2: produc1821101996_sc_sz] :
% 0.20/0.47 ( ( member1057565379_sc_sz @ X2 @ B )
% 0.20/0.47 => ( P @ X2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_Collect_iff
% 0.20/0.47 thf(fact_233_subset__Collect__iff,axiom,
% 0.20/0.47 ! [B: set_trm_sf_sz,A: set_trm_sf_sz,P: trm_sf_sz > $o] :
% 0.20/0.47 ( ( ord_le1697056455_sf_sz @ B @ A )
% 0.20/0.47 => ( ( ord_le1697056455_sf_sz @ B
% 0.20/0.47 @ ( collect_trm_sf_sz
% 0.20/0.47 @ ^ [X2: trm_sf_sz] :
% 0.20/0.47 ( ( member_trm_sf_sz @ X2 @ A )
% 0.20/0.47 & ( P @ X2 ) ) ) )
% 0.20/0.47 = ( ! [X2: trm_sf_sz] :
% 0.20/0.47 ( ( member_trm_sf_sz @ X2 @ B )
% 0.20/0.47 => ( P @ X2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_Collect_iff
% 0.20/0.47 thf(fact_234_subset__Collect__iff,axiom,
% 0.20/0.47 ! [B: set_trm_a_c,A: set_trm_a_c,P: trm_a_c > $o] :
% 0.20/0.47 ( ( ord_le1369644495rm_a_c @ B @ A )
% 0.20/0.47 => ( ( ord_le1369644495rm_a_c @ B
% 0.20/0.47 @ ( collect_trm_a_c
% 0.20/0.47 @ ^ [X2: trm_a_c] :
% 0.20/0.47 ( ( member_trm_a_c @ X2 @ A )
% 0.20/0.47 & ( P @ X2 ) ) ) )
% 0.20/0.47 = ( ! [X2: trm_a_c] :
% 0.20/0.47 ( ( member_trm_a_c @ X2 @ B )
% 0.20/0.47 => ( P @ X2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_Collect_iff
% 0.20/0.47 thf(fact_235_subset__Collect__iff,axiom,
% 0.20/0.47 ! [B: set_a,A: set_a,P: a > $o] :
% 0.20/0.47 ( ( ord_less_eq_set_a @ B @ A )
% 0.20/0.47 => ( ( ord_less_eq_set_a @ B
% 0.20/0.47 @ ( collect_a
% 0.20/0.47 @ ^ [X2: a] :
% 0.20/0.47 ( ( member_a @ X2 @ A )
% 0.20/0.47 & ( P @ X2 ) ) ) )
% 0.20/0.47 = ( ! [X2: a] :
% 0.20/0.47 ( ( member_a @ X2 @ B )
% 0.20/0.47 => ( P @ X2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_Collect_iff
% 0.20/0.47 thf(fact_236_subset__Collect__iff,axiom,
% 0.20/0.47 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,P: sum_su737395349um_b_c > $o] :
% 0.20/0.47 ( ( ord_le929608341um_b_c @ B @ A )
% 0.20/0.47 => ( ( ord_le929608341um_b_c @ B
% 0.20/0.47 @ ( collec2086029184um_b_c
% 0.20/0.47 @ ^ [X2: sum_su737395349um_b_c] :
% 0.20/0.47 ( ( member1893232190um_b_c @ X2 @ A )
% 0.20/0.47 & ( P @ X2 ) ) ) )
% 0.20/0.47 = ( ! [X2: sum_su737395349um_b_c] :
% 0.20/0.47 ( ( member1893232190um_b_c @ X2 @ B )
% 0.20/0.47 => ( P @ X2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_Collect_iff
% 0.20/0.47 thf(fact_237_subset__CollectI,axiom,
% 0.20/0.47 ! [B: set_Fi291318197eal_sz,A: set_Fi291318197eal_sz,Q: finite824932053eal_sz > $o,P: finite824932053eal_sz > $o] :
% 0.31/0.47 ( ( ord_le41263445eal_sz @ B @ A )
% 0.31/0.47 => ( ! [X3: finite824932053eal_sz] :
% 0.31/0.47 ( ( member1693951742eal_sz @ X3 @ B )
% 0.31/0.47 => ( ( Q @ X3 )
% 0.31/0.47 => ( P @ X3 ) ) )
% 0.31/0.47 => ( ord_le41263445eal_sz
% 0.31/0.47 @ ( collec1002602816eal_sz
% 0.31/0.47 @ ^ [X2: finite824932053eal_sz] :
% 0.31/0.47 ( ( member1693951742eal_sz @ X2 @ B )
% 0.31/0.47 & ( Q @ X2 ) ) )
% 0.31/0.47 @ ( collec1002602816eal_sz
% 0.31/0.47 @ ^ [X2: finite824932053eal_sz] :
% 0.31/0.47 ( ( member1693951742eal_sz @ X2 @ A )
% 0.31/0.47 & ( P @ X2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_CollectI
% 0.31/0.47 thf(fact_238_subset__CollectI,axiom,
% 0.31/0.47 ! [B: set_Pr1169339874_sc_sz,A: set_Pr1169339874_sc_sz,Q: produc1821101996_sc_sz > $o,P: produc1821101996_sc_sz > $o] :
% 0.31/0.47 ( ( ord_le1230423618_sc_sz @ B @ A )
% 0.31/0.47 => ( ! [X3: produc1821101996_sc_sz] :
% 0.31/0.47 ( ( member1057565379_sc_sz @ X3 @ B )
% 0.31/0.47 => ( ( Q @ X3 )
% 0.31/0.47 => ( P @ X3 ) ) )
% 0.31/0.47 => ( ord_le1230423618_sc_sz
% 0.31/0.47 @ ( collec1199592193_sc_sz
% 0.31/0.47 @ ^ [X2: produc1821101996_sc_sz] :
% 0.31/0.47 ( ( member1057565379_sc_sz @ X2 @ B )
% 0.31/0.47 & ( Q @ X2 ) ) )
% 0.31/0.47 @ ( collec1199592193_sc_sz
% 0.31/0.47 @ ^ [X2: produc1821101996_sc_sz] :
% 0.31/0.47 ( ( member1057565379_sc_sz @ X2 @ A )
% 0.31/0.47 & ( P @ X2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_CollectI
% 0.31/0.47 thf(fact_239_subset__CollectI,axiom,
% 0.31/0.47 ! [B: set_trm_sf_sz,A: set_trm_sf_sz,Q: trm_sf_sz > $o,P: trm_sf_sz > $o] :
% 0.31/0.47 ( ( ord_le1697056455_sf_sz @ B @ A )
% 0.31/0.47 => ( ! [X3: trm_sf_sz] :
% 0.31/0.47 ( ( member_trm_sf_sz @ X3 @ B )
% 0.31/0.47 => ( ( Q @ X3 )
% 0.31/0.47 => ( P @ X3 ) ) )
% 0.31/0.47 => ( ord_le1697056455_sf_sz
% 0.31/0.47 @ ( collect_trm_sf_sz
% 0.31/0.47 @ ^ [X2: trm_sf_sz] :
% 0.31/0.47 ( ( member_trm_sf_sz @ X2 @ B )
% 0.31/0.47 & ( Q @ X2 ) ) )
% 0.31/0.47 @ ( collect_trm_sf_sz
% 0.31/0.47 @ ^ [X2: trm_sf_sz] :
% 0.31/0.47 ( ( member_trm_sf_sz @ X2 @ A )
% 0.31/0.47 & ( P @ X2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_CollectI
% 0.31/0.47 thf(fact_240_subset__CollectI,axiom,
% 0.31/0.47 ! [B: set_trm_a_c,A: set_trm_a_c,Q: trm_a_c > $o,P: trm_a_c > $o] :
% 0.31/0.47 ( ( ord_le1369644495rm_a_c @ B @ A )
% 0.31/0.47 => ( ! [X3: trm_a_c] :
% 0.31/0.47 ( ( member_trm_a_c @ X3 @ B )
% 0.31/0.47 => ( ( Q @ X3 )
% 0.31/0.47 => ( P @ X3 ) ) )
% 0.31/0.47 => ( ord_le1369644495rm_a_c
% 0.31/0.47 @ ( collect_trm_a_c
% 0.31/0.47 @ ^ [X2: trm_a_c] :
% 0.31/0.47 ( ( member_trm_a_c @ X2 @ B )
% 0.31/0.47 & ( Q @ X2 ) ) )
% 0.31/0.47 @ ( collect_trm_a_c
% 0.31/0.47 @ ^ [X2: trm_a_c] :
% 0.31/0.47 ( ( member_trm_a_c @ X2 @ A )
% 0.31/0.47 & ( P @ X2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_CollectI
% 0.31/0.47 thf(fact_241_subset__CollectI,axiom,
% 0.31/0.47 ! [B: set_a,A: set_a,Q: a > $o,P: a > $o] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ B @ A )
% 0.31/0.47 => ( ! [X3: a] :
% 0.31/0.47 ( ( member_a @ X3 @ B )
% 0.31/0.47 => ( ( Q @ X3 )
% 0.31/0.47 => ( P @ X3 ) ) )
% 0.31/0.47 => ( ord_less_eq_set_a
% 0.31/0.47 @ ( collect_a
% 0.31/0.47 @ ^ [X2: a] :
% 0.31/0.47 ( ( member_a @ X2 @ B )
% 0.31/0.47 & ( Q @ X2 ) ) )
% 0.31/0.47 @ ( collect_a
% 0.31/0.47 @ ^ [X2: a] :
% 0.31/0.47 ( ( member_a @ X2 @ A )
% 0.31/0.47 & ( P @ X2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_CollectI
% 0.31/0.47 thf(fact_242_subset__CollectI,axiom,
% 0.31/0.47 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,Q: sum_su737395349um_b_c > $o,P: sum_su737395349um_b_c > $o] :
% 0.31/0.47 ( ( ord_le929608341um_b_c @ B @ A )
% 0.31/0.47 => ( ! [X3: sum_su737395349um_b_c] :
% 0.31/0.47 ( ( member1893232190um_b_c @ X3 @ B )
% 0.31/0.47 => ( ( Q @ X3 )
% 0.31/0.47 => ( P @ X3 ) ) )
% 0.31/0.47 => ( ord_le929608341um_b_c
% 0.31/0.47 @ ( collec2086029184um_b_c
% 0.31/0.47 @ ^ [X2: sum_su737395349um_b_c] :
% 0.31/0.47 ( ( member1893232190um_b_c @ X2 @ B )
% 0.31/0.47 & ( Q @ X2 ) ) )
% 0.31/0.47 @ ( collec2086029184um_b_c
% 0.31/0.47 @ ^ [X2: sum_su737395349um_b_c] :
% 0.31/0.47 ( ( member1893232190um_b_c @ X2 @ A )
% 0.31/0.47 & ( P @ X2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_CollectI
% 0.31/0.47 thf(fact_243_Pair__mono,axiom,
% 0.31/0.47 ! [X: set_a,X4: set_a,Y: set_a,Y5: set_a] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ X @ X4 )
% 0.31/0.47 => ( ( ord_less_eq_set_a @ Y @ Y5 )
% 0.31/0.47 => ( ord_le486764743_set_a @ ( produc1928581911_set_a @ X @ Y ) @ ( produc1928581911_set_a @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_244_Pair__mono,axiom,
% 0.31/0.47 ! [X: set_a,X4: set_a,Y: a > $o,Y5: a > $o] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ X @ X4 )
% 0.31/0.47 => ( ( ord_less_eq_a_o @ Y @ Y5 )
% 0.31/0.47 => ( ord_le501349868_a_a_o @ ( produc634809990_a_a_o @ X @ Y ) @ ( produc634809990_a_a_o @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_245_Pair__mono,axiom,
% 0.31/0.47 ! [X: a > $o,X4: a > $o,Y: set_a,Y5: set_a] :
% 0.31/0.47 ( ( ord_less_eq_a_o @ X @ X4 )
% 0.31/0.47 => ( ( ord_less_eq_set_a @ Y @ Y5 )
% 0.31/0.47 => ( ord_le72828020_set_a @ ( produc1916559302_set_a @ X @ Y ) @ ( produc1916559302_set_a @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_246_Pair__mono,axiom,
% 0.31/0.47 ! [X: finite1398487019real_c,X4: finite1398487019real_c,Y: finite1398487019real_c,Y5: finite1398487019real_c] :
% 0.31/0.47 ( ( ord_le775706699real_c @ X @ X4 )
% 0.31/0.47 => ( ( ord_le775706699real_c @ Y @ Y5 )
% 0.31/0.47 => ( ord_le850691415real_c @ ( produc394644079real_c @ X @ Y ) @ ( produc394644079real_c @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_247_Pair__mono,axiom,
% 0.31/0.47 ! [X: a > $o,X4: a > $o,Y: a > $o,Y5: a > $o] :
% 0.31/0.47 ( ( ord_less_eq_a_o @ X @ X4 )
% 0.31/0.47 => ( ( ord_less_eq_a_o @ Y @ Y5 )
% 0.31/0.47 => ( ord_le1883211903_o_a_o @ ( product_Pair_a_o_a_o @ X @ Y ) @ ( product_Pair_a_o_a_o @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_248_Pair__mono,axiom,
% 0.31/0.47 ! [X: set_Fi291318197eal_sz,X4: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,Y5: set_Fi291318197eal_sz] :
% 0.31/0.47 ( ( ord_le41263445eal_sz @ X @ X4 )
% 0.31/0.47 => ( ( ord_le41263445eal_sz @ Y @ Y5 )
% 0.31/0.47 => ( ord_le978883847eal_sz @ ( produc1235791063eal_sz @ X @ Y ) @ ( produc1235791063eal_sz @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_249_Pair__mono,axiom,
% 0.31/0.47 ! [X: set_a,X4: set_a,Y: trm_sf_sz > trm_sf_sz > $o,Y5: trm_sf_sz > trm_sf_sz > $o] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ X @ X4 )
% 0.31/0.47 => ( ( ord_le8515534f_sz_o @ Y @ Y5 )
% 0.31/0.47 => ( ord_le1884788375f_sz_o @ ( produc1174558183f_sz_o @ X @ Y ) @ ( produc1174558183f_sz_o @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_250_Pair__mono,axiom,
% 0.31/0.47 ! [X: trm_sf_sz > trm_sf_sz > $o,X4: trm_sf_sz > trm_sf_sz > $o,Y: set_a,Y5: set_a] :
% 0.31/0.47 ( ( ord_le8515534f_sz_o @ X @ X4 )
% 0.31/0.47 => ( ( ord_less_eq_set_a @ Y @ Y5 )
% 0.31/0.47 => ( ord_le1643089911_set_a @ ( produc1543226183_set_a @ X @ Y ) @ ( produc1543226183_set_a @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_251_Pair__mono,axiom,
% 0.31/0.47 ! [X: trm_sf_sz > trm_sf_sz > $o,X4: trm_sf_sz > trm_sf_sz > $o,Y: a > $o,Y5: a > $o] :
% 0.31/0.47 ( ( ord_le8515534f_sz_o @ X @ X4 )
% 0.31/0.47 => ( ( ord_less_eq_a_o @ Y @ Y5 )
% 0.31/0.47 => ( ord_le2132572860_o_a_o @ ( produc1152932438_o_a_o @ X @ Y ) @ ( produc1152932438_o_a_o @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_252_Pair__mono,axiom,
% 0.31/0.47 ! [X: a > $o,X4: a > $o,Y: trm_sf_sz > trm_sf_sz > $o,Y5: trm_sf_sz > trm_sf_sz > $o] :
% 0.31/0.47 ( ( ord_less_eq_a_o @ X @ X4 )
% 0.31/0.47 => ( ( ord_le8515534f_sz_o @ Y @ Y5 )
% 0.31/0.47 => ( ord_le472894788f_sz_o @ ( produc593159062f_sz_o @ X @ Y ) @ ( produc593159062f_sz_o @ X4 @ Y5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_mono
% 0.31/0.47 thf(fact_253_fst__mono,axiom,
% 0.31/0.47 ! [X: produc1149990247eal_sz,Y: produc1149990247eal_sz] :
% 0.31/0.47 ( ( ord_le473656583eal_sz @ X @ Y )
% 0.31/0.47 => ( ord_le787639925eal_sz @ ( produc1111759555eal_sz @ X ) @ ( produc1111759555eal_sz @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fst_mono
% 0.31/0.47 thf(fact_254_fst__mono,axiom,
% 0.31/0.47 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.31/0.47 ( ( ord_le850691415real_c @ X @ Y )
% 0.31/0.47 => ( ord_le775706699real_c @ ( produc2010422875real_c @ X ) @ ( produc2010422875real_c @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fst_mono
% 0.31/0.47 thf(fact_255_snd__mono,axiom,
% 0.31/0.47 ! [X: produc1149990247eal_sz,Y: produc1149990247eal_sz] :
% 0.31/0.47 ( ( ord_le473656583eal_sz @ X @ Y )
% 0.31/0.47 => ( ord_le787639925eal_sz @ ( produc1269210629eal_sz @ X ) @ ( produc1269210629eal_sz @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % snd_mono
% 0.31/0.47 thf(fact_256_snd__mono,axiom,
% 0.31/0.47 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.31/0.47 ( ( ord_le850691415real_c @ X @ Y )
% 0.31/0.47 => ( ord_le775706699real_c @ ( produc314122909real_c @ X ) @ ( produc314122909real_c @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % snd_mono
% 0.31/0.47 thf(fact_257_exE__realizer_H,axiom,
% 0.31/0.47 ! [P: finite824932053eal_sz > finite824932053eal_sz > $o,P2: produc1149990247eal_sz] :
% 0.31/0.47 ( ( P @ ( produc1269210629eal_sz @ P2 ) @ ( produc1111759555eal_sz @ P2 ) )
% 0.31/0.47 => ~ ! [X3: finite824932053eal_sz,Y3: finite824932053eal_sz] :
% 0.31/0.47 ~ ( P @ Y3 @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % exE_realizer'
% 0.31/0.47 thf(fact_258_exE__realizer_H,axiom,
% 0.31/0.47 ! [P: produc866628903_sc_sz > denota610675952t_unit > $o,P2: produc1821101996_sc_sz] :
% 0.31/0.47 ( ( P @ ( produc974239792_sc_sz @ P2 ) @ ( produc1503602930_sc_sz @ P2 ) )
% 0.31/0.47 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.31/0.47 ~ ( P @ Y3 @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % exE_realizer'
% 0.31/0.47 thf(fact_259_exE__realizer_H,axiom,
% 0.31/0.47 ! [P: finite1398487019real_c > finite1398487019real_c > $o,P2: produc190496183real_c] :
% 0.31/0.47 ( ( P @ ( produc314122909real_c @ P2 ) @ ( produc2010422875real_c @ P2 ) )
% 0.31/0.47 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.31/0.47 ~ ( P @ Y3 @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % exE_realizer'
% 0.31/0.47 thf(fact_260_sum_Oinject_I1_J,axiom,
% 0.31/0.47 ! [X1: a,Y1: a] :
% 0.31/0.47 ( ( ( sum_In2139678582um_b_c @ X1 )
% 0.31/0.47 = ( sum_In2139678582um_b_c @ Y1 ) )
% 0.31/0.47 = ( X1 = Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % sum.inject(1)
% 0.31/0.47 thf(fact_261_old_Osum_Oinject_I1_J,axiom,
% 0.31/0.47 ! [A2: a,A3: a] :
% 0.31/0.47 ( ( ( sum_In2139678582um_b_c @ A2 )
% 0.31/0.47 = ( sum_In2139678582um_b_c @ A3 ) )
% 0.31/0.47 = ( A2 = A3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.sum.inject(1)
% 0.31/0.47 thf(fact_262_good__interp__inverse,axiom,
% 0.31/0.47 ! [Y: denota231621370t_unit] :
% 0.31/0.47 ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.31/0.47 => ( ( freche1608036107_a_b_c @ ( freche1473475332_a_b_c @ Y ) )
% 0.31/0.47 = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % good_interp_inverse
% 0.31/0.47 thf(fact_263_good__interp__inverse,axiom,
% 0.31/0.47 ! [Y: denota610675952t_unit] :
% 0.31/0.47 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.31/0.47 => ( ( freche1421597129_sc_sz @ ( freche1784963216_sc_sz @ Y ) )
% 0.31/0.47 = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % good_interp_inverse
% 0.31/0.47 thf(fact_264_f0__def,axiom,
% 0.31/0.47 ( f0_sf_sz
% 0.31/0.47 = ( ^ [F: sf] : ( function_sf_sz @ F @ empty_sz_sf ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % f0_def
% 0.31/0.47 thf(fact_265_subsetI,axiom,
% 0.31/0.47 ! [A: set_Fi291318197eal_sz,B: set_Fi291318197eal_sz] :
% 0.31/0.47 ( ! [X3: finite824932053eal_sz] :
% 0.31/0.47 ( ( member1693951742eal_sz @ X3 @ A )
% 0.31/0.47 => ( member1693951742eal_sz @ X3 @ B ) )
% 0.31/0.47 => ( ord_le41263445eal_sz @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetI
% 0.31/0.47 thf(fact_266_subsetI,axiom,
% 0.31/0.47 ! [A: set_Pr1169339874_sc_sz,B: set_Pr1169339874_sc_sz] :
% 0.31/0.47 ( ! [X3: produc1821101996_sc_sz] :
% 0.31/0.47 ( ( member1057565379_sc_sz @ X3 @ A )
% 0.31/0.47 => ( member1057565379_sc_sz @ X3 @ B ) )
% 0.31/0.47 => ( ord_le1230423618_sc_sz @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetI
% 0.31/0.47 thf(fact_267_subsetI,axiom,
% 0.31/0.47 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.31/0.47 ( ! [X3: sum_su737395349um_b_c] :
% 0.31/0.47 ( ( member1893232190um_b_c @ X3 @ A )
% 0.31/0.47 => ( member1893232190um_b_c @ X3 @ B ) )
% 0.31/0.47 => ( ord_le929608341um_b_c @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetI
% 0.31/0.47 thf(fact_268_subsetI,axiom,
% 0.31/0.47 ! [A: set_trm_sf_sz,B: set_trm_sf_sz] :
% 0.31/0.47 ( ! [X3: trm_sf_sz] :
% 0.31/0.47 ( ( member_trm_sf_sz @ X3 @ A )
% 0.31/0.47 => ( member_trm_sf_sz @ X3 @ B ) )
% 0.31/0.47 => ( ord_le1697056455_sf_sz @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetI
% 0.31/0.47 thf(fact_269_subsetI,axiom,
% 0.31/0.47 ! [A: set_trm_a_c,B: set_trm_a_c] :
% 0.31/0.47 ( ! [X3: trm_a_c] :
% 0.31/0.47 ( ( member_trm_a_c @ X3 @ A )
% 0.31/0.47 => ( member_trm_a_c @ X3 @ B ) )
% 0.31/0.47 => ( ord_le1369644495rm_a_c @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetI
% 0.31/0.47 thf(fact_270_subsetI,axiom,
% 0.31/0.47 ! [A: set_a,B: set_a] :
% 0.31/0.47 ( ! [X3: a] :
% 0.31/0.47 ( ( member_a @ X3 @ A )
% 0.31/0.47 => ( member_a @ X3 @ B ) )
% 0.31/0.47 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetI
% 0.31/0.47 thf(fact_271_raw__interp__induct,axiom,
% 0.31/0.47 ! [Y: denota231621370t_unit,P: denota231621370t_unit > $o] :
% 0.31/0.47 ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.31/0.47 => ( ! [X3: freche914690577_a_b_c] : ( P @ ( freche1608036107_a_b_c @ X3 ) )
% 0.31/0.47 => ( P @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % raw_interp_induct
% 0.31/0.47 thf(fact_272_raw__interp__induct,axiom,
% 0.31/0.47 ! [Y: denota610675952t_unit,P: denota610675952t_unit > $o] :
% 0.31/0.47 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.31/0.47 => ( ! [X3: freche2095075217_sc_sz] : ( P @ ( freche1421597129_sc_sz @ X3 ) )
% 0.31/0.47 => ( P @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % raw_interp_induct
% 0.31/0.47 thf(fact_273_raw__interp__cases,axiom,
% 0.31/0.47 ! [Y: denota231621370t_unit] :
% 0.31/0.47 ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.31/0.47 => ~ ! [X3: freche914690577_a_b_c] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( freche1608036107_a_b_c @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % raw_interp_cases
% 0.31/0.47 thf(fact_274_raw__interp__cases,axiom,
% 0.31/0.47 ! [Y: denota610675952t_unit] :
% 0.31/0.47 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.31/0.47 => ~ ! [X3: freche2095075217_sc_sz] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( freche1421597129_sc_sz @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % raw_interp_cases
% 0.31/0.47 thf(fact_275_raw__interp,axiom,
% 0.31/0.47 ! [X: freche914690577_a_b_c] : ( member1777622435t_unit @ ( freche1608036107_a_b_c @ X ) @ ( collec451781861t_unit @ denota258389581_a_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % raw_interp
% 0.31/0.47 thf(fact_276_raw__interp,axiom,
% 0.31/0.47 ! [X: freche2095075217_sc_sz] : ( member754147591t_unit @ ( freche1421597129_sc_sz @ X ) @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ).
