%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP138^1 : 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 : n010.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 08:55:51 AM UTC 2026
% Result : Theorem 2.81s 1.74s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 227 ( 77 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 382 ( 51 ~; 38 |; 9 &; 270 @)
% ( 5 <=>; 7 =>; 0 <=; 2 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 263 ( 260 usr; 16 con; 0-3 aty)
% Number of variables : 66 ( 26 ^; 33 !; 7 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_o: $tType ).
thf(type_def_7,type,
set_set_o: $tType ).
thf(type_def_8,type,
set_list_char: $tType ).
thf(type_def_9,type,
set_set_list_char: $tType ).
thf(type_def_10,type,
set_Pa1764573435lle_tv: $tType ).
thf(type_def_11,type,
set_se800614875lle_tv: $tType ).
thf(type_def_12,type,
list_char: $tType ).
thf(type_def_13,type,
paraco1605129243lle_tv: $tType ).
thf(type_def_14,type,
set_nat: $tType ).
thf(type_def_15,type,
nat: $tType ).
thf(type_def_16,type,
paraco1604210848lle_fm: $tType ).
thf(type_def_17,type,
produc696645085lle_fm: $tType ).
thf(func_def_0,type,
produc696645085lle_fm: $tType ).
thf(func_def_1,type,
set_se800614875lle_tv: $tType ).
thf(func_def_2,type,
set_set_list_char: $tType ).
thf(func_def_3,type,
set_Pa1764573435lle_tv: $tType ).
thf(func_def_4,type,
set_list_char: $tType ).
thf(func_def_5,type,
paraco1605129243lle_tv: $tType ).
thf(func_def_6,type,
paraco1604210848lle_fm: $tType ).
thf(func_def_7,type,
set_set_o: $tType ).
thf(func_def_8,type,
list_char: $tType ).
thf(func_def_9,type,
set_nat: $tType ).
thf(func_def_10,type,
set_o: $tType ).
thf(func_def_11,type,
nat: $tType ).
thf(func_def_12,type,
complete_Sup_Sup_o: set_o > $o ).
thf(func_def_13,type,
finite_Fpow_o: set_o > set_set_o ).
thf(func_def_14,type,
finite1803457147t_char: set_list_char > set_set_list_char ).
thf(func_def_15,type,
finite2011762305lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv ).
thf(func_def_16,type,
ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_17,type,
ord_le1945897678char_o: ( list_char > $o ) > ( list_char > $o ) > $o ).
thf(func_def_18,type,
ord_le1632188418e_tv_o: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > $o ).
thf(func_def_19,type,
ord_less_eq_set_o: set_o > set_o > $o ).
thf(func_def_20,type,
ord_le1836582007t_char: set_list_char > set_list_char > $o ).
thf(func_def_21,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_22,type,
ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
thf(func_def_23,type,
ord_le2085948664_set_o: set_set_o > set_set_o > $o ).
thf(func_def_24,type,
ord_le263913851lle_tv: set_se800614875lle_tv > set_se800614875lle_tv > $o ).
thf(func_def_25,type,
order_Greatest_set_o: ( set_o > $o ) > set_o ).
thf(func_def_26,type,
order_350719188lle_tv: ( set_Pa1764573435lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(func_def_27,type,
top_top_o_o: $o > $o ).
thf(func_def_28,type,
top_top_list_char_o: list_char > $o ).
thf(func_def_29,type,
top_top_nat_o: nat > $o ).
thf(func_def_30,type,
top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
thf(func_def_31,type,
top_top_set_o: set_o ).
thf(func_def_32,type,
top_to748628679t_char: set_list_char ).
thf(func_def_33,type,
top_top_set_nat: set_nat ).
thf(func_def_34,type,
top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
thf(func_def_35,type,
top_top_set_set_o: set_set_o ).
thf(func_def_36,type,
top_to697846397t_char: set_set_list_char ).
thf(func_def_37,type,
paraco1933902578domain: set_nat > set_Pa1764573435lle_tv ).
thf(func_def_38,type,
paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
thf(func_def_39,type,
paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_40,type,
paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_41,type,
paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_42,type,
paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_43,type,
paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
thf(func_def_44,type,
paraco367965286_Truth: paraco1604210848lle_fm ).
thf(func_def_45,type,
paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
thf(func_def_46,type,
paraco327635598_valid: paraco1604210848lle_fm > $o ).
thf(func_def_47,type,
paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
thf(func_def_48,type,
produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
thf(func_def_49,type,
collect_o: ( $o > $o ) > set_o ).
thf(func_def_50,type,
collect_list_char: ( list_char > $o ) > set_list_char ).
thf(func_def_51,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_52,type,
collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(func_def_53,type,
pow_o: set_o > set_set_o ).
thf(func_def_54,type,
pow_list_char: set_list_char > set_set_list_char ).
thf(func_def_55,type,
pow_Pa475453624lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv ).
thf(func_def_56,type,
image_o_o: ( $o > $o ) > set_o > set_o ).
thf(func_def_57,type,
image_o_list_char: ( $o > list_char ) > set_o > set_list_char ).
thf(func_def_58,type,
image_o_nat: ( $o > nat ) > set_o > set_nat ).
thf(func_def_59,type,
image_1491822472lle_tv: ( $o > paraco1605129243lle_tv ) > set_o > set_Pa1764573435lle_tv ).
thf(func_def_60,type,
image_list_char_o: ( list_char > $o ) > set_list_char > set_o ).
thf(func_def_61,type,
image_890964937t_char: ( list_char > list_char ) > set_list_char > set_list_char ).
thf(func_def_62,type,
image_1187894195lle_tv: ( list_char > paraco1605129243lle_tv ) > set_list_char > set_Pa1764573435lle_tv ).
thf(func_def_63,type,
image_nat_o: ( nat > $o ) > set_nat > set_o ).
thf(func_def_64,type,
image_nat_list_char: ( nat > list_char ) > set_nat > set_list_char ).
thf(func_def_65,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_66,type,
image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
thf(func_def_67,type,
image_991799618e_tv_o: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv > set_o ).
thf(func_def_68,type,
image_1971766583t_char: ( paraco1605129243lle_tv > list_char ) > set_Pa1764573435lle_tv > set_list_char ).
thf(func_def_69,type,
image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
thf(func_def_70,type,
image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(func_def_71,type,
image_set_o_set_o: ( set_o > set_o ) > set_set_o > set_set_o ).
thf(func_def_72,type,
image_30320477lle_tv: ( set_list_char > set_Pa1764573435lle_tv ) > set_set_list_char > set_se800614875lle_tv ).
thf(func_def_73,type,
member_o: $o > set_o > $o ).
thf(func_def_74,type,
member_list_char: list_char > set_list_char > $o ).
thf(func_def_75,type,
member_nat: nat > set_nat > $o ).
thf(func_def_76,type,
member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
thf(func_def_77,type,
member_set_o: set_o > set_set_o > $o ).
thf(func_def_78,type,
member1875402276lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv > $o ).
thf(func_def_79,type,
p: paraco1604210848lle_fm ).
thf(func_def_91,type,
sP0: ( paraco1604210848lle_fm > $o ) > $o ).
thf(func_def_92,type,
sP1: ( paraco1604210848lle_fm > $o ) > $o ).
thf(func_def_93,type,
sK2: ( paraco1605129243lle_tv > list_char ) > list_char > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_94,type,
sK3: ( paraco1605129243lle_tv > list_char ) > set_list_char > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_95,type,
sK4: set_Pa1764573435lle_tv > ( list_char > paraco1605129243lle_tv ) > set_list_char > set_list_char ).
thf(func_def_96,type,
sK5: set_nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_97,type,
sK6: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_98,type,
sK7: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_99,type,
sK8: ( set_Pa1764573435lle_tv > $o ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(func_def_100,type,
sK9: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_101,type,
sK10: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_102,type,
sK11: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_103,type,
sK12: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_104,type,
sK13: produc696645085lle_fm > list_char ).
thf(func_def_105,type,
sK14: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_106,type,
sK15: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_107,type,
sK16: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_108,type,
sK17: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_109,type,
sK18: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_110,type,
sK19: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_111,type,
sK20: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_112,type,
sK21: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_113,type,
sK22: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_114,type,
sK23: set_o > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > $o ) > paraco1605129243lle_tv ).
thf(func_def_115,type,
sK24: ( list_char > $o ) > $o > list_char ).
thf(func_def_116,type,
sK25: set_list_char > ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > list_char ).
thf(func_def_117,type,
sK26: set_o > set_o > ( $o > $o ) > set_o ).
thf(func_def_118,type,
sK27: set_list_char > set_Pa1764573435lle_tv > ( list_char > paraco1605129243lle_tv ) > list_char ).
thf(func_def_119,type,
sK28: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_120,type,
sK29: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_121,type,
sK30: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_122,type,
sK31: set_nat > ( nat > $o ) > nat ).
thf(func_def_123,type,
sK32: ( list_char > paraco1605129243lle_tv ) > set_list_char > ( list_char > paraco1605129243lle_tv ) > list_char ).
thf(func_def_124,type,
sK33: paraco1605129243lle_tv > ( list_char > paraco1605129243lle_tv ) > set_list_char > list_char ).
thf(func_def_125,type,
sK34: ( $o > $o ) > ( $o > $o ) > set_o > $o ).
thf(func_def_126,type,
sK35: ( $o > $o ) > ( $o > $o ) > set_o > $o ).
thf(func_def_127,type,
sK36: set_Pa1764573435lle_tv > ( set_Pa1764573435lle_tv > $o ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_128,type,
sK37: set_Pa1764573435lle_tv > ( set_Pa1764573435lle_tv > $o ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_129,type,
sK38: set_list_char > set_list_char > list_char ).
thf(func_def_130,type,
sK39: set_o > ( $o > paraco1605129243lle_tv ) > paraco1605129243lle_tv > $o ).
thf(func_def_131,type,
sK40: ( set_o > set_Pa1764573435lle_tv ) > set_o ).
thf(func_def_132,type,
sK41: ( set_o > set_Pa1764573435lle_tv ) > set_o ).
thf(func_def_133,type,
sK42: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_134,type,
sK43: ( $o > $o ) > ( $o > $o ) > set_o > $o ).
thf(func_def_135,type,
sK44: set_list_char > set_list_char > ( list_char > list_char ) > list_char ).
thf(func_def_137,type,
sK46: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_138,type,
sK47: set_list_char > ( list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > $o ) > paraco1605129243lle_tv ).
thf(func_def_139,type,
sK48: ( $o > list_char ) > list_char > $o ).
thf(func_def_140,type,
sK49: set_Pa1764573435lle_tv > set_o > ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(func_def_141,type,
sK50: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > set_list_char > list_char ).
thf(func_def_142,type,
sK51: set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_143,type,
sK52: set_Pa1764573435lle_tv > ( nat > paraco1605129243lle_tv ) > ( nat > $o ) > nat ).
thf(func_def_144,type,
sK53: set_o > $o ).
thf(func_def_145,type,
sK54: set_o > set_o > ( $o > $o ) > $o ).
thf(func_def_146,type,
sK55: ( $o > $o ) > set_o > ( $o > $o ) > $o ).
thf(func_def_147,type,
sK56: ( set_Pa1764573435lle_tv > $o ) > set_list_char > ( list_char > paraco1605129243lle_tv ) > set_list_char ).
thf(func_def_148,type,
sK57: ( set_Pa1764573435lle_tv > $o ) > set_list_char > ( list_char > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_149,type,
sK58: set_list_char > ( list_char > $o ) > list_char ).
thf(func_def_150,type,
sK59: list_char > ( list_char > list_char ) > list_char ).
thf(func_def_151,type,
sK60: ( list_char > list_char ) > list_char ).
thf(func_def_152,type,
sK61: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_153,type,
sK62: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_154,type,
sK63: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_155,type,
sK64: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_156,type,
sK65: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_157,type,
sK66: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_158,type,
sK67: ( paraco1604210848lle_fm > $o ) > list_char ).
thf(func_def_159,type,
sK68: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).
thf(func_def_160,type,
sK69: set_list_char > ( list_char > list_char ) > list_char > list_char ).
thf(func_def_161,type,
sK70: ( list_char > paraco1605129243lle_tv ) > paraco1605129243lle_tv > list_char ).
thf(func_def_162,type,
sK71: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_163,type,
sK72: set_list_char > ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > list_char ) > paraco1605129243lle_tv ).
thf(func_def_164,type,
sK73: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > paraco1605129243lle_tv ).
thf(func_def_165,type,
sK74: set_list_char > ( list_char > $o ) > ( list_char > $o ) > list_char ).
thf(func_def_166,type,
sK75: $o > ( list_char > $o ) > list_char ).
thf(func_def_167,type,
sK76: ( list_char > $o ) > $o ).
thf(func_def_168,type,
sK77: list_char > ( list_char > list_char ) > list_char ).
thf(func_def_169,type,
sK78: ( list_char > $o ) > $o > list_char ).
thf(func_def_170,type,
sK79: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_171,type,
sK80: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_172,type,
sK81: ( list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > list_char ) > paraco1605129243lle_tv ).
thf(func_def_173,type,
sK82: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > $o ) > paraco1605129243lle_tv ).
thf(func_def_174,type,
sK83: ( $o > $o ) > $o ).
thf(func_def_175,type,
sK84: $o > ( $o > $o ) > $o ).
thf(func_def_176,type,
sK85: ( $o > list_char ) > list_char ).
thf(func_def_177,type,
sK86: list_char > ( $o > list_char ) > $o ).
thf(func_def_178,type,
sK87: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_179,type,
sK88: ( set_Pa1764573435lle_tv > $o ) > ( $o > paraco1605129243lle_tv ) > set_o > set_Pa1764573435lle_tv ).
thf(func_def_180,type,
sK89: ( set_Pa1764573435lle_tv > $o ) > ( $o > paraco1605129243lle_tv ) > set_o > set_o ).
thf(func_def_181,type,
sK90: ( list_char > $o ) > $o > list_char ).
thf(func_def_182,type,
sK91: ( $o > $o ) > set_o > ( $o > $o ) > $o ).
thf(func_def_183,type,
sK92: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_184,type,
sK93: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_185,type,
sK94: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_Pa1764573435lle_tv ).
thf(func_def_186,type,
sK95: ( $o > $o ) > set_o > $o ).
thf(func_def_187,type,
sK96: ( $o > $o ) > $o > $o ).
thf(func_def_188,type,
sK97: ( set_o > set_o ) > set_o ).
thf(func_def_189,type,
sK98: ( set_o > set_o ) > set_o ).
thf(func_def_190,type,
sK99: set_list_char > ( paraco1605129243lle_tv > $o ) > ( list_char > paraco1605129243lle_tv ) > list_char ).
thf(func_def_191,type,
sK100: ( set_o > set_Pa1764573435lle_tv ) > set_o ).
thf(func_def_192,type,
sK101: ( set_o > set_Pa1764573435lle_tv ) > set_o ).
thf(func_def_193,type,
sK102: ( $o > list_char ) > list_char > $o ).
thf(func_def_194,type,
sK103: ( list_char > list_char ) > ( list_char > list_char ) > list_char ).
thf(func_def_195,type,
sK104: ( set_o > set_Pa1764573435lle_tv ) > set_o ).
thf(func_def_196,type,
sK105: ( set_o > set_Pa1764573435lle_tv ) > set_o ).
thf(func_def_197,type,
sK106: list_char > ( $o > list_char ) > $o ).
thf(func_def_198,type,
sK107: list_char ).
thf(func_def_199,type,
sK108: list_char > ( list_char > list_char ) > list_char ).
thf(func_def_200,type,
sK109: $o > ( $o > $o ) > $o ).
thf(func_def_201,type,
sK110: ( list_char > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_202,type,
sK111: paraco1605129243lle_tv > ( list_char > paraco1605129243lle_tv ) > list_char ).
thf(func_def_203,type,
sK112: set_list_char > list_char ).
thf(func_def_204,type,
sK113: paraco1604210848lle_fm > list_char ).
thf(func_def_205,type,
sK114: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_206,type,
sK115: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_207,type,
sK116: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_208,type,
sK117: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_209,type,
sK118: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_210,type,
sK119: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_211,type,
sK120: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_212,type,
sK121: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_213,type,
sK122: ( $o > paraco1605129243lle_tv ) > paraco1605129243lle_tv > $o ).
thf(func_def_214,type,
sK123: ( $o > $o ) > ( $o > $o ) > set_o > $o ).
thf(func_def_215,type,
sK124: $o > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > $o ) > paraco1605129243lle_tv ).
thf(func_def_216,type,
sK125: ( set_o > set_o ) > set_o ).
thf(func_def_217,type,
sK126: ( set_o > set_o ) > set_o ).
thf(func_def_218,type,
sK127: ( $o > list_char ) > ( list_char > $o ) > $o ).
thf(func_def_219,type,
sK128: ( nat > $o ) > set_list_char > ( nat > list_char ) > nat ).
thf(func_def_220,type,
sK129: paraco1605129243lle_tv > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_221,type,
sK130: paraco1605129243lle_tv ).
thf(func_def_222,type,
sK131: ( set_o > set_o ) > set_o ).
thf(func_def_223,type,
sK132: ( set_o > set_o ) > set_o ).
thf(func_def_224,type,
sK133: ( list_char > $o ) > ( $o > list_char ) > list_char ).
thf(func_def_225,type,
sK134: set_o > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(func_def_226,type,
sK135: list_char > paraco1605129243lle_tv ).
thf(func_def_227,type,
sK136: list_char > paraco1605129243lle_tv ).
thf(func_def_228,type,
sK137: list_char > ( $o > list_char ) > set_o > $o ).
thf(func_def_229,type,
sK138: ( list_char > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_list_char > list_char ).
thf(func_def_230,type,
sK139: set_Pa1764573435lle_tv > ( $o > paraco1605129243lle_tv ) > set_o > $o ).
thf(func_def_231,type,
sK140: ( set_o > $o ) > ( set_o > $o ) > set_o ).
thf(func_def_232,type,
sK141: ( set_o > $o ) > set_o > set_o ).
thf(func_def_233,type,
sK142: set_Pa1764573435lle_tv > ( set_Pa1764573435lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(func_def_234,type,
sK143: ( set_Pa1764573435lle_tv > $o ) > ( set_Pa1764573435lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(func_def_235,type,
sK144: ( $o > paraco1605129243lle_tv ) > set_o > set_Pa1764573435lle_tv > set_o ).
thf(func_def_236,type,
sK145: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_237,type,
sK146: set_list_char > ( list_char > $o ) > set_o > list_char ).
thf(func_def_238,type,
sK147: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > paraco1605129243lle_tv ).
thf(func_def_239,type,
sK148: set_o > ( $o > $o ) > set_o > $o ).
thf(func_def_240,type,
sK149: ( set_o > set_o ) > set_o ).
thf(func_def_241,type,
sK150: ( set_o > set_o ) > set_o ).
thf(func_def_242,type,
sK151: ( set_Pa1764573435lle_tv > set_o ) > set_Pa1764573435lle_tv ).
thf(func_def_243,type,
sK152: ( set_Pa1764573435lle_tv > set_o ) > set_Pa1764573435lle_tv ).
thf(func_def_244,type,
sK153: set_Pa1764573435lle_tv > ( $o > paraco1605129243lle_tv ) > set_o > set_o ).
thf(func_def_245,type,
sK154: ( nat > $o ) > ( nat > $o ) > set_o > nat ).
thf(func_def_246,type,
sK155: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(func_def_247,type,
sK156: paraco1605129243lle_tv > ( list_char > paraco1605129243lle_tv ) > list_char ).
thf(func_def_248,type,
sK157: paraco1605129243lle_tv > set_list_char > ( list_char > paraco1605129243lle_tv ) > list_char ).
thf(func_def_249,type,
sK158: $o > ( $o > $o ) > $o ).
thf(func_def_250,type,
sK159: ( set_Pa1764573435lle_tv > set_o ) > set_Pa1764573435lle_tv ).
thf(func_def_251,type,
sK160: ( set_Pa1764573435lle_tv > set_o ) > set_Pa1764573435lle_tv ).
thf(func_def_252,type,
sK161: ( $o > $o ) > set_o > set_o > set_o ).
thf(func_def_253,type,
sK162: ( set_o > set_Pa1764573435lle_tv ) > set_o ).
thf(func_def_254,type,
sK163: ( set_o > set_Pa1764573435lle_tv ) > set_o ).
thf(func_def_255,type,
sK164: ( $o > $o ) > set_o > $o > $o ).
thf(func_def_256,type,
sK165: ( $o > $o ) > set_o > ( $o > $o ) > $o ).
thf(func_def_257,type,
sK166: $o > set_list_char > ( list_char > $o ) > list_char ).
thf(func_def_258,type,
sK167: ( $o > list_char ) > set_o > set_list_char > $o ).
thf(func_def_259,type,
sK168: ( set_o > $o ) > set_o > set_o ).
thf(func_def_260,type,
sK169: set_o > set_o > $o ).
thf(func_def_261,type,
sK170: $o > ( $o > $o ) > set_o > $o ).
thf(func_def_262,type,
sK171: ( list_char > paraco1605129243lle_tv ) > set_list_char > set_Pa1764573435lle_tv > set_list_char ).
thf(func_def_263,type,
sK172: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > set_o > paraco1605129243lle_tv ).
thf(func_def_264,type,
sK173: list_char > ( list_char > list_char ) > list_char ).
thf(func_def_265,type,
sK174: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_266,type,
sK175: ( list_char > paraco1605129243lle_tv ) > paraco1605129243lle_tv > list_char ).
thf(func_def_267,type,
sK176: set_Pa1764573435lle_tv > ( list_char > paraco1605129243lle_tv ) > ( list_char > $o ) > list_char ).
thf(func_def_268,type,
sK177: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > paraco1605129243lle_tv ).
thf(func_def_269,type,
sK178: ( set_Pa1764573435lle_tv > set_o ) > set_Pa1764573435lle_tv ).
thf(func_def_270,type,
sK179: ( set_Pa1764573435lle_tv > set_o ) > set_Pa1764573435lle_tv ).
thf(func_def_271,type,
sK180: ( set_Pa1764573435lle_tv > set_o ) > set_Pa1764573435lle_tv ).
thf(func_def_272,type,
sK181: ( set_Pa1764573435lle_tv > set_o ) > set_Pa1764573435lle_tv ).
thf(func_def_273,type,
sK182: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_274,type,
sK183: ( paraco1605129243lle_tv > $o ) > ( set_o > $o ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(func_def_275,type,
sK184: ( paraco1605129243lle_tv > $o ) > ( set_o > $o ) > set_Pa1764573435lle_tv > set_o ).
thf(func_def_276,type,
sK185: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > $o ) > paraco1605129243lle_tv ).
thf(func_def_277,type,
sK186: ( $o > $o ) > ( set_o > $o ) > set_o > set_o ).
thf(func_def_278,type,
sK187: ( $o > $o ) > ( set_o > $o ) > set_o > set_o ).
thf(func_def_280,type,
ph189:
!>[X0: $tType] : X0 ).
thf(f2453,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2352,f2361,f2373,f2376,f2448]) ).
thf(f2448,plain,
( spl188_2
| ~ spl188_1 ),
inference(avatar_split_clause,[status(thm)],[f2431,f2347,f2350]) ).
thf(f2350,definition,
( spl188_2
<=> ! [X2: list_char > paraco1605129243lle_tv] :
( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ p ) ) ),
introduced(definition,[new_symbols(naming,[spl188_2])],[avatar_definition]) ).
thf(f2347,definition,
( spl188_1
<=> ! [X3: list_char > paraco1605129243lle_tv] :
( ( ( paraco1325918602e_eval @ X3 @ p )
= ( paraco1344940915le_Det @ $true ) )
| ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X3 @ top_to748628679t_char ) @ top_to1057771083lle_tv )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl188_1])],[avatar_definition]) ).
thf(f2431,plain,
( ! [X0: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X0 @ p )
= ( paraco1344940915le_Det @ $true ) )
| ~ spl188_1 ),
inference(trivial_inequality_removal,[status(thm)],[f2424]) ).
thf(f2424,plain,
( ! [X0: list_char > paraco1605129243lle_tv] :
( ( $true != $true )
| ( ( paraco1325918602e_eval @ X0 @ p )
= ( paraco1344940915le_Det @ $true ) ) )
| ~ spl188_1 ),
inference(superposition,[status(thm)],[f2348,f2152]) ).
thf(f2152,plain,
! [X0: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ X0 @ top_to1057771083lle_tv )
= $true ),
inference(cnf_transformation,[status(thm)],[f502]) ).
thf(f502,plain,
! [X0: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ X0 @ top_to1057771083lle_tv )
= $true ),
inference(fool_elimination,[status(thm)],[f501]) ).
thf(f501,plain,
! [X0: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ X0 @ top_to1057771083lle_tv ),
inference(rectify,[status(thm)],[f214]) ).
thf(f214,axiom,
! [X18: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ X18 @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox/tmp/tmp.PTGbAxFx6h/DTF2THF_21650.p',fact_213_top__greatest) ).
thf(f2348,plain,
( ! [X3: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X3 @ top_to748628679t_char ) @ top_to1057771083lle_tv )
!= $true )
| ( ( paraco1325918602e_eval @ X3 @ p )
= ( paraco1344940915le_Det @ $true ) ) )
| ~ spl188_1 ),
inference(avatar_component_clause,[status(thm)],[f2347]) ).