% 0.31/0.47
% 0.31/0.47 % raw_interp
% 0.31/0.47 thf(fact_277_good__interp__cases,axiom,
% 0.31/0.47 ! [X: freche914690577_a_b_c] :
% 0.31/0.47 ~ ! [Y3: denota231621370t_unit] :
% 0.31/0.47 ( ( X
% 0.31/0.47 = ( freche1473475332_a_b_c @ Y3 ) )
% 0.31/0.47 => ~ ( member1777622435t_unit @ Y3 @ ( collec451781861t_unit @ denota258389581_a_b_c ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % good_interp_cases
% 0.31/0.47 thf(fact_278_good__interp__cases,axiom,
% 0.31/0.47 ! [X: freche2095075217_sc_sz] :
% 0.31/0.47 ~ ! [Y3: denota610675952t_unit] :
% 0.31/0.47 ( ( X
% 0.31/0.47 = ( freche1784963216_sc_sz @ Y3 ) )
% 0.31/0.47 => ~ ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % good_interp_cases
% 0.31/0.47 thf(fact_279_good__interp__induct,axiom,
% 0.31/0.47 ! [P: freche914690577_a_b_c > $o,X: freche914690577_a_b_c] :
% 0.31/0.47 ( ! [Y3: denota231621370t_unit] :
% 0.31/0.47 ( ( member1777622435t_unit @ Y3 @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.31/0.47 => ( P @ ( freche1473475332_a_b_c @ Y3 ) ) )
% 0.31/0.47 => ( P @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % good_interp_induct
% 0.31/0.47 thf(fact_280_good__interp__induct,axiom,
% 0.31/0.47 ! [P: freche2095075217_sc_sz > $o,X: freche2095075217_sc_sz] :
% 0.31/0.47 ( ! [Y3: denota610675952t_unit] :
% 0.31/0.47 ( ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.31/0.47 => ( P @ ( freche1784963216_sc_sz @ Y3 ) ) )
% 0.31/0.47 => ( P @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % good_interp_induct
% 0.31/0.47 thf(fact_281_good__interp__inject,axiom,
% 0.31/0.47 ! [X: denota231621370t_unit,Y: denota231621370t_unit] :
% 0.31/0.47 ( ( member1777622435t_unit @ X @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.31/0.47 => ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 0.31/0.47 => ( ( ( freche1473475332_a_b_c @ X )
% 0.31/0.47 = ( freche1473475332_a_b_c @ Y ) )
% 0.31/0.47 = ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % good_interp_inject
% 0.31/0.47 thf(fact_282_good__interp__inject,axiom,
% 0.31/0.47 ! [X: denota610675952t_unit,Y: denota610675952t_unit] :
% 0.31/0.47 ( ( member754147591t_unit @ X @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.31/0.47 => ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.31/0.47 => ( ( ( freche1784963216_sc_sz @ X )
% 0.31/0.47 = ( freche1784963216_sc_sz @ Y ) )
% 0.31/0.47 = ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % good_interp_inject
% 0.31/0.47 thf(fact_283_subset__antisym,axiom,
% 0.31/0.47 ! [A: set_a,B: set_a] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.31/0.47 => ( ( ord_less_eq_set_a @ B @ A )
% 0.31/0.47 => ( A = B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_antisym
% 0.31/0.47 thf(fact_284_Collect__mono__iff,axiom,
% 0.31/0.47 ! [P: finite824932053eal_sz > $o,Q: finite824932053eal_sz > $o] :
% 0.31/0.47 ( ( ord_le41263445eal_sz @ ( collec1002602816eal_sz @ P ) @ ( collec1002602816eal_sz @ Q ) )
% 0.31/0.47 = ( ! [X2: finite824932053eal_sz] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono_iff
% 0.31/0.47 thf(fact_285_Collect__mono__iff,axiom,
% 0.31/0.47 ! [P: produc1821101996_sc_sz > $o,Q: produc1821101996_sc_sz > $o] :
% 0.31/0.47 ( ( ord_le1230423618_sc_sz @ ( collec1199592193_sc_sz @ P ) @ ( collec1199592193_sc_sz @ Q ) )
% 0.31/0.47 = ( ! [X2: produc1821101996_sc_sz] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono_iff
% 0.31/0.47 thf(fact_286_Collect__mono__iff,axiom,
% 0.31/0.47 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 0.31/0.47 ( ( ord_le1697056455_sf_sz @ ( collect_trm_sf_sz @ P ) @ ( collect_trm_sf_sz @ Q ) )
% 0.31/0.47 = ( ! [X2: trm_sf_sz] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono_iff
% 0.31/0.47 thf(fact_287_Collect__mono__iff,axiom,
% 0.31/0.47 ! [P: trm_a_c > $o,Q: trm_a_c > $o] :
% 0.31/0.47 ( ( ord_le1369644495rm_a_c @ ( collect_trm_a_c @ P ) @ ( collect_trm_a_c @ Q ) )
% 0.31/0.47 = ( ! [X2: trm_a_c] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono_iff
% 0.31/0.47 thf(fact_288_Collect__mono__iff,axiom,
% 0.31/0.47 ! [P: a > $o,Q: a > $o] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.31/0.47 = ( ! [X2: a] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono_iff
% 0.31/0.47 thf(fact_289_Collect__mono__iff,axiom,
% 0.31/0.47 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.31/0.47 ( ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) )
% 0.31/0.47 = ( ! [X2: sum_su737395349um_b_c] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono_iff
% 0.31/0.47 thf(fact_290_set__eq__subset,axiom,
% 0.31/0.47 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.31/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 0.31/0.47 & ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % set_eq_subset
% 0.31/0.47 thf(fact_291_subset__trans,axiom,
% 0.31/0.47 ! [A: set_a,B: set_a,C3: set_a] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.31/0.47 => ( ( ord_less_eq_set_a @ B @ C3 )
% 0.31/0.47 => ( ord_less_eq_set_a @ A @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_trans
% 0.31/0.47 thf(fact_292_Collect__mono,axiom,
% 0.31/0.47 ! [P: produc1821101996_sc_sz > $o,Q: produc1821101996_sc_sz > $o] :
% 0.31/0.47 ( ! [X3: produc1821101996_sc_sz] :
% 0.31/0.47 ( ( P @ X3 )
% 0.31/0.47 => ( Q @ X3 ) )
% 0.31/0.47 => ( ord_le1230423618_sc_sz @ ( collec1199592193_sc_sz @ P ) @ ( collec1199592193_sc_sz @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono
% 0.31/0.47 thf(fact_293_Collect__mono,axiom,
% 0.31/0.47 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 0.31/0.47 ( ! [X3: trm_sf_sz] :
% 0.31/0.47 ( ( P @ X3 )
% 0.31/0.47 => ( Q @ X3 ) )
% 0.31/0.47 => ( ord_le1697056455_sf_sz @ ( collect_trm_sf_sz @ P ) @ ( collect_trm_sf_sz @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono
% 0.31/0.47 thf(fact_294_Collect__mono,axiom,
% 0.31/0.47 ! [P: trm_a_c > $o,Q: trm_a_c > $o] :
% 0.31/0.47 ( ! [X3: trm_a_c] :
% 0.31/0.47 ( ( P @ X3 )
% 0.31/0.47 => ( Q @ X3 ) )
% 0.31/0.47 => ( ord_le1369644495rm_a_c @ ( collect_trm_a_c @ P ) @ ( collect_trm_a_c @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono
% 0.31/0.47 thf(fact_295_Collect__mono,axiom,
% 0.31/0.47 ! [P: a > $o,Q: a > $o] :
% 0.31/0.47 ( ! [X3: a] :
% 0.31/0.47 ( ( P @ X3 )
% 0.31/0.47 => ( Q @ X3 ) )
% 0.31/0.47 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono
% 0.31/0.47 thf(fact_296_Collect__mono,axiom,
% 0.31/0.47 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.31/0.47 ( ! [X3: sum_su737395349um_b_c] :
% 0.31/0.47 ( ( P @ X3 )
% 0.31/0.47 => ( Q @ X3 ) )
% 0.31/0.47 => ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono
% 0.31/0.47 thf(fact_297_subset__iff,axiom,
% 0.31/0.47 ( ord_less_eq_set_a
% 0.31/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.31/0.47 ! [T: a] :
% 0.31/0.47 ( ( member_a @ T @ A5 )
% 0.31/0.47 => ( member_a @ T @ B5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_iff
% 0.31/0.47 thf(fact_298_subset__eq,axiom,
% 0.31/0.47 ( ord_less_eq_set_a
% 0.31/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.31/0.47 ! [X2: a] :
% 0.31/0.47 ( ( member_a @ X2 @ A5 )
% 0.31/0.47 => ( member_a @ X2 @ B5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_eq
% 0.31/0.47 thf(fact_299_subsetD,axiom,
% 0.31/0.47 ! [A: set_a,B: set_a,C2: a] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.31/0.47 => ( ( member_a @ C2 @ A )
% 0.31/0.47 => ( member_a @ C2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetD
% 0.31/0.47 thf(fact_300_in__mono,axiom,
% 0.31/0.47 ! [A: set_a,B: set_a,X: a] :
% 0.31/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.31/0.47 => ( ( member_a @ X @ A )
% 0.31/0.47 => ( member_a @ X @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_mono
% 0.31/0.47 thf(fact_301_Inl__inject,axiom,
% 0.31/0.47 ! [X: a,Y: a] :
% 0.31/0.47 ( ( ( sum_In2139678582um_b_c @ X )
% 0.31/0.47 = ( sum_In2139678582um_b_c @ Y ) )
% 0.31/0.47 => ( X = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % Inl_inject
% 0.31/0.47 thf(fact_302_Collect__subset,axiom,
% 0.31/0.47 ! [A: set_a,P: a > $o] :
% 0.31/0.47 ( ord_less_eq_set_a
% 0.31/0.47 @ ( collect_a
% 0.31/0.47 @ ^ [X2: a] :
% 0.31/0.47 ( ( member_a @ X2 @ A )
% 0.31/0.47 & ( P @ X2 ) ) )
% 0.31/0.47 @ A ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_subset
% 0.31/0.47 thf(fact_303_Collect__subset,axiom,
% 0.31/0.47 ! [A: set_Su1783761653um_b_c,P: sum_su737395349um_b_c > $o] :
% 0.31/0.47 ( ord_le929608341um_b_c
% 0.31/0.47 @ ( collec2086029184um_b_c
% 0.31/0.47 @ ^ [X2: sum_su737395349um_b_c] :
% 0.31/0.47 ( ( member1893232190um_b_c @ X2 @ A )
% 0.31/0.47 & ( P @ X2 ) ) )
% 0.31/0.47 @ A ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_subset
% 0.31/0.47 thf(fact_304_less__eq__set__def,axiom,
% 0.31/0.47 ( ord_less_eq_set_a
% 0.31/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.31/0.47 ( ord_less_eq_a_o
% 0.31/0.47 @ ^ [X2: a] : ( member_a @ X2 @ A5 )
% 0.31/0.47 @ ^ [X2: a] : ( member_a @ X2 @ B5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_eq_set_def
% 0.31/0.47 thf(fact_305_sterm__determines__frechet,axiom,
% 0.31/0.47 ! [I3: denota231621370t_unit,J: denota231621370t_unit,Theta_12: trm_a_c,Theta_22: trm_a_c,Nu: produc190496183real_c] :
% 0.31/0.47 ( ( denota258389581_a_b_c @ I3 )
% 0.31/0.47 => ( ( denota258389581_a_b_c @ J )
% 0.31/0.47 => ( ( dfree_a_c @ Theta_12 )
% 0.31/0.47 => ( ( dfree_a_c @ Theta_22 )
% 0.31/0.47 => ( ( ( denota2042094639_a_b_c @ I3 @ Theta_12 )
% 0.31/0.47 = ( denota2042094639_a_b_c @ J @ Theta_22 ) )
% 0.31/0.47 => ( ( denota229585092_a_b_c @ I3 @ Theta_12 @ ( produc2010422875real_c @ Nu ) @ ( produc314122909real_c @ Nu ) )
% 0.31/0.47 = ( denota229585092_a_b_c @ J @ Theta_22 @ ( produc2010422875real_c @ Nu ) @ ( produc314122909real_c @ Nu ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sterm_determines_frechet
% 0.31/0.47 thf(fact_306_sterm__determines__frechet,axiom,
% 0.31/0.47 ! [I3: denota610675952t_unit,J: denota610675952t_unit,Theta_12: trm_sf_sz,Theta_22: trm_sf_sz,Nu: produc1149990247eal_sz] :
% 0.31/0.47 ( ( denota1579475975_sc_sz @ I3 )
% 0.31/0.47 => ( ( denota1579475975_sc_sz @ J )
% 0.31/0.47 => ( ( dfree_sf_sz @ Theta_12 )
% 0.31/0.47 => ( ( dfree_sf_sz @ Theta_22 )
% 0.31/0.47 => ( ( ( denota1179238309_sc_sz @ I3 @ Theta_12 )
% 0.31/0.47 = ( denota1179238309_sc_sz @ J @ Theta_22 ) )
% 0.31/0.47 => ( ( denota1979904720_sc_sz @ I3 @ Theta_12 @ ( produc1111759555eal_sz @ Nu ) @ ( produc1269210629eal_sz @ Nu ) )
% 0.31/0.47 = ( denota1979904720_sc_sz @ J @ Theta_22 @ ( produc1111759555eal_sz @ Nu ) @ ( produc1269210629eal_sz @ Nu ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sterm_determines_frechet
% 0.31/0.47 thf(fact_307_type__definition__good__interp,axiom,
% 0.31/0.47 type_d1092523951t_unit @ freche1421597129_sc_sz @ freche1784963216_sc_sz @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ).
% 0.31/0.47
% 0.31/0.47 % type_definition_good_interp
% 0.31/0.47 thf(fact_308_image2__def,axiom,
% 0.31/0.47 ( bNF_Gr1775200401_sc_sz
% 0.31/0.47 = ( ^ [A5: set_a,F: a > denota610675952t_unit,G: a > produc866628903_sc_sz] :
% 0.31/0.47 ( collec1199592193_sc_sz
% 0.31/0.47 @ ^ [Uu: produc1821101996_sc_sz] :
% 0.31/0.47 ? [A6: a] :
% 0.31/0.47 ( ( Uu
% 0.31/0.47 = ( produc789536734_sc_sz @ ( F @ A6 ) @ ( G @ A6 ) ) )
% 0.31/0.47 & ( member_a @ A6 @ A5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % image2_def
% 0.31/0.47 thf(fact_309_image2__eqI,axiom,
% 0.31/0.47 ! [B2: denota610675952t_unit,F2: a > denota610675952t_unit,X: a,C2: produc866628903_sc_sz,G2: a > produc866628903_sc_sz,A: set_a] :
% 0.31/0.47 ( ( B2
% 0.31/0.47 = ( F2 @ X ) )
% 0.31/0.47 => ( ( C2
% 0.31/0.47 = ( G2 @ X ) )
% 0.31/0.47 => ( ( member_a @ X @ A )
% 0.31/0.47 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ B2 @ C2 ) @ ( bNF_Gr1775200401_sc_sz @ A @ F2 @ G2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % image2_eqI
% 0.31/0.47 thf(fact_310_coincidence__sterm_H,axiom,
% 0.31/0.47 ! [Theta: trm_a_c,Nu: produc190496183real_c,Nu2: produc190496183real_c,I3: denota231621370t_unit,J: denota231621370t_unit] :
% 0.31/0.47 ( ( dfree_a_c @ Theta )
% 0.31/0.47 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVT_a_c @ Theta ) )
% 0.31/0.47 => ( ( denota69106024_a_b_c @ I3 @ J
% 0.31/0.47 @ ( collec2086029184um_b_c
% 0.31/0.47 @ ^ [Uu: sum_su737395349um_b_c] :
% 0.31/0.47 ? [X2: a] :
% 0.31/0.47 ( ( Uu
% 0.31/0.47 = ( sum_In2139678582um_b_c @ X2 ) )
% 0.31/0.47 & ( member_a @ X2 @ ( static_SIGT_a_c @ Theta ) ) ) ) )
% 0.31/0.47 => ( ( denota2042094639_a_b_c @ I3 @ Theta @ ( produc2010422875real_c @ Nu ) )
% 0.31/0.47 = ( denota2042094639_a_b_c @ J @ Theta @ ( produc2010422875real_c @ Nu2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % coincidence_sterm'
% 0.31/0.47 thf(fact_311_pred__subset__eq,axiom,
% 0.31/0.47 ! [R: set_a,S3: set_a] :
% 0.31/0.47 ( ( ord_less_eq_a_o
% 0.31/0.47 @ ^ [X2: a] : ( member_a @ X2 @ R )
% 0.31/0.47 @ ^ [X2: a] : ( member_a @ X2 @ S3 ) )
% 0.31/0.47 = ( ord_less_eq_set_a @ R @ S3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pred_subset_eq
% 0.31/0.47 thf(fact_312_sterm__continuous_H,axiom,
% 0.31/0.47 ! [I3: denota610675952t_unit,Theta: trm_sf_sz,S3: set_Fi291318197eal_sz] :
% 0.31/0.47 ( ( denota1579475975_sc_sz @ I3 )
% 0.31/0.47 => ( ( dfree_sf_sz @ Theta )
% 0.31/0.47 => ( topolo1348430467z_real @ S3 @ ( denota1179238309_sc_sz @ I3 @ Theta ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sterm_continuous'
% 0.31/0.47 thf(fact_313_agree__func__fvt,axiom,
% 0.31/0.47 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,F2: sf,Args: sz > trm_sf_sz,I: sz] :
% 0.31/0.47 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVT_sf_sz @ ( function_sf_sz @ F2 @ Args ) ) )
% 0.31/0.47 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVT_sf_sz @ ( Args @ I ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % agree_func_fvt
% 0.31/0.47 thf(fact_314_subrelI,axiom,
% 0.31/0.47 ! [R2: set_Pr1169339874_sc_sz,S4: set_Pr1169339874_sc_sz] :
% 0.31/0.47 ( ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.31/0.47 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ R2 )
% 0.31/0.47 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ S4 ) )
% 0.31/0.47 => ( ord_le1230423618_sc_sz @ R2 @ S4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % subrelI
% 0.31/0.47 thf(fact_315_FVDiff__sub,axiom,
% 0.31/0.47 ! [F2: trm_a_c] : ( ord_le1772180283um_c_c @ ( static_FVT_a_c @ F2 ) @ ( static_FVDiff_a_c @ F2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % FVDiff_sub
% 0.31/0.47 thf(fact_316_pred__equals__eq2,axiom,
% 0.31/0.47 ! [R: set_Pr1169339874_sc_sz,S3: set_Pr1169339874_sc_sz] :
% 0.31/0.47 ( ( ( ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ R ) )
% 0.31/0.47 = ( ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ S3 ) ) )
% 0.31/0.47 = ( R = S3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pred_equals_eq2
% 0.31/0.47 thf(fact_317_pred__subset__eq2,axiom,
% 0.31/0.47 ! [R: set_Pr1169339874_sc_sz,S3: set_Pr1169339874_sc_sz] :
% 0.31/0.47 ( ( ord_le108471557c_sz_o
% 0.31/0.47 @ ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ R )
% 0.31/0.47 @ ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ S3 ) )
% 0.31/0.47 = ( ord_le1230423618_sc_sz @ R @ S3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pred_subset_eq2
% 0.31/0.47 thf(fact_318_sterm__continuous,axiom,
% 0.31/0.47 ! [I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.31/0.47 ( ( denota1579475975_sc_sz @ I3 )
% 0.31/0.47 => ( ( dfree_sf_sz @ Theta )
% 0.31/0.47 => ( topolo1348430467z_real @ top_to1873962757eal_sz @ ( denota1179238309_sc_sz @ I3 @ Theta ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sterm_continuous
% 0.31/0.47 thf(fact_319_continuous__on__cases__le,axiom,
% 0.31/0.47 ! [S4: set_Fi291318197eal_sz,H: finite824932053eal_sz > real,A2: real,F2: finite824932053eal_sz > bounde472938360z_real,G2: finite824932053eal_sz > bounde472938360z_real] :
% 0.31/0.47 ( ( topolo885751137z_real
% 0.31/0.47 @ ( collec1002602816eal_sz
% 0.31/0.47 @ ^ [T: finite824932053eal_sz] :
% 0.31/0.47 ( ( member1693951742eal_sz @ T @ S4 )
% 0.31/0.47 & ( ord_less_eq_real @ ( H @ T ) @ A2 ) ) )
% 0.31/0.47 @ F2 )
% 0.31/0.47 => ( ( topolo885751137z_real
% 0.31/0.47 @ ( collec1002602816eal_sz
% 0.31/0.47 @ ^ [T: finite824932053eal_sz] :
% 0.31/0.47 ( ( member1693951742eal_sz @ T @ S4 )
% 0.31/0.47 & ( ord_less_eq_real @ A2 @ ( H @ T ) ) ) )
% 0.31/0.47 @ G2 )
% 0.31/0.47 => ( ( topolo1348430467z_real @ S4 @ H )
% 0.31/0.47 => ( ! [T4: finite824932053eal_sz] :
% 0.31/0.47 ( ( member1693951742eal_sz @ T4 @ S4 )
% 0.31/0.47 => ( ( ( H @ T4 )
% 0.31/0.47 = A2 )
% 0.31/0.47 => ( ( F2 @ T4 )
% 0.31/0.47 = ( G2 @ T4 ) ) ) )
% 0.31/0.47 => ( topolo885751137z_real @ S4
% 0.31/0.47 @ ^ [T: finite824932053eal_sz] : ( if_Bou1785791806z_real @ ( ord_less_eq_real @ ( H @ T ) @ A2 ) @ ( F2 @ T ) @ ( G2 @ T ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % continuous_on_cases_le
% 0.31/0.47 thf(fact_320_UNIV__I,axiom,
% 0.31/0.47 ! [X: a] : ( member_a @ X @ top_top_set_a ) ).
% 0.31/0.47
% 0.31/0.47 % UNIV_I
% 0.31/0.47 thf(fact_321_UNIV__I,axiom,
% 0.31/0.47 ! [X: finite824932053eal_sz] : ( member1693951742eal_sz @ X @ top_to1873962757eal_sz ) ).
% 0.31/0.47
% 0.31/0.47 % UNIV_I
% 0.31/0.47 thf(fact_322_top_Oextremum__uniqueI,axiom,
% 0.31/0.47 ! [A2: set_Fi291318197eal_sz] :
% 0.31/0.47 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A2 )
% 0.31/0.47 => ( A2 = top_to1873962757eal_sz ) ) ).
% 0.31/0.47
% 0.31/0.47 % top.extremum_uniqueI
% 0.31/0.47 thf(fact_323_top_Oextremum__unique,axiom,
% 0.31/0.47 ! [A2: set_Fi291318197eal_sz] :
% 0.31/0.47 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A2 )
% 0.31/0.47 = ( A2 = top_to1873962757eal_sz ) ) ).
% 0.31/0.47
% 0.31/0.47 % top.extremum_unique
% 0.31/0.47 thf(fact_324_top__greatest,axiom,
% 0.31/0.47 ! [A2: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A2 @ top_to1873962757eal_sz ) ).
% 0.31/0.47
% 0.31/0.47 % top_greatest
% 0.31/0.47 thf(fact_325_subset__UNIV,axiom,
% 0.31/0.47 ! [A: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A @ top_to1873962757eal_sz ) ).
% 0.31/0.47
% 0.31/0.47 % subset_UNIV
% 0.31/0.47 thf(fact_326_ids_Oseq__sem_Ocases,axiom,
% 0.31/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,X: produc1821101996_sc_sz] :
% 0.31/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.31/0.47 => ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( produc789536734_sc_sz @ I2 @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ids.seq_sem.cases
% 0.31/0.47 thf(fact_327_UNIV__def,axiom,
% 0.31/0.47 ( top_to524132421um_b_c
% 0.31/0.47 = ( collec2086029184um_b_c
% 0.31/0.47 @ ^ [X2: sum_su737395349um_b_c] : $true ) ) ).
% 0.31/0.47
% 0.31/0.47 % UNIV_def
% 0.31/0.47 thf(fact_328_UNIV__def,axiom,
% 0.31/0.47 ( top_to1873962757eal_sz
% 0.31/0.47 = ( collec1002602816eal_sz
% 0.31/0.47 @ ^ [X2: finite824932053eal_sz] : $true ) ) ).
% 0.31/0.47
% 0.31/0.47 % UNIV_def
% 0.31/0.47 thf(fact_329_UNIV__witness,axiom,
% 0.31/0.47 ? [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).
% 0.31/0.47
% 0.31/0.47 % UNIV_witness
% 0.31/0.47 thf(fact_330_UNIV__witness,axiom,
% 0.31/0.47 ? [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ top_to1873962757eal_sz ) ).
% 0.31/0.47
% 0.31/0.47 % UNIV_witness
% 0.31/0.47 thf(fact_331_UNIV__eq__I,axiom,
% 0.31/0.47 ! [A: set_a] :
% 0.31/0.47 ( ! [X3: a] : ( member_a @ X3 @ A )
% 0.31/0.47 => ( top_top_set_a = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % UNIV_eq_I
% 0.31/0.47 thf(fact_332_UNIV__eq__I,axiom,
% 0.31/0.47 ! [A: set_Fi291318197eal_sz] :
% 0.31/0.47 ( ! [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ A )
% 0.31/0.47 => ( top_to1873962757eal_sz = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % UNIV_eq_I
% 0.31/0.47 thf(fact_333_top__prod__def,axiom,
% 0.31/0.47 ( top_to1787697847eal_sz
% 0.31/0.47 = ( produc1235791063eal_sz @ top_to1873962757eal_sz @ top_to1873962757eal_sz ) ) ).
% 0.31/0.47
% 0.31/0.47 % top_prod_def
% 0.31/0.47 thf(fact_334_ids_OP__def,axiom,
% 0.31/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P2: sc] :
% 0.31/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.31/0.47 => ( ( p_sc_sf_sz @ P2 )
% 0.31/0.47 = ( predic913887884_sf_sz @ P2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ids.P_def
% 0.31/0.47 thf(fact_335_frechet__continuous,axiom,
% 0.31/0.47 ! [I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.31/0.47 ( ( denota1579475975_sc_sz @ I3 )
% 0.31/0.47 => ( ( dfree_sf_sz @ Theta )
% 0.31/0.47 => ( topolo885751137z_real @ top_to1873962757eal_sz @ ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % frechet_continuous
% 0.31/0.47 thf(fact_336_top__empty__eq2,axiom,
% 0.31/0.47 ( top_to1399053141c_sz_o
% 0.31/0.47 = ( ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ top_to1499569298_sc_sz ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % top_empty_eq2
% 0.31/0.47 thf(fact_337_top__set__def,axiom,
% 0.31/0.47 ( top_to524132421um_b_c
% 0.31/0.47 = ( collec2086029184um_b_c @ top_to1201357528_b_c_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % top_set_def
% 0.31/0.47 thf(fact_338_top__set__def,axiom,
% 0.31/0.47 ( top_to1873962757eal_sz
% 0.31/0.47 = ( collec1002602816eal_sz @ top_to646513176l_sz_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % top_set_def
% 0.31/0.47 thf(fact_339_Vagree__univ,axiom,
% 0.31/0.47 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 0.31/0.47 ( ( denota1997846518gree_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc394644079real_c @ C2 @ D ) @ top_to1660572043um_c_c )
% 0.31/0.47 => ( ( A2 = C2 )
% 0.31/0.47 & ( B2 = D ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Vagree_univ
% 0.31/0.47 thf(fact_340_agree__UNIV__eq,axiom,
% 0.31/0.47 ! [Nu: produc190496183real_c,Omega: produc190496183real_c] :
% 0.31/0.47 ( ( denota1997846518gree_c @ Nu @ Omega @ top_to1660572043um_c_c )
% 0.31/0.47 => ( Nu = Omega ) ) ).
% 0.31/0.47
% 0.31/0.47 % agree_UNIV_eq
% 0.31/0.47 thf(fact_341_ids_Ofrechet__continuous,axiom,
% 0.31/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.31/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.31/0.47 => ( ( denota1579475975_sc_sz @ I3 )
% 0.31/0.47 => ( ( dfree_sf_sz @ Theta )
% 0.31/0.47 => ( topolo885751137z_real @ top_to1873962757eal_sz @ ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ids.frechet_continuous
% 0.31/0.47 thf(fact_342_frechet__blin,axiom,
% 0.31/0.47 ! [I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.31/0.47 ( ( denota1579475975_sc_sz @ I3 )
% 0.31/0.47 => ( ( dfree_sf_sz @ Theta )
% 0.31/0.47 => ( ( ^ [V2: finite824932053eal_sz] : ( bounde397081123z_real @ ( denota1979904720_sc_sz @ I3 @ Theta @ V2 ) ) )
% 0.31/0.47 = ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % frechet_blin
% 0.31/0.47 thf(fact_343_continuous__on__const,axiom,
% 0.31/0.47 ! [S4: set_Fi291318197eal_sz,C2: bounde472938360z_real] :
% 0.31/0.47 ( topolo885751137z_real @ S4
% 0.31/0.47 @ ^ [X2: finite824932053eal_sz] : C2 ) ).
% 0.31/0.47
% 0.31/0.47 % continuous_on_const
% 0.31/0.47 thf(fact_344_continuous__on__subset,axiom,
% 0.31/0.47 ! [S4: set_Fi291318197eal_sz,F2: finite824932053eal_sz > bounde472938360z_real,T3: set_Fi291318197eal_sz] :
% 0.31/0.47 ( ( topolo885751137z_real @ S4 @ F2 )
% 0.31/0.47 => ( ( ord_le41263445eal_sz @ T3 @ S4 )
% 0.31/0.47 => ( topolo885751137z_real @ T3 @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % continuous_on_subset
% 0.31/0.47 thf(fact_345_continuous__on__Pair,axiom,
% 0.31/0.47 ! [S4: set_Fi291318197eal_sz,F2: finite824932053eal_sz > bounde472938360z_real,G2: finite824932053eal_sz > bounde472938360z_real] :
% 0.31/0.47 ( ( topolo885751137z_real @ S4 @ F2 )
% 0.31/0.47 => ( ( topolo885751137z_real @ S4 @ G2 )
% 0.31/0.47 => ( topolo1027477648z_real @ S4
% 0.31/0.47 @ ^ [X2: finite824932053eal_sz] : ( produc784663575z_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % continuous_on_Pair
% 0.31/0.47 thf(fact_346_ids_Ofrechet__blin,axiom,
% 0.31/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.31/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.31/0.47 => ( ( denota1579475975_sc_sz @ I3 )
% 0.31/0.47 => ( ( dfree_sf_sz @ Theta )
% 0.31/0.47 => ( ( ^ [V2: finite824932053eal_sz] : ( bounde397081123z_real @ ( denota1979904720_sc_sz @ I3 @ Theta @ V2 ) ) )
% 0.31/0.47 = ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ids.frechet_blin
% 0.31/0.47 thf(fact_347_blin__frechet_Oabs__eq,axiom,
% 0.31/0.47 ! [Xb: denota610675952t_unit,Xa: trm_sf_sz,X: finite824932053eal_sz] :
% 0.31/0.47 ( ( bNF_eq1660582207t_unit @ denota1579475975_sc_sz @ Xb @ Xb )
% 0.31/0.47 => ( ( bNF_eq_onp_trm_sf_sz @ dfree_sf_sz @ Xa @ Xa )
% 0.31/0.47 => ( ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ Xb ) @ ( freche1046279700_sf_sz @ Xa ) @ X )
% 0.31/0.47 = ( bounde397081123z_real @ ( denota1979904720_sc_sz @ Xb @ Xa @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % blin_frechet.abs_eq
% 0.31/0.47 thf(fact_348_ids_Oblin__frechet_Oabs__eq,axiom,
% 0.31/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,Xb: denota610675952t_unit,Xa: trm_sf_sz,X: finite824932053eal_sz] :
% 0.31/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.31/0.47 => ( ( bNF_eq1660582207t_unit @ denota1579475975_sc_sz @ Xb @ Xb )
% 0.31/0.47 => ( ( bNF_eq_onp_trm_sf_sz @ dfree_sf_sz @ Xa @ Xa )
% 0.31/0.47 => ( ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ Xb ) @ ( freche1046279700_sf_sz @ Xa ) @ X )
% 0.31/0.47 = ( bounde397081123z_real @ ( denota1979904720_sc_sz @ Xb @ Xa @ X ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ids.blin_frechet.abs_eq
% 0.31/0.47 thf(fact_349_Quotient__good__interp,axiom,
% 0.31/0.47 quotie842200089_sc_sz @ ( bNF_eq1660582207t_unit @ denota1579475975_sc_sz ) @ freche1784963216_sc_sz @ freche1421597129_sc_sz @ freche58918398_sc_sz ).
% 0.31/0.47
% 0.31/0.47 % Quotient_good_interp
% 0.31/0.47 thf(fact_350_Quotient__strm,axiom,
% 0.31/0.47 quotie1467858509rm_a_c @ ( bNF_eq_onp_trm_a_c @ dfree_a_c ) @ freche665377492rm_a_c @ frechet_raw_term_a_c @ frechet_cr_strm_a_c ).
% 0.31/0.47
% 0.31/0.47 % Quotient_strm
% 0.31/0.47 thf(fact_351_Quotient__strm,axiom,
% 0.31/0.47 quotie1549861309_sf_sz @ ( bNF_eq_onp_trm_sf_sz @ dfree_sf_sz ) @ freche1046279700_sf_sz @ freche782854530_sf_sz @ freche1244000341_sf_sz ).
% 0.31/0.47
% 0.31/0.47 % Quotient_strm
% 0.31/0.47 thf(fact_352_eq__onp__le__eq,axiom,
% 0.31/0.47 ! [P: denota610675952t_unit > $o] :
% 0.31/0.47 ( ord_le2003534918unit_o @ ( bNF_eq1660582207t_unit @ P )
% 0.31/0.47 @ ^ [Y4: denota610675952t_unit,Z: denota610675952t_unit] : ( Y4 = Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_onp_le_eq
% 0.31/0.47 thf(fact_353_eq__onp__le__eq,axiom,
% 0.31/0.47 ! [P: trm_sf_sz > $o] :
% 0.31/0.47 ( ord_le8515534f_sz_o @ ( bNF_eq_onp_trm_sf_sz @ P )
% 0.31/0.47 @ ^ [Y4: trm_sf_sz,Z: trm_sf_sz] : ( Y4 = Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_onp_le_eq
% 0.31/0.47
% 0.31/0.47 % Helper facts (3)
% 0.31/0.47 thf(help_If_3_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 0.31/0.47 ! [P: $o] :
% 0.31/0.47 ( ( P = $true )
% 0.31/0.47 | ( P = $false ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_2_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 0.31/0.47 ! [X: bounde472938360z_real,Y: bounde472938360z_real] :
% 0.31/0.47 ( ( if_Bou1785791806z_real @ $false @ X @ Y )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_1_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 0.31/0.47 ! [X: bounde472938360z_real,Y: bounde472938360z_real] :
% 0.31/0.47 ( ( if_Bou1785791806z_real @ $true @ X @ Y )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 3.17/1.82 ---- Embedded in THF ---
% 3.17/1.82 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.17/1.82 %%% Generated on Tue Feb 24 08:24:25 EST 2026
% 3.17/1.82 %%% using '$$dhol' embedding, version 1.3.0.
% 3.17/1.82 %%% Logic specification used:
% 3.17/1.82 %%% thf(spec, logic, $$dhol).
% 3.17/1.82
% 3.17/1.82 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VtE5UpiK52/DTF2DTF30300.p
% See solution above
% 3.17/1.82 ------------------------
% 3.17/1.86 ---- Cleaned THF ---
% 3.17/1.86 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_J,type,
% 3.17/1.86 set_Pr1169339874_sc_sz: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 3.17/1.86 produc1821101996_sc_sz: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_It__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_Mt__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_J,type,
% 3.17/1.86 produc1892666919z_real: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J_J,type,
% 3.17/1.86 produc1241881959eal_sz: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 3.17/1.86 produc1149990247eal_sz: $tType ).
% 3.17/1.86
% 3.17/1.86 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,
% 3.17/1.86 produc190496183real_c: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 3.17/1.86 produc866628903_sc_sz: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_Eo_J_J_J,type,
% 3.17/1.86 produc1144880887f_sz_o: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_I_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_Eo_J_J_Mt__Set__Oset_Itf__a_J_J,type,
% 3.17/1.86 produc903182423_set_a: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__a_M_Eo_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_Eo_J_J_J,type,
% 3.17/1.86 produc1553439972f_sz_o: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_I_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_Eo_J_J_M_062_Itf__a_M_Eo_J_J,type,
% 3.17/1.86 produc1065634396_o_a_o: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J,type,
% 3.17/1.86 bounde472938360z_real: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Set__Oset_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 3.17/1.86 set_De208295462t_unit: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Set__Oset_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J_J,type,
% 3.17/1.86 set_De455519194t_unit: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 3.17/1.86 denota610675952t_unit: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J,type,
% 3.17/1.86 denota231621370t_unit: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J_J,type,
% 3.17/1.86 set_Su1783761653um_b_c: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 3.17/1.86 set_Fi291318197eal_sz: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Frechet____Correctness__Oids__Ogood____interp_Itf__sf_Mtf__sc_Mtf__sz_J,type,
% 3.17/1.86 freche2095075217_sc_sz: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_Mt__Set__Oset_Itf__a_J_J,type,
% 3.17/1.86 produc1691597095_set_a: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Frechet____Correctness__Oids__Ogood____interp_Itf__a_Mtf__b_Mtf__c_J,type,
% 3.17/1.86 freche914690577_a_b_c: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_M_062_Itf__a_M_Eo_J_J,type,
% 3.17/1.86 produc1989635468_a_a_o: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__a_M_Eo_J_Mt__Set__Oset_Itf__a_J_J,type,
% 3.17/1.86 produc1561113620_set_a: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J,type,
% 3.17/1.86 sum_su737395349um_b_c: $tType ).