thf(f2376,plain,
( ~ spl188_2
| spl188_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f2375]) ).
thf(f2375,plain,
( $false
| ~ spl188_2
| spl188_3 ),
inference(trivial_inequality_removal,[status(thm)],[f2374]) ).
thf(f2374,plain,
( ( ( paraco1344940915le_Det @ $true )
!= ( paraco1344940915le_Det @ $true ) )
| ~ spl188_2
| spl188_3 ),
inference(superposition,[status(thm)],[f2356,f2351]) ).
thf(f2351,plain,
( ! [X2: list_char > paraco1605129243lle_tv] :
( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ p ) )
| ~ spl188_2 ),
inference(avatar_component_clause,[status(thm)],[f2350]) ).
thf(f2356,plain,
( ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ sK135 @ p ) )
| spl188_3 ),
inference(avatar_component_clause,[status(thm)],[f2354]) ).
thf(f2354,definition,
( spl188_3
<=> ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ sK135 @ p ) ) ),
introduced(definition,[new_symbols(naming,[spl188_3])],[avatar_definition]) ).
thf(f2373,plain,
( ~ spl188_2
| spl188_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f2372]) ).
thf(f2372,plain,
( $false
| ~ spl188_2
| spl188_4 ),
inference(trivial_inequality_removal,[status(thm)],[f2371]) ).
thf(f2371,plain,
( ( ( paraco1344940915le_Det @ $true )
!= ( paraco1344940915le_Det @ $true ) )
| ~ spl188_2
| spl188_4 ),
inference(superposition,[status(thm)],[f2360,f2351]) ).
thf(f2360,plain,
( ( ( paraco1325918602e_eval @ sK136 @ p )
!= ( paraco1344940915le_Det @ $true ) )
| spl188_4 ),
inference(avatar_component_clause,[status(thm)],[f2358]) ).
thf(f2358,definition,
( spl188_4
<=> ( ( paraco1325918602e_eval @ sK136 @ p )
= ( paraco1344940915le_Det @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl188_4])],[avatar_definition]) ).
thf(f2361,plain,
( ~ spl188_3
| ~ spl188_4 ),
inference(avatar_split_clause,[status(thm)],[f2091,f2358,f2354]) ).
thf(f2091,plain,
( ( ( paraco1325918602e_eval @ sK136 @ p )
!= ( paraco1344940915le_Det @ $true ) )
| ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ sK135 @ p ) ) ),
inference(cnf_transformation,[status(thm)],[f1593]) ).
thf(f1593,plain,
( ( ( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ sK135 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
= $true )
& ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ sK135 @ p ) ) )
| ( ( paraco1325918602e_eval @ sK136 @ p )
!= ( paraco1344940915le_Det @ $true ) ) )
& ( ! [X2: list_char > paraco1605129243lle_tv] :
( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ p ) )
| ! [X3: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X3 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
!= $true )
| ( ( paraco1325918602e_eval @ X3 @ p )
= ( paraco1344940915le_Det @ $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK135,sK136])],[f1590,f1592,f1591]) ).
thf(f1591,plain,
( ? [X0: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X0 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
= $true )
& ( ( paraco1325918602e_eval @ X0 @ p )
!= ( paraco1344940915le_Det @ $true ) ) )
=> ( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ sK135 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
= $true )
& ( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval @ sK135 @ p ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1592,plain,
( ? [X1: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X1 @ p )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ sK136 @ p )
!= ( paraco1344940915le_Det @ $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1590,plain,
( ( ? [X0: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X0 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
= $true )
& ( ( paraco1325918602e_eval @ X0 @ p )
!= ( paraco1344940915le_Det @ $true ) ) )
| ? [X1: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X1 @ p )
!= ( paraco1344940915le_Det @ $true ) ) )
& ( ! [X2: list_char > paraco1605129243lle_tv] :
( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ p ) )
| ! [X3: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X3 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
!= $true )
| ( ( paraco1325918602e_eval @ X3 @ p )
= ( paraco1344940915le_Det @ $true ) ) ) ) ),
inference(rectify,[status(thm)],[f1589]) ).
thf(f1589,plain,
( ( ? [X0: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X0 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
= $true )
& ( ( paraco1325918602e_eval @ X0 @ p )
!= ( paraco1344940915le_Det @ $true ) ) )
| ? [X1: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X1 @ p )
!= ( paraco1344940915le_Det @ $true ) ) )
& ( ! [X1: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X1 @ p )
= ( paraco1344940915le_Det @ $true ) )
| ! [X0: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X0 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
!= $true )
| ( ( paraco1325918602e_eval @ X0 @ p )
= ( paraco1344940915le_Det @ $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1183]) ).
thf(f1183,plain,
( ? [X0: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X0 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
= $true )
& ( ( paraco1325918602e_eval @ X0 @ p )
!= ( paraco1344940915le_Det @ $true ) ) )
<=> ! [X1: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X1 @ p )
= ( paraco1344940915le_Det @ $true ) ) ),
inference(ennf_transformation,[status(thm)],[f979]) ).
thf(f979,plain,
~ ( ~ ! [X0: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X0 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
= $true )
=> ( ( paraco1325918602e_eval @ X0 @ p )
= ( paraco1344940915le_Det @ $true ) ) )
<~> ! [X1: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X1 @ p )
= ( paraco1344940915le_Det @ $true ) ) ),
inference(rectify,[status(thm)],[f414]) ).
thf(f414,plain,
~ ( ~ ! [X0: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X0 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
= $true )
=> ( ( paraco1325918602e_eval @ X0 @ p )
= ( paraco1344940915le_Det @ $true ) ) )
<~> ! [X2: list_char > paraco1605129243lle_tv] :
( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ p ) ) ),
inference(fool_elimination,[status(thm)],[f413]) ).
thf(f413,plain,
~ ~ ! [X0: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X0 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : $true ) ) )
=> ( ( paraco1325918602e_eval @ X0 @ p )
= ( paraco1344940915le_Det @ $true ) ) )
!= ( ! [X2: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X2 @ p )
= ( paraco1344940915le_Det @ $true ) ) ) ),
inference(rectify,[status(thm)],[f356]) ).
thf(f356,negated_conjecture,
~ ~ ! [X6: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X6 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X0: nat] : $true ) ) )
=> ( ( paraco1325918602e_eval @ X6 @ p )
= ( paraco1344940915le_Det @ $true ) ) )
!= ( ! [X6: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X6 @ p )
= ( paraco1344940915le_Det @ $true ) ) ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f355,conjecture,
~ ! [X6: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X6 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X0: nat] : $true ) ) )
=> ( ( paraco1325918602e_eval @ X6 @ p )
= ( paraco1344940915le_Det @ $true ) ) )
!= ( ! [X6: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X6 @ p )
= ( paraco1344940915le_Det @ $true ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PTGbAxFx6h/DTF2THF_21650.p',conj_0) ).
thf(f2352,plain,
( spl188_1
| spl188_2 ),
inference(avatar_split_clause,[status(thm)],[f2345,f2350,f2347]) ).
thf(f2345,plain,
! [X2: list_char > paraco1605129243lle_tv,X3: list_char > paraco1605129243lle_tv] :
( ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ p ) )
| ( ( paraco1325918602e_eval @ X3 @ p )
= ( paraco1344940915le_Det @ $true ) )
| ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X3 @ top_to748628679t_char ) @ top_to1057771083lle_tv )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f2344,f1916]) ).
thf(f1916,plain,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv
@ ^ [Y0: paraco1605129243lle_tv] : $true ) ),
inference(cnf_transformation,[status(thm)],[f799]) ).
thf(f799,plain,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv
@ ^ [Y0: paraco1605129243lle_tv] : $true ) ),
inference(fool_elimination,[status(thm)],[f798]) ).
thf(f798,plain,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv
@ ^ [X0: paraco1605129243lle_tv] : $true ) ),
inference(rectify,[status(thm)],[f204]) ).
thf(f204,axiom,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv
@ ^ [X1: paraco1605129243lle_tv] : $true ) ),
file('/export/starexec/sandbox/tmp/tmp.PTGbAxFx6h/DTF2THF_21650.p',fact_203_UNIV__def) ).
thf(f2344,plain,
! [X2: list_char > paraco1605129243lle_tv,X3: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X3 @ top_to748628679t_char )
@ ( collec1111687558lle_tv
@ ^ [Y0: paraco1605129243lle_tv] : $true ) )
!= $true )
| ( ( paraco1325918602e_eval @ X3 @ p )
= ( paraco1344940915le_Det @ $true ) )
| ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ p ) ) ),
inference(forward_demodulation,[status(thm)],[f2090,f2207]) ).
thf(f2207,plain,
( ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) )
= ( collec1111687558lle_tv
@ ^ [Y0: paraco1605129243lle_tv] : $true ) ),
inference(cnf_transformation,[status(thm)],[f531]) ).
thf(f531,plain,
( ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) )
= ( collec1111687558lle_tv
@ ^ [Y0: paraco1605129243lle_tv] : $true ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( paraco1933902578domain
@ ( collect_nat
@ ^ [X0: nat] : $true ) )
= ( collec1111687558lle_tv
@ ^ [X1: paraco1605129243lle_tv] : $true ) ),
file('/export/starexec/sandbox/tmp/tmp.PTGbAxFx6h/DTF2THF_21650.p',fact_0_universal__domain) ).
thf(f2090,plain,
! [X2: list_char > paraco1605129243lle_tv,X3: list_char > paraco1605129243lle_tv] :
( ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X3 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [Y0: nat] : $true ) ) )
!= $true )
| ( ( paraco1344940915le_Det @ $true )
= ( paraco1325918602e_eval @ X2 @ p ) )
| ( ( paraco1325918602e_eval @ X3 @ p )
= ( paraco1344940915le_Det @ $true ) ) ),
inference(cnf_transformation,[status(thm)],[f1593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP138^1 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n010.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 08:27:03 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : ITP138^1 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.46 % Domain : Interactive Theorem Proving
% 0.28/0.46 % Problem : Sledgehammer Paraconsistency problem prob_525__3267638_1
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Des21]
% 0.28/0.46 % Names : Paraconsistency/prob_525__3267638_1 [Des21]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0, 0.36 v7.5.0
% 0.28/0.46 % Syntax : Number of formulae : 435 ( 153 unt; 80 typ; 0 def)
% 0.28/0.46 % Number of atoms : 994 ( 360 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 16 ( 2 avg)
% 0.28/0.46 % Number of connectives : 2958 ( 96 ~; 0 |; 84 &;2337 @)
% 0.28/0.46 % ( 0 <=>; 441 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 16 ( 7 avg)
% 0.28/0.46 % Number of types : 13 ( 12 usr)
% 0.28/0.47 % Number of type conns : 419 ( 419 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 71 ( 68 usr; 10 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 1164 ( 139 ^;1001 !; 24 ?;1164 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:36:45.032
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % Could-be-implicit typings (12)
% 0.28/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.28/0.47 produc696645085lle_fm: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.28/0.47 set_se800614875lle_tv: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J,type,
% 0.28/0.47 set_set_list_char: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.28/0.47 set_Pa1764573435lle_tv: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
% 0.28/0.47 set_list_char: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.28/0.47 paraco1605129243lle_tv: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.28/0.47 paraco1604210848lle_fm: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 0.28/0.47 set_set_o: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 0.28/0.47 list_char: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47 set_nat: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 0.28/0.47 set_o: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.28/0.47 nat: $tType ).
% 0.28/0.47
% 0.28/0.47 % Explicit typings (68)
% 0.28/0.47 thf(sy_c_Complete__Lattices_OSup__class_OSup_001_Eo,type,
% 0.28/0.47 complete_Sup_Sup_o: set_o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Finite__Set_OFpow_001_Eo,type,
% 0.28/0.47 finite_Fpow_o: set_o > set_set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Finite__Set_OFpow_001t__List__Olist_It__String__Ochar_J,type,
% 0.28/0.47 finite1803457147t_char: set_list_char > set_set_list_char ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Finite__Set_OFpow_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.28/0.47 finite2011762305lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_Eo_J,type,
% 0.28/0.47 ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 0.28/0.47 ord_le1945897678char_o: ( list_char > $o ) > ( list_char > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 0.28/0.47 ord_le1632188418e_tv_o: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
% 0.28/0.47 ord_less_eq_set_o: set_o > set_o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
% 0.28/0.47 ord_le1836582007t_char: set_list_char > set_list_char > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.28/0.47 ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 0.28/0.47 ord_le2085948664_set_o: set_set_o > set_set_o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.28/0.47 ord_le263913851lle_tv: set_se800614875lle_tv > set_se800614875lle_tv > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_I_Eo_J,type,
% 0.28/0.47 order_Greatest_set_o: ( set_o > $o ) > set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.28/0.47 order_350719188lle_tv: ( set_Pa1764573435lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_M_Eo_J,type,
% 0.28/0.47 top_top_o_o: $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 0.28/0.47 top_top_list_char_o: list_char > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.28/0.47 top_top_nat_o: nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 0.28/0.47 top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 0.28/0.47 top_top_set_o: set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
% 0.28/0.47 top_to748628679t_char: set_list_char ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47 top_top_set_nat: set_nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.28/0.47 top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 0.28/0.47 top_top_set_set_o: set_set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J,type,
% 0.28/0.47 top_to697846397t_char: set_set_list_char ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Odomain,type,
% 0.28/0.47 paraco1933902578domain: set_nat > set_Pa1764573435lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Oeval,type,
% 0.28/0.47 paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OCon_H,type,
% 0.28/0.47 paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql,type,
% 0.28/0.47 paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql_H,type,
% 0.28/0.47 paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_ONeg_H,type,
% 0.28/0.47 paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OPro,type,
% 0.28/0.47 paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OTruth,type,
% 0.28/0.47 paraco367965286_Truth: paraco1604210848lle_fm ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_ODet,type,
% 0.28/0.47 paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid,type,
% 0.28/0.47 paraco327635598_valid: paraco1604210848lle_fm > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid__in,type,
% 0.28/0.47 paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.28/0.47 produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OCollect_001_Eo,type,
% 0.28/0.47 collect_o: ( $o > $o ) > set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OCollect_001t__List__Olist_It__String__Ochar_J,type,
% 0.28/0.47 collect_list_char: ( list_char > $o ) > set_list_char ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.28/0.47 collect_nat: ( nat > $o ) > set_nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OCollect_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.28/0.47 collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OPow_001_Eo,type,
% 0.28/0.47 pow_o: set_o > set_set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OPow_001t__List__Olist_It__String__Ochar_J,type,
% 0.28/0.47 pow_list_char: set_list_char > set_set_list_char ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OPow_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.28/0.47 pow_Pa475453624lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001_Eo_001_Eo,type,
% 0.28/0.47 image_o_o: ( $o > $o ) > set_o > set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001_Eo_001t__List__Olist_It__String__Ochar_J,type,
% 0.28/0.47 image_o_list_char: ( $o > list_char ) > set_o > set_list_char ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001_Eo_001t__Nat__Onat,type,
% 0.28/0.47 image_o_nat: ( $o > nat ) > set_o > set_nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001_Eo_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.28/0.47 image_1491822472lle_tv: ( $o > paraco1605129243lle_tv ) > set_o > set_Pa1764573435lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__List__Olist_It__String__Ochar_J_001_Eo,type,
% 0.28/0.47 image_list_char_o: ( list_char > $o ) > set_list_char > set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
% 0.28/0.47 image_890964937t_char: ( list_char > list_char ) > set_list_char > set_list_char ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__List__Olist_It__String__Ochar_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.28/0.47 image_1187894195lle_tv: ( list_char > paraco1605129243lle_tv ) > set_list_char > set_Pa1764573435lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Nat__Onat_001_Eo,type,
% 0.28/0.47 image_nat_o: ( nat > $o ) > set_nat > set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
% 0.28/0.47 image_nat_list_char: ( nat > list_char ) > set_nat > set_list_char ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.47 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.28/0.47 image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_Eo,type,
% 0.28/0.47 image_991799618e_tv_o: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv > set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__List__Olist_It__String__Ochar_J,type,
% 0.28/0.47 image_1971766583t_char: ( paraco1605129243lle_tv > list_char ) > set_Pa1764573435lle_tv > set_list_char ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.28/0.47 image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.28/0.47 image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
% 0.28/0.47 image_set_o_set_o: ( set_o > set_o ) > set_set_o > set_set_o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.28/0.47 image_30320477lle_tv: ( set_list_char > set_Pa1764573435lle_tv ) > set_set_list_char > set_se800614875lle_tv ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member_001_Eo,type,
% 0.28/0.47 member_o: $o > set_o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member_001t__List__Olist_It__String__Ochar_J,type,
% 0.28/0.47 member_list_char: list_char > set_list_char > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member_001t__Nat__Onat,type,
% 0.28/0.47 member_nat: nat > set_nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.28/0.47 member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member_001t__Set__Oset_I_Eo_J,type,
% 0.28/0.47 member_set_o: set_o > set_set_o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.28/0.47 member1875402276lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_p,type,
% 0.28/0.47 p: paraco1604210848lle_fm ).
% 0.28/0.47
% 0.28/0.47 % Relevant facts (354)
% 0.28/0.47 thf(fact_0_universal__domain,axiom,
% 0.28/0.47 ( ( paraco1933902578domain
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [N: nat] : $true ) )
% 0.28/0.47 = ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] : $true ) ) ).
% 0.28/0.47
% 0.28/0.47 % universal_domain
% 0.28/0.47 thf(fact_1_tv_Oinject_I1_J,axiom,
% 0.28/0.47 ! [X1: $o,Y1: $o] :
% 0.28/0.47 ( ( ( paraco1344940915le_Det @ X1 )
% 0.28/0.47 = ( paraco1344940915le_Det @ Y1 ) )
% 0.28/0.47 = ( X1 = Y1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % tv.inject(1)
% 0.28/0.47 thf(fact_2_valid__in__def,axiom,
% 0.28/0.47 ( paraco55203475lid_in
% 0.28/0.47 = ( ^ [U: set_nat,P: paraco1604210848lle_fm] :
% 0.28/0.47 ! [I: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ I @ top_to748628679t_char ) @ ( paraco1933902578domain @ U ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I @ P )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % valid_in_def
% 0.28/0.47 thf(fact_3_image__ident,axiom,
% 0.28/0.47 ! [Y: set_o] :
% 0.28/0.47 ( ( image_o_o
% 0.28/0.47 @ ^ [X: $o] : X
% 0.28/0.47 @ Y )
% 0.28/0.47 = Y ) ).
% 0.28/0.47
% 0.28/0.47 % image_ident
% 0.28/0.47 thf(fact_4_UNIV__I,axiom,
% 0.28/0.47 ! [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_I
% 0.28/0.47 thf(fact_5_UNIV__I,axiom,
% 0.28/0.47 ! [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_I
% 0.28/0.47 thf(fact_6_UNIV__I,axiom,
% 0.28/0.47 ! [X2: list_char] : ( member_list_char @ X2 @ top_to748628679t_char ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_I
% 0.28/0.47 thf(fact_7_iso__tuple__UNIV__I,axiom,
% 0.28/0.47 ! [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ).
% 0.28/0.47
% 0.28/0.47 % iso_tuple_UNIV_I
% 0.28/0.47 thf(fact_8_iso__tuple__UNIV__I,axiom,
% 0.28/0.47 ! [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ).
% 0.28/0.47
% 0.28/0.47 % iso_tuple_UNIV_I
% 0.28/0.47 thf(fact_9_iso__tuple__UNIV__I,axiom,
% 0.28/0.47 ! [X2: list_char] : ( member_list_char @ X2 @ top_to748628679t_char ) ).
% 0.28/0.47
% 0.28/0.47 % iso_tuple_UNIV_I
% 0.28/0.47 thf(fact_10_subsetI,axiom,
% 0.28/0.47 ! [A: set_list_char,B: set_list_char] :
% 0.28/0.47 ( ! [X3: list_char] :
% 0.28/0.47 ( ( member_list_char @ X3 @ A )
% 0.28/0.47 => ( member_list_char @ X3 @ B ) )
% 0.28/0.47 => ( ord_le1836582007t_char @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetI
% 0.28/0.47 thf(fact_11_subsetI,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o] :
% 0.28/0.47 ( ! [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ A )
% 0.28/0.47 => ( member_o @ X3 @ B ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetI
% 0.28/0.47 thf(fact_12_subsetI,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X3 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ X3 @ B ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetI
% 0.28/0.47 thf(fact_13_subset__antisym,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_antisym
% 0.28/0.47 thf(fact_14_subset__antisym,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A @ B )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_antisym
% 0.28/0.47 thf(fact_15_image__eqI,axiom,
% 0.28/0.47 ! [B2: list_char,F: $o > list_char,X2: $o,A: set_o] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( member_list_char @ B2 @ ( image_o_list_char @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_16_image__eqI,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv,X2: $o,A: set_o] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_17_image__eqI,axiom,
% 0.28/0.47 ! [B2: $o,F: list_char > $o,X2: list_char,A: set_list_char] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( member_o @ B2 @ ( image_list_char_o @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_18_image__eqI,axiom,
% 0.28/0.47 ! [B2: list_char,F: list_char > list_char,X2: list_char,A: set_list_char] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( member_list_char @ B2 @ ( image_890964937t_char @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_19_image__eqI,axiom,
% 0.28/0.47 ! [B2: $o,F: paraco1605129243lle_tv > $o,X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( member_o @ B2 @ ( image_991799618e_tv_o @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_20_image__eqI,axiom,
% 0.28/0.47 ! [B2: list_char,F: paraco1605129243lle_tv > list_char,X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( member_list_char @ B2 @ ( image_1971766583t_char @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_21_image__eqI,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_22_image__eqI,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv,X2: list_char,A: set_list_char] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_23_image__eqI,axiom,
% 0.28/0.47 ! [B2: $o,F: $o > $o,X2: $o,A: set_o] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( member_o @ B2 @ ( image_o_o @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_24_order__refl,axiom,
% 0.28/0.47 ! [X2: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ X2 @ X2 ) ).
% 0.28/0.47
% 0.28/0.47 % order_refl
% 0.28/0.47 thf(fact_25_order__refl,axiom,
% 0.28/0.47 ! [X2: set_o] : ( ord_less_eq_set_o @ X2 @ X2 ) ).