% 3.17/1.86
% 3.17/1.86 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__a_M_Eo_J_M_062_Itf__a_M_Eo_J_J,type,
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% 3.17/1.86 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_Itf__a_J_001_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_062_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_M_Eo_J_J,type,
% 3.17/1.86 produc407510293f_sz_o: produc1144880887f_sz_o > trm_sf_sz > trm_sf_sz > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_Itf__a_J_001_062_Itf__a_M_Eo_J,type,
% 3.17/1.86 produc23639768_a_a_o: produc1989635468_a_a_o > a > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
% 3.17/1.86 produc918972485_set_a: produc1691597095_set_a > set_a ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Set_OCollect_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J,type,
% 3.17/1.86 collec451781861t_unit: ( denota231621370t_unit > $o ) > set_De455519194t_unit ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Set_OCollect_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 3.17/1.86 collec1767975749t_unit: ( denota610675952t_unit > $o ) > set_De208295462t_unit ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Set_OCollect_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 3.17/1.86 collec1002602816eal_sz: ( finite824932053eal_sz > $o ) > set_Fi291318197eal_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 3.17/1.86 collec1199592193_sc_sz: ( produc1821101996_sc_sz > $o ) > set_Pr1169339874_sc_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J,type,
% 3.17/1.86 collec2086029184um_b_c: ( sum_su737395349um_b_c > $o ) > set_Su1783761653um_b_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Set_OCollect_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 3.17/1.86 collect_trm_a_c: ( trm_a_c > $o ) > set_trm_a_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Set_OCollect_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 3.17/1.86 collect_trm_sf_sz: ( trm_sf_sz > $o ) > set_trm_sf_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Set_OCollect_001tf__a,type,
% 3.17/1.86 collect_a: ( a > $o ) > set_a ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Static__Semantics_OFVDiff_001tf__a_001tf__c,type,
% 3.17/1.86 static_FVDiff_a_c: trm_a_c > set_Sum_sum_c_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Static__Semantics_OFVDiff_001tf__sf_001tf__sz,type,
% 3.17/1.86 static_FVDiff_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Static__Semantics_OFVT_001tf__a_001tf__c,type,
% 3.17/1.86 static_FVT_a_c: trm_a_c > set_Sum_sum_c_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Static__Semantics_OFVT_001tf__sf_001tf__sz,type,
% 3.17/1.86 static_FVT_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Static__Semantics_OSIGT_001tf__a_001tf__c,type,
% 3.17/1.86 static_SIGT_a_c: trm_a_c > set_a ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Sum__Type_OInl_001tf__a_001t__Sum____Type__Osum_Itf__b_Mtf__c_J,type,
% 3.17/1.86 sum_In2139678582um_b_c: a > sum_su737395349um_b_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_OPredicational_001tf__sc_001tf__sf_001tf__sz,type,
% 3.17/1.86 predic913887884_sf_sz: sc > formula_sf_sc_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Odfree_001tf__a_001tf__c,type,
% 3.17/1.86 dfree_a_c: trm_a_c > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Odfree_001tf__sf_001tf__sz,type,
% 3.17/1.86 dfree_sf_sz: trm_sf_sz > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Oids_OP_001tf__sc_001tf__sf_001tf__sz,type,
% 3.17/1.86 p_sc_sf_sz: sc > formula_sf_sc_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Oids_Oempty_001tf__sz_001tf__sf,type,
% 3.17/1.86 empty_sz_sf: sz > trm_sf_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Oids_Of0_001tf__sf_001tf__sz,type,
% 3.17/1.86 f0_sf_sz: sf > trm_sf_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Otrm_OFunction_001tf__a_001tf__c,type,
% 3.17/1.86 function_a_c: a > ( c > trm_a_c ) > trm_a_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Otrm_OFunction_001tf__sf_001tf__sz,type,
% 3.17/1.86 function_sf_sz: sf > ( sz > trm_sf_sz ) > trm_sf_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Otrm_OPlus_001tf__a_001tf__c,type,
% 3.17/1.86 plus_a_c: trm_a_c > trm_a_c > trm_a_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Otrm_OPlus_001tf__sf_001tf__sz,type,
% 3.17/1.86 plus_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Otrm_OTimes_001tf__a_001tf__c,type,
% 3.17/1.86 times_a_c: trm_a_c > trm_a_c > trm_a_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Syntax_Otrm_OTimes_001tf__sf_001tf__sz,type,
% 3.17/1.86 times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J,type,
% 3.17/1.86 topolo885751137z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > bounde472938360z_real ) > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_001t__Product____Type__Oprod_It__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_Mt__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_J,type,
% 3.17/1.86 topolo1027477648z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > produc1892666919z_real ) > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_001t__Real__Oreal,type,
% 3.17/1.86 topolo1348430467z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > real ) > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Typedef_Otype__definition_001t__Frechet____Correctness__Oids__Ogood____interp_Itf__sf_Mtf__sc_Mtf__sz_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 3.17/1.86 type_d1092523951t_unit: ( freche2095075217_sc_sz > denota610675952t_unit ) > ( denota610675952t_unit > freche2095075217_sc_sz ) > set_De208295462t_unit > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Typedef_Otype__definition_001t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__c_J_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 3.17/1.86 type_d1238563341rm_a_c: ( frechet_strm_a_c > trm_a_c ) > ( trm_a_c > frechet_strm_a_c ) > set_trm_a_c > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_Typedef_Otype__definition_001t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 3.17/1.86 type_d46389773_sf_sz: ( frechet_strm_sf_sz > trm_sf_sz ) > ( trm_sf_sz > frechet_strm_sf_sz ) > set_trm_sf_sz > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_member_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J,type,
% 3.17/1.86 member1777622435t_unit: denota231621370t_unit > set_De455519194t_unit > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_member_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 3.17/1.86 member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_member_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 3.17/1.86 member1693951742eal_sz: finite824932053eal_sz > set_Fi291318197eal_sz > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_member_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 3.17/1.86 member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_member_001t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J,type,
% 3.17/1.86 member1893232190um_b_c: sum_su737395349um_b_c > set_Su1783761653um_b_c > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_member_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 3.17/1.86 member_trm_a_c: trm_a_c > set_trm_a_c > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_member_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 3.17/1.86 member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_c_member_001tf__a,type,
% 3.17/1.86 member_a: a > set_a > $o ).
% 3.17/1.86
% 3.17/1.86 thf(sy_v_I,type,
% 3.17/1.86 i: denota231621370t_unit ).
% 3.17/1.86
% 3.17/1.86 thf(sy_v_J,type,
% 3.17/1.86 j: denota231621370t_unit ).
% 3.17/1.86
% 3.17/1.86 thf(sy_v__092_060nu_062,type,
% 3.17/1.86 nu: produc190496183real_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_v__092_060nu_062_H,type,
% 3.17/1.86 nu2: produc190496183real_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_v_t1____,type,
% 3.17/1.86 t1: trm_a_c ).
% 3.17/1.86
% 3.17/1.86 thf(sy_v_t2____,type,
% 3.17/1.86 t2: trm_a_c ).
% 3.17/1.86
% 3.17/1.86 thf(fact_0_agree__plus2,axiom,
% 3.17/1.86 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 3.17/1.86 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( plus_sf_sz @ T1 @ T2 ) ) )
% 3.17/1.86 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_1_agree__plus2,axiom,
% 3.17/1.86 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 3.17/1.86 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ T1 @ T2 ) ) )
% 3.17/1.86 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_2_agree,axiom,
% 3.17/1.86 denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ t1 @ t2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_3_agree1,axiom,
% 3.17/1.86 denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t1 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_4_dfree2,axiom,
% 3.17/1.86 dfree_a_c @ t2 ).
% 3.17/1.86
% 3.17/1.86 thf(fact_5_agree__plus1,axiom,
% 3.17/1.86 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 3.17/1.86 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( plus_sf_sz @ T1 @ T2 ) ) )
% 3.17/1.86 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T1 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_6_agree__plus1,axiom,
% 3.17/1.86 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 3.17/1.86 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ T1 @ T2 ) ) )
% 3.17/1.86 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T1 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_7_agree__comm,axiom,
% 3.17/1.86 ! [A: produc1149990247eal_sz,B: produc1149990247eal_sz,V: set_Sum_sum_sz_sz] :
% 3.17/1.86 ( ( denota102713844ree_sz @ A @ B @ V )
% 3.17/1.86 => ( denota102713844ree_sz @ B @ A @ V ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_8_agree__comm,axiom,
% 3.17/1.86 ! [A: produc190496183real_c,B: produc190496183real_c,V: set_Sum_sum_c_c] :
% 3.17/1.86 ( ( denota1997846518gree_c @ A @ B @ V )
% 3.17/1.86 => ( denota1997846518gree_c @ B @ A @ V ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_9_agree__refl,axiom,
% 3.17/1.86 ! [Nu: produc1149990247eal_sz,A: set_Sum_sum_sz_sz] : ( denota102713844ree_sz @ Nu @ Nu @ A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_10_agree__refl,axiom,
% 3.17/1.86 ! [Nu: produc190496183real_c,A: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu @ Nu @ A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_11_dfree1,axiom,
% 3.17/1.86 dfree_a_c @ t1 ).
% 3.17/1.86
% 3.17/1.86 thf(fact_12_raw__interp__inject,axiom,
% 3.17/1.86 ! [X: freche2095075217_sc_sz,Y: freche2095075217_sc_sz] :
% 3.17/1.86 ( ( ( freche1421597129_sc_sz @ X )
% 3.17/1.86 = ( freche1421597129_sc_sz @ Y ) )
% 3.17/1.86 = ( X = Y ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_13_raw__term__inject,axiom,
% 3.17/1.86 ! [X: frechet_strm_sf_sz,Y: frechet_strm_sf_sz] :
% 3.17/1.86 ( ( ( freche782854530_sf_sz @ X )
% 3.17/1.86 = ( freche782854530_sf_sz @ Y ) )
% 3.17/1.86 = ( X = Y ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_14_raw__term__inject,axiom,
% 3.17/1.86 ! [X: frechet_strm_a_c,Y: frechet_strm_a_c] :
% 3.17/1.86 ( ( ( frechet_raw_term_a_c @ X )
% 3.17/1.86 = ( frechet_raw_term_a_c @ Y ) )
% 3.17/1.86 = ( X = Y ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_15_agree__times1,axiom,
% 3.17/1.86 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 3.17/1.86 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 3.17/1.86 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T1 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_16_agree__times1,axiom,
% 3.17/1.86 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 3.17/1.86 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 3.17/1.86 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T1 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_17_agree__times2,axiom,
% 3.17/1.86 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 3.17/1.86 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 3.17/1.86 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_18_agree__times2,axiom,
% 3.17/1.86 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 3.17/1.86 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 3.17/1.86 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_19_agree__func,axiom,
% 3.17/1.86 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,Var: sf,Args: sz > trm_sf_sz,I: sz] :
% 3.17/1.86 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( function_sf_sz @ Var @ Args ) ) )
% 3.17/1.86 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( Args @ I ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_20_agree__func,axiom,
% 3.17/1.86 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Var: a,Args: c > trm_a_c,I: c] :
% 3.17/1.86 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( function_a_c @ Var @ Args ) ) )
% 3.17/1.86 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( Args @ I ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_21_P__def,axiom,
% 3.17/1.86 p_sc_sf_sz = predic913887884_sf_sz ).
% 3.17/1.86
% 3.17/1.86 thf(fact_22_IH2,axiom,
% 3.17/1.86 ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) )
% 3.17/1.86 => ( ( denota69106024_a_b_c @ i @ j
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) ) )
% 3.17/1.86 => ( ( denota229585092_a_b_c @ i @ t2 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
% 3.17/1.86 = ( denota229585092_a_b_c @ j @ t2 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_23_seq__sem_Ocases,axiom,
% 3.17/1.86 ! [X: produc1821101996_sc_sz] :
% 3.17/1.86 ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 3.17/1.86 ( X
% 3.17/1.86 != ( produc789536734_sc_sz @ I2 @ S ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_24_raw__term,axiom,
% 3.17/1.86 ! [X: frechet_strm_a_c] : ( member_trm_a_c @ ( frechet_raw_term_a_c @ X ) @ ( collect_trm_a_c @ dfree_a_c ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_25_raw__term,axiom,
% 3.17/1.86 ! [X: frechet_strm_sf_sz] : ( member_trm_sf_sz @ ( freche782854530_sf_sz @ X ) @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_26_raw__term__cases,axiom,
% 3.17/1.86 ! [Y: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 3.17/1.86 => ~ ! [X3: frechet_strm_a_c] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( frechet_raw_term_a_c @ X3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_27_raw__term__cases,axiom,
% 3.17/1.86 ! [Y: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 3.17/1.86 => ~ ! [X3: frechet_strm_sf_sz] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( freche782854530_sf_sz @ X3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_28_raw__term__induct,axiom,
% 3.17/1.86 ! [Y: trm_a_c,P: trm_a_c > $o] :
% 3.17/1.86 ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 3.17/1.86 => ( ! [X3: frechet_strm_a_c] : ( P @ ( frechet_raw_term_a_c @ X3 ) )
% 3.17/1.86 => ( P @ Y ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_29_raw__term__induct,axiom,
% 3.17/1.86 ! [Y: trm_sf_sz,P: trm_sf_sz > $o] :
% 3.17/1.86 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 3.17/1.86 => ( ! [X3: frechet_strm_sf_sz] : ( P @ ( freche782854530_sf_sz @ X3 ) )
% 3.17/1.86 => ( P @ Y ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_30_coincidence__frechet,axiom,
% 3.17/1.86 ! [Theta: trm_a_c,Nu: produc190496183real_c,Nu2: produc190496183real_c,I3: denota231621370t_unit] :
% 3.17/1.86 ( ( dfree_a_c @ Theta )
% 3.17/1.86 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ Theta ) )
% 3.17/1.86 => ( ( denota229585092_a_b_c @ I3 @ Theta @ ( produc2010422875real_c @ Nu ) @ ( produc314122909real_c @ Nu ) )
% 3.17/1.86 = ( denota229585092_a_b_c @ I3 @ Theta @ ( produc2010422875real_c @ Nu2 ) @ ( produc314122909real_c @ Nu2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_31_coincidence__frechet,axiom,
% 3.17/1.86 ! [Theta: trm_sf_sz,Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,I3: denota610675952t_unit] :
% 3.17/1.86 ( ( dfree_sf_sz @ Theta )
% 3.17/1.86 => ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ Theta ) )
% 3.17/1.86 => ( ( denota1979904720_sc_sz @ I3 @ Theta @ ( produc1111759555eal_sz @ Nu ) @ ( produc1269210629eal_sz @ Nu ) )
% 3.17/1.86 = ( denota1979904720_sc_sz @ I3 @ Theta @ ( produc1111759555eal_sz @ Nu2 ) @ ( produc1269210629eal_sz @ Nu2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_32_IA,axiom,
% 3.17/1.86 ( denota69106024_a_b_c @ i @ j
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_33_IA1,axiom,
% 3.17/1.86 ( denota69106024_a_b_c @ i @ j
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_34_IA2,axiom,
% 3.17/1.86 ( denota69106024_a_b_c @ i @ j
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_35_IH1,axiom,
% 3.17/1.86 ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t1 ) )
% 3.17/1.86 => ( ( denota69106024_a_b_c @ i @ j
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) ) )
% 3.17/1.86 => ( ( denota229585092_a_b_c @ i @ t1 @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
% 3.17/1.86 = ( denota229585092_a_b_c @ j @ t1 @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_36_Iagree__comm,axiom,
% 3.17/1.86 ! [A: denota231621370t_unit,B: denota231621370t_unit,V: set_Su1783761653um_b_c] :
% 3.17/1.86 ( ( denota69106024_a_b_c @ A @ B @ V )
% 3.17/1.86 => ( denota69106024_a_b_c @ B @ A @ V ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_37_Iagree__refl,axiom,
% 3.17/1.86 ! [I3: denota231621370t_unit,A: set_Su1783761653um_b_c] : ( denota69106024_a_b_c @ I3 @ I3 @ A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_38_subs_I2_J,axiom,
% 3.17/1.86 ( ord_le929608341um_b_c
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ t2 ) ) ) )
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_39_subs_I1_J,axiom,
% 3.17/1.86 ( ord_le929608341um_b_c
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ t1 ) ) ) )
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ ( plus_a_c @ t1 @ t2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_40_simple__term__inverse,axiom,
% 3.17/1.86 ! [Y: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 3.17/1.86 => ( ( frechet_raw_term_a_c @ ( freche665377492rm_a_c @ Y ) )
% 3.17/1.86 = Y ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_41_simple__term__inverse,axiom,
% 3.17/1.86 ! [Y: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 3.17/1.86 => ( ( freche782854530_sf_sz @ ( freche1046279700_sf_sz @ Y ) )
% 3.17/1.86 = Y ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_42_prod_Ocollapse,axiom,
% 3.17/1.86 ! [Prod: produc866628903_sc_sz] :
% 3.17/1.86 ( ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) )
% 3.17/1.86 = Prod ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_43_prod_Ocollapse,axiom,
% 3.17/1.86 ! [Prod: produc1241881959eal_sz] :
% 3.17/1.86 ( ( produc1235791063eal_sz @ ( produc286845635eal_sz @ Prod ) @ ( produc1746886149eal_sz @ Prod ) )
% 3.17/1.86 = Prod ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_44_prod_Ocollapse,axiom,
% 3.17/1.86 ! [Prod: produc1892666919z_real] :
% 3.17/1.86 ( ( produc784663575z_real @ ( produc870616579z_real @ Prod ) @ ( produc1422611269z_real @ Prod ) )
% 3.17/1.86 = Prod ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_45_prod_Ocollapse,axiom,
% 3.17/1.86 ! [Prod: produc1149990247eal_sz] :
% 3.17/1.86 ( ( produc1308130519eal_sz @ ( produc1111759555eal_sz @ Prod ) @ ( produc1269210629eal_sz @ Prod ) )
% 3.17/1.86 = Prod ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_46_prod_Ocollapse,axiom,
% 3.17/1.86 ! [Prod: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) )
% 3.17/1.86 = Prod ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_47_prod_Ocollapse,axiom,
% 3.17/1.86 ! [Prod: produc190496183real_c] :
% 3.17/1.86 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 3.17/1.86 = Prod ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_48_cr__good__interp__def,axiom,
% 3.17/1.86 ( freche58918398_sc_sz
% 3.17/1.86 = ( ^ [X2: denota610675952t_unit,Y2: freche2095075217_sc_sz] :
% 3.17/1.86 ( X2
% 3.17/1.86 = ( freche1421597129_sc_sz @ Y2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_49_cr__strm__def,axiom,
% 3.17/1.86 ( freche1244000341_sf_sz
% 3.17/1.86 = ( ^ [X2: trm_sf_sz,Y2: frechet_strm_sf_sz] :
% 3.17/1.86 ( X2
% 3.17/1.86 = ( freche782854530_sf_sz @ Y2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_50_cr__strm__def,axiom,
% 3.17/1.86 ( frechet_cr_strm_a_c
% 3.17/1.86 = ( ^ [X2: trm_a_c,Y2: frechet_strm_a_c] :
% 3.17/1.86 ( X2
% 3.17/1.86 = ( frechet_raw_term_a_c @ Y2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_51_dfree__Times__simps,axiom,
% 3.17/1.86 ! [A2: trm_a_c,B2: trm_a_c] :
% 3.17/1.86 ( ( dfree_a_c @ ( times_a_c @ A2 @ B2 ) )
% 3.17/1.86 = ( ( dfree_a_c @ A2 )
% 3.17/1.86 & ( dfree_a_c @ B2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_52_dfree__Times__simps,axiom,
% 3.17/1.86 ! [A2: trm_sf_sz,B2: trm_sf_sz] :
% 3.17/1.86 ( ( dfree_sf_sz @ ( times_sf_sz @ A2 @ B2 ) )
% 3.17/1.86 = ( ( dfree_sf_sz @ A2 )
% 3.17/1.86 & ( dfree_sf_sz @ B2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_53_dfree__Plus__simps,axiom,
% 3.17/1.86 ! [A2: trm_sf_sz,B2: trm_sf_sz] :
% 3.17/1.86 ( ( dfree_sf_sz @ ( plus_sf_sz @ A2 @ B2 ) )
% 3.17/1.86 = ( ( dfree_sf_sz @ A2 )
% 3.17/1.86 & ( dfree_sf_sz @ B2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_54_dfree__Plus__simps,axiom,
% 3.17/1.86 ! [A2: trm_a_c,B2: trm_a_c] :
% 3.17/1.86 ( ( dfree_a_c @ ( plus_a_c @ A2 @ B2 ) )
% 3.17/1.86 = ( ( dfree_a_c @ A2 )
% 3.17/1.86 & ( dfree_a_c @ B2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_55_dfree__Fun__simps,axiom,
% 3.17/1.86 ! [I: a,Args: c > trm_a_c] :
% 3.17/1.86 ( ( dfree_a_c @ ( function_a_c @ I @ Args ) )
% 3.17/1.86 = ( ! [X2: c] : ( dfree_a_c @ ( Args @ X2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_56_dfree__Fun__simps,axiom,
% 3.17/1.86 ! [I: sf,Args: sz > trm_sf_sz] :
% 3.17/1.86 ( ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) )
% 3.17/1.86 = ( ! [X2: sz] : ( dfree_sf_sz @ ( Args @ X2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_57_simple__term__cases,axiom,
% 3.17/1.86 ! [X: frechet_strm_a_c] :
% 3.17/1.86 ~ ! [Y3: trm_a_c] :
% 3.17/1.86 ( ( X
% 3.17/1.86 = ( freche665377492rm_a_c @ Y3 ) )
% 3.17/1.86 => ~ ( member_trm_a_c @ Y3 @ ( collect_trm_a_c @ dfree_a_c ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_58_simple__term__cases,axiom,
% 3.17/1.86 ! [X: frechet_strm_sf_sz] :
% 3.17/1.86 ~ ! [Y3: trm_sf_sz] :
% 3.17/1.86 ( ( X
% 3.17/1.86 = ( freche1046279700_sf_sz @ Y3 ) )
% 3.17/1.86 => ~ ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_59_raw__term__inverse,axiom,
% 3.17/1.86 ! [X: frechet_strm_a_c] :
% 3.17/1.86 ( ( freche665377492rm_a_c @ ( frechet_raw_term_a_c @ X ) )
% 3.17/1.86 = X ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_60_raw__term__inverse,axiom,
% 3.17/1.86 ! [X: frechet_strm_sf_sz] :
% 3.17/1.86 ( ( freche1046279700_sf_sz @ ( freche782854530_sf_sz @ X ) )
% 3.17/1.86 = X ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_61_simple__term__inject,axiom,
% 3.17/1.86 ! [X: trm_a_c,Y: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ X @ ( collect_trm_a_c @ dfree_a_c ) )
% 3.17/1.86 => ( ( member_trm_a_c @ Y @ ( collect_trm_a_c @ dfree_a_c ) )
% 3.17/1.86 => ( ( ( freche665377492rm_a_c @ X )
% 3.17/1.86 = ( freche665377492rm_a_c @ Y ) )
% 3.17/1.86 = ( X = Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_62_simple__term__inject,axiom,
% 3.17/1.86 ! [X: trm_sf_sz,Y: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ X @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 3.17/1.86 => ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 3.17/1.86 => ( ( ( freche1046279700_sf_sz @ X )
% 3.17/1.86 = ( freche1046279700_sf_sz @ Y ) )
% 3.17/1.86 = ( X = Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_63_simple__term__induct,axiom,
% 3.17/1.86 ! [P: frechet_strm_a_c > $o,X: frechet_strm_a_c] :
% 3.17/1.86 ( ! [Y3: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ Y3 @ ( collect_trm_a_c @ dfree_a_c ) )
% 3.17/1.86 => ( P @ ( freche665377492rm_a_c @ Y3 ) ) )
% 3.17/1.86 => ( P @ X ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_64_simple__term__induct,axiom,
% 3.17/1.86 ! [P: frechet_strm_sf_sz > $o,X: frechet_strm_sf_sz] :
% 3.17/1.86 ( ! [Y3: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 3.17/1.86 => ( P @ ( freche1046279700_sf_sz @ Y3 ) ) )
% 3.17/1.86 => ( P @ X ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_65_old_Oprod_Oinject,axiom,
% 3.17/1.86 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 3.17/1.86 ( ( ( produc394644079real_c @ A2 @ B2 )
% 3.17/1.86 = ( produc394644079real_c @ A3 @ B3 ) )
% 3.17/1.86 = ( ( A2 = A3 )
% 3.17/1.86 & ( B2 = B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_66_old_Oprod_Oinject,axiom,
% 3.17/1.86 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 3.17/1.86 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 3.17/1.86 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 3.17/1.86 = ( ( A2 = A3 )
% 3.17/1.86 & ( B2 = B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_67_old_Oprod_Oinject,axiom,
% 3.17/1.86 ! [A2: set_Fi291318197eal_sz,B2: set_Fi291318197eal_sz,A3: set_Fi291318197eal_sz,B3: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( ( produc1235791063eal_sz @ A2 @ B2 )
% 3.17/1.86 = ( produc1235791063eal_sz @ A3 @ B3 ) )
% 3.17/1.86 = ( ( A2 = A3 )
% 3.17/1.86 & ( B2 = B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_68_old_Oprod_Oinject,axiom,
% 3.17/1.86 ! [A2: bounde472938360z_real,B2: bounde472938360z_real,A3: bounde472938360z_real,B3: bounde472938360z_real] :
% 3.17/1.86 ( ( ( produc784663575z_real @ A2 @ B2 )
% 3.17/1.86 = ( produc784663575z_real @ A3 @ B3 ) )
% 3.17/1.86 = ( ( A2 = A3 )
% 3.17/1.86 & ( B2 = B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_69_old_Oprod_Oinject,axiom,
% 3.17/1.86 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 3.17/1.86 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 3.17/1.86 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 3.17/1.86 = ( ( A2 = A3 )
% 3.17/1.86 & ( B2 = B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_70_prod_Oinject,axiom,
% 3.17/1.86 ! [X1: finite1398487019real_c,X22: finite1398487019real_c,Y1: finite1398487019real_c,Y22: finite1398487019real_c] :
% 3.17/1.86 ( ( ( produc394644079real_c @ X1 @ X22 )
% 3.17/1.86 = ( produc394644079real_c @ Y1 @ Y22 ) )
% 3.17/1.86 = ( ( X1 = Y1 )
% 3.17/1.86 & ( X22 = Y22 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_71_prod_Oinject,axiom,
% 3.17/1.86 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz,Y1: list_f1238882004_sc_sz,Y22: list_f1238882004_sc_sz] :
% 3.17/1.86 ( ( ( produc1822718231_sc_sz @ X1 @ X22 )
% 3.17/1.86 = ( produc1822718231_sc_sz @ Y1 @ Y22 ) )
% 3.17/1.86 = ( ( X1 = Y1 )
% 3.17/1.86 & ( X22 = Y22 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_72_prod_Oinject,axiom,
% 3.17/1.86 ! [X1: set_Fi291318197eal_sz,X22: set_Fi291318197eal_sz,Y1: set_Fi291318197eal_sz,Y22: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( ( produc1235791063eal_sz @ X1 @ X22 )
% 3.17/1.86 = ( produc1235791063eal_sz @ Y1 @ Y22 ) )
% 3.17/1.86 = ( ( X1 = Y1 )
% 3.17/1.86 & ( X22 = Y22 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_73_prod_Oinject,axiom,
% 3.17/1.86 ! [X1: bounde472938360z_real,X22: bounde472938360z_real,Y1: bounde472938360z_real,Y22: bounde472938360z_real] :
% 3.17/1.86 ( ( ( produc784663575z_real @ X1 @ X22 )
% 3.17/1.86 = ( produc784663575z_real @ Y1 @ Y22 ) )
% 3.17/1.86 = ( ( X1 = Y1 )
% 3.17/1.86 & ( X22 = Y22 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_74_prod_Oinject,axiom,
% 3.17/1.86 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz,Y1: denota610675952t_unit,Y22: produc866628903_sc_sz] :
% 3.17/1.86 ( ( ( produc789536734_sc_sz @ X1 @ X22 )
% 3.17/1.86 = ( produc789536734_sc_sz @ Y1 @ Y22 ) )
% 3.17/1.86 = ( ( X1 = Y1 )
% 3.17/1.86 & ( X22 = Y22 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_75_trm_Oinject_I3_J,axiom,
% 3.17/1.86 ! [X31: a,X32: c > trm_a_c,Y31: a,Y32: c > trm_a_c] :
% 3.17/1.86 ( ( ( function_a_c @ X31 @ X32 )
% 3.17/1.86 = ( function_a_c @ Y31 @ Y32 ) )
% 3.17/1.86 = ( ( X31 = Y31 )
% 3.17/1.86 & ( X32 = Y32 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_76_trm_Oinject_I3_J,axiom,
% 3.17/1.86 ! [X31: sf,X32: sz > trm_sf_sz,Y31: sf,Y32: sz > trm_sf_sz] :
% 3.17/1.86 ( ( ( function_sf_sz @ X31 @ X32 )
% 3.17/1.86 = ( function_sf_sz @ Y31 @ Y32 ) )
% 3.17/1.86 = ( ( X31 = Y31 )
% 3.17/1.86 & ( X32 = Y32 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_77_trm_Oinject_I4_J,axiom,
% 3.17/1.86 ! [X41: trm_sf_sz,X42: trm_sf_sz,Y41: trm_sf_sz,Y42: trm_sf_sz] :
% 3.17/1.86 ( ( ( plus_sf_sz @ X41 @ X42 )
% 3.17/1.86 = ( plus_sf_sz @ Y41 @ Y42 ) )
% 3.17/1.86 = ( ( X41 = Y41 )
% 3.17/1.86 & ( X42 = Y42 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_78_trm_Oinject_I4_J,axiom,
% 3.17/1.86 ! [X41: trm_a_c,X42: trm_a_c,Y41: trm_a_c,Y42: trm_a_c] :
% 3.17/1.86 ( ( ( plus_a_c @ X41 @ X42 )
% 3.17/1.86 = ( plus_a_c @ Y41 @ Y42 ) )
% 3.17/1.86 = ( ( X41 = Y41 )
% 3.17/1.86 & ( X42 = Y42 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_79_trm_Oinject_I5_J,axiom,
% 3.17/1.86 ! [X51: trm_a_c,X52: trm_a_c,Y51: trm_a_c,Y52: trm_a_c] :