% 0.28/0.47
% 0.28/0.47 % order_refl
% 0.28/0.47 thf(fact_26_rangeE,axiom,
% 0.28/0.47 ! [B2: $o,F: list_char > $o] :
% 0.28/0.47 ( ( member_o @ B2 @ ( image_list_char_o @ F @ top_to748628679t_char ) )
% 0.28/0.47 => ~ ! [X3: list_char] :
% 0.28/0.47 ( B2
% 0.28/0.47 = ( ~ ( F @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeE
% 0.28/0.47 thf(fact_27_rangeE,axiom,
% 0.28/0.47 ! [B2: list_char,F: list_char > list_char] :
% 0.28/0.47 ( ( member_list_char @ B2 @ ( image_890964937t_char @ F @ top_to748628679t_char ) )
% 0.28/0.47 => ~ ! [X3: list_char] :
% 0.28/0.47 ( B2
% 0.28/0.47 != ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeE
% 0.28/0.47 thf(fact_28_rangeE,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ top_to748628679t_char ) )
% 0.28/0.47 => ~ ! [X3: list_char] :
% 0.28/0.47 ( B2
% 0.28/0.47 != ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeE
% 0.28/0.47 thf(fact_29_rangeE,axiom,
% 0.28/0.47 ! [B2: $o,F: $o > $o] :
% 0.28/0.47 ( ( member_o @ B2 @ ( image_o_o @ F @ top_top_set_o ) )
% 0.28/0.47 => ~ ! [X3: $o] :
% 0.28/0.47 ( B2
% 0.28/0.47 = ( ~ ( F @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeE
% 0.28/0.47 thf(fact_30_rangeE,axiom,
% 0.28/0.47 ! [B2: list_char,F: $o > list_char] :
% 0.28/0.47 ( ( member_list_char @ B2 @ ( image_o_list_char @ F @ top_top_set_o ) )
% 0.28/0.47 => ~ ! [X3: $o] :
% 0.28/0.47 ( B2
% 0.28/0.47 != ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeE
% 0.28/0.47 thf(fact_31_rangeE,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ top_top_set_o ) )
% 0.28/0.47 => ~ ! [X3: $o] :
% 0.28/0.47 ( B2
% 0.28/0.47 != ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeE
% 0.28/0.47 thf(fact_32_range__composition,axiom,
% 0.28/0.47 ! [F: $o > $o,G: list_char > $o] :
% 0.28/0.47 ( ( image_list_char_o
% 0.28/0.47 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 0.28/0.47 @ top_to748628679t_char )
% 0.28/0.47 = ( image_o_o @ F @ ( image_list_char_o @ G @ top_to748628679t_char ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_composition
% 0.28/0.47 thf(fact_33_range__composition,axiom,
% 0.28/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( image_1187894195lle_tv
% 0.28/0.47 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 0.28/0.47 @ top_to748628679t_char )
% 0.28/0.47 = ( image_335818702lle_tv @ F @ ( image_1187894195lle_tv @ G @ top_to748628679t_char ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_composition
% 0.28/0.47 thf(fact_34_range__composition,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,G: list_char > list_char] :
% 0.28/0.47 ( ( image_1187894195lle_tv
% 0.28/0.47 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 0.28/0.47 @ top_to748628679t_char )
% 0.28/0.47 = ( image_1187894195lle_tv @ F @ ( image_890964937t_char @ G @ top_to748628679t_char ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_composition
% 0.28/0.47 thf(fact_35_range__composition,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,G: $o > list_char] :
% 0.28/0.47 ( ( image_1491822472lle_tv
% 0.28/0.47 @ ^ [X: $o] : ( F @ ( G @ X ) )
% 0.28/0.47 @ top_top_set_o )
% 0.28/0.47 = ( image_1187894195lle_tv @ F @ ( image_o_list_char @ G @ top_top_set_o ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_composition
% 0.28/0.47 thf(fact_36_range__composition,axiom,
% 0.28/0.47 ! [F: $o > $o,G: $o > $o] :
% 0.28/0.47 ( ( image_o_o
% 0.28/0.47 @ ^ [X: $o] : ( F @ ( G @ X ) )
% 0.28/0.47 @ top_top_set_o )
% 0.28/0.47 = ( image_o_o @ F @ ( image_o_o @ G @ top_top_set_o ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_composition
% 0.28/0.47 thf(fact_37_image__Collect__subsetI,axiom,
% 0.28/0.47 ! [P2: nat > $o,F: nat > list_char,B: set_list_char] :
% 0.28/0.47 ( ! [X3: nat] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le1836582007t_char @ ( image_nat_list_char @ F @ ( collect_nat @ P2 ) ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Collect_subsetI
% 0.28/0.47 thf(fact_38_image__Collect__subsetI,axiom,
% 0.28/0.47 ! [P2: paraco1605129243lle_tv > $o,F: paraco1605129243lle_tv > list_char,B: set_list_char] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le1836582007t_char @ ( image_1971766583t_char @ F @ ( collec1111687558lle_tv @ P2 ) ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Collect_subsetI
% 0.28/0.47 thf(fact_39_image__Collect__subsetI,axiom,
% 0.28/0.47 ! [P2: list_char > $o,F: list_char > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ! [X3: list_char] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ ( collect_list_char @ P2 ) ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Collect_subsetI
% 0.28/0.47 thf(fact_40_image__Collect__subsetI,axiom,
% 0.28/0.47 ! [P2: nat > $o,F: nat > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ! [X3: nat] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( image_1151963140lle_tv @ F @ ( collect_nat @ P2 ) ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Collect_subsetI
% 0.28/0.47 thf(fact_41_image__Collect__subsetI,axiom,
% 0.28/0.47 ! [P2: paraco1605129243lle_tv > $o,F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ ( collec1111687558lle_tv @ P2 ) ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Collect_subsetI
% 0.28/0.47 thf(fact_42_image__Collect__subsetI,axiom,
% 0.28/0.47 ! [P2: $o > $o,F: $o > $o,B: set_o] :
% 0.28/0.47 ( ! [X3: $o] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( member_o @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( image_o_o @ F @ ( collect_o @ P2 ) ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Collect_subsetI
% 0.28/0.47 thf(fact_43_image__Collect__subsetI,axiom,
% 0.28/0.47 ! [P2: nat > $o,F: nat > $o,B: set_o] :
% 0.28/0.47 ( ! [X3: nat] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( member_o @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( image_nat_o @ F @ ( collect_nat @ P2 ) ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Collect_subsetI
% 0.28/0.47 thf(fact_44_image__Collect__subsetI,axiom,
% 0.28/0.47 ! [P2: paraco1605129243lle_tv > $o,F: paraco1605129243lle_tv > $o,B: set_o] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( member_o @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ F @ ( collec1111687558lle_tv @ P2 ) ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Collect_subsetI
% 0.28/0.47 thf(fact_45_top__set__def,axiom,
% 0.28/0.47 ( top_top_set_nat
% 0.28/0.47 = ( collect_nat @ top_top_nat_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % top_set_def
% 0.28/0.47 thf(fact_46_top__set__def,axiom,
% 0.28/0.47 ( top_to1057771083lle_tv
% 0.28/0.47 = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % top_set_def
% 0.28/0.47 thf(fact_47_top__set__def,axiom,
% 0.28/0.47 ( top_to748628679t_char
% 0.28/0.47 = ( collect_list_char @ top_top_list_char_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % top_set_def
% 0.28/0.47 thf(fact_48_top__set__def,axiom,
% 0.28/0.47 ( top_top_set_o
% 0.28/0.47 = ( collect_o @ top_top_o_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % top_set_def
% 0.28/0.47 thf(fact_49_less__eq__set__def,axiom,
% 0.28/0.47 ( ord_le1836582007t_char
% 0.28/0.47 = ( ^ [A2: set_list_char,B3: set_list_char] :
% 0.28/0.47 ( ord_le1945897678char_o
% 0.28/0.47 @ ^ [X: list_char] : ( member_list_char @ X @ A2 )
% 0.28/0.47 @ ^ [X: list_char] : ( member_list_char @ X @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_set_def
% 0.28/0.47 thf(fact_50_less__eq__set__def,axiom,
% 0.28/0.47 ( ord_le241064091lle_tv
% 0.28/0.47 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ord_le1632188418e_tv_o
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ A2 )
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_set_def
% 0.28/0.47 thf(fact_51_less__eq__set__def,axiom,
% 0.28/0.47 ( ord_less_eq_set_o
% 0.28/0.47 = ( ^ [A2: set_o,B3: set_o] :
% 0.28/0.47 ( ord_less_eq_o_o
% 0.28/0.47 @ ^ [X: $o] : ( member_o @ X @ A2 )
% 0.28/0.47 @ ^ [X: $o] : ( member_o @ X @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_set_def
% 0.28/0.47 thf(fact_52_dual__order_Oantisym,axiom,
% 0.28/0.47 ! [B2: set_Pa1764573435lle_tv,A3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B2 @ A3 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 0.28/0.47 => ( A3 = B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.antisym
% 0.28/0.47 thf(fact_53_dual__order_Oantisym,axiom,
% 0.28/0.47 ! [B2: set_o,A3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B2 @ A3 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ A3 @ B2 )
% 0.28/0.47 => ( A3 = B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.antisym
% 0.28/0.47 thf(fact_54_dual__order_Oeq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_Pa1764573435lle_tv,Z: set_Pa1764573435lle_tv] : ( Y2 = Z ) )
% 0.28/0.47 = ( ^ [A4: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B4 @ A4 )
% 0.28/0.47 & ( ord_le241064091lle_tv @ A4 @ B4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.eq_iff
% 0.28/0.47 thf(fact_55_dual__order_Oeq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_o,Z: set_o] : ( Y2 = Z ) )
% 0.28/0.47 = ( ^ [A4: set_o,B4: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B4 @ A4 )
% 0.28/0.47 & ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.eq_iff
% 0.28/0.47 thf(fact_56_dual__order_Otrans,axiom,
% 0.28/0.47 ! [B2: set_Pa1764573435lle_tv,A3: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B2 @ A3 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ C @ B2 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ C @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.trans
% 0.28/0.47 thf(fact_57_dual__order_Otrans,axiom,
% 0.28/0.47 ! [B2: set_o,A3: set_o,C: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B2 @ A3 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ C @ B2 )
% 0.28/0.47 => ( ord_less_eq_set_o @ C @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.trans
% 0.28/0.47 thf(fact_58_dual__order_Orefl,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A3 @ A3 ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.refl
% 0.28/0.47 thf(fact_59_dual__order_Orefl,axiom,
% 0.28/0.47 ! [A3: set_o] : ( ord_less_eq_set_o @ A3 @ A3 ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.refl
% 0.28/0.47 thf(fact_60_order__trans,axiom,
% 0.28/0.47 ! [X2: set_Pa1764573435lle_tv,Y3: set_Pa1764573435lle_tv,Z2: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X2 @ Y3 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ Y3 @ Z2 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ X2 @ Z2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_trans
% 0.28/0.47 thf(fact_61_order__trans,axiom,
% 0.28/0.47 ! [X2: set_o,Y3: set_o,Z2: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X2 @ Y3 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ Y3 @ Z2 )
% 0.28/0.47 => ( ord_less_eq_set_o @ X2 @ Z2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_trans
% 0.28/0.47 thf(fact_62_order__class_Oorder_Oantisym,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B2 @ A3 )
% 0.28/0.47 => ( A3 = B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.antisym
% 0.28/0.47 thf(fact_63_order__class_Oorder_Oantisym,axiom,
% 0.28/0.47 ! [A3: set_o,B2: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B2 @ A3 )
% 0.28/0.47 => ( A3 = B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.antisym
% 0.28/0.47 thf(fact_64_ord__le__eq__trans,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 0.28/0.47 => ( ( B2 = C )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_trans
% 0.28/0.47 thf(fact_65_ord__le__eq__trans,axiom,
% 0.28/0.47 ! [A3: set_o,B2: set_o,C: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 0.28/0.47 => ( ( B2 = C )
% 0.28/0.47 => ( ord_less_eq_set_o @ A3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_trans
% 0.28/0.47 thf(fact_66_ord__eq__le__trans,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( A3 = B2 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_trans
% 0.28/0.47 thf(fact_67_ord__eq__le__trans,axiom,
% 0.28/0.47 ! [A3: set_o,B2: set_o,C: set_o] :
% 0.28/0.47 ( ( A3 = B2 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B2 @ C )
% 0.28/0.47 => ( ord_less_eq_set_o @ A3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_trans
% 0.28/0.47 thf(fact_68_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_Pa1764573435lle_tv,Z: set_Pa1764573435lle_tv] : ( Y2 = Z ) )
% 0.28/0.47 = ( ^ [A4: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A4 @ B4 )
% 0.28/0.47 & ( ord_le241064091lle_tv @ B4 @ A4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.eq_iff
% 0.28/0.47 thf(fact_69_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_o,Z: set_o] : ( Y2 = Z ) )
% 0.28/0.47 = ( ^ [A4: set_o,B4: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 0.28/0.47 & ( ord_less_eq_set_o @ B4 @ A4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.eq_iff
% 0.28/0.47 thf(fact_70_antisym__conv,axiom,
% 0.28/0.47 ! [Y3: set_Pa1764573435lle_tv,X2: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ Y3 @ X2 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ X2 @ Y3 )
% 0.28/0.47 = ( X2 = Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym_conv
% 0.28/0.47 thf(fact_71_antisym__conv,axiom,
% 0.28/0.47 ! [Y3: set_o,X2: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ Y3 @ X2 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ X2 @ Y3 )
% 0.28/0.47 = ( X2 = Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym_conv
% 0.28/0.47 thf(fact_72_order_Otrans,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.trans
% 0.28/0.47 thf(fact_73_order_Otrans,axiom,
% 0.28/0.47 ! [A3: set_o,B2: set_o,C: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B2 @ C )