% 3.17/1.86 ( ( ( times_a_c @ X51 @ X52 )
% 3.17/1.86 = ( times_a_c @ Y51 @ Y52 ) )
% 3.17/1.86 = ( ( X51 = Y51 )
% 3.17/1.86 & ( X52 = Y52 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_80_trm_Oinject_I5_J,axiom,
% 3.17/1.86 ! [X51: trm_sf_sz,X52: trm_sf_sz,Y51: trm_sf_sz,Y52: trm_sf_sz] :
% 3.17/1.86 ( ( ( times_sf_sz @ X51 @ X52 )
% 3.17/1.86 = ( times_sf_sz @ Y51 @ Y52 ) )
% 3.17/1.86 = ( ( X51 = Y51 )
% 3.17/1.86 & ( X52 = Y52 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_81_mem__Collect__eq,axiom,
% 3.17/1.86 ! [A2: finite824932053eal_sz,P: finite824932053eal_sz > $o] :
% 3.17/1.86 ( ( member1693951742eal_sz @ A2 @ ( collec1002602816eal_sz @ P ) )
% 3.17/1.86 = ( P @ A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_82_mem__Collect__eq,axiom,
% 3.17/1.86 ! [A2: produc1821101996_sc_sz,P: produc1821101996_sc_sz > $o] :
% 3.17/1.86 ( ( member1057565379_sc_sz @ A2 @ ( collec1199592193_sc_sz @ P ) )
% 3.17/1.86 = ( P @ A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_83_mem__Collect__eq,axiom,
% 3.17/1.86 ! [A2: trm_sf_sz,P: trm_sf_sz > $o] :
% 3.17/1.86 ( ( member_trm_sf_sz @ A2 @ ( collect_trm_sf_sz @ P ) )
% 3.17/1.86 = ( P @ A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_84_mem__Collect__eq,axiom,
% 3.17/1.86 ! [A2: trm_a_c,P: trm_a_c > $o] :
% 3.17/1.86 ( ( member_trm_a_c @ A2 @ ( collect_trm_a_c @ P ) )
% 3.17/1.86 = ( P @ A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_85_mem__Collect__eq,axiom,
% 3.17/1.86 ! [A2: a,P: a > $o] :
% 3.17/1.86 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 3.17/1.86 = ( P @ A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_86_mem__Collect__eq,axiom,
% 3.17/1.86 ! [A2: sum_su737395349um_b_c,P: sum_su737395349um_b_c > $o] :
% 3.17/1.86 ( ( member1893232190um_b_c @ A2 @ ( collec2086029184um_b_c @ P ) )
% 3.17/1.86 = ( P @ A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_87_Collect__mem__eq,axiom,
% 3.17/1.86 ! [A: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( collec1002602816eal_sz
% 3.17/1.86 @ ^ [X2: finite824932053eal_sz] : ( member1693951742eal_sz @ X2 @ A ) )
% 3.17/1.86 = A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_88_Collect__mem__eq,axiom,
% 3.17/1.86 ! [A: set_Pr1169339874_sc_sz] :
% 3.17/1.86 ( ( collec1199592193_sc_sz
% 3.17/1.86 @ ^ [X2: produc1821101996_sc_sz] : ( member1057565379_sc_sz @ X2 @ A ) )
% 3.17/1.86 = A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_89_Collect__mem__eq,axiom,
% 3.17/1.86 ! [A: set_trm_sf_sz] :
% 3.17/1.86 ( ( collect_trm_sf_sz
% 3.17/1.86 @ ^ [X2: trm_sf_sz] : ( member_trm_sf_sz @ X2 @ A ) )
% 3.17/1.86 = A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_90_Collect__mem__eq,axiom,
% 3.17/1.86 ! [A: set_trm_a_c] :
% 3.17/1.86 ( ( collect_trm_a_c
% 3.17/1.86 @ ^ [X2: trm_a_c] : ( member_trm_a_c @ X2 @ A ) )
% 3.17/1.86 = A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_91_Collect__mem__eq,axiom,
% 3.17/1.86 ! [A: set_a] :
% 3.17/1.86 ( ( collect_a
% 3.17/1.86 @ ^ [X2: a] : ( member_a @ X2 @ A ) )
% 3.17/1.86 = A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_92_Collect__mem__eq,axiom,
% 3.17/1.86 ! [A: set_Su1783761653um_b_c] :
% 3.17/1.86 ( ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [X2: sum_su737395349um_b_c] : ( member1893232190um_b_c @ X2 @ A ) )
% 3.17/1.86 = A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_93_Collect__cong,axiom,
% 3.17/1.86 ! [P: finite824932053eal_sz > $o,Q: finite824932053eal_sz > $o] :
% 3.17/1.86 ( ! [X3: finite824932053eal_sz] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 = ( Q @ X3 ) )
% 3.17/1.86 => ( ( collec1002602816eal_sz @ P )
% 3.17/1.86 = ( collec1002602816eal_sz @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_94_Collect__cong,axiom,
% 3.17/1.86 ! [P: produc1821101996_sc_sz > $o,Q: produc1821101996_sc_sz > $o] :
% 3.17/1.86 ( ! [X3: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 = ( Q @ X3 ) )
% 3.17/1.86 => ( ( collec1199592193_sc_sz @ P )
% 3.17/1.86 = ( collec1199592193_sc_sz @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_95_Collect__cong,axiom,
% 3.17/1.86 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 3.17/1.86 ( ! [X3: trm_sf_sz] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 = ( Q @ X3 ) )
% 3.17/1.86 => ( ( collect_trm_sf_sz @ P )
% 3.17/1.86 = ( collect_trm_sf_sz @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_96_Collect__cong,axiom,
% 3.17/1.86 ! [P: trm_a_c > $o,Q: trm_a_c > $o] :
% 3.17/1.86 ( ! [X3: trm_a_c] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 = ( Q @ X3 ) )
% 3.17/1.86 => ( ( collect_trm_a_c @ P )
% 3.17/1.86 = ( collect_trm_a_c @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_97_Collect__cong,axiom,
% 3.17/1.86 ! [P: a > $o,Q: a > $o] :
% 3.17/1.86 ( ! [X3: a] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 = ( Q @ X3 ) )
% 3.17/1.86 => ( ( collect_a @ P )
% 3.17/1.86 = ( collect_a @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_98_Collect__cong,axiom,
% 3.17/1.86 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 3.17/1.86 ( ! [X3: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 = ( Q @ X3 ) )
% 3.17/1.86 => ( ( collec2086029184um_b_c @ P )
% 3.17/1.86 = ( collec2086029184um_b_c @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_99_agree__sub,axiom,
% 3.17/1.86 ! [A: set_Sum_sum_sz_sz,B: set_Sum_sum_sz_sz,Nu: produc1149990247eal_sz,Omega: produc1149990247eal_sz] :
% 3.17/1.86 ( ( ord_le1110131657_sz_sz @ A @ B )
% 3.17/1.86 => ( ( denota102713844ree_sz @ Nu @ Omega @ B )
% 3.17/1.86 => ( denota102713844ree_sz @ Nu @ Omega @ A ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_100_agree__sub,axiom,
% 3.17/1.86 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,Nu: produc190496183real_c,Omega: produc190496183real_c] :
% 3.17/1.86 ( ( ord_le1772180283um_c_c @ A @ B )
% 3.17/1.86 => ( ( denota1997846518gree_c @ Nu @ Omega @ B )
% 3.17/1.86 => ( denota1997846518gree_c @ Nu @ Omega @ A ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_101_agree__supset,axiom,
% 3.17/1.86 ! [B: set_Sum_sum_sz_sz,A: set_Sum_sum_sz_sz,Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz] :
% 3.17/1.86 ( ( ord_le1110131657_sz_sz @ B @ A )
% 3.17/1.86 => ( ( denota102713844ree_sz @ Nu @ Nu2 @ A )
% 3.17/1.86 => ( denota102713844ree_sz @ Nu @ Nu2 @ B ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_102_agree__supset,axiom,
% 3.17/1.86 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,Nu: produc190496183real_c,Nu2: produc190496183real_c] :
% 3.17/1.86 ( ( ord_le1772180283um_c_c @ B @ A )
% 3.17/1.86 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ A )
% 3.17/1.86 => ( denota1997846518gree_c @ Nu @ Nu2 @ B ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_103_old_Oprod_Oinducts,axiom,
% 3.17/1.86 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 3.17/1.86 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ Prod ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_104_old_Oprod_Oinducts,axiom,
% 3.17/1.86 ! [P: produc866628903_sc_sz > $o,Prod: produc866628903_sc_sz] :
% 3.17/1.86 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ Prod ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_105_old_Oprod_Oinducts,axiom,
% 3.17/1.86 ! [P: produc1241881959eal_sz > $o,Prod: produc1241881959eal_sz] :
% 3.17/1.86 ( ! [A4: set_Fi291318197eal_sz,B4: set_Fi291318197eal_sz] : ( P @ ( produc1235791063eal_sz @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ Prod ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_106_old_Oprod_Oinducts,axiom,
% 3.17/1.86 ! [P: produc1892666919z_real > $o,Prod: produc1892666919z_real] :
% 3.17/1.86 ( ! [A4: bounde472938360z_real,B4: bounde472938360z_real] : ( P @ ( produc784663575z_real @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ Prod ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_107_old_Oprod_Oinducts,axiom,
% 3.17/1.86 ! [P: produc1821101996_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 3.17/1.86 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ Prod ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_108_old_Oprod_Oexhaust,axiom,
% 3.17/1.86 ! [Y: produc190496183real_c] :
% 3.17/1.86 ~ ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( produc394644079real_c @ A4 @ B4 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_109_old_Oprod_Oexhaust,axiom,
% 3.17/1.86 ! [Y: produc866628903_sc_sz] :
% 3.17/1.86 ~ ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( produc1822718231_sc_sz @ A4 @ B4 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_110_old_Oprod_Oexhaust,axiom,
% 3.17/1.86 ! [Y: produc1241881959eal_sz] :
% 3.17/1.86 ~ ! [A4: set_Fi291318197eal_sz,B4: set_Fi291318197eal_sz] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( produc1235791063eal_sz @ A4 @ B4 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_111_old_Oprod_Oexhaust,axiom,
% 3.17/1.86 ! [Y: produc1892666919z_real] :
% 3.17/1.86 ~ ! [A4: bounde472938360z_real,B4: bounde472938360z_real] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( produc784663575z_real @ A4 @ B4 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_112_old_Oprod_Oexhaust,axiom,
% 3.17/1.86 ! [Y: produc1821101996_sc_sz] :
% 3.17/1.86 ~ ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( produc789536734_sc_sz @ A4 @ B4 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_113_Pair__inject,axiom,
% 3.17/1.86 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 3.17/1.86 ( ( ( produc394644079real_c @ A2 @ B2 )
% 3.17/1.86 = ( produc394644079real_c @ A3 @ B3 ) )
% 3.17/1.86 => ~ ( ( A2 = A3 )
% 3.17/1.86 => ( B2 != B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_114_Pair__inject,axiom,
% 3.17/1.86 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 3.17/1.86 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 3.17/1.86 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 3.17/1.86 => ~ ( ( A2 = A3 )
% 3.17/1.86 => ( B2 != B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_115_Pair__inject,axiom,
% 3.17/1.86 ! [A2: set_Fi291318197eal_sz,B2: set_Fi291318197eal_sz,A3: set_Fi291318197eal_sz,B3: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( ( produc1235791063eal_sz @ A2 @ B2 )
% 3.17/1.86 = ( produc1235791063eal_sz @ A3 @ B3 ) )
% 3.17/1.86 => ~ ( ( A2 = A3 )
% 3.17/1.86 => ( B2 != B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_116_Pair__inject,axiom,
% 3.17/1.86 ! [A2: bounde472938360z_real,B2: bounde472938360z_real,A3: bounde472938360z_real,B3: bounde472938360z_real] :
% 3.17/1.86 ( ( ( produc784663575z_real @ A2 @ B2 )
% 3.17/1.86 = ( produc784663575z_real @ A3 @ B3 ) )
% 3.17/1.86 => ~ ( ( A2 = A3 )
% 3.17/1.86 => ( B2 != B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_117_Pair__inject,axiom,
% 3.17/1.86 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 3.17/1.86 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 3.17/1.86 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 3.17/1.86 => ~ ( ( A2 = A3 )
% 3.17/1.86 => ( B2 != B3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_118_prod__cases,axiom,
% 3.17/1.86 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 3.17/1.86 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ P2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_119_prod__cases,axiom,
% 3.17/1.86 ! [P: produc866628903_sc_sz > $o,P2: produc866628903_sc_sz] :
% 3.17/1.86 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ P2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_120_prod__cases,axiom,
% 3.17/1.86 ! [P: produc1241881959eal_sz > $o,P2: produc1241881959eal_sz] :
% 3.17/1.86 ( ! [A4: set_Fi291318197eal_sz,B4: set_Fi291318197eal_sz] : ( P @ ( produc1235791063eal_sz @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ P2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_121_prod__cases,axiom,
% 3.17/1.86 ! [P: produc1892666919z_real > $o,P2: produc1892666919z_real] :
% 3.17/1.86 ( ! [A4: bounde472938360z_real,B4: bounde472938360z_real] : ( P @ ( produc784663575z_real @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ P2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_122_prod__cases,axiom,
% 3.17/1.86 ! [P: produc1821101996_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 3.17/1.86 => ( P @ P2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_123_surj__pair,axiom,
% 3.17/1.86 ! [P2: produc190496183real_c] :
% 3.17/1.86 ? [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.17/1.86 ( P2
% 3.17/1.86 = ( produc394644079real_c @ X3 @ Y3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_124_surj__pair,axiom,
% 3.17/1.86 ! [P2: produc866628903_sc_sz] :
% 3.17/1.86 ? [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 3.17/1.86 ( P2
% 3.17/1.86 = ( produc1822718231_sc_sz @ X3 @ Y3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_125_surj__pair,axiom,
% 3.17/1.86 ! [P2: produc1241881959eal_sz] :
% 3.17/1.86 ? [X3: set_Fi291318197eal_sz,Y3: set_Fi291318197eal_sz] :
% 3.17/1.86 ( P2
% 3.17/1.86 = ( produc1235791063eal_sz @ X3 @ Y3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_126_surj__pair,axiom,
% 3.17/1.86 ! [P2: produc1892666919z_real] :
% 3.17/1.86 ? [X3: bounde472938360z_real,Y3: bounde472938360z_real] :
% 3.17/1.86 ( P2
% 3.17/1.86 = ( produc784663575z_real @ X3 @ Y3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_127_surj__pair,axiom,
% 3.17/1.86 ! [P2: produc1821101996_sc_sz] :
% 3.17/1.86 ? [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.17/1.86 ( P2
% 3.17/1.86 = ( produc789536734_sc_sz @ X3 @ Y3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_128_prod__induct3,axiom,
% 3.17/1.86 ! [P: produc1821101996_sc_sz > $o,X: produc1821101996_sc_sz] :
% 3.17/1.86 ( ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) )
% 3.17/1.86 => ( P @ X ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_129_prod__cases3,axiom,
% 3.17/1.86 ! [Y: produc1821101996_sc_sz] :
% 3.17/1.86 ~ ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_130_fst__conv,axiom,
% 3.17/1.86 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 3.17/1.86 ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 3.17/1.86 = X1 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_131_fst__conv,axiom,
% 3.17/1.86 ! [X1: set_Fi291318197eal_sz,X22: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( produc286845635eal_sz @ ( produc1235791063eal_sz @ X1 @ X22 ) )
% 3.17/1.86 = X1 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_132_fst__conv,axiom,
% 3.17/1.86 ! [X1: bounde472938360z_real,X22: bounde472938360z_real] :
% 3.17/1.86 ( ( produc870616579z_real @ ( produc784663575z_real @ X1 @ X22 ) )
% 3.17/1.86 = X1 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_133_fst__conv,axiom,
% 3.17/1.86 ! [X1: finite824932053eal_sz,X22: finite824932053eal_sz] :
% 3.17/1.86 ( ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ X1 @ X22 ) )
% 3.17/1.86 = X1 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_134_fst__conv,axiom,
% 3.17/1.86 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 3.17/1.86 ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 3.17/1.86 = X1 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_135_fst__conv,axiom,
% 3.17/1.86 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 3.17/1.86 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 3.17/1.86 = X1 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_136_fst__eqD,axiom,
% 3.17/1.86 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A2: list_f1238882004_sc_sz] :
% 3.17/1.86 ( ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( X = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_137_fst__eqD,axiom,
% 3.17/1.86 ! [X: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,A2: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( ( produc286845635eal_sz @ ( produc1235791063eal_sz @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( X = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_138_fst__eqD,axiom,
% 3.17/1.86 ! [X: bounde472938360z_real,Y: bounde472938360z_real,A2: bounde472938360z_real] :
% 3.17/1.86 ( ( ( produc870616579z_real @ ( produc784663575z_real @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( X = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_139_fst__eqD,axiom,
% 3.17/1.86 ! [X: finite824932053eal_sz,Y: finite824932053eal_sz,A2: finite824932053eal_sz] :
% 3.17/1.86 ( ( ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( X = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_140_fst__eqD,axiom,
% 3.17/1.86 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: denota610675952t_unit] :
% 3.17/1.86 ( ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( X = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_141_fst__eqD,axiom,
% 3.17/1.86 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A2: finite1398487019real_c] :
% 3.17/1.86 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( X = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_142_snd__conv,axiom,
% 3.17/1.86 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 3.17/1.86 ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 3.17/1.86 = X22 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_143_snd__conv,axiom,
% 3.17/1.86 ! [X1: set_Fi291318197eal_sz,X22: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ X1 @ X22 ) )
% 3.17/1.86 = X22 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_144_snd__conv,axiom,
% 3.17/1.86 ! [X1: bounde472938360z_real,X22: bounde472938360z_real] :
% 3.17/1.86 ( ( produc1422611269z_real @ ( produc784663575z_real @ X1 @ X22 ) )
% 3.17/1.86 = X22 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_145_snd__conv,axiom,
% 3.17/1.86 ! [X1: finite824932053eal_sz,X22: finite824932053eal_sz] :
% 3.17/1.86 ( ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ X1 @ X22 ) )
% 3.17/1.86 = X22 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_146_snd__conv,axiom,
% 3.17/1.86 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 3.17/1.86 ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 3.17/1.86 = X22 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_147_snd__conv,axiom,
% 3.17/1.86 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 3.17/1.86 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 3.17/1.86 = X22 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_148_snd__eqD,axiom,
% 3.17/1.86 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A2: list_f1238882004_sc_sz] :
% 3.17/1.86 ( ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( Y = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_149_snd__eqD,axiom,
% 3.17/1.86 ! [X: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,A2: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( Y = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_150_snd__eqD,axiom,
% 3.17/1.86 ! [X: bounde472938360z_real,Y: bounde472938360z_real,A2: bounde472938360z_real] :
% 3.17/1.86 ( ( ( produc1422611269z_real @ ( produc784663575z_real @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( Y = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_151_snd__eqD,axiom,
% 3.17/1.86 ! [X: finite824932053eal_sz,Y: finite824932053eal_sz,A2: finite824932053eal_sz] :
% 3.17/1.86 ( ( ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( Y = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_152_snd__eqD,axiom,
% 3.17/1.86 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: produc866628903_sc_sz] :
% 3.17/1.86 ( ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( Y = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_153_snd__eqD,axiom,
% 3.17/1.86 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A2: finite1398487019real_c] :
% 3.17/1.86 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( Y = A2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_154_prod__eq__iff,axiom,
% 3.17/1.86 ( ( ^ [Y4: produc1149990247eal_sz,Z: produc1149990247eal_sz] : ( Y4 = Z ) )
% 3.17/1.86 = ( ^ [S2: produc1149990247eal_sz,T: produc1149990247eal_sz] :
% 3.17/1.86 ( ( ( produc1111759555eal_sz @ S2 )
% 3.17/1.86 = ( produc1111759555eal_sz @ T ) )
% 3.17/1.86 & ( ( produc1269210629eal_sz @ S2 )
% 3.17/1.86 = ( produc1269210629eal_sz @ T ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_155_prod__eq__iff,axiom,
% 3.17/1.86 ( ( ^ [Y4: produc1821101996_sc_sz,Z: produc1821101996_sc_sz] : ( Y4 = Z ) )
% 3.17/1.86 = ( ^ [S2: produc1821101996_sc_sz,T: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( ( produc1503602930_sc_sz @ S2 )
% 3.17/1.86 = ( produc1503602930_sc_sz @ T ) )
% 3.17/1.86 & ( ( produc974239792_sc_sz @ S2 )
% 3.17/1.86 = ( produc974239792_sc_sz @ T ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_156_prod__eq__iff,axiom,
% 3.17/1.86 ( ( ^ [Y4: produc190496183real_c,Z: produc190496183real_c] : ( Y4 = Z ) )
% 3.17/1.86 = ( ^ [S2: produc190496183real_c,T: produc190496183real_c] :
% 3.17/1.86 ( ( ( produc2010422875real_c @ S2 )
% 3.17/1.86 = ( produc2010422875real_c @ T ) )
% 3.17/1.86 & ( ( produc314122909real_c @ S2 )
% 3.17/1.86 = ( produc314122909real_c @ T ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_157_prod_Oexpand,axiom,
% 3.17/1.86 ! [Prod: produc1149990247eal_sz,Prod2: produc1149990247eal_sz] :
% 3.17/1.86 ( ( ( ( produc1111759555eal_sz @ Prod )
% 3.17/1.86 = ( produc1111759555eal_sz @ Prod2 ) )
% 3.17/1.86 & ( ( produc1269210629eal_sz @ Prod )
% 3.17/1.86 = ( produc1269210629eal_sz @ Prod2 ) ) )
% 3.17/1.86 => ( Prod = Prod2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_158_prod_Oexpand,axiom,
% 3.17/1.86 ! [Prod: produc1821101996_sc_sz,Prod2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( ( ( produc1503602930_sc_sz @ Prod )
% 3.17/1.86 = ( produc1503602930_sc_sz @ Prod2 ) )
% 3.17/1.86 & ( ( produc974239792_sc_sz @ Prod )
% 3.17/1.86 = ( produc974239792_sc_sz @ Prod2 ) ) )
% 3.17/1.86 => ( Prod = Prod2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_159_prod_Oexpand,axiom,
% 3.17/1.86 ! [Prod: produc190496183real_c,Prod2: produc190496183real_c] :
% 3.17/1.86 ( ( ( ( produc2010422875real_c @ Prod )
% 3.17/1.86 = ( produc2010422875real_c @ Prod2 ) )
% 3.17/1.86 & ( ( produc314122909real_c @ Prod )
% 3.17/1.86 = ( produc314122909real_c @ Prod2 ) ) )
% 3.17/1.86 => ( Prod = Prod2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_160_prod__eqI,axiom,
% 3.17/1.86 ! [P2: produc1149990247eal_sz,Q2: produc1149990247eal_sz] :
% 3.17/1.86 ( ( ( produc1111759555eal_sz @ P2 )
% 3.17/1.86 = ( produc1111759555eal_sz @ Q2 ) )
% 3.17/1.86 => ( ( ( produc1269210629eal_sz @ P2 )
% 3.17/1.86 = ( produc1269210629eal_sz @ Q2 ) )
% 3.17/1.86 => ( P2 = Q2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_161_prod__eqI,axiom,
% 3.17/1.86 ! [P2: produc1821101996_sc_sz,Q2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( ( produc1503602930_sc_sz @ P2 )
% 3.17/1.86 = ( produc1503602930_sc_sz @ Q2 ) )
% 3.17/1.86 => ( ( ( produc974239792_sc_sz @ P2 )
% 3.17/1.86 = ( produc974239792_sc_sz @ Q2 ) )
% 3.17/1.86 => ( P2 = Q2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_162_prod__eqI,axiom,
% 3.17/1.86 ! [P2: produc190496183real_c,Q2: produc190496183real_c] :
% 3.17/1.86 ( ( ( produc2010422875real_c @ P2 )
% 3.17/1.86 = ( produc2010422875real_c @ Q2 ) )
% 3.17/1.86 => ( ( ( produc314122909real_c @ P2 )
% 3.17/1.86 = ( produc314122909real_c @ Q2 ) )
% 3.17/1.86 => ( P2 = Q2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_163_dfree__Fun,axiom,
% 3.17/1.86 ! [Args: c > trm_a_c,I: a] :
% 3.17/1.86 ( ! [I4: c] : ( dfree_a_c @ ( Args @ I4 ) )
% 3.17/1.86 => ( dfree_a_c @ ( function_a_c @ I @ Args ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_164_dfree__Fun,axiom,
% 3.17/1.86 ! [Args: sz > trm_sf_sz,I: sf] :
% 3.17/1.86 ( ! [I4: sz] : ( dfree_sf_sz @ ( Args @ I4 ) )
% 3.17/1.86 => ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_165_dfree_Odfree__Plus,axiom,
% 3.17/1.86 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 3.17/1.86 ( ( dfree_sf_sz @ Theta_1 )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta_2 )
% 3.17/1.86 => ( dfree_sf_sz @ ( plus_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_166_dfree_Odfree__Plus,axiom,
% 3.17/1.86 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 3.17/1.86 ( ( dfree_a_c @ Theta_1 )
% 3.17/1.86 => ( ( dfree_a_c @ Theta_2 )
% 3.17/1.86 => ( dfree_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_167_dfree__Times,axiom,
% 3.17/1.86 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 3.17/1.86 ( ( dfree_a_c @ Theta_1 )
% 3.17/1.86 => ( ( dfree_a_c @ Theta_2 )
% 3.17/1.86 => ( dfree_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_168_dfree__Times,axiom,
% 3.17/1.86 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 3.17/1.86 ( ( dfree_sf_sz @ Theta_1 )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta_2 )
% 3.17/1.86 => ( dfree_sf_sz @ ( times_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_169_trm_Odistinct_I23_J,axiom,
% 3.17/1.86 ! [X31: a,X32: c > trm_a_c,X41: trm_a_c,X42: trm_a_c] :
% 3.17/1.86 ( ( function_a_c @ X31 @ X32 )
% 3.17/1.86 != ( plus_a_c @ X41 @ X42 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_170_trm_Odistinct_I23_J,axiom,
% 3.17/1.86 ! [X31: sf,X32: sz > trm_sf_sz,X41: trm_sf_sz,X42: trm_sf_sz] :
% 3.17/1.86 ( ( function_sf_sz @ X31 @ X32 )
% 3.17/1.86 != ( plus_sf_sz @ X41 @ X42 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_171_trm_Odistinct_I25_J,axiom,
% 3.17/1.86 ! [X31: a,X32: c > trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 3.17/1.86 ( ( function_a_c @ X31 @ X32 )
% 3.17/1.86 != ( times_a_c @ X51 @ X52 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_172_trm_Odistinct_I25_J,axiom,
% 3.17/1.86 ! [X31: sf,X32: sz > trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 3.17/1.86 ( ( function_sf_sz @ X31 @ X32 )
% 3.17/1.86 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_173_trm_Odistinct_I31_J,axiom,
% 3.17/1.86 ! [X41: trm_sf_sz,X42: trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 3.17/1.86 ( ( plus_sf_sz @ X41 @ X42 )
% 3.17/1.86 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_174_trm_Odistinct_I31_J,axiom,
% 3.17/1.86 ! [X41: trm_a_c,X42: trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 3.17/1.86 ( ( plus_a_c @ X41 @ X42 )
% 3.17/1.86 != ( times_a_c @ X51 @ X52 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_175_surjective__pairing,axiom,
% 3.17/1.86 ! [T3: produc866628903_sc_sz] :
% 3.17/1.86 ( T3
% 3.17/1.86 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ T3 ) @ ( produc4753477_sc_sz @ T3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_176_surjective__pairing,axiom,
% 3.17/1.86 ! [T3: produc1241881959eal_sz] :
% 3.17/1.86 ( T3
% 3.17/1.86 = ( produc1235791063eal_sz @ ( produc286845635eal_sz @ T3 ) @ ( produc1746886149eal_sz @ T3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_177_surjective__pairing,axiom,
% 3.17/1.86 ! [T3: produc1892666919z_real] :
% 3.17/1.86 ( T3
% 3.17/1.86 = ( produc784663575z_real @ ( produc870616579z_real @ T3 ) @ ( produc1422611269z_real @ T3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_178_surjective__pairing,axiom,
% 3.17/1.86 ! [T3: produc1149990247eal_sz] :
% 3.17/1.86 ( T3
% 3.17/1.86 = ( produc1308130519eal_sz @ ( produc1111759555eal_sz @ T3 ) @ ( produc1269210629eal_sz @ T3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_179_surjective__pairing,axiom,
% 3.17/1.86 ! [T3: produc1821101996_sc_sz] :
% 3.17/1.86 ( T3
% 3.17/1.86 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ T3 ) @ ( produc974239792_sc_sz @ T3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_180_surjective__pairing,axiom,
% 3.17/1.86 ! [T3: produc190496183real_c] :
% 3.17/1.86 ( T3
% 3.17/1.86 = ( produc394644079real_c @ ( produc2010422875real_c @ T3 ) @ ( produc314122909real_c @ T3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_181_prod_Oexhaust__sel,axiom,
% 3.17/1.86 ! [Prod: produc866628903_sc_sz] :
% 3.17/1.86 ( Prod
% 3.17/1.86 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_182_prod_Oexhaust__sel,axiom,
% 3.17/1.86 ! [Prod: produc1241881959eal_sz] :
% 3.17/1.86 ( Prod
% 3.17/1.86 = ( produc1235791063eal_sz @ ( produc286845635eal_sz @ Prod ) @ ( produc1746886149eal_sz @ Prod ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_183_prod_Oexhaust__sel,axiom,
% 3.17/1.86 ! [Prod: produc1892666919z_real] :
% 3.17/1.86 ( Prod
% 3.17/1.86 = ( produc784663575z_real @ ( produc870616579z_real @ Prod ) @ ( produc1422611269z_real @ Prod ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_184_prod_Oexhaust__sel,axiom,
% 3.17/1.86 ! [Prod: produc1149990247eal_sz] :
% 3.17/1.86 ( Prod
% 3.17/1.86 = ( produc1308130519eal_sz @ ( produc1111759555eal_sz @ Prod ) @ ( produc1269210629eal_sz @ Prod ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_185_prod_Oexhaust__sel,axiom,
% 3.17/1.86 ! [Prod: produc1821101996_sc_sz] :
% 3.17/1.86 ( Prod
% 3.17/1.86 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_186_prod_Oexhaust__sel,axiom,
% 3.17/1.86 ! [Prod: produc190496183real_c] :
% 3.17/1.86 ( Prod
% 3.17/1.86 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_187_Pair__le,axiom,
% 3.17/1.86 ! [A2: set_a,B2: set_a,C2: set_a,D: set_a] :
% 3.17/1.86 ( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A2 @ B2 ) @ ( produc1928581911_set_a @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_less_eq_set_a @ A2 @ C2 )