% 0.28/0.47 => ( ord_less_eq_set_o @ A3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.trans
% 0.28/0.47 thf(fact_74_eq__refl,axiom,
% 0.28/0.47 ! [X2: set_Pa1764573435lle_tv,Y3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( X2 = Y3 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ X2 @ Y3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_refl
% 0.28/0.47 thf(fact_75_eq__refl,axiom,
% 0.28/0.47 ! [X2: set_o,Y3: set_o] :
% 0.28/0.47 ( ( X2 = Y3 )
% 0.28/0.47 => ( ord_less_eq_set_o @ X2 @ Y3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_refl
% 0.28/0.47 thf(fact_76_antisym,axiom,
% 0.28/0.47 ! [X2: set_Pa1764573435lle_tv,Y3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X2 @ Y3 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ Y3 @ X2 )
% 0.28/0.47 => ( X2 = Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym
% 0.28/0.47 thf(fact_77_antisym,axiom,
% 0.28/0.47 ! [X2: set_o,Y3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X2 @ Y3 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ Y3 @ X2 )
% 0.28/0.47 => ( X2 = Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym
% 0.28/0.47 thf(fact_78_eq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_Pa1764573435lle_tv,Z: set_Pa1764573435lle_tv] : ( Y2 = Z ) )
% 0.28/0.47 = ( ^ [X: set_Pa1764573435lle_tv,Y4: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X @ Y4 )
% 0.28/0.47 & ( ord_le241064091lle_tv @ Y4 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_iff
% 0.28/0.47 thf(fact_79_eq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_o,Z: set_o] : ( Y2 = Z ) )
% 0.28/0.47 = ( ^ [X: set_o,Y4: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X @ Y4 )
% 0.28/0.47 & ( ord_less_eq_set_o @ Y4 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_iff
% 0.28/0.47 thf(fact_80_ord__le__eq__subst,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 0.28/0.47 => ( ( ( F @ B2 )
% 0.28/0.47 = C )
% 0.28/0.47 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_subst
% 0.28/0.47 thf(fact_81_ord__le__eq__subst,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_o,C: set_o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 0.28/0.47 => ( ( ( F @ B2 )
% 0.28/0.47 = C )
% 0.28/0.47 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_subst
% 0.28/0.47 thf(fact_82_ord__le__eq__subst,axiom,
% 0.28/0.47 ! [A3: set_o,B2: set_o,F: set_o > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 0.28/0.47 => ( ( ( F @ B2 )
% 0.28/0.47 = C )
% 0.28/0.47 => ( ! [X3: set_o,Y5: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_subst
% 0.28/0.47 thf(fact_83_ord__le__eq__subst,axiom,
% 0.28/0.47 ! [A3: set_o,B2: set_o,F: set_o > set_o,C: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 0.28/0.47 => ( ( ( F @ B2 )
% 0.28/0.47 = C )
% 0.28/0.47 => ( ! [X3: set_o,Y5: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_subst
% 0.28/0.47 thf(fact_84_ord__eq__le__subst,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( A3
% 0.28/0.47 = ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 0.28/0.47 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_subst
% 0.28/0.47 thf(fact_85_ord__eq__le__subst,axiom,
% 0.28/0.47 ! [A3: set_o,F: set_Pa1764573435lle_tv > set_o,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( A3
% 0.28/0.47 = ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 0.28/0.47 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_subst
% 0.28/0.47 thf(fact_86_ord__eq__le__subst,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,F: set_o > set_Pa1764573435lle_tv,B2: set_o,C: set_o] :
% 0.28/0.47 ( ( A3
% 0.28/0.47 = ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B2 @ C )
% 0.28/0.47 => ( ! [X3: set_o,Y5: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_subst
% 0.28/0.47 thf(fact_87_ord__eq__le__subst,axiom,
% 0.28/0.47 ! [A3: set_o,F: set_o > set_o,B2: set_o,C: set_o] :
% 0.28/0.47 ( ( A3
% 0.28/0.47 = ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B2 @ C )
% 0.28/0.47 => ( ! [X3: set_o,Y5: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_subst
% 0.28/0.47 thf(fact_88_order__subst2,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ ( F @ B2 ) @ C )
% 0.28/0.47 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst2
% 0.28/0.47 thf(fact_89_order__subst2,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_o,C: set_o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ ( F @ B2 ) @ C )
% 0.28/0.47 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst2
% 0.28/0.47 thf(fact_90_order__subst2,axiom,
% 0.28/0.47 ! [A3: set_o,B2: set_o,F: set_o > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ ( F @ B2 ) @ C )
% 0.28/0.47 => ( ! [X3: set_o,Y5: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst2
% 0.28/0.47 thf(fact_91_order__subst2,axiom,
% 0.28/0.47 ! [A3: set_o,B2: set_o,F: set_o > set_o,C: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ ( F @ B2 ) @ C )
% 0.28/0.47 => ( ! [X3: set_o,Y5: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst2
% 0.28/0.47 thf(fact_92_order__subst1,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A3 @ ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 0.28/0.47 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst1
% 0.28/0.47 thf(fact_93_order__subst1,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv,F: set_o > set_Pa1764573435lle_tv,B2: set_o,C: set_o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A3 @ ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B2 @ C )
% 0.28/0.47 => ( ! [X3: set_o,Y5: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst1
% 0.28/0.47 thf(fact_94_order__subst1,axiom,
% 0.28/0.47 ! [A3: set_o,F: set_Pa1764573435lle_tv > set_o,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A3 @ ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 0.28/0.47 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst1
% 0.28/0.47 thf(fact_95_order__subst1,axiom,
% 0.28/0.47 ! [A3: set_o,F: set_o > set_o,B2: set_o,C: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A3 @ ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B2 @ C )
% 0.28/0.47 => ( ! [X3: set_o,Y5: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst1
% 0.28/0.47 thf(fact_96_rev__image__eqI,axiom,
% 0.28/0.47 ! [X2: $o,A: set_o,B2: $o,F: $o > $o] :
% 0.28/0.47 ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_o @ B2 @ ( image_o_o @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_97_rev__image__eqI,axiom,
% 0.28/0.47 ! [X2: $o,A: set_o,B2: list_char,F: $o > list_char] :
% 0.28/0.47 ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_list_char @ B2 @ ( image_o_list_char @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_98_rev__image__eqI,axiom,
% 0.28/0.47 ! [X2: $o,A: set_o,B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_99_rev__image__eqI,axiom,
% 0.28/0.47 ! [X2: list_char,A: set_list_char,B2: $o,F: list_char > $o] :
% 0.28/0.47 ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_o @ B2 @ ( image_list_char_o @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_100_rev__image__eqI,axiom,
% 0.28/0.47 ! [X2: list_char,A: set_list_char,B2: list_char,F: list_char > list_char] :
% 0.28/0.47 ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_list_char @ B2 @ ( image_890964937t_char @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_101_rev__image__eqI,axiom,
% 0.28/0.47 ! [X2: list_char,A: set_list_char,B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_102_rev__image__eqI,axiom,
% 0.28/0.47 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: $o,F: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_o @ B2 @ ( image_991799618e_tv_o @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_103_rev__image__eqI,axiom,
% 0.28/0.47 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: list_char,F: paraco1605129243lle_tv > list_char] :
% 0.28/0.47 ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_list_char @ B2 @ ( image_1971766583t_char @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_104_rev__image__eqI,axiom,
% 0.28/0.47 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_105_ball__imageD,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X3 @ ( image_1187894195lle_tv @ F @ A ) )
% 0.28/0.47 => ( P2 @ X3 ) )
% 0.28/0.47 => ! [X4: list_char] :
% 0.28/0.47 ( ( member_list_char @ X4 @ A )
% 0.28/0.47 => ( P2 @ ( F @ X4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ball_imageD
% 0.28/0.47 thf(fact_106_ball__imageD,axiom,
% 0.28/0.47 ! [F: $o > $o,A: set_o,P2: $o > $o] :
% 0.28/0.47 ( ! [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ ( image_o_o @ F @ A ) )
% 0.28/0.47 => ( P2 @ X3 ) )
% 0.28/0.47 => ! [X4: $o] :
% 0.28/0.47 ( ( member_o @ X4 @ A )
% 0.28/0.47 => ( P2 @ ( F @ X4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ball_imageD
% 0.28/0.47 thf(fact_107_image__cong,axiom,
% 0.28/0.47 ! [M: set_o,N2: set_o,F: $o > $o,G: $o > $o] :
% 0.28/0.47 ( ( M = N2 )
% 0.28/0.47 => ( ! [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ N2 )
% 0.28/0.47 => ( ( F @ X3 )
% 0.28/0.47 = ( G @ X3 ) ) )
% 0.28/0.47 => ( ( image_o_o @ F @ M )
% 0.28/0.47 = ( image_o_o @ G @ N2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_cong
% 0.28/0.47 thf(fact_108_image__cong,axiom,
% 0.28/0.47 ! [M: set_list_char,N2: set_list_char,F: list_char > paraco1605129243lle_tv,G: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( M = N2 )
% 0.28/0.47 => ( ! [X3: list_char] :
% 0.28/0.47 ( ( member_list_char @ X3 @ N2 )
% 0.28/0.47 => ( ( F @ X3 )
% 0.28/0.47 = ( G @ X3 ) ) )
% 0.28/0.47 => ( ( image_1187894195lle_tv @ F @ M )
% 0.28/0.47 = ( image_1187894195lle_tv @ G @ N2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_cong
% 0.28/0.47 thf(fact_109_mem__Collect__eq,axiom,
% 0.28/0.47 ! [A3: $o,P2: $o > $o] :
% 0.28/0.47 ( ( member_o @ A3 @ ( collect_o @ P2 ) )
% 0.28/0.47 = ( P2 @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem_Collect_eq
% 0.28/0.47 thf(fact_110_mem__Collect__eq,axiom,
% 0.28/0.47 ! [A3: list_char,P2: list_char > $o] :
% 0.28/0.47 ( ( member_list_char @ A3 @ ( collect_list_char @ P2 ) )
% 0.28/0.47 = ( P2 @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem_Collect_eq
% 0.28/0.47 thf(fact_111_mem__Collect__eq,axiom,
% 0.28/0.47 ! [A3: nat,P2: nat > $o] :
% 0.28/0.47 ( ( member_nat @ A3 @ ( collect_nat @ P2 ) )
% 0.28/0.47 = ( P2 @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem_Collect_eq
% 0.28/0.47 thf(fact_112_mem__Collect__eq,axiom,
% 0.28/0.47 ! [A3: paraco1605129243lle_tv,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( member266900804lle_tv @ A3 @ ( collec1111687558lle_tv @ P2 ) )
% 0.28/0.47 = ( P2 @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem_Collect_eq
% 0.28/0.47 thf(fact_113_Collect__mem__eq,axiom,
% 0.28/0.47 ! [A: set_o] :
% 0.28/0.47 ( ( collect_o
% 0.28/0.47 @ ^ [X: $o] : ( member_o @ X @ A ) )
% 0.28/0.47 = A ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mem_eq
% 0.28/0.47 thf(fact_114_Collect__mem__eq,axiom,
% 0.28/0.47 ! [A: set_list_char] :
% 0.28/0.47 ( ( collect_list_char
% 0.28/0.47 @ ^ [X: list_char] : ( member_list_char @ X @ A ) )
% 0.28/0.47 = A ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mem_eq
% 0.28/0.47 thf(fact_115_Collect__mem__eq,axiom,
% 0.28/0.47 ! [A: set_nat] :
% 0.28/0.47 ( ( collect_nat
% 0.28/0.47 @ ^ [X: nat] : ( member_nat @ X @ A ) )
% 0.28/0.47 = A ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mem_eq
% 0.28/0.47 thf(fact_116_Collect__mem__eq,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ A ) )
% 0.28/0.47 = A ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mem_eq
% 0.28/0.47 thf(fact_117_Collect__cong,axiom,
% 0.28/0.47 ! [P2: nat > $o,Q: nat > $o] :
% 0.28/0.47 ( ! [X3: nat] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 = ( Q @ X3 ) )
% 0.28/0.47 => ( ( collect_nat @ P2 )
% 0.28/0.47 = ( collect_nat @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_cong
% 0.28/0.47 thf(fact_118_Collect__cong,axiom,
% 0.28/0.47 ! [P2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 = ( Q @ X3 ) )
% 0.28/0.47 => ( ( collec1111687558lle_tv @ P2 )
% 0.28/0.47 = ( collec1111687558lle_tv @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_cong
% 0.28/0.47 thf(fact_119_bex__imageD,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ? [X4: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X4 @ ( image_1187894195lle_tv @ F @ A ) )
% 0.28/0.47 & ( P2 @ X4 ) )
% 0.28/0.47 => ? [X3: list_char] :
% 0.28/0.47 ( ( member_list_char @ X3 @ A )
% 0.28/0.47 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bex_imageD
% 0.28/0.47 thf(fact_120_bex__imageD,axiom,
% 0.28/0.47 ! [F: $o > $o,A: set_o,P2: $o > $o] :
% 0.28/0.47 ( ? [X4: $o] :
% 0.28/0.47 ( ( member_o @ X4 @ ( image_o_o @ F @ A ) )
% 0.28/0.47 & ( P2 @ X4 ) )
% 0.28/0.47 => ? [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ A )
% 0.28/0.47 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bex_imageD
% 0.28/0.47 thf(fact_121_image__iff,axiom,
% 0.28/0.47 ! [Z2: $o,F: $o > $o,A: set_o] :
% 0.28/0.47 ( ( member_o @ Z2 @ ( image_o_o @ F @ A ) )
% 0.28/0.47 = ( ? [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ A )
% 0.28/0.47 & ( Z2
% 0.28/0.47 = ( F @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_iff
% 0.28/0.47 thf(fact_122_image__iff,axiom,
% 0.28/0.47 ! [Z2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 0.28/0.47 ( ( member266900804lle_tv @ Z2 @ ( image_1187894195lle_tv @ F @ A ) )
% 0.28/0.47 = ( ? [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ A )
% 0.28/0.47 & ( Z2
% 0.28/0.47 = ( F @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_iff
% 0.28/0.47 thf(fact_123_imageI,axiom,