% 3.17/1.86 & ( ord_less_eq_set_a @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_188_Pair__le,axiom,
% 3.17/1.86 ! [A2: set_a,B2: a > $o,C2: set_a,D: a > $o] :
% 3.17/1.86 ( ( ord_le501349868_a_a_o @ ( produc634809990_a_a_o @ A2 @ B2 ) @ ( produc634809990_a_a_o @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_less_eq_set_a @ A2 @ C2 )
% 3.17/1.86 & ( ord_less_eq_a_o @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_189_Pair__le,axiom,
% 3.17/1.86 ! [A2: a > $o,B2: set_a,C2: a > $o,D: set_a] :
% 3.17/1.86 ( ( ord_le72828020_set_a @ ( produc1916559302_set_a @ A2 @ B2 ) @ ( produc1916559302_set_a @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_less_eq_a_o @ A2 @ C2 )
% 3.17/1.86 & ( ord_less_eq_set_a @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_190_Pair__le,axiom,
% 3.17/1.86 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 3.17/1.86 ( ( ord_le850691415real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc394644079real_c @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_le775706699real_c @ A2 @ C2 )
% 3.17/1.86 & ( ord_le775706699real_c @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_191_Pair__le,axiom,
% 3.17/1.86 ! [A2: a > $o,B2: a > $o,C2: a > $o,D: a > $o] :
% 3.17/1.86 ( ( ord_le1883211903_o_a_o @ ( product_Pair_a_o_a_o @ A2 @ B2 ) @ ( product_Pair_a_o_a_o @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_less_eq_a_o @ A2 @ C2 )
% 3.17/1.86 & ( ord_less_eq_a_o @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_192_Pair__le,axiom,
% 3.17/1.86 ! [A2: set_Fi291318197eal_sz,B2: set_Fi291318197eal_sz,C2: set_Fi291318197eal_sz,D: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( ord_le978883847eal_sz @ ( produc1235791063eal_sz @ A2 @ B2 ) @ ( produc1235791063eal_sz @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_le41263445eal_sz @ A2 @ C2 )
% 3.17/1.86 & ( ord_le41263445eal_sz @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_193_Pair__le,axiom,
% 3.17/1.86 ! [A2: set_a,B2: trm_sf_sz > trm_sf_sz > $o,C2: set_a,D: trm_sf_sz > trm_sf_sz > $o] :
% 3.17/1.86 ( ( ord_le1884788375f_sz_o @ ( produc1174558183f_sz_o @ A2 @ B2 ) @ ( produc1174558183f_sz_o @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_less_eq_set_a @ A2 @ C2 )
% 3.17/1.86 & ( ord_le8515534f_sz_o @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_194_Pair__le,axiom,
% 3.17/1.86 ! [A2: trm_sf_sz > trm_sf_sz > $o,B2: set_a,C2: trm_sf_sz > trm_sf_sz > $o,D: set_a] :
% 3.17/1.86 ( ( ord_le1643089911_set_a @ ( produc1543226183_set_a @ A2 @ B2 ) @ ( produc1543226183_set_a @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_le8515534f_sz_o @ A2 @ C2 )
% 3.17/1.86 & ( ord_less_eq_set_a @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_195_Pair__le,axiom,
% 3.17/1.86 ! [A2: trm_sf_sz > trm_sf_sz > $o,B2: a > $o,C2: trm_sf_sz > trm_sf_sz > $o,D: a > $o] :
% 3.17/1.86 ( ( ord_le2132572860_o_a_o @ ( produc1152932438_o_a_o @ A2 @ B2 ) @ ( produc1152932438_o_a_o @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_le8515534f_sz_o @ A2 @ C2 )
% 3.17/1.86 & ( ord_less_eq_a_o @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_196_Pair__le,axiom,
% 3.17/1.86 ! [A2: a > $o,B2: trm_sf_sz > trm_sf_sz > $o,C2: a > $o,D: trm_sf_sz > trm_sf_sz > $o] :
% 3.17/1.86 ( ( ord_le472894788f_sz_o @ ( produc593159062f_sz_o @ A2 @ B2 ) @ ( produc593159062f_sz_o @ C2 @ D ) )
% 3.17/1.86 = ( ( ord_less_eq_a_o @ A2 @ C2 )
% 3.17/1.86 & ( ord_le8515534f_sz_o @ B2 @ D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_197_directional__derivative__def,axiom,
% 3.17/1.86 ( denota2112424896_a_b_c
% 3.17/1.86 = ( ^ [I5: denota231621370t_unit,T: trm_a_c,V2: produc190496183real_c] : ( denota229585092_a_b_c @ I5 @ T @ ( produc2010422875real_c @ V2 ) @ ( produc314122909real_c @ V2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_198_directional__derivative__def,axiom,
% 3.17/1.86 ( denota453121236_sc_sz
% 3.17/1.86 = ( ^ [I5: denota610675952t_unit,T: trm_sf_sz,V2: produc1149990247eal_sz] : ( denota1979904720_sc_sz @ I5 @ T @ ( produc1111759555eal_sz @ V2 ) @ ( produc1269210629eal_sz @ V2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_199_raw__interp__inverse,axiom,
% 3.17/1.86 ! [X: freche2095075217_sc_sz] :
% 3.17/1.86 ( ( freche1784963216_sc_sz @ ( freche1421597129_sc_sz @ X ) )
% 3.17/1.86 = X ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_200_type__definition__strm,axiom,
% 3.17/1.86 type_d1238563341rm_a_c @ frechet_raw_term_a_c @ freche665377492rm_a_c @ ( collect_trm_a_c @ dfree_a_c ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_201_type__definition__strm,axiom,
% 3.17/1.86 type_d46389773_sf_sz @ freche782854530_sf_sz @ freche1046279700_sf_sz @ ( collect_trm_sf_sz @ dfree_sf_sz ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_202_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.17/1.86 ! [P: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A2: produc866628903_sc_sz] :
% 3.17/1.86 ( ( P @ X @ Y )
% 3.17/1.86 => ( ( A2
% 3.17/1.86 = ( produc1822718231_sc_sz @ X @ Y ) )
% 3.17/1.86 => ( P @ ( produc548504323_sc_sz @ A2 ) @ ( produc4753477_sc_sz @ A2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_203_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.17/1.86 ! [P: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o,X: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,A2: produc1241881959eal_sz] :
% 3.17/1.86 ( ( P @ X @ Y )
% 3.17/1.86 => ( ( A2
% 3.17/1.86 = ( produc1235791063eal_sz @ X @ Y ) )
% 3.17/1.86 => ( P @ ( produc286845635eal_sz @ A2 ) @ ( produc1746886149eal_sz @ A2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_204_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.17/1.86 ! [P: bounde472938360z_real > bounde472938360z_real > $o,X: bounde472938360z_real,Y: bounde472938360z_real,A2: produc1892666919z_real] :
% 3.17/1.86 ( ( P @ X @ Y )
% 3.17/1.86 => ( ( A2
% 3.17/1.86 = ( produc784663575z_real @ X @ Y ) )
% 3.17/1.86 => ( P @ ( produc870616579z_real @ A2 ) @ ( produc1422611269z_real @ A2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_205_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.17/1.86 ! [P: finite824932053eal_sz > finite824932053eal_sz > $o,X: finite824932053eal_sz,Y: finite824932053eal_sz,A2: produc1149990247eal_sz] :
% 3.17/1.86 ( ( P @ X @ Y )
% 3.17/1.86 => ( ( A2
% 3.17/1.86 = ( produc1308130519eal_sz @ X @ Y ) )
% 3.17/1.86 => ( P @ ( produc1111759555eal_sz @ A2 ) @ ( produc1269210629eal_sz @ A2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_206_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.17/1.86 ! [P: denota610675952t_unit > produc866628903_sc_sz > $o,X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( P @ X @ Y )
% 3.17/1.86 => ( ( A2
% 3.17/1.86 = ( produc789536734_sc_sz @ X @ Y ) )
% 3.17/1.86 => ( P @ ( produc1503602930_sc_sz @ A2 ) @ ( produc974239792_sc_sz @ A2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_207_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.17/1.86 ! [P: finite1398487019real_c > finite1398487019real_c > $o,X: finite1398487019real_c,Y: finite1398487019real_c,A2: produc190496183real_c] :
% 3.17/1.86 ( ( P @ X @ Y )
% 3.17/1.86 => ( ( A2
% 3.17/1.86 = ( produc394644079real_c @ X @ Y ) )
% 3.17/1.86 => ( P @ ( produc2010422875real_c @ A2 ) @ ( produc314122909real_c @ A2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_208_conjI__realizer,axiom,
% 3.17/1.86 ! [P: list_f1238882004_sc_sz > $o,P2: list_f1238882004_sc_sz,Q: list_f1238882004_sc_sz > $o,Q2: list_f1238882004_sc_sz] :
% 3.17/1.86 ( ( P @ P2 )
% 3.17/1.86 => ( ( Q @ Q2 )
% 3.17/1.86 => ( ( P @ ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ P2 @ Q2 ) ) )
% 3.17/1.86 & ( Q @ ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_209_conjI__realizer,axiom,
% 3.17/1.86 ! [P: set_Fi291318197eal_sz > $o,P2: set_Fi291318197eal_sz,Q: set_Fi291318197eal_sz > $o,Q2: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( P @ P2 )
% 3.17/1.86 => ( ( Q @ Q2 )
% 3.17/1.86 => ( ( P @ ( produc286845635eal_sz @ ( produc1235791063eal_sz @ P2 @ Q2 ) ) )
% 3.17/1.86 & ( Q @ ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_210_conjI__realizer,axiom,
% 3.17/1.86 ! [P: bounde472938360z_real > $o,P2: bounde472938360z_real,Q: bounde472938360z_real > $o,Q2: bounde472938360z_real] :
% 3.17/1.86 ( ( P @ P2 )
% 3.17/1.86 => ( ( Q @ Q2 )
% 3.17/1.86 => ( ( P @ ( produc870616579z_real @ ( produc784663575z_real @ P2 @ Q2 ) ) )
% 3.17/1.86 & ( Q @ ( produc1422611269z_real @ ( produc784663575z_real @ P2 @ Q2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_211_conjI__realizer,axiom,
% 3.17/1.86 ! [P: finite824932053eal_sz > $o,P2: finite824932053eal_sz,Q: finite824932053eal_sz > $o,Q2: finite824932053eal_sz] :
% 3.17/1.86 ( ( P @ P2 )
% 3.17/1.86 => ( ( Q @ Q2 )
% 3.17/1.86 => ( ( P @ ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ P2 @ Q2 ) ) )
% 3.17/1.86 & ( Q @ ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_212_conjI__realizer,axiom,
% 3.17/1.86 ! [P: denota610675952t_unit > $o,P2: denota610675952t_unit,Q: produc866628903_sc_sz > $o,Q2: produc866628903_sc_sz] :
% 3.17/1.86 ( ( P @ P2 )
% 3.17/1.86 => ( ( Q @ Q2 )
% 3.17/1.86 => ( ( P @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q2 ) ) )
% 3.17/1.86 & ( Q @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_213_conjI__realizer,axiom,
% 3.17/1.86 ! [P: finite1398487019real_c > $o,P2: finite1398487019real_c,Q: finite1398487019real_c > $o,Q2: finite1398487019real_c] :
% 3.17/1.86 ( ( P @ P2 )
% 3.17/1.86 => ( ( Q @ Q2 )
% 3.17/1.86 => ( ( P @ ( produc2010422875real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) )
% 3.17/1.86 & ( Q @ ( produc314122909real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_214_exI__realizer,axiom,
% 3.17/1.86 ! [P: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,Y: list_f1238882004_sc_sz,X: list_f1238882004_sc_sz] :
% 3.17/1.86 ( ( P @ Y @ X )
% 3.17/1.86 => ( P @ ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) ) @ ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_215_exI__realizer,axiom,
% 3.17/1.86 ! [P: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o,Y: set_Fi291318197eal_sz,X: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( P @ Y @ X )
% 3.17/1.86 => ( P @ ( produc1746886149eal_sz @ ( produc1235791063eal_sz @ X @ Y ) ) @ ( produc286845635eal_sz @ ( produc1235791063eal_sz @ X @ Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_216_exI__realizer,axiom,
% 3.17/1.86 ! [P: bounde472938360z_real > bounde472938360z_real > $o,Y: bounde472938360z_real,X: bounde472938360z_real] :
% 3.17/1.86 ( ( P @ Y @ X )
% 3.17/1.86 => ( P @ ( produc1422611269z_real @ ( produc784663575z_real @ X @ Y ) ) @ ( produc870616579z_real @ ( produc784663575z_real @ X @ Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_217_exI__realizer,axiom,
% 3.17/1.86 ! [P: finite824932053eal_sz > finite824932053eal_sz > $o,Y: finite824932053eal_sz,X: finite824932053eal_sz] :
% 3.17/1.86 ( ( P @ Y @ X )
% 3.17/1.86 => ( P @ ( produc1269210629eal_sz @ ( produc1308130519eal_sz @ X @ Y ) ) @ ( produc1111759555eal_sz @ ( produc1308130519eal_sz @ X @ Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_218_exI__realizer,axiom,
% 3.17/1.86 ! [P: produc866628903_sc_sz > denota610675952t_unit > $o,Y: produc866628903_sc_sz,X: denota610675952t_unit] :
% 3.17/1.86 ( ( P @ Y @ X )
% 3.17/1.86 => ( P @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_219_exI__realizer,axiom,
% 3.17/1.86 ! [P: finite1398487019real_c > finite1398487019real_c > $o,Y: finite1398487019real_c,X: finite1398487019real_c] :
% 3.17/1.86 ( ( P @ Y @ X )
% 3.17/1.86 => ( P @ ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) ) @ ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_220_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le850691415real_c
% 3.17/1.86 = ( ^ [X2: produc190496183real_c,Y2: produc190496183real_c] :
% 3.17/1.86 ( ( ord_le775706699real_c @ ( produc2010422875real_c @ X2 ) @ ( produc2010422875real_c @ Y2 ) )
% 3.17/1.86 & ( ord_le775706699real_c @ ( produc314122909real_c @ X2 ) @ ( produc314122909real_c @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_221_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le486764743_set_a
% 3.17/1.86 = ( ^ [X2: produc1691597095_set_a,Y2: produc1691597095_set_a] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ ( produc1926412547_set_a @ X2 ) @ ( produc1926412547_set_a @ Y2 ) )
% 3.17/1.86 & ( ord_less_eq_set_a @ ( produc918972485_set_a @ X2 ) @ ( produc918972485_set_a @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_222_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le501349868_a_a_o
% 3.17/1.86 = ( ^ [X2: produc1989635468_a_a_o,Y2: produc1989635468_a_a_o] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ ( produc1911461786_a_a_o @ X2 ) @ ( produc1911461786_a_a_o @ Y2 ) )
% 3.17/1.86 & ( ord_less_eq_a_o @ ( produc23639768_a_a_o @ X2 ) @ ( produc23639768_a_a_o @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_223_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le72828020_set_a
% 3.17/1.86 = ( ^ [X2: produc1561113620_set_a,Y2: produc1561113620_set_a] :
% 3.17/1.86 ( ( ord_less_eq_a_o @ ( produc1045727450_set_a @ X2 ) @ ( produc1045727450_set_a @ Y2 ) )
% 3.17/1.86 & ( ord_less_eq_set_a @ ( produc1305389080_set_a @ X2 ) @ ( produc1305389080_set_a @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_224_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le473656583eal_sz
% 3.17/1.86 = ( ^ [X2: produc1149990247eal_sz,Y2: produc1149990247eal_sz] :
% 3.17/1.86 ( ( ord_le787639925eal_sz @ ( produc1111759555eal_sz @ X2 ) @ ( produc1111759555eal_sz @ Y2 ) )
% 3.17/1.86 & ( ord_le787639925eal_sz @ ( produc1269210629eal_sz @ X2 ) @ ( produc1269210629eal_sz @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_225_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le1883211903_o_a_o
% 3.17/1.86 = ( ^ [X2: product_prod_a_o_a_o,Y2: product_prod_a_o_a_o] :
% 3.17/1.86 ( ( ord_less_eq_a_o @ ( product_fst_a_o_a_o @ X2 ) @ ( product_fst_a_o_a_o @ Y2 ) )
% 3.17/1.86 & ( ord_less_eq_a_o @ ( product_snd_a_o_a_o @ X2 ) @ ( product_snd_a_o_a_o @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_226_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le1884788375f_sz_o
% 3.17/1.86 = ( ^ [X2: produc1144880887f_sz_o,Y2: produc1144880887f_sz_o] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ ( produc38604755f_sz_o @ X2 ) @ ( produc38604755f_sz_o @ Y2 ) )
% 3.17/1.86 & ( ord_le8515534f_sz_o @ ( produc407510293f_sz_o @ X2 ) @ ( produc407510293f_sz_o @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_227_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le1643089911_set_a
% 3.17/1.86 = ( ^ [X2: produc903182423_set_a,Y2: produc903182423_set_a] :
% 3.17/1.86 ( ( ord_le8515534f_sz_o @ ( produc407272755_set_a @ X2 ) @ ( produc407272755_set_a @ Y2 ) )
% 3.17/1.86 & ( ord_less_eq_set_a @ ( produc776178293_set_a @ X2 ) @ ( produc776178293_set_a @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_228_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le2132572860_o_a_o
% 3.17/1.86 = ( ^ [X2: produc1065634396_o_a_o,Y2: produc1065634396_o_a_o] :
% 3.17/1.86 ( ( ord_le8515534f_sz_o @ ( produc2013638506_o_a_o @ X2 ) @ ( produc2013638506_o_a_o @ Y2 ) )
% 3.17/1.86 & ( ord_less_eq_a_o @ ( produc1630531752_o_a_o @ X2 ) @ ( produc1630531752_o_a_o @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_229_less__eq__prod__def,axiom,
% 3.17/1.86 ( ord_le472894788f_sz_o
% 3.17/1.86 = ( ^ [X2: produc1553439972f_sz_o,Y2: produc1553439972f_sz_o] :
% 3.17/1.86 ( ( ord_less_eq_a_o @ ( produc1453865130f_sz_o @ X2 ) @ ( produc1453865130f_sz_o @ Y2 ) )
% 3.17/1.86 & ( ord_le8515534f_sz_o @ ( produc1070758376f_sz_o @ X2 ) @ ( produc1070758376f_sz_o @ Y2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_230_Iagree__sub,axiom,
% 3.17/1.86 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,I3: denota231621370t_unit,J: denota231621370t_unit] :
% 3.17/1.86 ( ( ord_le929608341um_b_c @ A @ B )
% 3.17/1.86 => ( ( denota69106024_a_b_c @ I3 @ J @ B )
% 3.17/1.86 => ( denota69106024_a_b_c @ I3 @ J @ A ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_231_subset__Collect__iff,axiom,
% 3.17/1.86 ! [B: set_Fi291318197eal_sz,A: set_Fi291318197eal_sz,P: finite824932053eal_sz > $o] :
% 3.17/1.86 ( ( ord_le41263445eal_sz @ B @ A )
% 3.17/1.86 => ( ( ord_le41263445eal_sz @ B
% 3.17/1.86 @ ( collec1002602816eal_sz
% 3.17/1.86 @ ^ [X2: finite824932053eal_sz] :
% 3.17/1.86 ( ( member1693951742eal_sz @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) )
% 3.17/1.86 = ( ! [X2: finite824932053eal_sz] :
% 3.17/1.86 ( ( member1693951742eal_sz @ X2 @ B )
% 3.17/1.86 => ( P @ X2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_232_subset__Collect__iff,axiom,
% 3.17/1.86 ! [B: set_Pr1169339874_sc_sz,A: set_Pr1169339874_sc_sz,P: produc1821101996_sc_sz > $o] :
% 3.17/1.86 ( ( ord_le1230423618_sc_sz @ B @ A )
% 3.17/1.86 => ( ( ord_le1230423618_sc_sz @ B
% 3.17/1.86 @ ( collec1199592193_sc_sz
% 3.17/1.86 @ ^ [X2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( member1057565379_sc_sz @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) )
% 3.17/1.86 = ( ! [X2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( member1057565379_sc_sz @ X2 @ B )
% 3.17/1.86 => ( P @ X2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_233_subset__Collect__iff,axiom,
% 3.17/1.86 ! [B: set_trm_sf_sz,A: set_trm_sf_sz,P: trm_sf_sz > $o] :
% 3.17/1.86 ( ( ord_le1697056455_sf_sz @ B @ A )
% 3.17/1.86 => ( ( ord_le1697056455_sf_sz @ B
% 3.17/1.86 @ ( collect_trm_sf_sz
% 3.17/1.86 @ ^ [X2: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) )
% 3.17/1.86 = ( ! [X2: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ X2 @ B )
% 3.17/1.86 => ( P @ X2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_234_subset__Collect__iff,axiom,
% 3.17/1.86 ! [B: set_trm_a_c,A: set_trm_a_c,P: trm_a_c > $o] :
% 3.17/1.86 ( ( ord_le1369644495rm_a_c @ B @ A )
% 3.17/1.86 => ( ( ord_le1369644495rm_a_c @ B
% 3.17/1.86 @ ( collect_trm_a_c
% 3.17/1.86 @ ^ [X2: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) )
% 3.17/1.86 = ( ! [X2: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ X2 @ B )
% 3.17/1.86 => ( P @ X2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_235_subset__Collect__iff,axiom,
% 3.17/1.86 ! [B: set_a,A: set_a,P: a > $o] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ B @ A )
% 3.17/1.86 => ( ( ord_less_eq_set_a @ B
% 3.17/1.86 @ ( collect_a
% 3.17/1.86 @ ^ [X2: a] :
% 3.17/1.86 ( ( member_a @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) )
% 3.17/1.86 = ( ! [X2: a] :
% 3.17/1.86 ( ( member_a @ X2 @ B )
% 3.17/1.86 => ( P @ X2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_236_subset__Collect__iff,axiom,
% 3.17/1.86 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,P: sum_su737395349um_b_c > $o] :
% 3.17/1.86 ( ( ord_le929608341um_b_c @ B @ A )
% 3.17/1.86 => ( ( ord_le929608341um_b_c @ B
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [X2: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( member1893232190um_b_c @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) )
% 3.17/1.86 = ( ! [X2: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( member1893232190um_b_c @ X2 @ B )
% 3.17/1.86 => ( P @ X2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_237_subset__CollectI,axiom,
% 3.17/1.86 ! [B: set_Fi291318197eal_sz,A: set_Fi291318197eal_sz,Q: finite824932053eal_sz > $o,P: finite824932053eal_sz > $o] :
% 3.17/1.86 ( ( ord_le41263445eal_sz @ B @ A )
% 3.17/1.86 => ( ! [X3: finite824932053eal_sz] :
% 3.17/1.86 ( ( member1693951742eal_sz @ X3 @ B )
% 3.17/1.86 => ( ( Q @ X3 )
% 3.17/1.86 => ( P @ X3 ) ) )
% 3.17/1.86 => ( ord_le41263445eal_sz
% 3.17/1.86 @ ( collec1002602816eal_sz
% 3.17/1.86 @ ^ [X2: finite824932053eal_sz] :
% 3.17/1.86 ( ( member1693951742eal_sz @ X2 @ B )
% 3.17/1.86 & ( Q @ X2 ) ) )
% 3.17/1.86 @ ( collec1002602816eal_sz
% 3.17/1.86 @ ^ [X2: finite824932053eal_sz] :
% 3.17/1.86 ( ( member1693951742eal_sz @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_238_subset__CollectI,axiom,
% 3.17/1.86 ! [B: set_Pr1169339874_sc_sz,A: set_Pr1169339874_sc_sz,Q: produc1821101996_sc_sz > $o,P: produc1821101996_sc_sz > $o] :
% 3.17/1.86 ( ( ord_le1230423618_sc_sz @ B @ A )
% 3.17/1.86 => ( ! [X3: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( member1057565379_sc_sz @ X3 @ B )
% 3.17/1.86 => ( ( Q @ X3 )
% 3.17/1.86 => ( P @ X3 ) ) )
% 3.17/1.86 => ( ord_le1230423618_sc_sz
% 3.17/1.86 @ ( collec1199592193_sc_sz
% 3.17/1.86 @ ^ [X2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( member1057565379_sc_sz @ X2 @ B )
% 3.17/1.86 & ( Q @ X2 ) ) )
% 3.17/1.86 @ ( collec1199592193_sc_sz
% 3.17/1.86 @ ^ [X2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( member1057565379_sc_sz @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_239_subset__CollectI,axiom,
% 3.17/1.86 ! [B: set_trm_sf_sz,A: set_trm_sf_sz,Q: trm_sf_sz > $o,P: trm_sf_sz > $o] :
% 3.17/1.86 ( ( ord_le1697056455_sf_sz @ B @ A )
% 3.17/1.86 => ( ! [X3: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ X3 @ B )
% 3.17/1.86 => ( ( Q @ X3 )
% 3.17/1.86 => ( P @ X3 ) ) )
% 3.17/1.86 => ( ord_le1697056455_sf_sz
% 3.17/1.86 @ ( collect_trm_sf_sz
% 3.17/1.86 @ ^ [X2: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ X2 @ B )
% 3.17/1.86 & ( Q @ X2 ) ) )
% 3.17/1.86 @ ( collect_trm_sf_sz
% 3.17/1.86 @ ^ [X2: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_240_subset__CollectI,axiom,
% 3.17/1.86 ! [B: set_trm_a_c,A: set_trm_a_c,Q: trm_a_c > $o,P: trm_a_c > $o] :
% 3.17/1.86 ( ( ord_le1369644495rm_a_c @ B @ A )
% 3.17/1.86 => ( ! [X3: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ X3 @ B )
% 3.17/1.86 => ( ( Q @ X3 )
% 3.17/1.86 => ( P @ X3 ) ) )
% 3.17/1.86 => ( ord_le1369644495rm_a_c
% 3.17/1.86 @ ( collect_trm_a_c
% 3.17/1.86 @ ^ [X2: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ X2 @ B )
% 3.17/1.86 & ( Q @ X2 ) ) )
% 3.17/1.86 @ ( collect_trm_a_c
% 3.17/1.86 @ ^ [X2: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_241_subset__CollectI,axiom,
% 3.17/1.86 ! [B: set_a,A: set_a,Q: a > $o,P: a > $o] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ B @ A )
% 3.17/1.86 => ( ! [X3: a] :
% 3.17/1.86 ( ( member_a @ X3 @ B )
% 3.17/1.86 => ( ( Q @ X3 )
% 3.17/1.86 => ( P @ X3 ) ) )
% 3.17/1.86 => ( ord_less_eq_set_a
% 3.17/1.86 @ ( collect_a
% 3.17/1.86 @ ^ [X2: a] :
% 3.17/1.86 ( ( member_a @ X2 @ B )
% 3.17/1.86 & ( Q @ X2 ) ) )
% 3.17/1.86 @ ( collect_a
% 3.17/1.86 @ ^ [X2: a] :
% 3.17/1.86 ( ( member_a @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_242_subset__CollectI,axiom,
% 3.17/1.86 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,Q: sum_su737395349um_b_c > $o,P: sum_su737395349um_b_c > $o] :
% 3.17/1.86 ( ( ord_le929608341um_b_c @ B @ A )
% 3.17/1.86 => ( ! [X3: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( member1893232190um_b_c @ X3 @ B )
% 3.17/1.86 => ( ( Q @ X3 )
% 3.17/1.86 => ( P @ X3 ) ) )
% 3.17/1.86 => ( ord_le929608341um_b_c
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [X2: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( member1893232190um_b_c @ X2 @ B )
% 3.17/1.86 & ( Q @ X2 ) ) )
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [X2: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( member1893232190um_b_c @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_243_Pair__mono,axiom,
% 3.17/1.86 ! [X: set_a,X4: set_a,Y: set_a,Y5: set_a] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ X @ X4 )
% 3.17/1.86 => ( ( ord_less_eq_set_a @ Y @ Y5 )
% 3.17/1.86 => ( ord_le486764743_set_a @ ( produc1928581911_set_a @ X @ Y ) @ ( produc1928581911_set_a @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_244_Pair__mono,axiom,
% 3.17/1.86 ! [X: set_a,X4: set_a,Y: a > $o,Y5: a > $o] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ X @ X4 )
% 3.17/1.86 => ( ( ord_less_eq_a_o @ Y @ Y5 )
% 3.17/1.86 => ( ord_le501349868_a_a_o @ ( produc634809990_a_a_o @ X @ Y ) @ ( produc634809990_a_a_o @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_245_Pair__mono,axiom,
% 3.17/1.86 ! [X: a > $o,X4: a > $o,Y: set_a,Y5: set_a] :
% 3.17/1.86 ( ( ord_less_eq_a_o @ X @ X4 )
% 3.17/1.86 => ( ( ord_less_eq_set_a @ Y @ Y5 )
% 3.17/1.86 => ( ord_le72828020_set_a @ ( produc1916559302_set_a @ X @ Y ) @ ( produc1916559302_set_a @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_246_Pair__mono,axiom,
% 3.17/1.86 ! [X: finite1398487019real_c,X4: finite1398487019real_c,Y: finite1398487019real_c,Y5: finite1398487019real_c] :
% 3.17/1.86 ( ( ord_le775706699real_c @ X @ X4 )
% 3.17/1.86 => ( ( ord_le775706699real_c @ Y @ Y5 )
% 3.17/1.86 => ( ord_le850691415real_c @ ( produc394644079real_c @ X @ Y ) @ ( produc394644079real_c @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_247_Pair__mono,axiom,
% 3.17/1.86 ! [X: a > $o,X4: a > $o,Y: a > $o,Y5: a > $o] :
% 3.17/1.86 ( ( ord_less_eq_a_o @ X @ X4 )
% 3.17/1.86 => ( ( ord_less_eq_a_o @ Y @ Y5 )
% 3.17/1.86 => ( ord_le1883211903_o_a_o @ ( product_Pair_a_o_a_o @ X @ Y ) @ ( product_Pair_a_o_a_o @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_248_Pair__mono,axiom,
% 3.17/1.86 ! [X: set_Fi291318197eal_sz,X4: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,Y5: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( ord_le41263445eal_sz @ X @ X4 )
% 3.17/1.86 => ( ( ord_le41263445eal_sz @ Y @ Y5 )
% 3.17/1.86 => ( ord_le978883847eal_sz @ ( produc1235791063eal_sz @ X @ Y ) @ ( produc1235791063eal_sz @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_249_Pair__mono,axiom,
% 3.17/1.86 ! [X: set_a,X4: set_a,Y: trm_sf_sz > trm_sf_sz > $o,Y5: trm_sf_sz > trm_sf_sz > $o] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ X @ X4 )
% 3.17/1.86 => ( ( ord_le8515534f_sz_o @ Y @ Y5 )
% 3.17/1.86 => ( ord_le1884788375f_sz_o @ ( produc1174558183f_sz_o @ X @ Y ) @ ( produc1174558183f_sz_o @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_250_Pair__mono,axiom,
% 3.17/1.86 ! [X: trm_sf_sz > trm_sf_sz > $o,X4: trm_sf_sz > trm_sf_sz > $o,Y: set_a,Y5: set_a] :
% 3.17/1.86 ( ( ord_le8515534f_sz_o @ X @ X4 )
% 3.17/1.86 => ( ( ord_less_eq_set_a @ Y @ Y5 )
% 3.17/1.86 => ( ord_le1643089911_set_a @ ( produc1543226183_set_a @ X @ Y ) @ ( produc1543226183_set_a @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_251_Pair__mono,axiom,
% 3.17/1.86 ! [X: trm_sf_sz > trm_sf_sz > $o,X4: trm_sf_sz > trm_sf_sz > $o,Y: a > $o,Y5: a > $o] :
% 3.17/1.86 ( ( ord_le8515534f_sz_o @ X @ X4 )
% 3.17/1.86 => ( ( ord_less_eq_a_o @ Y @ Y5 )
% 3.17/1.86 => ( ord_le2132572860_o_a_o @ ( produc1152932438_o_a_o @ X @ Y ) @ ( produc1152932438_o_a_o @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_252_Pair__mono,axiom,
% 3.17/1.86 ! [X: a > $o,X4: a > $o,Y: trm_sf_sz > trm_sf_sz > $o,Y5: trm_sf_sz > trm_sf_sz > $o] :
% 3.17/1.86 ( ( ord_less_eq_a_o @ X @ X4 )
% 3.17/1.86 => ( ( ord_le8515534f_sz_o @ Y @ Y5 )
% 3.17/1.86 => ( ord_le472894788f_sz_o @ ( produc593159062f_sz_o @ X @ Y ) @ ( produc593159062f_sz_o @ X4 @ Y5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_253_fst__mono,axiom,
% 3.17/1.86 ! [X: produc1149990247eal_sz,Y: produc1149990247eal_sz] :
% 3.17/1.86 ( ( ord_le473656583eal_sz @ X @ Y )
% 3.17/1.86 => ( ord_le787639925eal_sz @ ( produc1111759555eal_sz @ X ) @ ( produc1111759555eal_sz @ Y ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_254_fst__mono,axiom,
% 3.17/1.86 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 3.17/1.86 ( ( ord_le850691415real_c @ X @ Y )
% 3.17/1.86 => ( ord_le775706699real_c @ ( produc2010422875real_c @ X ) @ ( produc2010422875real_c @ Y ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_255_snd__mono,axiom,
% 3.17/1.86 ! [X: produc1149990247eal_sz,Y: produc1149990247eal_sz] :
% 3.17/1.86 ( ( ord_le473656583eal_sz @ X @ Y )
% 3.17/1.86 => ( ord_le787639925eal_sz @ ( produc1269210629eal_sz @ X ) @ ( produc1269210629eal_sz @ Y ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_256_snd__mono,axiom,
% 3.17/1.86 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 3.17/1.86 ( ( ord_le850691415real_c @ X @ Y )
% 3.17/1.86 => ( ord_le775706699real_c @ ( produc314122909real_c @ X ) @ ( produc314122909real_c @ Y ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_257_exE__realizer_H,axiom,
% 3.17/1.86 ! [P: finite824932053eal_sz > finite824932053eal_sz > $o,P2: produc1149990247eal_sz] :
% 3.17/1.86 ( ( P @ ( produc1269210629eal_sz @ P2 ) @ ( produc1111759555eal_sz @ P2 ) )
% 3.17/1.86 => ~ ! [X3: finite824932053eal_sz,Y3: finite824932053eal_sz] :
% 3.17/1.86 ~ ( P @ Y3 @ X3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_258_exE__realizer_H,axiom,
% 3.17/1.86 ! [P: produc866628903_sc_sz > denota610675952t_unit > $o,P2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( P @ ( produc974239792_sc_sz @ P2 ) @ ( produc1503602930_sc_sz @ P2 ) )
% 3.17/1.86 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.17/1.86 ~ ( P @ Y3 @ X3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_259_exE__realizer_H,axiom,
% 3.17/1.86 ! [P: finite1398487019real_c > finite1398487019real_c > $o,P2: produc190496183real_c] :
% 3.17/1.86 ( ( P @ ( produc314122909real_c @ P2 ) @ ( produc2010422875real_c @ P2 ) )
% 3.17/1.86 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.17/1.86 ~ ( P @ Y3 @ X3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_260_sum_Oinject_I1_J,axiom,
% 3.17/1.86 ! [X1: a,Y1: a] :
% 3.17/1.86 ( ( ( sum_In2139678582um_b_c @ X1 )
% 3.17/1.86 = ( sum_In2139678582um_b_c @ Y1 ) )
% 3.17/1.86 = ( X1 = Y1 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_261_old_Osum_Oinject_I1_J,axiom,
% 3.17/1.86 ! [A2: a,A3: a] :
% 3.17/1.86 ( ( ( sum_In2139678582um_b_c @ A2 )
% 3.17/1.86 = ( sum_In2139678582um_b_c @ A3 ) )
% 3.17/1.86 = ( A2 = A3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_262_good__interp__inverse,axiom,
% 3.17/1.86 ! [Y: denota231621370t_unit] :
% 3.17/1.86 ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 3.17/1.86 => ( ( freche1608036107_a_b_c @ ( freche1473475332_a_b_c @ Y ) )
% 3.17/1.86 = Y ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_263_good__interp__inverse,axiom,
% 3.17/1.86 ! [Y: denota610675952t_unit] :
% 3.17/1.86 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 3.17/1.86 => ( ( freche1421597129_sc_sz @ ( freche1784963216_sc_sz @ Y ) )
% 3.17/1.86 = Y ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_264_f0__def,axiom,
% 3.17/1.86 ( f0_sf_sz
% 3.17/1.86 = ( ^ [F: sf] : ( function_sf_sz @ F @ empty_sz_sf ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_265_subsetI,axiom,
% 3.17/1.86 ! [A: set_Fi291318197eal_sz,B: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ! [X3: finite824932053eal_sz] :
% 3.17/1.86 ( ( member1693951742eal_sz @ X3 @ A )
% 3.17/1.86 => ( member1693951742eal_sz @ X3 @ B ) )
% 3.17/1.86 => ( ord_le41263445eal_sz @ A @ B ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_266_subsetI,axiom,
% 3.17/1.86 ! [A: set_Pr1169339874_sc_sz,B: set_Pr1169339874_sc_sz] :
% 3.17/1.86 ( ! [X3: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( member1057565379_sc_sz @ X3 @ A )
% 3.17/1.86 => ( member1057565379_sc_sz @ X3 @ B ) )
% 3.17/1.86 => ( ord_le1230423618_sc_sz @ A @ B ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_267_subsetI,axiom,
% 3.17/1.86 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.17/1.86 ( ! [X3: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( member1893232190um_b_c @ X3 @ A )
% 3.17/1.86 => ( member1893232190um_b_c @ X3 @ B ) )
% 3.17/1.86 => ( ord_le929608341um_b_c @ A @ B ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_268_subsetI,axiom,
% 3.17/1.86 ! [A: set_trm_sf_sz,B: set_trm_sf_sz] :
% 3.17/1.86 ( ! [X3: trm_sf_sz] :
% 3.17/1.86 ( ( member_trm_sf_sz @ X3 @ A )
% 3.17/1.86 => ( member_trm_sf_sz @ X3 @ B ) )
% 3.17/1.86 => ( ord_le1697056455_sf_sz @ A @ B ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_269_subsetI,axiom,
% 3.17/1.86 ! [A: set_trm_a_c,B: set_trm_a_c] :
% 3.17/1.86 ( ! [X3: trm_a_c] :
% 3.17/1.86 ( ( member_trm_a_c @ X3 @ A )
% 3.17/1.86 => ( member_trm_a_c @ X3 @ B ) )
% 3.17/1.86 => ( ord_le1369644495rm_a_c @ A @ B ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_270_subsetI,axiom,
% 3.17/1.86 ! [A: set_a,B: set_a] :
% 3.17/1.86 ( ! [X3: a] :
% 3.17/1.86 ( ( member_a @ X3 @ A )
% 3.17/1.86 => ( member_a @ X3 @ B ) )
% 3.17/1.86 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_271_raw__interp__induct,axiom,
% 3.17/1.86 ! [Y: denota231621370t_unit,P: denota231621370t_unit > $o] :
% 3.17/1.86 ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 3.17/1.86 => ( ! [X3: freche914690577_a_b_c] : ( P @ ( freche1608036107_a_b_c @ X3 ) )
% 3.17/1.86 => ( P @ Y ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_272_raw__interp__induct,axiom,
% 3.17/1.86 ! [Y: denota610675952t_unit,P: denota610675952t_unit > $o] :
% 3.17/1.86 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 3.17/1.86 => ( ! [X3: freche2095075217_sc_sz] : ( P @ ( freche1421597129_sc_sz @ X3 ) )
% 3.17/1.86 => ( P @ Y ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_273_raw__interp__cases,axiom,
% 3.17/1.86 ! [Y: denota231621370t_unit] :
% 3.17/1.86 ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 3.17/1.86 => ~ ! [X3: freche914690577_a_b_c] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( freche1608036107_a_b_c @ X3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_274_raw__interp__cases,axiom,
% 3.17/1.86 ! [Y: denota610675952t_unit] :
% 3.17/1.86 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 3.17/1.86 => ~ ! [X3: freche2095075217_sc_sz] :
% 3.17/1.86 ( Y
% 3.17/1.86 != ( freche1421597129_sc_sz @ X3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_275_raw__interp,axiom,
% 3.17/1.86 ! [X: freche914690577_a_b_c] : ( member1777622435t_unit @ ( freche1608036107_a_b_c @ X ) @ ( collec451781861t_unit @ denota258389581_a_b_c ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_276_raw__interp,axiom,
% 3.17/1.86 ! [X: freche2095075217_sc_sz] : ( member754147591t_unit @ ( freche1421597129_sc_sz @ X ) @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_277_good__interp__cases,axiom,
% 3.17/1.86 ! [X: freche914690577_a_b_c] :
% 3.17/1.86 ~ ! [Y3: denota231621370t_unit] :
% 3.17/1.86 ( ( X
% 3.17/1.86 = ( freche1473475332_a_b_c @ Y3 ) )
% 3.17/1.86 => ~ ( member1777622435t_unit @ Y3 @ ( collec451781861t_unit @ denota258389581_a_b_c ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_278_good__interp__cases,axiom,
% 3.17/1.86 ! [X: freche2095075217_sc_sz] :
% 3.17/1.86 ~ ! [Y3: denota610675952t_unit] :
% 3.17/1.86 ( ( X
% 3.17/1.86 = ( freche1784963216_sc_sz @ Y3 ) )
% 3.17/1.86 => ~ ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_279_good__interp__induct,axiom,
% 3.17/1.86 ! [P: freche914690577_a_b_c > $o,X: freche914690577_a_b_c] :
% 3.17/1.86 ( ! [Y3: denota231621370t_unit] :
% 3.17/1.86 ( ( member1777622435t_unit @ Y3 @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 3.17/1.86 => ( P @ ( freche1473475332_a_b_c @ Y3 ) ) )
% 3.17/1.86 => ( P @ X ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_280_good__interp__induct,axiom,
% 3.17/1.86 ! [P: freche2095075217_sc_sz > $o,X: freche2095075217_sc_sz] :
% 3.17/1.86 ( ! [Y3: denota610675952t_unit] :
% 3.17/1.86 ( ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 3.17/1.86 => ( P @ ( freche1784963216_sc_sz @ Y3 ) ) )
% 3.17/1.86 => ( P @ X ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_281_good__interp__inject,axiom,
% 3.17/1.86 ! [X: denota231621370t_unit,Y: denota231621370t_unit] :
% 3.17/1.86 ( ( member1777622435t_unit @ X @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 3.17/1.86 => ( ( member1777622435t_unit @ Y @ ( collec451781861t_unit @ denota258389581_a_b_c ) )
% 3.17/1.86 => ( ( ( freche1473475332_a_b_c @ X )
% 3.17/1.86 = ( freche1473475332_a_b_c @ Y ) )
% 3.17/1.86 = ( X = Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_282_good__interp__inject,axiom,
% 3.17/1.86 ! [X: denota610675952t_unit,Y: denota610675952t_unit] :
% 3.17/1.86 ( ( member754147591t_unit @ X @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 3.17/1.86 => ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 3.17/1.86 => ( ( ( freche1784963216_sc_sz @ X )
% 3.17/1.86 = ( freche1784963216_sc_sz @ Y ) )
% 3.17/1.86 = ( X = Y ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_283_subset__antisym,axiom,
% 3.17/1.86 ! [A: set_a,B: set_a] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ A @ B )
% 3.17/1.86 => ( ( ord_less_eq_set_a @ B @ A )
% 3.17/1.86 => ( A = B ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_284_Collect__mono__iff,axiom,
% 3.17/1.86 ! [P: finite824932053eal_sz > $o,Q: finite824932053eal_sz > $o] :
% 3.17/1.86 ( ( ord_le41263445eal_sz @ ( collec1002602816eal_sz @ P ) @ ( collec1002602816eal_sz @ Q ) )
% 3.17/1.86 = ( ! [X2: finite824932053eal_sz] :
% 3.17/1.86 ( ( P @ X2 )
% 3.17/1.86 => ( Q @ X2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_285_Collect__mono__iff,axiom,
% 3.17/1.86 ! [P: produc1821101996_sc_sz > $o,Q: produc1821101996_sc_sz > $o] :
% 3.17/1.86 ( ( ord_le1230423618_sc_sz @ ( collec1199592193_sc_sz @ P ) @ ( collec1199592193_sc_sz @ Q ) )
% 3.17/1.86 = ( ! [X2: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( P @ X2 )
% 3.17/1.86 => ( Q @ X2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_286_Collect__mono__iff,axiom,
% 3.17/1.86 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 3.17/1.86 ( ( ord_le1697056455_sf_sz @ ( collect_trm_sf_sz @ P ) @ ( collect_trm_sf_sz @ Q ) )
% 3.17/1.86 = ( ! [X2: trm_sf_sz] :
% 3.17/1.86 ( ( P @ X2 )
% 3.17/1.86 => ( Q @ X2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_287_Collect__mono__iff,axiom,
% 3.17/1.86 ! [P: trm_a_c > $o,Q: trm_a_c > $o] :
% 3.17/1.86 ( ( ord_le1369644495rm_a_c @ ( collect_trm_a_c @ P ) @ ( collect_trm_a_c @ Q ) )
% 3.17/1.86 = ( ! [X2: trm_a_c] :
% 3.17/1.86 ( ( P @ X2 )
% 3.17/1.86 => ( Q @ X2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_288_Collect__mono__iff,axiom,
% 3.17/1.86 ! [P: a > $o,Q: a > $o] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 3.17/1.86 = ( ! [X2: a] :
% 3.17/1.86 ( ( P @ X2 )
% 3.17/1.86 => ( Q @ X2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_289_Collect__mono__iff,axiom,
% 3.17/1.86 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 3.17/1.86 ( ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) )
% 3.17/1.86 = ( ! [X2: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( P @ X2 )
% 3.17/1.86 => ( Q @ X2 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_290_set__eq__subset,axiom,
% 3.17/1.86 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 3.17/1.86 = ( ^ [A5: set_a,B5: set_a] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 3.17/1.86 & ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_291_subset__trans,axiom,
% 3.17/1.86 ! [A: set_a,B: set_a,C3: set_a] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ A @ B )
% 3.17/1.86 => ( ( ord_less_eq_set_a @ B @ C3 )
% 3.17/1.86 => ( ord_less_eq_set_a @ A @ C3 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_292_Collect__mono,axiom,
% 3.17/1.86 ! [P: produc1821101996_sc_sz > $o,Q: produc1821101996_sc_sz > $o] :
% 3.17/1.86 ( ! [X3: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 => ( Q @ X3 ) )
% 3.17/1.86 => ( ord_le1230423618_sc_sz @ ( collec1199592193_sc_sz @ P ) @ ( collec1199592193_sc_sz @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_293_Collect__mono,axiom,
% 3.17/1.86 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 3.17/1.86 ( ! [X3: trm_sf_sz] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 => ( Q @ X3 ) )
% 3.17/1.86 => ( ord_le1697056455_sf_sz @ ( collect_trm_sf_sz @ P ) @ ( collect_trm_sf_sz @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_294_Collect__mono,axiom,
% 3.17/1.86 ! [P: trm_a_c > $o,Q: trm_a_c > $o] :
% 3.17/1.86 ( ! [X3: trm_a_c] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 => ( Q @ X3 ) )
% 3.17/1.86 => ( ord_le1369644495rm_a_c @ ( collect_trm_a_c @ P ) @ ( collect_trm_a_c @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_295_Collect__mono,axiom,
% 3.17/1.86 ! [P: a > $o,Q: a > $o] :
% 3.17/1.86 ( ! [X3: a] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 => ( Q @ X3 ) )
% 3.17/1.86 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_296_Collect__mono,axiom,
% 3.17/1.86 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 3.17/1.86 ( ! [X3: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( P @ X3 )
% 3.17/1.86 => ( Q @ X3 ) )
% 3.17/1.86 => ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_297_subset__iff,axiom,
% 3.17/1.86 ( ord_less_eq_set_a
% 3.17/1.86 = ( ^ [A5: set_a,B5: set_a] :
% 3.17/1.86 ! [T: a] :
% 3.17/1.86 ( ( member_a @ T @ A5 )
% 3.17/1.86 => ( member_a @ T @ B5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_298_subset__eq,axiom,
% 3.17/1.86 ( ord_less_eq_set_a
% 3.17/1.86 = ( ^ [A5: set_a,B5: set_a] :
% 3.17/1.86 ! [X2: a] :
% 3.17/1.86 ( ( member_a @ X2 @ A5 )
% 3.17/1.86 => ( member_a @ X2 @ B5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_299_subsetD,axiom,
% 3.17/1.86 ! [A: set_a,B: set_a,C2: a] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ A @ B )
% 3.17/1.86 => ( ( member_a @ C2 @ A )
% 3.17/1.86 => ( member_a @ C2 @ B ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_300_in__mono,axiom,
% 3.17/1.86 ! [A: set_a,B: set_a,X: a] :
% 3.17/1.86 ( ( ord_less_eq_set_a @ A @ B )
% 3.17/1.86 => ( ( member_a @ X @ A )
% 3.17/1.86 => ( member_a @ X @ B ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_301_Inl__inject,axiom,
% 3.17/1.86 ! [X: a,Y: a] :
% 3.17/1.86 ( ( ( sum_In2139678582um_b_c @ X )
% 3.17/1.86 = ( sum_In2139678582um_b_c @ Y ) )
% 3.17/1.86 => ( X = Y ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_302_Collect__subset,axiom,
% 3.17/1.86 ! [A: set_a,P: a > $o] :
% 3.17/1.86 ( ord_less_eq_set_a
% 3.17/1.86 @ ( collect_a
% 3.17/1.86 @ ^ [X2: a] :
% 3.17/1.86 ( ( member_a @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) )
% 3.17/1.86 @ A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_303_Collect__subset,axiom,
% 3.17/1.86 ! [A: set_Su1783761653um_b_c,P: sum_su737395349um_b_c > $o] :
% 3.17/1.86 ( ord_le929608341um_b_c
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [X2: sum_su737395349um_b_c] :
% 3.17/1.86 ( ( member1893232190um_b_c @ X2 @ A )
% 3.17/1.86 & ( P @ X2 ) ) )
% 3.17/1.86 @ A ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_304_less__eq__set__def,axiom,
% 3.17/1.86 ( ord_less_eq_set_a
% 3.17/1.86 = ( ^ [A5: set_a,B5: set_a] :
% 3.17/1.86 ( ord_less_eq_a_o
% 3.17/1.86 @ ^ [X2: a] : ( member_a @ X2 @ A5 )
% 3.17/1.86 @ ^ [X2: a] : ( member_a @ X2 @ B5 ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_305_sterm__determines__frechet,axiom,
% 3.17/1.86 ! [I3: denota231621370t_unit,J: denota231621370t_unit,Theta_12: trm_a_c,Theta_22: trm_a_c,Nu: produc190496183real_c] :
% 3.17/1.86 ( ( denota258389581_a_b_c @ I3 )
% 3.17/1.86 => ( ( denota258389581_a_b_c @ J )
% 3.17/1.86 => ( ( dfree_a_c @ Theta_12 )
% 3.17/1.86 => ( ( dfree_a_c @ Theta_22 )
% 3.17/1.86 => ( ( ( denota2042094639_a_b_c @ I3 @ Theta_12 )
% 3.17/1.86 = ( denota2042094639_a_b_c @ J @ Theta_22 ) )
% 3.17/1.86 => ( ( denota229585092_a_b_c @ I3 @ Theta_12 @ ( produc2010422875real_c @ Nu ) @ ( produc314122909real_c @ Nu ) )
% 3.17/1.86 = ( denota229585092_a_b_c @ J @ Theta_22 @ ( produc2010422875real_c @ Nu ) @ ( produc314122909real_c @ Nu ) ) ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_306_sterm__determines__frechet,axiom,
% 3.17/1.86 ! [I3: denota610675952t_unit,J: denota610675952t_unit,Theta_12: trm_sf_sz,Theta_22: trm_sf_sz,Nu: produc1149990247eal_sz] :
% 3.17/1.86 ( ( denota1579475975_sc_sz @ I3 )
% 3.17/1.86 => ( ( denota1579475975_sc_sz @ J )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta_12 )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta_22 )
% 3.17/1.86 => ( ( ( denota1179238309_sc_sz @ I3 @ Theta_12 )
% 3.17/1.86 = ( denota1179238309_sc_sz @ J @ Theta_22 ) )
% 3.17/1.86 => ( ( denota1979904720_sc_sz @ I3 @ Theta_12 @ ( produc1111759555eal_sz @ Nu ) @ ( produc1269210629eal_sz @ Nu ) )
% 3.17/1.86 = ( denota1979904720_sc_sz @ J @ Theta_22 @ ( produc1111759555eal_sz @ Nu ) @ ( produc1269210629eal_sz @ Nu ) ) ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_307_type__definition__good__interp,axiom,
% 3.17/1.86 type_d1092523951t_unit @ freche1421597129_sc_sz @ freche1784963216_sc_sz @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_308_image2__def,axiom,
% 3.17/1.86 ( bNF_Gr1775200401_sc_sz
% 3.17/1.86 = ( ^ [A5: set_a,F: a > denota610675952t_unit,G: a > produc866628903_sc_sz] :
% 3.17/1.86 ( collec1199592193_sc_sz
% 3.17/1.86 @ ^ [Uu: produc1821101996_sc_sz] :
% 3.17/1.86 ? [A6: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( produc789536734_sc_sz @ ( F @ A6 ) @ ( G @ A6 ) ) )
% 3.17/1.86 & ( member_a @ A6 @ A5 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_309_image2__eqI,axiom,
% 3.17/1.86 ! [B2: denota610675952t_unit,F2: a > denota610675952t_unit,X: a,C2: produc866628903_sc_sz,G2: a > produc866628903_sc_sz,A: set_a] :
% 3.17/1.86 ( ( B2
% 3.17/1.86 = ( F2 @ X ) )
% 3.17/1.86 => ( ( C2
% 3.17/1.86 = ( G2 @ X ) )
% 3.17/1.86 => ( ( member_a @ X @ A )
% 3.17/1.86 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ B2 @ C2 ) @ ( bNF_Gr1775200401_sc_sz @ A @ F2 @ G2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_310_coincidence__sterm_H,axiom,
% 3.17/1.86 ! [Theta: trm_a_c,Nu: produc190496183real_c,Nu2: produc190496183real_c,I3: denota231621370t_unit,J: denota231621370t_unit] :
% 3.17/1.86 ( ( dfree_a_c @ Theta )
% 3.17/1.86 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVT_a_c @ Theta ) )
% 3.17/1.86 => ( ( denota69106024_a_b_c @ I3 @ J
% 3.17/1.86 @ ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [Uu: sum_su737395349um_b_c] :
% 3.17/1.86 ? [X2: a] :
% 3.17/1.86 ( ( Uu
% 3.17/1.86 = ( sum_In2139678582um_b_c @ X2 ) )
% 3.17/1.86 & ( member_a @ X2 @ ( static_SIGT_a_c @ Theta ) ) ) ) )
% 3.17/1.86 => ( ( denota2042094639_a_b_c @ I3 @ Theta @ ( produc2010422875real_c @ Nu ) )
% 3.17/1.86 = ( denota2042094639_a_b_c @ J @ Theta @ ( produc2010422875real_c @ Nu2 ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_311_pred__subset__eq,axiom,
% 3.17/1.86 ! [R: set_a,S3: set_a] :
% 3.17/1.86 ( ( ord_less_eq_a_o
% 3.17/1.86 @ ^ [X2: a] : ( member_a @ X2 @ R )
% 3.17/1.86 @ ^ [X2: a] : ( member_a @ X2 @ S3 ) )
% 3.17/1.86 = ( ord_less_eq_set_a @ R @ S3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_312_sterm__continuous_H,axiom,
% 3.17/1.86 ! [I3: denota610675952t_unit,Theta: trm_sf_sz,S3: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( denota1579475975_sc_sz @ I3 )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta )
% 3.17/1.86 => ( topolo1348430467z_real @ S3 @ ( denota1179238309_sc_sz @ I3 @ Theta ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_313_agree__func__fvt,axiom,
% 3.17/1.86 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,F2: sf,Args: sz > trm_sf_sz,I: sz] :
% 3.17/1.86 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVT_sf_sz @ ( function_sf_sz @ F2 @ Args ) ) )
% 3.17/1.86 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVT_sf_sz @ ( Args @ I ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_314_subrelI,axiom,
% 3.17/1.86 ! [R2: set_Pr1169339874_sc_sz,S4: set_Pr1169339874_sc_sz] :
% 3.17/1.86 ( ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.17/1.86 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ R2 )
% 3.17/1.86 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ S4 ) )
% 3.17/1.86 => ( ord_le1230423618_sc_sz @ R2 @ S4 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_315_FVDiff__sub,axiom,
% 3.17/1.86 ! [F2: trm_a_c] : ( ord_le1772180283um_c_c @ ( static_FVT_a_c @ F2 ) @ ( static_FVDiff_a_c @ F2 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_316_pred__equals__eq2,axiom,
% 3.17/1.86 ! [R: set_Pr1169339874_sc_sz,S3: set_Pr1169339874_sc_sz] :
% 3.17/1.86 ( ( ( ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ R ) )
% 3.17/1.86 = ( ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ S3 ) ) )
% 3.17/1.86 = ( R = S3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_317_pred__subset__eq2,axiom,
% 3.17/1.86 ! [R: set_Pr1169339874_sc_sz,S3: set_Pr1169339874_sc_sz] :
% 3.17/1.86 ( ( ord_le108471557c_sz_o
% 3.17/1.86 @ ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ R )
% 3.17/1.86 @ ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ S3 ) )
% 3.17/1.86 = ( ord_le1230423618_sc_sz @ R @ S3 ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_318_sterm__continuous,axiom,
% 3.17/1.86 ! [I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 3.17/1.86 ( ( denota1579475975_sc_sz @ I3 )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta )
% 3.17/1.86 => ( topolo1348430467z_real @ top_to1873962757eal_sz @ ( denota1179238309_sc_sz @ I3 @ Theta ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_319_continuous__on__cases__le,axiom,
% 3.17/1.86 ! [S4: set_Fi291318197eal_sz,H: finite824932053eal_sz > real,A2: real,F2: finite824932053eal_sz > bounde472938360z_real,G2: finite824932053eal_sz > bounde472938360z_real] :
% 3.17/1.86 ( ( topolo885751137z_real
% 3.17/1.86 @ ( collec1002602816eal_sz
% 3.17/1.86 @ ^ [T: finite824932053eal_sz] :
% 3.17/1.86 ( ( member1693951742eal_sz @ T @ S4 )
% 3.17/1.86 & ( ord_less_eq_real @ ( H @ T ) @ A2 ) ) )
% 3.17/1.86 @ F2 )
% 3.17/1.86 => ( ( topolo885751137z_real
% 3.17/1.86 @ ( collec1002602816eal_sz
% 3.17/1.86 @ ^ [T: finite824932053eal_sz] :
% 3.17/1.86 ( ( member1693951742eal_sz @ T @ S4 )
% 3.17/1.86 & ( ord_less_eq_real @ A2 @ ( H @ T ) ) ) )
% 3.17/1.86 @ G2 )
% 3.17/1.86 => ( ( topolo1348430467z_real @ S4 @ H )
% 3.17/1.86 => ( ! [T4: finite824932053eal_sz] :
% 3.17/1.86 ( ( member1693951742eal_sz @ T4 @ S4 )
% 3.17/1.86 => ( ( ( H @ T4 )
% 3.17/1.86 = A2 )
% 3.17/1.86 => ( ( F2 @ T4 )
% 3.17/1.86 = ( G2 @ T4 ) ) ) )
% 3.17/1.86 => ( topolo885751137z_real @ S4
% 3.17/1.86 @ ^ [T: finite824932053eal_sz] : ( if_Bou1785791806z_real @ ( ord_less_eq_real @ ( H @ T ) @ A2 ) @ ( F2 @ T ) @ ( G2 @ T ) ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_320_UNIV__I,axiom,
% 3.17/1.86 ! [X: a] : ( member_a @ X @ top_top_set_a ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_321_UNIV__I,axiom,
% 3.17/1.86 ! [X: finite824932053eal_sz] : ( member1693951742eal_sz @ X @ top_to1873962757eal_sz ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_322_top_Oextremum__uniqueI,axiom,
% 3.17/1.86 ! [A2: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A2 )
% 3.17/1.86 => ( A2 = top_to1873962757eal_sz ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_323_top_Oextremum__unique,axiom,
% 3.17/1.86 ! [A2: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A2 )
% 3.17/1.86 = ( A2 = top_to1873962757eal_sz ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_324_top__greatest,axiom,
% 3.17/1.86 ! [A2: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A2 @ top_to1873962757eal_sz ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_325_subset__UNIV,axiom,
% 3.17/1.86 ! [A: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A @ top_to1873962757eal_sz ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_326_ids_Oseq__sem_Ocases,axiom,
% 3.17/1.86 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,X: produc1821101996_sc_sz] :
% 3.17/1.86 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.17/1.86 => ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 3.17/1.86 ( X
% 3.17/1.86 != ( produc789536734_sc_sz @ I2 @ S ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_327_UNIV__def,axiom,
% 3.17/1.86 ( top_to524132421um_b_c
% 3.17/1.86 = ( collec2086029184um_b_c
% 3.17/1.86 @ ^ [X2: sum_su737395349um_b_c] : $true ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_328_UNIV__def,axiom,
% 3.17/1.86 ( top_to1873962757eal_sz
% 3.17/1.86 = ( collec1002602816eal_sz
% 3.17/1.86 @ ^ [X2: finite824932053eal_sz] : $true ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_329_UNIV__witness,axiom,
% 3.17/1.86 ? [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_330_UNIV__witness,axiom,
% 3.17/1.86 ? [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ top_to1873962757eal_sz ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_331_UNIV__eq__I,axiom,
% 3.17/1.86 ! [A: set_a] :
% 3.17/1.86 ( ! [X3: a] : ( member_a @ X3 @ A )
% 3.17/1.86 => ( top_top_set_a = A ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_332_UNIV__eq__I,axiom,
% 3.17/1.86 ! [A: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ! [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ A )
% 3.17/1.86 => ( top_to1873962757eal_sz = A ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_333_top__prod__def,axiom,
% 3.17/1.86 ( top_to1787697847eal_sz
% 3.17/1.86 = ( produc1235791063eal_sz @ top_to1873962757eal_sz @ top_to1873962757eal_sz ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_334_ids_OP__def,axiom,
% 3.17/1.86 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P2: sc] :
% 3.17/1.86 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.17/1.86 => ( ( p_sc_sf_sz @ P2 )
% 3.17/1.86 = ( predic913887884_sf_sz @ P2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_335_frechet__continuous,axiom,
% 3.17/1.86 ! [I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 3.17/1.86 ( ( denota1579475975_sc_sz @ I3 )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta )
% 3.17/1.86 => ( topolo885751137z_real @ top_to1873962757eal_sz @ ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_336_top__empty__eq2,axiom,
% 3.17/1.86 ( top_to1399053141c_sz_o
% 3.17/1.86 = ( ^ [X2: denota610675952t_unit,Y2: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X2 @ Y2 ) @ top_to1499569298_sc_sz ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_337_top__set__def,axiom,
% 3.17/1.86 ( top_to524132421um_b_c
% 3.17/1.86 = ( collec2086029184um_b_c @ top_to1201357528_b_c_o ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_338_top__set__def,axiom,
% 3.17/1.86 ( top_to1873962757eal_sz
% 3.17/1.86 = ( collec1002602816eal_sz @ top_to646513176l_sz_o ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_339_Vagree__univ,axiom,
% 3.17/1.86 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 3.17/1.86 ( ( denota1997846518gree_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc394644079real_c @ C2 @ D ) @ top_to1660572043um_c_c )
% 3.17/1.86 => ( ( A2 = C2 )
% 3.17/1.86 & ( B2 = D ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_340_agree__UNIV__eq,axiom,
% 3.17/1.86 ! [Nu: produc190496183real_c,Omega: produc190496183real_c] :
% 3.17/1.86 ( ( denota1997846518gree_c @ Nu @ Omega @ top_to1660572043um_c_c )
% 3.17/1.86 => ( Nu = Omega ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_341_ids_Ofrechet__continuous,axiom,
% 3.17/1.86 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 3.17/1.86 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.17/1.86 => ( ( denota1579475975_sc_sz @ I3 )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta )
% 3.17/1.86 => ( topolo885751137z_real @ top_to1873962757eal_sz @ ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_342_frechet__blin,axiom,
% 3.17/1.86 ! [I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 3.17/1.86 ( ( denota1579475975_sc_sz @ I3 )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta )
% 3.17/1.86 => ( ( ^ [V2: finite824932053eal_sz] : ( bounde397081123z_real @ ( denota1979904720_sc_sz @ I3 @ Theta @ V2 ) ) )
% 3.17/1.86 = ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_343_continuous__on__const,axiom,
% 3.17/1.86 ! [S4: set_Fi291318197eal_sz,C2: bounde472938360z_real] :
% 3.17/1.86 ( topolo885751137z_real @ S4
% 3.17/1.86 @ ^ [X2: finite824932053eal_sz] : C2 ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_344_continuous__on__subset,axiom,
% 3.17/1.86 ! [S4: set_Fi291318197eal_sz,F2: finite824932053eal_sz > bounde472938360z_real,T3: set_Fi291318197eal_sz] :
% 3.17/1.86 ( ( topolo885751137z_real @ S4 @ F2 )
% 3.17/1.86 => ( ( ord_le41263445eal_sz @ T3 @ S4 )
% 3.17/1.86 => ( topolo885751137z_real @ T3 @ F2 ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_345_continuous__on__Pair,axiom,
% 3.17/1.86 ! [S4: set_Fi291318197eal_sz,F2: finite824932053eal_sz > bounde472938360z_real,G2: finite824932053eal_sz > bounde472938360z_real] :
% 3.17/1.86 ( ( topolo885751137z_real @ S4 @ F2 )
% 3.17/1.86 => ( ( topolo885751137z_real @ S4 @ G2 )
% 3.17/1.86 => ( topolo1027477648z_real @ S4
% 3.17/1.86 @ ^ [X2: finite824932053eal_sz] : ( produc784663575z_real @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_346_ids_Ofrechet__blin,axiom,
% 3.17/1.86 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,I3: denota610675952t_unit,Theta: trm_sf_sz] :
% 3.17/1.86 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.17/1.86 => ( ( denota1579475975_sc_sz @ I3 )
% 3.17/1.86 => ( ( dfree_sf_sz @ Theta )
% 3.17/1.86 => ( ( ^ [V2: finite824932053eal_sz] : ( bounde397081123z_real @ ( denota1979904720_sc_sz @ I3 @ Theta @ V2 ) ) )
% 3.17/1.86 = ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I3 ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_347_blin__frechet_Oabs__eq,axiom,
% 3.17/1.86 ! [Xb: denota610675952t_unit,Xa: trm_sf_sz,X: finite824932053eal_sz] :
% 3.17/1.86 ( ( bNF_eq1660582207t_unit @ denota1579475975_sc_sz @ Xb @ Xb )
% 3.17/1.86 => ( ( bNF_eq_onp_trm_sf_sz @ dfree_sf_sz @ Xa @ Xa )
% 3.17/1.86 => ( ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ Xb ) @ ( freche1046279700_sf_sz @ Xa ) @ X )
% 3.17/1.86 = ( bounde397081123z_real @ ( denota1979904720_sc_sz @ Xb @ Xa @ X ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_348_ids_Oblin__frechet_Oabs__eq,axiom,
% 3.17/1.86 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,Xb: denota610675952t_unit,Xa: trm_sf_sz,X: finite824932053eal_sz] :
% 3.17/1.86 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.17/1.86 => ( ( bNF_eq1660582207t_unit @ denota1579475975_sc_sz @ Xb @ Xb )
% 3.17/1.86 => ( ( bNF_eq_onp_trm_sf_sz @ dfree_sf_sz @ Xa @ Xa )
% 3.17/1.86 => ( ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ Xb ) @ ( freche1046279700_sf_sz @ Xa ) @ X )
% 3.17/1.86 = ( bounde397081123z_real @ ( denota1979904720_sc_sz @ Xb @ Xa @ X ) ) ) ) ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_349_Quotient__good__interp,axiom,
% 3.17/1.86 quotie842200089_sc_sz @ ( bNF_eq1660582207t_unit @ denota1579475975_sc_sz ) @ freche1784963216_sc_sz @ freche1421597129_sc_sz @ freche58918398_sc_sz ).