% 0.28/0.47 ! [X2: $o,A: set_o,F: $o > $o] :
% 0.28/0.47 ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( member_o @ ( F @ X2 ) @ ( image_o_o @ F @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_124_imageI,axiom,
% 0.28/0.47 ! [X2: $o,A: set_o,F: $o > list_char] :
% 0.28/0.47 ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( member_list_char @ ( F @ X2 ) @ ( image_o_list_char @ F @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_125_imageI,axiom,
% 0.28/0.47 ! [X2: $o,A: set_o,F: $o > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X2 ) @ ( image_1491822472lle_tv @ F @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_126_imageI,axiom,
% 0.28/0.47 ! [X2: list_char,A: set_list_char,F: list_char > $o] :
% 0.28/0.47 ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( member_o @ ( F @ X2 ) @ ( image_list_char_o @ F @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_127_imageI,axiom,
% 0.28/0.47 ! [X2: list_char,A: set_list_char,F: list_char > list_char] :
% 0.28/0.47 ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( member_list_char @ ( F @ X2 ) @ ( image_890964937t_char @ F @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_128_imageI,axiom,
% 0.28/0.47 ! [X2: list_char,A: set_list_char,F: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X2 ) @ ( image_1187894195lle_tv @ F @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_129_imageI,axiom,
% 0.28/0.47 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( member_o @ ( F @ X2 ) @ ( image_991799618e_tv_o @ F @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_130_imageI,axiom,
% 0.28/0.47 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > list_char] :
% 0.28/0.47 ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( member_list_char @ ( F @ X2 ) @ ( image_1971766583t_char @ F @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_131_imageI,axiom,
% 0.28/0.47 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X2 ) @ ( image_335818702lle_tv @ F @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_132_Collect__mono__iff,axiom,
% 0.28/0.47 ! [P2: nat > $o,Q: nat > $o] :
% 0.28/0.47 ( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) )
% 0.28/0.47 = ( ! [X: nat] :
% 0.28/0.47 ( ( P2 @ X )
% 0.28/0.47 => ( Q @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono_iff
% 0.28/0.47 thf(fact_133_Collect__mono__iff,axiom,
% 0.28/0.47 ! [P2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ ( collec1111687558lle_tv @ P2 ) @ ( collec1111687558lle_tv @ Q ) )
% 0.28/0.47 = ( ! [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( P2 @ X )
% 0.28/0.47 => ( Q @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono_iff
% 0.28/0.47 thf(fact_134_Collect__mono__iff,axiom,
% 0.28/0.47 ! [P2: $o > $o,Q: $o > $o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q ) )
% 0.28/0.47 = ( ! [X: $o] :
% 0.28/0.47 ( ( P2 @ X )
% 0.28/0.47 => ( Q @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono_iff
% 0.28/0.47 thf(fact_135_set__eq__subset,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_Pa1764573435lle_tv,Z: set_Pa1764573435lle_tv] : ( Y2 = Z ) )
% 0.28/0.47 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A2 @ B3 )
% 0.28/0.47 & ( ord_le241064091lle_tv @ B3 @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_eq_subset
% 0.28/0.47 thf(fact_136_set__eq__subset,axiom,
% 0.28/0.47 ( ( ^ [Y2: set_o,Z: set_o] : ( Y2 = Z ) )
% 0.28/0.47 = ( ^ [A2: set_o,B3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A2 @ B3 )
% 0.28/0.47 & ( ord_less_eq_set_o @ B3 @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_eq_subset
% 0.28/0.47 thf(fact_137_subset__trans,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C2: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A @ B )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B @ C2 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_trans
% 0.28/0.47 thf(fact_138_subset__trans,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o,C2: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B @ C2 )
% 0.28/0.47 => ( ord_less_eq_set_o @ A @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_trans
% 0.28/0.47 thf(fact_139_Collect__mono,axiom,
% 0.28/0.47 ! [P2: nat > $o,Q: nat > $o] :
% 0.28/0.47 ( ! [X3: nat] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( Q @ X3 ) )
% 0.28/0.47 => ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono
% 0.28/0.47 thf(fact_140_Collect__mono,axiom,
% 0.28/0.47 ! [P2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( Q @ X3 ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( collec1111687558lle_tv @ P2 ) @ ( collec1111687558lle_tv @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono
% 0.28/0.47 thf(fact_141_Collect__mono,axiom,
% 0.28/0.47 ! [P2: $o > $o,Q: $o > $o] :
% 0.28/0.47 ( ! [X3: $o] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( Q @ X3 ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono
% 0.28/0.47 thf(fact_142_subset__refl,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ A ) ).
% 0.28/0.47
% 0.28/0.47 % subset_refl
% 0.28/0.47 thf(fact_143_subset__refl,axiom,
% 0.28/0.47 ! [A: set_o] : ( ord_less_eq_set_o @ A @ A ) ).
% 0.28/0.47
% 0.28/0.47 % subset_refl
% 0.28/0.47 thf(fact_144_subset__iff,axiom,
% 0.28/0.47 ( ord_le1836582007t_char
% 0.28/0.47 = ( ^ [A2: set_list_char,B3: set_list_char] :
% 0.28/0.47 ! [T: list_char] :
% 0.28/0.47 ( ( member_list_char @ T @ A2 )
% 0.28/0.47 => ( member_list_char @ T @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff
% 0.28/0.47 thf(fact_145_subset__iff,axiom,
% 0.28/0.47 ( ord_le241064091lle_tv
% 0.28/0.47 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ! [T: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ T @ A2 )
% 0.28/0.47 => ( member266900804lle_tv @ T @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff
% 0.28/0.47 thf(fact_146_subset__iff,axiom,
% 0.28/0.47 ( ord_less_eq_set_o
% 0.28/0.47 = ( ^ [A2: set_o,B3: set_o] :
% 0.28/0.47 ! [T: $o] :
% 0.28/0.47 ( ( member_o @ T @ A2 )
% 0.28/0.47 => ( member_o @ T @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff
% 0.28/0.47 thf(fact_147_equalityD2,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_le241064091lle_tv @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD2
% 0.28/0.47 thf(fact_148_equalityD2,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_less_eq_set_o @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD2
% 0.28/0.47 thf(fact_149_equalityD1,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_le241064091lle_tv @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD1
% 0.28/0.47 thf(fact_150_equalityD1,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ord_less_eq_set_o @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD1
% 0.28/0.47 thf(fact_151_subset__eq,axiom,
% 0.28/0.47 ( ord_le1836582007t_char
% 0.28/0.47 = ( ^ [A2: set_list_char,B3: set_list_char] :
% 0.28/0.47 ! [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ A2 )
% 0.28/0.47 => ( member_list_char @ X @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_eq
% 0.28/0.47 thf(fact_152_subset__eq,axiom,
% 0.28/0.47 ( ord_le241064091lle_tv
% 0.28/0.47 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ! [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ A2 )
% 0.28/0.47 => ( member266900804lle_tv @ X @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_eq
% 0.28/0.47 thf(fact_153_subset__eq,axiom,
% 0.28/0.47 ( ord_less_eq_set_o
% 0.28/0.47 = ( ^ [A2: set_o,B3: set_o] :
% 0.28/0.47 ! [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ A2 )
% 0.28/0.47 => ( member_o @ X @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_eq
% 0.28/0.47 thf(fact_154_equalityE,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ~ ( ( ord_le241064091lle_tv @ A @ B )
% 0.28/0.47 => ~ ( ord_le241064091lle_tv @ B @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityE
% 0.28/0.47 thf(fact_155_equalityE,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ~ ( ( ord_less_eq_set_o @ A @ B )
% 0.28/0.47 => ~ ( ord_less_eq_set_o @ B @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityE
% 0.28/0.47 thf(fact_156_subsetD,axiom,
% 0.28/0.47 ! [A: set_list_char,B: set_list_char,C: list_char] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ A @ B )
% 0.28/0.47 => ( ( member_list_char @ C @ A )
% 0.28/0.47 => ( member_list_char @ C @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetD
% 0.28/0.47 thf(fact_157_subsetD,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A @ B )
% 0.28/0.47 => ( ( member266900804lle_tv @ C @ A )
% 0.28/0.47 => ( member266900804lle_tv @ C @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetD
% 0.28/0.47 thf(fact_158_subsetD,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o,C: $o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.28/0.47 => ( ( member_o @ C @ A )
% 0.28/0.47 => ( member_o @ C @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetD
% 0.28/0.47 thf(fact_159_in__mono,axiom,
% 0.28/0.47 ! [A: set_list_char,B: set_list_char,X2: list_char] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ A @ B )
% 0.28/0.47 => ( ( member_list_char @ X2 @ A )
% 0.28/0.47 => ( member_list_char @ X2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_mono
% 0.28/0.47 thf(fact_160_in__mono,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,X2: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A @ B )
% 0.28/0.47 => ( ( member266900804lle_tv @ X2 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ X2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_mono
% 0.28/0.47 thf(fact_161_in__mono,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o,X2: $o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.28/0.47 => ( ( member_o @ X2 @ A )
% 0.28/0.47 => ( member_o @ X2 @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_mono
% 0.28/0.47 thf(fact_162_UNIV__witness,axiom,
% 0.28/0.47 ? [X3: paraco1605129243lle_tv] : ( member266900804lle_tv @ X3 @ top_to1057771083lle_tv ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_witness
% 0.28/0.47 thf(fact_163_UNIV__witness,axiom,
% 0.28/0.47 ? [X3: list_char] : ( member_list_char @ X3 @ top_to748628679t_char ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_witness
% 0.28/0.47 thf(fact_164_UNIV__witness,axiom,
% 0.28/0.47 ? [X3: $o] : ( member_o @ X3 @ top_top_set_o ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_witness
% 0.28/0.47 thf(fact_165_UNIV__eq__I,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] : ( member266900804lle_tv @ X3 @ A )
% 0.28/0.47 => ( top_to1057771083lle_tv = A ) ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_eq_I
% 0.28/0.47 thf(fact_166_UNIV__eq__I,axiom,
% 0.28/0.47 ! [A: set_list_char] :
% 0.28/0.47 ( ! [X3: list_char] : ( member_list_char @ X3 @ A )
% 0.28/0.47 => ( top_to748628679t_char = A ) ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_eq_I
% 0.28/0.47 thf(fact_167_UNIV__eq__I,axiom,
% 0.28/0.47 ! [A: set_o] :
% 0.28/0.47 ( ! [X3: $o] : ( member_o @ X3 @ A )
% 0.28/0.47 => ( top_top_set_o = A ) ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_eq_I
% 0.28/0.47 thf(fact_168_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: $o > $o,A: set_o,P2: $o > $o] :
% 0.28/0.47 ( ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ ( image_o_o @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_o_o @ F
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_169_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: nat > $o,A: set_nat,P2: $o > $o] :
% 0.28/0.47 ( ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ ( image_nat_o @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_nat_o @ F
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_170_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv,P2: $o > $o] :
% 0.28/0.47 ( ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ ( image_991799618e_tv_o @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_991799618e_tv_o @ F
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_171_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: $o > nat,A: set_o,P2: nat > $o] :
% 0.28/0.47 ( ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ ( image_o_nat @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_o_nat @ F
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_172_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: nat > nat,A: set_nat,P2: nat > $o] :
% 0.28/0.47 ( ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ ( image_nat_nat @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_nat_nat @ F
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_173_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: paraco1605129243lle_tv > nat,A: set_Pa1764573435lle_tv,P2: nat > $o] :
% 0.28/0.47 ( ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ ( image_376325286tv_nat @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_376325286tv_nat @ F
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_174_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: $o > paraco1605129243lle_tv,A: set_o,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ ( image_1491822472lle_tv @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_1491822472lle_tv @ F
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_175_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: nat > paraco1605129243lle_tv,A: set_nat,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ ( image_1151963140lle_tv @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_1151963140lle_tv @ F
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_176_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_335818702lle_tv @ F