% 3.17/1.86
% 3.17/1.86 thf(fact_350_Quotient__strm,axiom,
% 3.17/1.86 quotie1467858509rm_a_c @ ( bNF_eq_onp_trm_a_c @ dfree_a_c ) @ freche665377492rm_a_c @ frechet_raw_term_a_c @ frechet_cr_strm_a_c ).
% 3.17/1.86
% 3.17/1.86 thf(fact_351_Quotient__strm,axiom,
% 3.17/1.86 quotie1549861309_sf_sz @ ( bNF_eq_onp_trm_sf_sz @ dfree_sf_sz ) @ freche1046279700_sf_sz @ freche782854530_sf_sz @ freche1244000341_sf_sz ).
% 3.17/1.86
% 3.17/1.86 thf(fact_352_eq__onp__le__eq,axiom,
% 3.17/1.86 ! [P: denota610675952t_unit > $o] :
% 3.17/1.86 ( ord_le2003534918unit_o @ ( bNF_eq1660582207t_unit @ P )
% 3.17/1.86 @ ^ [Y4: denota610675952t_unit,Z: denota610675952t_unit] : ( Y4 = Z ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(fact_353_eq__onp__le__eq,axiom,
% 3.17/1.86 ! [P: trm_sf_sz > $o] :
% 3.17/1.86 ( ord_le8515534f_sz_o @ ( bNF_eq_onp_trm_sf_sz @ P )
% 3.17/1.86 @ ^ [Y4: trm_sf_sz,Z: trm_sf_sz] : ( Y4 = Z ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(help_If_3_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 3.17/1.86 ! [P: $o] :
% 3.17/1.86 ( ( P = $true )
% 3.17/1.86 | ( P = $false ) ) ).
% 3.17/1.86
% 3.17/1.86 thf(help_If_2_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 3.17/1.86 ! [X: bounde472938360z_real,Y: bounde472938360z_real] :
% 3.17/1.86 ( ( if_Bou1785791806z_real @ $false @ X @ Y )
% 3.17/1.86 = Y ) ).
% 3.17/1.86
% 3.17/1.86 thf(help_If_1_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 3.17/1.86 ! [X: bounde472938360z_real,Y: bounde472938360z_real] :
% 3.17/1.86 ( ( if_Bou1785791806z_real @ $true @ X @ Y )
% 3.17/1.86 = X ) ).
% 3.17/1.86
% 3.17/1.86 thf(conj_0,conjecture,
% 3.17/1.86 denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ t2 ) ).
% 3.17/1.86 ------------------------
% 3.17/1.89 % (30406)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/183Mi)
% 3.17/1.89 % (30408)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_30300 for (2999ds/27Mi)
% 3.17/1.90 % (30410)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_30300 for (2999ds/2Mi)
% 3.17/1.90 % (30412)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/18Mi)
% 3.17/1.90 % (30409)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/2Mi)
% 3.17/1.90 % (30411)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_30300 for (2999ds/275Mi)
% 3.25/1.90 % (30410)Instruction limit reached!
% 3.25/1.90 % (30410)------------------------------
% 3.25/1.90 % (30410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.90 % (30410)Termination reason: Unknown
% 3.25/1.90 % (30410)Termination phase: shuffling
% 3.25/1.90
% 3.25/1.90 % (30410)Memory used [KB]: 1535
% 3.25/1.90 % (30410)Time elapsed: 0.003 s
% 3.25/1.90 % (30410)Instructions burned: 2 (million)
% 3.25/1.90 % (30410)------------------------------
% 3.25/1.90 % (30410)------------------------------
% 3.25/1.90 % (30409)Instruction limit reached!
% 3.25/1.90 % (30409)------------------------------
% 3.25/1.90 % (30409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.90 % (30409)Termination reason: Unknown
% 3.25/1.90 % (30409)Termination phase: shuffling
% 3.25/1.90
% 3.25/1.90 % (30409)Memory used [KB]: 1535
% 3.25/1.90 % (30409)Time elapsed: 0.003 s
% 3.25/1.90 % (30409)Instructions burned: 3 (million)
% 3.25/1.90 % (30409)------------------------------
% 3.25/1.90 % (30409)------------------------------
% 3.25/1.90 % (30407)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_30300 for (2999ds/4Mi)
% 3.25/1.90 % (30407)Instruction limit reached!
% 3.25/1.90 % (30407)------------------------------
% 3.25/1.90 % (30407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.90 % (30407)Termination reason: Unknown
% 3.25/1.90 % (30407)Termination phase: shuffling
% 3.25/1.90
% 3.25/1.90 % (30407)Memory used [KB]: 1663
% 3.25/1.90 % (30407)Time elapsed: 0.003 s
% 3.25/1.90 % (30407)Instructions burned: 6 (million)
% 3.25/1.90 % (30407)------------------------------
% 3.25/1.90 % (30407)------------------------------
% 3.25/1.91 % (30412)Instruction limit reached!
% 3.25/1.91 % (30412)------------------------------
% 3.25/1.91 % (30412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.91 % (30412)Termination reason: Unknown
% 3.25/1.91 % (30412)Termination phase: shuffling
% 3.25/1.91
% 3.25/1.91 % (30412)Memory used [KB]: 1918
% 3.25/1.91 % (30412)Time elapsed: 0.013 s
% 3.25/1.91 % (30412)Instructions burned: 19 (million)
% 3.25/1.91 % (30412)------------------------------
% 3.25/1.91 % (30412)------------------------------
% 3.25/1.91 % (30408)Instruction limit reached!
% 3.25/1.91 % (30408)------------------------------
% 3.25/1.91 % (30408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.91 % (30408)Termination reason: Unknown
% 3.25/1.91 % (30408)Termination phase: Property scanning
% 3.25/1.91
% 3.25/1.91 % (30408)Memory used [KB]: 2174
% 3.25/1.91 % (30408)Time elapsed: 0.015 s
% 3.25/1.91 % (30408)Instructions burned: 30 (million)
% 3.25/1.91 % (30408)------------------------------
% 3.25/1.91 % (30408)------------------------------
% 3.25/1.92 % (30413)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/3Mi)
% 3.25/1.92 % (30414)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_30300 for (2999ds/37Mi)
% 3.25/1.92 % (30413)Instruction limit reached!
% 3.25/1.92 % (30413)------------------------------
% 3.25/1.92 % (30413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.92 % (30413)Termination reason: Unknown
% 3.25/1.92 % (30413)Termination phase: shuffling
% 3.25/1.92
% 3.25/1.92 % (30413)Memory used [KB]: 1535
% 3.25/1.92 % (30413)Time elapsed: 0.004 s
% 3.25/1.92 % (30413)Instructions burned: 3 (million)
% 3.25/1.92 % (30413)------------------------------
% 3.25/1.92 % (30413)------------------------------
% 3.25/1.93 % (30416)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_30300 for (2999ds/3Mi)
% 3.25/1.93 % (30415)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_30300 for (2999ds/15Mi)
% 3.25/1.93 % (30417)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_30300 for (2999ds/1041Mi)
% 3.25/1.93 % (30418)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/7Mi)
% 3.25/1.93 % (30416)Instruction limit reached!
% 3.25/1.93 % (30416)------------------------------
% 3.25/1.93 % (30416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.93 % (30416)Termination reason: Unknown
% 3.25/1.93 % (30416)Termination phase: shuffling
% 3.25/1.93
% 3.25/1.93 % (30416)Memory used [KB]: 1535
% 3.25/1.93 % (30416)Time elapsed: 0.003 s
% 3.25/1.93 % (30416)Instructions burned: 3 (million)
% 3.25/1.93 % (30416)------------------------------
% 3.25/1.93 % (30416)------------------------------
% 3.25/1.93 % (30418)Instruction limit reached!
% 3.25/1.93 % (30418)------------------------------
% 3.25/1.93 % (30418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.93 % (30418)Termination reason: Unknown
% 3.25/1.93 % (30418)Termination phase: shuffling
% 3.25/1.93
% 3.25/1.93 % (30418)Memory used [KB]: 1791
% 3.25/1.93 % (30418)Time elapsed: 0.004 s
% 3.25/1.93 % (30418)Instructions burned: 9 (million)
% 3.25/1.93 % (30418)------------------------------
% 3.25/1.93 % (30418)------------------------------
% 3.25/1.93 % (30411)Refutation not found, incomplete strategy
% 3.25/1.93 % (30411)------------------------------
% 3.25/1.93 % (30411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.93 % (30411)Termination reason: Refutation not found, incomplete strategy
% 3.25/1.93
% 3.25/1.93
% 3.25/1.93 % (30411)Memory used [KB]: 6652
% 3.25/1.93 % (30411)Time elapsed: 0.035 s
% 3.25/1.93 % (30411)Instructions burned: 59 (million)
% 3.25/1.93 % (30411)------------------------------
% 3.25/1.93 % (30411)------------------------------
% 3.25/1.93 % (30415)Instruction limit reached!
% 3.25/1.93 % (30415)------------------------------
% 3.25/1.93 % (30415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.93 % (30415)Termination reason: Unknown
% 3.25/1.93 % (30415)Termination phase: shuffling
% 3.25/1.93
% 3.25/1.93 % (30415)Memory used [KB]: 1918
% 3.25/1.93 % (30415)Time elapsed: 0.011 s
% 3.25/1.93 % (30415)Instructions burned: 16 (million)
% 3.25/1.93 % (30415)------------------------------
% 3.25/1.93 % (30415)------------------------------
% 3.25/1.93 % (30414)Instruction limit reached!
% 3.25/1.93 % (30414)------------------------------
% 3.25/1.93 % (30414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.93 % (30414)Termination reason: Unknown
% 3.25/1.93 % (30414)Termination phase: shuffling
% 3.25/1.93
% 3.25/1.93 % (30414)Memory used [KB]: 2302
% 3.25/1.93 % (30414)Time elapsed: 0.021 s
% 3.25/1.93 % (30414)Instructions burned: 37 (million)
% 3.25/1.93 % (30414)------------------------------
% 3.25/1.93 % (30414)------------------------------
% 3.25/1.94 % (30420)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_30300 for (2999ds/3Mi)
% 3.25/1.94 % (30420)Instruction limit reached!
% 3.25/1.94 % (30420)------------------------------
% 3.25/1.94 % (30420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.94 % (30420)Termination reason: Unknown
% 3.25/1.94 % (30420)Termination phase: shuffling
% 3.25/1.94
% 3.25/1.94 % (30420)Memory used [KB]: 1535
% 3.25/1.94 % (30420)Time elapsed: 0.002 s
% 3.25/1.94 % (30420)Instructions burned: 3 (million)
% 3.25/1.94 % (30420)------------------------------
% 3.25/1.94 % (30420)------------------------------
% 3.25/1.94 % (30406)Instruction limit reached!
% 3.25/1.94 % (30406)------------------------------
% 3.25/1.94 % (30406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.94 % (30406)Termination reason: Unknown
% 3.25/1.94 % (30406)Termination phase: Saturation
% 3.25/1.94
% 3.25/1.94 % (30406)Memory used [KB]: 7547
% 3.25/1.94 % (30406)Time elapsed: 0.055 s
% 3.25/1.94 % (30406)Instructions burned: 183 (million)
% 3.25/1.94 % (30406)------------------------------
% 3.25/1.94 % (30406)------------------------------
% 3.25/1.95 % (30419)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/16Mi)
% 3.25/1.95 % (30424)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/4Mi)
% 3.25/1.95 % (30425)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/18Mi)
% 3.25/1.95 % (30421)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_30300 for (2999ds/3Mi)
% 3.25/1.95 % (30424)Instruction limit reached!
% 3.25/1.95 % (30424)------------------------------
% 3.25/1.95 % (30424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.95 % (30424)Termination reason: Unknown
% 3.25/1.95 % (30424)Termination phase: shuffling
% 3.25/1.95
% 3.25/1.95 % (30424)Memory used [KB]: 1663
% 3.25/1.95 % (30424)Time elapsed: 0.003 s
% 3.25/1.95 % (30424)Instructions burned: 6 (million)
% 3.25/1.95 % (30424)------------------------------
% 3.25/1.95 % (30424)------------------------------
% 3.25/1.95 % (30421)Instruction limit reached!
% 3.25/1.95 % (30421)------------------------------
% 3.25/1.95 % (30421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.95 % (30421)Termination reason: Unknown
% 3.25/1.95 % (30421)Termination phase: shuffling
% 3.25/1.95
% 3.25/1.95 % (30421)Memory used [KB]: 1535
% 3.25/1.95 % (30421)Time elapsed: 0.004 s
% 3.25/1.95 % (30421)Instructions burned: 3 (million)
% 3.25/1.95 % (30421)------------------------------
% 3.25/1.95 % (30421)------------------------------
% 3.25/1.95 % (30423)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/3Mi)
% 3.25/1.95 % (30422)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/7Mi)
% 3.25/1.95 % (30423)Instruction limit reached!
% 3.25/1.95 % (30423)------------------------------
% 3.25/1.95 % (30423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.95 % (30423)Termination reason: Unknown
% 3.25/1.95 % (30423)Termination phase: shuffling
% 3.25/1.95
% 3.25/1.95 % (30423)Memory used [KB]: 1535
% 3.25/1.95 % (30423)Time elapsed: 0.003 s
% 3.25/1.95 % (30423)Instructions burned: 3 (million)
% 3.25/1.95 % (30423)------------------------------
% 3.25/1.95 % (30423)------------------------------
% 3.25/1.95 % (30419)Instruction limit reached!
% 3.25/1.95 % (30419)------------------------------
% 3.25/1.95 % (30419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.95 % (30419)Termination reason: Unknown
% 3.25/1.95 % (30419)Termination phase: shuffling
% 3.25/1.95
% 3.25/1.95 % (30419)Memory used [KB]: 1918
% 3.25/1.95 % (30419)Time elapsed: 0.011 s
% 3.25/1.95 % (30419)Instructions burned: 17 (million)
% 3.25/1.95 % (30419)------------------------------
% 3.25/1.95 % (30419)------------------------------
% 3.25/1.96 % (30425)Instruction limit reached!
% 3.25/1.96 % (30425)------------------------------
% 3.25/1.96 % (30425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.96 % (30425)Termination reason: Unknown
% 3.25/1.96 % (30425)Termination phase: shuffling
% 3.25/1.96
% 3.25/1.96 % (30425)Memory used [KB]: 1918
% 3.25/1.96 % (30425)Time elapsed: 0.007 s
% 3.25/1.96 % (30425)Instructions burned: 19 (million)
% 3.25/1.96 % (30425)------------------------------
% 3.25/1.96 % (30425)------------------------------
% 3.25/1.96 % (30422)Instruction limit reached!
% 3.25/1.96 % (30422)------------------------------
% 3.25/1.96 % (30422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.96 % (30422)Termination reason: Unknown
% 3.25/1.96 % (30422)Termination phase: shuffling
% 3.25/1.96
% 3.25/1.96 % (30422)Memory used [KB]: 1791
% 3.25/1.96 % (30422)Time elapsed: 0.006 s
% 3.25/1.96 % (30422)Instructions burned: 8 (million)
% 3.25/1.96 % (30422)------------------------------
% 3.25/1.96 % (30422)------------------------------
% 3.25/1.96 % (30426)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/710Mi)
% 3.25/1.97 % (30428)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/902Mi)
% 3.25/1.97 % (30427)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/6Mi)
% 3.25/1.97 % (30429)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/21Mi)
% 3.25/1.97 % (30427)Instruction limit reached!
% 3.25/1.97 % (30427)------------------------------
% 3.25/1.97 % (30427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.97 % (30427)Termination reason: Unknown
% 3.25/1.97 % (30427)Termination phase: shuffling
% 3.25/1.97
% 3.25/1.97 % (30427)Memory used [KB]: 1663
% 3.25/1.97 % (30427)Time elapsed: 0.006 s
% 3.25/1.97 % (30427)Instructions burned: 7 (million)
% 3.25/1.97 % (30427)------------------------------
% 3.25/1.97 % (30427)------------------------------
% 3.25/1.98 % (30430)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/5Mi)
% 3.25/1.98 % (30430)Instruction limit reached!
% 3.25/1.98 % (30430)------------------------------
% 3.25/1.98 % (30430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.98 % (30430)Termination reason: Unknown
% 3.25/1.98 % (30430)Termination phase: shuffling
% 3.25/1.98
% 3.25/1.98 % (30430)Memory used [KB]: 1663
% 3.25/1.98 % (30430)Time elapsed: 0.004 s
% 3.25/1.98 % (30430)Instructions burned: 5 (million)
% 3.25/1.98 % (30430)------------------------------
% 3.25/1.98 % (30430)------------------------------
% 3.25/1.98 % (30431)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/6Mi)
% 3.25/1.98 % (30426)Refutation not found, incomplete strategy
% 3.25/1.98 % (30426)------------------------------
% 3.25/1.98 % (30426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.98 % (30426)Termination reason: Refutation not found, incomplete strategy
% 3.25/1.98
% 3.25/1.98
% 3.25/1.98 % (30426)Memory used [KB]: 6780
% 3.25/1.98 % (30426)Time elapsed: 0.020 s
% 3.25/1.98 % (30426)Instructions burned: 61 (million)
% 3.25/1.98 % (30426)------------------------------
% 3.25/1.98 % (30426)------------------------------
% 3.25/1.98 % (30431)Instruction limit reached!
% 3.25/1.98 % (30431)------------------------------
% 3.25/1.98 % (30431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.98 % (30431)Termination reason: Unknown
% 3.25/1.98 % (30431)Termination phase: shuffling
% 3.25/1.98
% 3.25/1.98 % (30431)Memory used [KB]: 1663
% 3.25/1.98 % (30431)Time elapsed: 0.005 s
% 3.25/1.98 % (30431)Instructions burned: 6 (million)
% 3.25/1.98 % (30431)------------------------------
% 3.25/1.98 % (30431)------------------------------
% 3.25/1.98 % (30429)Instruction limit reached!
% 3.25/1.98 % (30429)------------------------------
% 3.25/1.98 % (30429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.98 % (30429)Termination reason: Unknown
% 3.25/1.98 % (30429)Termination phase: shuffling
% 3.25/1.98
% 3.25/1.98 % (30429)Memory used [KB]: 2046
% 3.25/1.98 % (30429)Time elapsed: 0.013 s
% 3.25/1.98 % (30429)Instructions burned: 22 (million)
% 3.25/1.98 % (30429)------------------------------
% 3.25/1.98 % (30429)------------------------------
% 3.25/1.99 % (30435)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30300 for (2998ds/879Mi)
% 3.25/2.00 % (30432)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30300 for (2999ds/377Mi)
% 3.25/2.00 % (30433)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_30300 for (2998ds/779Mi)
% 3.25/2.00 % (30434)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_30300 for (2998ds/19Mi)
% 3.25/2.00 % (30436)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30300 for (2998ds/17Mi)
% 3.25/2.01 % (30434)Instruction limit reached!
% 3.25/2.01 % (30434)------------------------------
% 3.25/2.01 % (30434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/2.01 % (30434)Termination reason: Unknown
% 3.25/2.01 % (30434)Termination phase: shuffling
% 3.25/2.01
% 3.25/2.01 % (30434)Memory used [KB]: 2046
% 3.25/2.01 % (30434)Time elapsed: 0.012 s
% 3.25/2.01 % (30434)Instructions burned: 20 (million)
% 3.25/2.01 % (30434)------------------------------
% 3.25/2.01 % (30434)------------------------------
% 3.25/2.01 % (30436)Instruction limit reached!
% 3.25/2.01 % (30436)------------------------------
% 3.25/2.01 % (30436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/2.01 % (30436)Termination reason: Unknown
% 3.25/2.01 % (30436)Termination phase: shuffling
% 3.25/2.01
% 3.25/2.01 % (30436)Memory used [KB]: 1918
% 3.25/2.01 % (30436)Time elapsed: 0.011 s
% 3.25/2.01 % (30436)Instructions burned: 17 (million)
% 3.25/2.01 % (30436)------------------------------
% 3.25/2.01 % (30436)------------------------------
% 3.25/2.02 % (30435)First to succeed.
% 4.15/2.03 % (30437)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30300 for (2998ds/3Mi)
% 4.15/2.03 % (30435)Refutation found. Thanks to Tanya!
% 4.15/2.03 % SZS status Theorem for DTF2THF_30300
% 4.15/2.03 % SZS output start Proof for DTF2THF_30300
% 4.15/2.03 thf(type_def_5, type, denota610675952t_unit: $tType).
% 4.15/2.03 thf(type_def_7, type, trm_a_c: $tType).
% 4.15/2.03 thf(type_def_8, type, trm_sf_sz: $tType).
% 4.15/2.03 thf(type_def_9, type, set_a: $tType).
% 4.15/2.03 thf(type_def_10, type, a: $tType).
% 4.15/2.03 thf(type_def_11, type, produc866628903_sc_sz: $tType).
% 4.15/2.03 thf(type_def_12, type, set_Pr1169339874_sc_sz: $tType).
% 4.15/2.03 thf(type_def_13, type, finite824932053eal_sz: $tType).
% 4.15/2.03 thf(type_def_14, type, real: $tType).
% 4.15/2.03 thf(type_def_15, type, bounde472938360z_real: $tType).
% 4.15/2.03 thf(type_def_16, type, denota231621370t_unit: $tType).
% 4.15/2.03 thf(type_def_17, type, set_Su1783761653um_b_c: $tType).
% 4.15/2.03 thf(type_def_18, type, produc190496183real_c: $tType).
% 4.15/2.03 thf(type_def_19, type, set_Sum_sum_c_c: $tType).
% 4.15/2.03 thf(type_def_20, type, produc1149990247eal_sz: $tType).
% 4.15/2.03 thf(type_def_21, type, set_Sum_sum_sz_sz: $tType).
% 4.15/2.03 thf(type_def_22, type, finite1398487019real_c: $tType).
% 4.15/2.03 thf(type_def_23, type, freche2095075217_sc_sz: $tType).
% 4.15/2.03 thf(type_def_24, type, frechet_strm_sf_sz: $tType).
% 4.15/2.03 thf(type_def_25, type, frechet_strm_a_c: $tType).
% 4.15/2.03 thf(type_def_26, type, freche914690577_a_b_c: $tType).
% 4.15/2.03 thf(type_def_27, type, sz: $tType).
% 4.15/2.03 thf(type_def_28, type, sf: $tType).
% 4.15/2.03 thf(type_def_29, type, sc: $tType).
% 4.15/2.03 thf(type_def_30, type, produc1065634396_o_a_o: $tType).
% 4.15/2.03 thf(type_def_31, type, produc903182423_set_a: $tType).
% 4.15/2.03 thf(type_def_32, type, produc1553439972f_sz_o: $tType).
% 4.15/2.03 thf(type_def_33, type, product_prod_a_o_a_o: $tType).
% 4.15/2.03 thf(type_def_34, type, produc1561113620_set_a: $tType).
% 4.15/2.03 thf(type_def_35, type, produc1241881959eal_sz: $tType).
% 4.15/2.03 thf(type_def_36, type, produc1144880887f_sz_o: $tType).
% 4.15/2.03 thf(type_def_37, type, produc1989635468_a_a_o: $tType).
% 4.15/2.03 thf(type_def_38, type, produc1691597095_set_a: $tType).
% 4.15/2.03 thf(type_def_39, type, set_Fi291318197eal_sz: $tType).
% 4.15/2.03 thf(type_def_40, type, set_trm_a_c: $tType).
% 4.15/2.03 thf(type_def_41, type, set_trm_sf_sz: $tType).
% 4.15/2.03 thf(type_def_42, type, sum_su737395349um_b_c: $tType).
% 4.15/2.03 thf(type_def_43, type, produc1892666919z_real: $tType).
% 4.15/2.03 thf(type_def_44, type, produc1821101996_sc_sz: $tType).
% 4.15/2.03 thf(type_def_45, type, list_f1238882004_sc_sz: $tType).
% 4.15/2.03 thf(type_def_46, type, set_De455519194t_unit: $tType).
% 4.15/2.03 thf(type_def_47, type, set_De208295462t_unit: $tType).
% 4.15/2.03 thf(type_def_48, type, formula_sf_sc_sz: $tType).
% 4.15/2.03 thf(type_def_49, type, c: $tType).
% 4.15/2.03 thf(func_def_0, type, set_Pr1169339874_sc_sz: $tType).
% 4.15/2.03 thf(func_def_1, type, produc1821101996_sc_sz: $tType).
% 4.15/2.03 thf(func_def_2, type, produc1892666919z_real: $tType).
% 4.15/2.03 thf(func_def_3, type, produc1241881959eal_sz: $tType).
% 4.15/2.03 thf(func_def_4, type, produc1149990247eal_sz: $tType).
% 4.15/2.03 thf(func_def_5, type, produc190496183real_c: $tType).
% 4.15/2.03 thf(func_def_6, type, produc866628903_sc_sz: $tType).
% 4.15/2.03 thf(func_def_7, type, produc1144880887f_sz_o: $tType).
% 4.15/2.03 thf(func_def_8, type, produc903182423_set_a: $tType).
% 4.15/2.03 thf(func_def_9, type, produc1553439972f_sz_o: $tType).
% 4.15/2.03 thf(func_def_10, type, produc1065634396_o_a_o: $tType).
% 4.15/2.03 thf(func_def_11, type, bounde472938360z_real: $tType).
% 4.15/2.03 thf(func_def_12, type, set_De208295462t_unit: $tType).
% 4.15/2.03 thf(func_def_13, type, set_De455519194t_unit: $tType).
% 4.15/2.03 thf(func_def_14, type, denota610675952t_unit: $tType).
% 4.15/2.03 thf(func_def_15, type, denota231621370t_unit: $tType).
% 4.15/2.03 thf(func_def_16, type, set_Su1783761653um_b_c: $tType).
% 4.15/2.03 thf(func_def_17, type, set_Fi291318197eal_sz: $tType).
% 4.15/2.03 thf(func_def_18, type, freche2095075217_sc_sz: $tType).
% 4.15/2.03 thf(func_def_19, type, produc1691597095_set_a: $tType).
% 4.15/2.03 thf(func_def_20, type, freche914690577_a_b_c: $tType).
% 4.15/2.03 thf(func_def_21, type, produc1989635468_a_a_o: $tType).
% 4.15/2.03 thf(func_def_22, type, produc1561113620_set_a: $tType).
% 4.15/2.03 thf(func_def_23, type, sum_su737395349um_b_c: $tType).
% 4.15/2.03 thf(func_def_24, type, product_prod_a_o_a_o: $tType).
% 4.15/2.03 thf(func_def_25, type, finite824932053eal_sz: $tType).
% 4.15/2.03 thf(func_def_26, type, finite1398487019real_c: $tType).
% 4.15/2.03 thf(func_def_27, type, list_f1238882004_sc_sz: $tType).
% 4.15/2.03 thf(func_def_28, type, frechet_strm_sf_sz: $tType).
% 4.15/2.03 thf(func_def_29, type, set_Sum_sum_sz_sz: $tType).
% 4.15/2.03 thf(func_def_30, type, frechet_strm_a_c: $tType).
% 4.15/2.03 thf(func_def_31, type, set_Sum_sum_c_c: $tType).
% 4.15/2.03 thf(func_def_32, type, set_trm_sf_sz: $tType).
% 4.15/2.03 thf(func_def_33, type, set_trm_a_c: $tType).
% 4.15/2.03 thf(func_def_34, type, formula_sf_sc_sz: $tType).
% 4.15/2.03 thf(func_def_35, type, trm_sf_sz: $tType).
% 4.15/2.03 thf(func_def_36, type, trm_a_c: $tType).
% 4.15/2.03 thf(func_def_37, type, set_a: $tType).
% 4.15/2.03 thf(func_def_38, type, real: $tType).
% 4.15/2.03 thf(func_def_39, type, sz: $tType).
% 4.15/2.03 thf(func_def_40, type, sf: $tType).
% 4.15/2.03 thf(func_def_41, type, sc: $tType).
% 4.15/2.03 thf(func_def_42, type, c: $tType).
% 4.15/2.03 thf(func_def_43, type, a: $tType).
% 4.15/2.03 thf(func_def_44, type, bNF_eq1660582207t_unit: (denota610675952t_unit > $o) > denota610675952t_unit > denota610675952t_unit > $o).
% 4.15/2.03 thf(func_def_45, type, bNF_eq_onp_trm_a_c: (trm_a_c > $o) > trm_a_c > trm_a_c > $o).
% 4.15/2.03 thf(func_def_46, type, bNF_eq_onp_trm_sf_sz: (trm_sf_sz > $o) > trm_sf_sz > trm_sf_sz > $o).
% 4.15/2.03 thf(func_def_47, type, bNF_Gr1775200401_sc_sz: set_a > (a > denota610675952t_unit) > (a > produc866628903_sc_sz) > set_Pr1169339874_sc_sz).
% 4.15/2.03 thf(func_def_48, type, bounde397081123z_real: (finite824932053eal_sz > real) > bounde472938360z_real).
% 4.15/2.03 thf(func_def_49, type, denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o).
% 4.15/2.03 thf(func_def_50, type, denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o).
% 4.15/2.03 thf(func_def_51, type, denota102713844ree_sz: produc1149990247eal_sz > produc1149990247eal_sz > set_Sum_sum_sz_sz > $o).
% 4.15/2.03 thf(func_def_52, type, denota2112424896_a_b_c: denota231621370t_unit > trm_a_c > produc190496183real_c > real).
% 4.15/2.03 thf(func_def_53, type, denota453121236_sc_sz: denota610675952t_unit > trm_sf_sz > produc1149990247eal_sz > real).
% 4.15/2.03 thf(func_def_54, type, denota229585092_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > finite1398487019real_c > real).
% 4.15/2.03 thf(func_def_55, type, denota1979904720_sc_sz: denota610675952t_unit > trm_sf_sz > finite824932053eal_sz > finite824932053eal_sz > real).
% 4.15/2.03 thf(func_def_56, type, denota258389581_a_b_c: denota231621370t_unit > $o).
% 4.15/2.03 thf(func_def_57, type, denota1579475975_sc_sz: denota610675952t_unit > $o).
% 4.15/2.03 thf(func_def_58, type, denota2042094639_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > real).
% 4.15/2.03 thf(func_def_59, type, denota1179238309_sc_sz: denota610675952t_unit > trm_sf_sz > finite824932053eal_sz > real).
% 4.15/2.03 thf(func_def_60, type, freche585307148_sc_sz: freche2095075217_sc_sz > frechet_strm_sf_sz > finite824932053eal_sz > bounde472938360z_real).
% 4.15/2.03 thf(func_def_61, type, freche58918398_sc_sz: denota610675952t_unit > freche2095075217_sc_sz > $o).
% 4.15/2.03 thf(func_def_62, type, frechet_cr_strm_a_c: trm_a_c > frechet_strm_a_c > $o).
% 4.15/2.03 thf(func_def_63, type, freche1244000341_sf_sz: trm_sf_sz > frechet_strm_sf_sz > $o).
% 4.15/2.03 thf(func_def_64, type, freche1473475332_a_b_c: denota231621370t_unit > freche914690577_a_b_c).
% 4.15/2.03 thf(func_def_65, type, freche1784963216_sc_sz: denota610675952t_unit > freche2095075217_sc_sz).
% 4.15/2.03 thf(func_def_66, type, freche1608036107_a_b_c: freche914690577_a_b_c > denota231621370t_unit).
% 4.15/2.03 thf(func_def_67, type, freche1421597129_sc_sz: freche2095075217_sc_sz > denota610675952t_unit).
% 4.15/2.03 thf(func_def_68, type, frechet_raw_term_a_c: frechet_strm_a_c > trm_a_c).
% 4.15/2.03 thf(func_def_69, type, freche782854530_sf_sz: frechet_strm_sf_sz > trm_sf_sz).
% 4.15/2.03 thf(func_def_70, type, freche665377492rm_a_c: trm_a_c > frechet_strm_a_c).
% 4.15/2.03 thf(func_def_71, type, freche1046279700_sf_sz: trm_sf_sz > frechet_strm_sf_sz).
% 4.15/2.03 thf(func_def_72, type, ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o).
% 4.15/2.03 thf(func_def_73, type, if_Bou1785791806z_real: $o > bounde472938360z_real > bounde472938360z_real > bounde472938360z_real).
% 4.15/2.03 thf(func_def_74, type, quotie842200089_sc_sz: (denota610675952t_unit > denota610675952t_unit > $o) > (denota610675952t_unit > freche2095075217_sc_sz) > (freche2095075217_sc_sz > denota610675952t_unit) > (denota610675952t_unit > freche2095075217_sc_sz > $o) > $o).
% 4.15/2.03 thf(func_def_75, type, quotie1467858509rm_a_c: (trm_a_c > trm_a_c > $o) > (trm_a_c > frechet_strm_a_c) > (frechet_strm_a_c > trm_a_c) > (trm_a_c > frechet_strm_a_c > $o) > $o).
% 4.15/2.03 thf(func_def_76, type, quotie1549861309_sf_sz: (trm_sf_sz > trm_sf_sz > $o) > (trm_sf_sz > frechet_strm_sf_sz) > (frechet_strm_sf_sz > trm_sf_sz) > (trm_sf_sz > frechet_strm_sf_sz > $o) > $o).
% 4.15/2.03 thf(func_def_77, type, ord_le2003534918unit_o: (denota610675952t_unit > denota610675952t_unit > $o) > (denota610675952t_unit > denota610675952t_unit > $o) > $o).
% 4.15/2.03 thf(func_def_78, type, ord_le108471557c_sz_o: (denota610675952t_unit > produc866628903_sc_sz > $o) > (denota610675952t_unit > produc866628903_sc_sz > $o) > $o).
% 4.15/2.03 thf(func_def_79, type, ord_le8515534f_sz_o: (trm_sf_sz > trm_sf_sz > $o) > (trm_sf_sz > trm_sf_sz > $o) > $o).
% 4.15/2.03 thf(func_def_80, type, ord_less_eq_a_o: (a > $o) > (a > $o) > $o).
% 4.15/2.03 thf(func_def_81, type, ord_le775706699real_c: finite1398487019real_c > finite1398487019real_c > $o).
% 4.15/2.03 thf(func_def_82, type, ord_le787639925eal_sz: finite824932053eal_sz > finite824932053eal_sz > $o).
% 4.15/2.03 thf(func_def_83, type, ord_le2132572860_o_a_o: produc1065634396_o_a_o > produc1065634396_o_a_o > $o).
% 4.15/2.03 thf(func_def_84, type, ord_le1643089911_set_a: produc903182423_set_a > produc903182423_set_a > $o).
% 4.15/2.03 thf(func_def_85, type, ord_le472894788f_sz_o: produc1553439972f_sz_o > produc1553439972f_sz_o > $o).
% 4.15/2.03 thf(func_def_86, type, ord_le1883211903_o_a_o: product_prod_a_o_a_o > product_prod_a_o_a_o > $o).
% 4.15/2.03 thf(func_def_87, type, ord_le72828020_set_a: produc1561113620_set_a > produc1561113620_set_a > $o).
% 4.15/2.03 thf(func_def_88, type, ord_le850691415real_c: produc190496183real_c > produc190496183real_c > $o).
% 4.15/2.03 thf(func_def_89, type, ord_le473656583eal_sz: produc1149990247eal_sz > produc1149990247eal_sz > $o).
% 4.15/2.03 thf(func_def_90, type, ord_le978883847eal_sz: produc1241881959eal_sz > produc1241881959eal_sz > $o).
% 4.15/2.03 thf(func_def_91, type, ord_le1884788375f_sz_o: produc1144880887f_sz_o > produc1144880887f_sz_o > $o).
% 4.15/2.03 thf(func_def_92, type, ord_le501349868_a_a_o: produc1989635468_a_a_o > produc1989635468_a_a_o > $o).
% 4.15/2.03 thf(func_def_93, type, ord_le486764743_set_a: produc1691597095_set_a > produc1691597095_set_a > $o).
% 4.15/2.03 thf(func_def_94, type, ord_less_eq_real: real > real > $o).
% 4.15/2.03 thf(func_def_95, type, ord_le41263445eal_sz: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o).
% 4.15/2.03 thf(func_def_96, type, ord_le1230423618_sc_sz: set_Pr1169339874_sc_sz > set_Pr1169339874_sc_sz > $o).
% 4.15/2.03 thf(func_def_97, type, ord_le929608341um_b_c: set_Su1783761653um_b_c > set_Su1783761653um_b_c > $o).
% 4.15/2.03 thf(func_def_98, type, ord_le1772180283um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > $o).
% 4.15/2.03 thf(func_def_99, type, ord_le1110131657_sz_sz: set_Sum_sum_sz_sz > set_Sum_sum_sz_sz > $o).
% 4.15/2.03 thf(func_def_100, type, ord_le1369644495rm_a_c: set_trm_a_c > set_trm_a_c > $o).
% 4.15/2.03 thf(func_def_101, type, ord_le1697056455_sf_sz: set_trm_sf_sz > set_trm_sf_sz > $o).
% 4.15/2.03 thf(func_def_102, type, ord_less_eq_set_a: set_a > set_a > $o).
% 4.15/2.03 thf(func_def_103, type, top_to1399053141c_sz_o: denota610675952t_unit > produc866628903_sc_sz > $o).
% 4.15/2.03 thf(func_def_104, type, top_to646513176l_sz_o: finite824932053eal_sz > $o).
% 4.15/2.03 thf(func_def_105, type, top_to1201357528_b_c_o: sum_su737395349um_b_c > $o).
% 4.15/2.03 thf(func_def_106, type, top_to1787697847eal_sz: produc1241881959eal_sz).
% 4.15/2.03 thf(func_def_107, type, top_to1873962757eal_sz: set_Fi291318197eal_sz).
% 4.15/2.03 thf(func_def_108, type, top_to1499569298_sc_sz: set_Pr1169339874_sc_sz).
% 4.15/2.03 thf(func_def_109, type, top_to524132421um_b_c: set_Su1783761653um_b_c).
% 4.15/2.03 thf(func_def_110, type, top_to1660572043um_c_c: set_Sum_sum_c_c).
% 4.15/2.03 thf(func_def_111, type, top_top_set_a: set_a).
% 4.15/2.03 thf(func_def_112, type, produc1152932438_o_a_o: (trm_sf_sz > trm_sf_sz > $o) > (a > $o) > produc1065634396_o_a_o).
% 4.15/2.03 thf(func_def_113, type, produc1543226183_set_a: (trm_sf_sz > trm_sf_sz > $o) > set_a > produc903182423_set_a).
% 4.15/2.03 thf(func_def_114, type, produc593159062f_sz_o: (a > $o) > (trm_sf_sz > trm_sf_sz > $o) > produc1553439972f_sz_o).
% 4.15/2.03 thf(func_def_115, type, product_Pair_a_o_a_o: (a > $o) > (a > $o) > product_prod_a_o_a_o).
% 4.15/2.03 thf(func_def_116, type, produc1916559302_set_a: (a > $o) > set_a > produc1561113620_set_a).
% 4.15/2.03 thf(func_def_117, type, produc784663575z_real: bounde472938360z_real > bounde472938360z_real > produc1892666919z_real).
% 4.15/2.03 thf(func_def_118, type, produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz).
% 4.15/2.03 thf(func_def_119, type, produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c).
% 4.15/2.03 thf(func_def_120, type, produc1308130519eal_sz: finite824932053eal_sz > finite824932053eal_sz > produc1149990247eal_sz).
% 4.15/2.03 thf(func_def_121, type, produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz).
% 4.15/2.03 thf(func_def_122, type, produc1235791063eal_sz: set_Fi291318197eal_sz > set_Fi291318197eal_sz > produc1241881959eal_sz).
% 4.15/2.03 thf(func_def_123, type, produc1174558183f_sz_o: set_a > (trm_sf_sz > trm_sf_sz > $o) > produc1144880887f_sz_o).
% 4.15/2.03 thf(func_def_124, type, produc634809990_a_a_o: set_a > (a > $o) > produc1989635468_a_a_o).
% 4.15/2.03 thf(func_def_125, type, produc1928581911_set_a: set_a > set_a > produc1691597095_set_a).
% 4.15/2.03 thf(func_def_126, type, produc2013638506_o_a_o: produc1065634396_o_a_o > trm_sf_sz > trm_sf_sz > $o).
% 4.15/2.03 thf(func_def_127, type, produc407272755_set_a: produc903182423_set_a > trm_sf_sz > trm_sf_sz > $o).
% 4.15/2.03 thf(func_def_128, type, produc1453865130f_sz_o: produc1553439972f_sz_o > a > $o).
% 4.15/2.03 thf(func_def_129, type, product_fst_a_o_a_o: product_prod_a_o_a_o > a > $o).
% 4.15/2.03 thf(func_def_130, type, produc1045727450_set_a: produc1561113620_set_a > a > $o).
% 4.15/2.03 thf(func_def_131, type, produc870616579z_real: produc1892666919z_real > bounde472938360z_real).
% 4.15/2.03 thf(func_def_132, type, produc1503602930_sc_sz: produc1821101996_sc_sz > denota610675952t_unit).
% 4.15/2.03 thf(func_def_133, type, produc2010422875real_c: produc190496183real_c > finite1398487019real_c).
% 4.15/2.03 thf(func_def_134, type, produc1111759555eal_sz: produc1149990247eal_sz > finite824932053eal_sz).
% 4.15/2.03 thf(func_def_135, type, produc548504323_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz).
% 4.15/2.03 thf(func_def_136, type, produc286845635eal_sz: produc1241881959eal_sz > set_Fi291318197eal_sz).
% 4.15/2.03 thf(func_def_137, type, produc38604755f_sz_o: produc1144880887f_sz_o > set_a).
% 4.15/2.03 thf(func_def_138, type, produc1911461786_a_a_o: produc1989635468_a_a_o > set_a).
% 4.15/2.03 thf(func_def_139, type, produc1926412547_set_a: produc1691597095_set_a > set_a).
% 4.15/2.03 thf(func_def_140, type, produc1630531752_o_a_o: produc1065634396_o_a_o > a > $o).
% 4.15/2.03 thf(func_def_141, type, produc776178293_set_a: produc903182423_set_a > set_a).
% 4.15/2.03 thf(func_def_142, type, produc1070758376f_sz_o: produc1553439972f_sz_o > trm_sf_sz > trm_sf_sz > $o).
% 4.15/2.03 thf(func_def_143, type, product_snd_a_o_a_o: product_prod_a_o_a_o > a > $o).
% 4.15/2.03 thf(func_def_144, type, produc1305389080_set_a: produc1561113620_set_a > set_a).
% 4.15/2.03 thf(func_def_145, type, produc1422611269z_real: produc1892666919z_real > bounde472938360z_real).
% 4.15/2.03 thf(func_def_146, type, produc974239792_sc_sz: produc1821101996_sc_sz > produc866628903_sc_sz).
% 4.15/2.03 thf(func_def_147, type, produc314122909real_c: produc190496183real_c > finite1398487019real_c).
% 4.15/2.03 thf(func_def_148, type, produc1269210629eal_sz: produc1149990247eal_sz > finite824932053eal_sz).
% 4.15/2.03 thf(func_def_149, type, produc4753477_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz).
% 4.15/2.03 thf(func_def_150, type, produc1746886149eal_sz: produc1241881959eal_sz > set_Fi291318197eal_sz).
% 4.15/2.03 thf(func_def_151, type, produc407510293f_sz_o: produc1144880887f_sz_o > trm_sf_sz > trm_sf_sz > $o).
% 4.15/2.03 thf(func_def_152, type, produc23639768_a_a_o: produc1989635468_a_a_o > a > $o).
% 4.15/2.03 thf(func_def_153, type, produc918972485_set_a: produc1691597095_set_a > set_a).
% 4.15/2.03 thf(func_def_154, type, collec451781861t_unit: (denota231621370t_unit > $o) > set_De455519194t_unit).
% 4.15/2.03 thf(func_def_155, type, collec1767975749t_unit: (denota610675952t_unit > $o) > set_De208295462t_unit).
% 4.15/2.03 thf(func_def_156, type, collec1002602816eal_sz: (finite824932053eal_sz > $o) > set_Fi291318197eal_sz).
% 4.15/2.03 thf(func_def_157, type, collec1199592193_sc_sz: (produc1821101996_sc_sz > $o) > set_Pr1169339874_sc_sz).
% 4.15/2.03 thf(func_def_158, type, collec2086029184um_b_c: (sum_su737395349um_b_c > $o) > set_Su1783761653um_b_c).
% 4.15/2.03 thf(func_def_159, type, collect_trm_a_c: (trm_a_c > $o) > set_trm_a_c).
% 4.15/2.03 thf(func_def_160, type, collect_trm_sf_sz: (trm_sf_sz > $o) > set_trm_sf_sz).
% 4.15/2.03 thf(func_def_161, type, collect_a: (a > $o) > set_a).
% 4.15/2.03 thf(func_def_162, type, static_FVDiff_a_c: trm_a_c > set_Sum_sum_c_c).
% 4.15/2.03 thf(func_def_163, type, static_FVDiff_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz).
% 4.15/2.03 thf(func_def_164, type, static_FVT_a_c: trm_a_c > set_Sum_sum_c_c).
% 4.15/2.03 thf(func_def_165, type, static_FVT_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz).
% 4.15/2.03 thf(func_def_166, type, static_SIGT_a_c: trm_a_c > set_a).
% 4.15/2.03 thf(func_def_167, type, sum_In2139678582um_b_c: a > sum_su737395349um_b_c).
% 4.15/2.03 thf(func_def_168, type, predic913887884_sf_sz: sc > formula_sf_sc_sz).
% 4.15/2.03 thf(func_def_169, type, dfree_a_c: trm_a_c > $o).
% 4.15/2.03 thf(func_def_170, type, dfree_sf_sz: trm_sf_sz > $o).
% 4.15/2.03 thf(func_def_171, type, p_sc_sf_sz: sc > formula_sf_sc_sz).
% 4.15/2.03 thf(func_def_172, type, empty_sz_sf: sz > trm_sf_sz).
% 4.15/2.03 thf(func_def_173, type, f0_sf_sz: sf > trm_sf_sz).
% 4.15/2.03 thf(func_def_174, type, function_a_c: a > (c > trm_a_c) > trm_a_c).
% 4.15/2.03 thf(func_def_175, type, function_sf_sz: sf > (sz > trm_sf_sz) > trm_sf_sz).
% 4.15/2.03 thf(func_def_176, type, plus_a_c: trm_a_c > trm_a_c > trm_a_c).
% 4.15/2.03 thf(func_def_177, type, plus_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz).
% 4.15/2.03 thf(func_def_178, type, times_a_c: trm_a_c > trm_a_c > trm_a_c).
% 4.15/2.03 thf(func_def_179, type, times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz).
% 4.15/2.03 thf(func_def_180, type, topolo885751137z_real: set_Fi291318197eal_sz > (finite824932053eal_sz > bounde472938360z_real) > $o).
% 4.15/2.03 thf(func_def_181, type, topolo1027477648z_real: set_Fi291318197eal_sz > (finite824932053eal_sz > produc1892666919z_real) > $o).
% 4.15/2.03 thf(func_def_182, type, topolo1348430467z_real: set_Fi291318197eal_sz > (finite824932053eal_sz > real) > $o).
% 4.15/2.03 thf(func_def_183, type, type_d1092523951t_unit: (freche2095075217_sc_sz > denota610675952t_unit) > (denota610675952t_unit > freche2095075217_sc_sz) > set_De208295462t_unit > $o).
% 4.15/2.03 thf(func_def_184, type, type_d1238563341rm_a_c: (frechet_strm_a_c > trm_a_c) > (trm_a_c > frechet_strm_a_c) > set_trm_a_c > $o).
% 4.15/2.03 thf(func_def_185, type, type_d46389773_sf_sz: (frechet_strm_sf_sz > trm_sf_sz) > (trm_sf_sz > frechet_strm_sf_sz) > set_trm_sf_sz > $o).
% 4.15/2.03 thf(func_def_186, type, member1777622435t_unit: denota231621370t_unit > set_De455519194t_unit > $o).
% 4.15/2.03 thf(func_def_187, type, member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o).
% 4.15/2.03 thf(func_def_188, type, member1693951742eal_sz: finite824932053eal_sz > set_Fi291318197eal_sz > $o).
% 4.15/2.03 thf(func_def_189, type, member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o).
% 4.15/2.03 thf(func_def_190, type, member1893232190um_b_c: sum_su737395349um_b_c > set_Su1783761653um_b_c > $o).
% 4.15/2.03 thf(func_def_191, type, member_trm_a_c: trm_a_c > set_trm_a_c > $o).
% 4.15/2.03 thf(func_def_192, type, member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o).
% 4.15/2.03 thf(func_def_193, type, member_a: a > set_a > $o).
% 4.15/2.03 thf(func_def_194, type, i: denota231621370t_unit).
% 4.15/2.03 thf(func_def_195, type, j: denota231621370t_unit).
% 4.15/2.03 thf(func_def_196, type, nu: produc190496183real_c).
% 4.15/2.03 thf(func_def_197, type, nu2: produc190496183real_c).
% 4.15/2.03 thf(func_def_198, type, t1: trm_a_c).
% 4.15/2.03 thf(func_def_199, type, t2: trm_a_c).
% 4.15/2.03 thf(func_def_214, type, sK0: produc190496183real_c > finite1398487019real_c).
% 4.15/2.03 thf(func_def_215, type, sK1: produc190496183real_c > finite1398487019real_c).
% 4.15/2.03 thf(func_def_216, type, sK2: (produc190496183real_c > $o) > finite1398487019real_c).
% 4.15/2.03 thf(func_def_217, type, sK3: (produc190496183real_c > $o) > finite1398487019real_c).
% 4.15/2.03 thf(func_def_218, type, sK4: produc190496183real_c > finite1398487019real_c).
% 4.15/2.03 thf(func_def_219, type, sK5: produc190496183real_c > finite1398487019real_c).
% 4.15/2.03 thf(func_def_220, type, sK6: (finite1398487019real_c > finite1398487019real_c > $o) > finite1398487019real_c).
% 4.15/2.03 thf(func_def_221, type, sK7: (finite1398487019real_c > finite1398487019real_c > $o) > finite1398487019real_c).
% 4.15/2.03 thf(func_def_222, type, sK8: (produc190496183real_c > $o) > finite1398487019real_c).
% 4.15/2.03 thf(func_def_223, type, sK9: (produc190496183real_c > $o) > finite1398487019real_c).
% 4.15/2.03 thf(func_def_226, type, ph11: !>[X0: $tType]:(X0)).
% 4.15/2.03 thf(f1201,plain,(
% 4.15/2.03 $false),
% 4.15/2.03 inference(avatar_sat_refutation,[status(thm)],[f1117,f1200])).
% 4.15/2.03 thf(f1200,plain,(
% 4.15/2.03 spl10_7),
% 4.15/2.03 inference(avatar_contradiction_clause,[status(thm)],[f1199])).
% 4.15/2.03 thf(f1199,plain,(
% 4.15/2.03 $false | spl10_7),
% 4.15/2.03 inference(subsumption_resolution,[status(thm)],[f1197,f1113])).
% 4.15/2.03 thf(f1113,plain,(
% 4.15/2.03 ((denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2)) != $true) | spl10_7),
% 4.15/2.03 inference(avatar_component_clause,[status(thm)],[f1111])).
% 4.15/2.03 thf(f1111,definition,(
% 4.15/2.03 spl10_7 <=> ((denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2)) = $true)),
% 4.15/2.03 introduced(definition,[new_symbols(naming,[spl10_7])],[avatar_definition])).
% 4.15/2.03 thf(f1197,plain,(
% 4.15/2.03 ((denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2)) = $true)),
% 4.15/2.03 inference(trivial_inequality_removal,[status(thm)],[f1193])).
% 4.15/2.03 thf(f1193,plain,(
% 4.15/2.03 ((denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2)) = $true) | ($true != $true)),
% 4.15/2.03 inference(superposition,[status(thm)],[f987,f990])).
% 4.15/2.03 thf(f990,plain,(
% 4.15/2.03 ((denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ (plus_a_c @ t1 @ t2))) = $true)),
% 4.15/2.03 inference(cnf_transformation,[status(thm)],[f484])).
% 4.15/2.03 thf(f484,plain,(
% 4.15/2.03 ((denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ (plus_a_c @ t1 @ t2))) = $true)),
% 4.15/2.03 inference(fool_elimination,[status(thm)],[f483])).
% 4.15/2.03 thf(f483,plain,(
% 4.15/2.03 (denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ (plus_a_c @ t1 @ t2)))),
% 4.15/2.03 inference(rectify,[status(thm)],[f3])).
% 4.15/2.03 thf(f3,axiom,(
% 4.15/2.03 (denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ (plus_a_c @ t1 @ t2)))),
% 4.15/2.03 file('/export/starexec/sandbox/tmp/tmp.VtE5UpiK52/DTF2THF_30300.p',fact_2_agree)).
% 4.15/2.03 thf(f987,plain,(
% 4.15/2.03 ( ! [X2 : trm_a_c,X3 : produc190496183real_c,X0 : produc190496183real_c,X1 : trm_a_c] : (((denota1997846518gree_c @ X3 @ X0 @ (static_FVDiff_a_c @ (plus_a_c @ X1 @ X2))) != $true) | ((denota1997846518gree_c @ X3 @ X0 @ (static_FVDiff_a_c @ X2)) = $true)) )),
% 4.15/2.03 inference(cnf_transformation,[status(thm)],[f922])).
% 4.15/2.03 thf(f922,plain,(
% 4.15/2.03 ! [X0 : produc190496183real_c,X1 : trm_a_c,X2 : trm_a_c,X3 : produc190496183real_c] : (((denota1997846518gree_c @ X3 @ X0 @ (static_FVDiff_a_c @ X2)) = $true) | ((denota1997846518gree_c @ X3 @ X0 @ (static_FVDiff_a_c @ (plus_a_c @ X1 @ X2))) != $true))),
% 4.15/2.03 inference(ennf_transformation,[status(thm)],[f492])).
% 4.15/2.03 thf(f492,plain,(
% 4.15/2.03 ! [X0 : produc190496183real_c,X1 : trm_a_c,X2 : trm_a_c,X3 : produc190496183real_c] : (((denota1997846518gree_c @ X3 @ X0 @ (static_FVDiff_a_c @ (plus_a_c @ X1 @ X2))) = $true) => ((denota1997846518gree_c @ X3 @ X0 @ (static_FVDiff_a_c @ X2)) = $true))),
% 4.15/2.03 inference(fool_elimination,[status(thm)],[f491])).
% 4.15/2.03 thf(f491,plain,(
% 4.15/2.03 ! [X0 : produc190496183real_c,X1 : trm_a_c,X2 : trm_a_c,X3 : produc190496183real_c] : ((denota1997846518gree_c @ X3 @ X0 @ (static_FVDiff_a_c @ (plus_a_c @ X1 @ X2))) => (denota1997846518gree_c @ X3 @ X0 @ (static_FVDiff_a_c @ X2)))),
% 4.15/2.03 inference(rectify,[status(thm)],[f2])).
% 4.15/2.03 thf(f2,axiom,(
% 4.15/2.03 ! [X1 : produc190496183real_c,X2 : trm_a_c,X3 : trm_a_c,X0 : produc190496183real_c] : ((denota1997846518gree_c @ X0 @ X1 @ (static_FVDiff_a_c @ (plus_a_c @ X2 @ X3))) => (denota1997846518gree_c @ X0 @ X1 @ (static_FVDiff_a_c @ X3)))),
% 4.15/2.03 file('/export/starexec/sandbox/tmp/tmp.VtE5UpiK52/DTF2THF_30300.p',fact_1_agree__plus2)).
% 4.15/2.03 thf(f1117,plain,(
% 4.15/2.03 ~spl10_7),
% 4.15/2.03 inference(avatar_split_clause,[status(thm)],[f964,f1111])).
% 4.15/2.03 thf(f964,plain,(
% 4.15/2.03 ((denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2)) != $true)),
% 4.15/2.03 inference(cnf_transformation,[status(thm)],[f895])).
% 4.15/2.03 thf(f895,plain,(
% 4.15/2.03 ((denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2)) != $true)),
% 4.15/2.03 inference(flattening,[status(thm)],[f742])).
% 4.15/2.03 thf(f742,plain,(
% 4.15/2.03 ~((denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2)) = $true)),
% 4.15/2.03 inference(fool_elimination,[status(thm)],[f741])).
% 4.15/2.03 thf(f741,plain,(
% 4.15/2.03 ~(denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2))),
% 4.15/2.03 inference(rectify,[status(thm)],[f359])).
% 4.15/2.03 thf(f359,negated_conjecture,(
% 4.15/2.03 ~(denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2))),
% 4.15/2.03 inference(negated_conjecture,[status(cth)],[f358])).
% 4.15/2.03 thf(f358,conjecture,(
% 4.15/2.03 (denota1997846518gree_c @ nu @ nu2 @ (static_FVDiff_a_c @ t2))),
% 4.15/2.03 file('/export/starexec/sandbox/tmp/tmp.VtE5UpiK52/DTF2THF_30300.p',conj_0)).
% 4.15/2.03 % SZS output end Proof for DTF2THF_30300
% 4.15/2.03 % (30435)------------------------------
% 4.15/2.03 % (30435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.15/2.03 % (30435)Termination reason: Refutation
% 4.15/2.03
% 4.15/2.03 % (30435)Memory used [KB]: 7036
% 4.15/2.03 % (30435)Time elapsed: 0.035 s
% 4.15/2.03 % (30435)Instructions burned: 102 (million)
% 4.15/2.03 % (30435)------------------------------
% 4.15/2.03 % (30435)------------------------------
% 4.15/2.03 % (30405)Success in time 0.154 s
%------------------------------------------------------------------------------