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_177_Compr__image__eq,axiom,
% 0.28/0.47 ! [F: list_char > $o,A: set_list_char,P2: $o > $o] :
% 0.28/0.47 ( ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ ( image_list_char_o @ F @ A ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( image_list_char_o @ F
% 0.28/0.47 @ ( collect_list_char
% 0.28/0.47 @ ^ [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ A )
% 0.28/0.47 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Compr_image_eq
% 0.28/0.47 thf(fact_178_image__image,axiom,
% 0.28/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 0.28/0.47 ( ( image_335818702lle_tv @ F @ ( image_1187894195lle_tv @ G @ A ) )
% 0.28/0.47 = ( image_1187894195lle_tv
% 0.28/0.47 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 0.28/0.47 @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_image
% 0.28/0.47 thf(fact_179_image__image,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,G: list_char > list_char,A: set_list_char] :
% 0.28/0.47 ( ( image_1187894195lle_tv @ F @ ( image_890964937t_char @ G @ A ) )
% 0.28/0.47 = ( image_1187894195lle_tv
% 0.28/0.47 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 0.28/0.47 @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_image
% 0.28/0.47 thf(fact_180_image__image,axiom,
% 0.28/0.47 ! [F: $o > $o,G: $o > $o,A: set_o] :
% 0.28/0.47 ( ( image_o_o @ F @ ( image_o_o @ G @ A ) )
% 0.28/0.47 = ( image_o_o
% 0.28/0.47 @ ^ [X: $o] : ( F @ ( G @ X ) )
% 0.28/0.47 @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_image
% 0.28/0.47 thf(fact_181_imageE,axiom,
% 0.28/0.47 ! [B2: $o,F: $o > $o,A: set_o] :
% 0.28/0.47 ( ( member_o @ B2 @ ( image_o_o @ F @ A ) )
% 0.28/0.47 => ~ ! [X3: $o] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X3 ) )
% 0.28/0.47 => ~ ( member_o @ X3 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageE
% 0.28/0.47 thf(fact_182_imageE,axiom,
% 0.28/0.47 ! [B2: $o,F: list_char > $o,A: set_list_char] :
% 0.28/0.47 ( ( member_o @ B2 @ ( image_list_char_o @ F @ A ) )
% 0.28/0.47 => ~ ! [X3: list_char] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X3 ) )
% 0.28/0.47 => ~ ( member_list_char @ X3 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageE
% 0.28/0.47 thf(fact_183_imageE,axiom,
% 0.28/0.47 ! [B2: $o,F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( member_o @ B2 @ ( image_991799618e_tv_o @ F @ A ) )
% 0.28/0.47 => ~ ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X3 ) )
% 0.28/0.47 => ~ ( member266900804lle_tv @ X3 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageE
% 0.28/0.47 thf(fact_184_imageE,axiom,
% 0.28/0.47 ! [B2: list_char,F: $o > list_char,A: set_o] :
% 0.28/0.47 ( ( member_list_char @ B2 @ ( image_o_list_char @ F @ A ) )
% 0.28/0.47 => ~ ! [X3: $o] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X3 ) )
% 0.28/0.47 => ~ ( member_o @ X3 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageE
% 0.28/0.47 thf(fact_185_imageE,axiom,
% 0.28/0.47 ! [B2: list_char,F: list_char > list_char,A: set_list_char] :
% 0.28/0.47 ( ( member_list_char @ B2 @ ( image_890964937t_char @ F @ A ) )
% 0.28/0.47 => ~ ! [X3: list_char] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X3 ) )
% 0.28/0.47 => ~ ( member_list_char @ X3 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageE
% 0.28/0.47 thf(fact_186_imageE,axiom,
% 0.28/0.47 ! [B2: list_char,F: paraco1605129243lle_tv > list_char,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( member_list_char @ B2 @ ( image_1971766583t_char @ F @ A ) )
% 0.28/0.47 => ~ ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X3 ) )
% 0.28/0.47 => ~ ( member266900804lle_tv @ X3 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageE
% 0.28/0.47 thf(fact_187_imageE,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv,A: set_o] :
% 0.28/0.47 ( ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ A ) )
% 0.28/0.47 => ~ ! [X3: $o] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X3 ) )
% 0.28/0.47 => ~ ( member_o @ X3 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageE
% 0.28/0.47 thf(fact_188_imageE,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 0.28/0.47 ( ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ A ) )
% 0.28/0.47 => ~ ! [X3: list_char] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X3 ) )
% 0.28/0.47 => ~ ( member_list_char @ X3 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageE
% 0.28/0.47 thf(fact_189_imageE,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) )
% 0.28/0.47 => ~ ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X3 ) )
% 0.28/0.47 => ~ ( member266900804lle_tv @ X3 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageE
% 0.28/0.47 thf(fact_190_Collect__restrict,axiom,
% 0.28/0.47 ! [X5: set_list_char,P2: list_char > $o] :
% 0.28/0.47 ( ord_le1836582007t_char
% 0.28/0.47 @ ( collect_list_char
% 0.28/0.47 @ ^ [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ X5 )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 @ X5 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_restrict
% 0.28/0.47 thf(fact_191_Collect__restrict,axiom,
% 0.28/0.47 ! [X5: set_nat,P2: nat > $o] :
% 0.28/0.47 ( ord_less_eq_set_nat
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ X5 )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 @ X5 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_restrict
% 0.28/0.47 thf(fact_192_Collect__restrict,axiom,
% 0.28/0.47 ! [X5: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ord_le241064091lle_tv
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ X5 )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 @ X5 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_restrict
% 0.28/0.47 thf(fact_193_Collect__restrict,axiom,
% 0.28/0.47 ! [X5: set_o,P2: $o > $o] :
% 0.28/0.47 ( ord_less_eq_set_o
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ X5 )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 @ X5 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_restrict
% 0.28/0.47 thf(fact_194_prop__restrict,axiom,
% 0.28/0.47 ! [X2: list_char,Z3: set_list_char,X5: set_list_char,P2: list_char > $o] :
% 0.28/0.47 ( ( member_list_char @ X2 @ Z3 )
% 0.28/0.47 => ( ( ord_le1836582007t_char @ Z3
% 0.28/0.47 @ ( collect_list_char
% 0.28/0.47 @ ^ [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ X5 )
% 0.28/0.47 & ( P2 @ X ) ) ) )
% 0.28/0.47 => ( P2 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prop_restrict
% 0.28/0.47 thf(fact_195_prop__restrict,axiom,
% 0.28/0.47 ! [X2: nat,Z3: set_nat,X5: set_nat,P2: nat > $o] :
% 0.28/0.47 ( ( member_nat @ X2 @ Z3 )
% 0.28/0.47 => ( ( ord_less_eq_set_nat @ Z3
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ X5 )
% 0.28/0.47 & ( P2 @ X ) ) ) )
% 0.28/0.47 => ( P2 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prop_restrict
% 0.28/0.47 thf(fact_196_prop__restrict,axiom,
% 0.28/0.47 ! [X2: paraco1605129243lle_tv,Z3: set_Pa1764573435lle_tv,X5: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( member266900804lle_tv @ X2 @ Z3 )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ Z3
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ X5 )
% 0.28/0.47 & ( P2 @ X ) ) ) )
% 0.28/0.47 => ( P2 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prop_restrict
% 0.28/0.47 thf(fact_197_prop__restrict,axiom,
% 0.28/0.47 ! [X2: $o,Z3: set_o,X5: set_o,P2: $o > $o] :
% 0.28/0.47 ( ( member_o @ X2 @ Z3 )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ Z3
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ X5 )
% 0.28/0.47 & ( P2 @ X ) ) ) )
% 0.28/0.47 => ( P2 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prop_restrict
% 0.28/0.47 thf(fact_198_Collect__subset,axiom,
% 0.28/0.47 ! [A: set_list_char,P2: list_char > $o] :
% 0.28/0.47 ( ord_le1836582007t_char
% 0.28/0.47 @ ( collect_list_char
% 0.28/0.47 @ ^ [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 @ A ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_subset
% 0.28/0.47 thf(fact_199_Collect__subset,axiom,
% 0.28/0.47 ! [A: set_nat,P2: nat > $o] :
% 0.28/0.47 ( ord_less_eq_set_nat
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 @ A ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_subset
% 0.28/0.47 thf(fact_200_Collect__subset,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ord_le241064091lle_tv
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 @ A ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_subset
% 0.28/0.47 thf(fact_201_Collect__subset,axiom,
% 0.28/0.47 ! [A: set_o,P2: $o > $o] :
% 0.28/0.47 ( ord_less_eq_set_o
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 @ A ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_subset
% 0.28/0.47 thf(fact_202_UNIV__def,axiom,
% 0.28/0.47 ( top_top_set_nat
% 0.28/0.47 = ( collect_nat
% 0.28/0.47 @ ^ [X: nat] : $true ) ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_def
% 0.28/0.47 thf(fact_203_UNIV__def,axiom,
% 0.28/0.47 ( top_to1057771083lle_tv
% 0.28/0.47 = ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] : $true ) ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_def
% 0.28/0.47 thf(fact_204_UNIV__def,axiom,
% 0.28/0.47 ( top_to748628679t_char
% 0.28/0.47 = ( collect_list_char
% 0.28/0.47 @ ^ [X: list_char] : $true ) ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_def
% 0.28/0.47 thf(fact_205_UNIV__def,axiom,
% 0.28/0.47 ( top_top_set_o
% 0.28/0.47 = ( collect_o
% 0.28/0.47 @ ^ [X: $o] : $true ) ) ).
% 0.28/0.47
% 0.28/0.47 % UNIV_def
% 0.28/0.47 thf(fact_206_top_Oextremum__uniqueI,axiom,
% 0.28/0.47 ! [A3: set_list_char] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ top_to748628679t_char @ A3 )
% 0.28/0.47 => ( A3 = top_to748628679t_char ) ) ).
% 0.28/0.47
% 0.28/0.47 % top.extremum_uniqueI
% 0.28/0.47 thf(fact_207_top_Oextremum__uniqueI,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A3 )
% 0.28/0.47 => ( A3 = top_to1057771083lle_tv ) ) ).
% 0.28/0.47
% 0.28/0.47 % top.extremum_uniqueI
% 0.28/0.47 thf(fact_208_top_Oextremum__uniqueI,axiom,
% 0.28/0.47 ! [A3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ top_top_set_o @ A3 )
% 0.28/0.47 => ( A3 = top_top_set_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % top.extremum_uniqueI
% 0.28/0.47 thf(fact_209_top_Oextremum__unique,axiom,
% 0.28/0.47 ! [A3: set_list_char] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ top_to748628679t_char @ A3 )
% 0.28/0.47 = ( A3 = top_to748628679t_char ) ) ).
% 0.28/0.47
% 0.28/0.47 % top.extremum_unique
% 0.28/0.47 thf(fact_210_top_Oextremum__unique,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A3 )
% 0.28/0.47 = ( A3 = top_to1057771083lle_tv ) ) ).
% 0.28/0.47
% 0.28/0.47 % top.extremum_unique
% 0.28/0.47 thf(fact_211_top_Oextremum__unique,axiom,
% 0.28/0.47 ! [A3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ top_top_set_o @ A3 )
% 0.28/0.47 = ( A3 = top_top_set_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % top.extremum_unique
% 0.28/0.47 thf(fact_212_top__greatest,axiom,
% 0.28/0.47 ! [A3: set_list_char] : ( ord_le1836582007t_char @ A3 @ top_to748628679t_char ) ).
% 0.28/0.47
% 0.28/0.47 % top_greatest
% 0.28/0.47 thf(fact_213_top__greatest,axiom,
% 0.28/0.47 ! [A3: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A3 @ top_to1057771083lle_tv ) ).
% 0.28/0.47
% 0.28/0.47 % top_greatest
% 0.28/0.47 thf(fact_214_top__greatest,axiom,
% 0.28/0.47 ! [A3: set_o] : ( ord_less_eq_set_o @ A3 @ top_top_set_o ) ).
% 0.28/0.47
% 0.28/0.47 % top_greatest
% 0.28/0.47 thf(fact_215_subset__image__iff,axiom,
% 0.28/0.47 ! [B: set_Pa1764573435lle_tv,F: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B @ ( image_1187894195lle_tv @ F @ A ) )
% 0.28/0.47 = ( ? [AA: set_list_char] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ AA @ A )
% 0.28/0.47 & ( B
% 0.28/0.47 = ( image_1187894195lle_tv @ F @ AA ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_image_iff
% 0.28/0.47 thf(fact_216_subset__image__iff,axiom,
% 0.28/0.47 ! [B: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B @ ( image_335818702lle_tv @ F @ A ) )
% 0.28/0.47 = ( ? [AA: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ AA @ A )
% 0.28/0.47 & ( B
% 0.28/0.47 = ( image_335818702lle_tv @ F @ AA ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_image_iff
% 0.28/0.47 thf(fact_217_subset__image__iff,axiom,
% 0.28/0.47 ! [B: set_Pa1764573435lle_tv,F: $o > paraco1605129243lle_tv,A: set_o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B @ ( image_1491822472lle_tv @ F @ A ) )
% 0.28/0.47 = ( ? [AA: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ AA @ A )
% 0.28/0.47 & ( B
% 0.28/0.47 = ( image_1491822472lle_tv @ F @ AA ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_image_iff
% 0.28/0.47 thf(fact_218_subset__image__iff,axiom,
% 0.28/0.47 ! [B: set_o,F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B @ ( image_991799618e_tv_o @ F @ A ) )
% 0.28/0.47 = ( ? [AA: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ AA @ A )
% 0.28/0.47 & ( B
% 0.28/0.47 = ( image_991799618e_tv_o @ F @ AA ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_image_iff
% 0.28/0.47 thf(fact_219_subset__image__iff,axiom,
% 0.28/0.47 ! [B: set_o,F: $o > $o,A: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B @ ( image_o_o @ F @ A ) )
% 0.28/0.47 = ( ? [AA: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ AA @ A )
% 0.28/0.47 & ( B
% 0.28/0.47 = ( image_o_o @ F @ AA ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_image_iff
% 0.28/0.47 thf(fact_220_image__subset__iff,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ B )
% 0.28/0.47 = ( ! [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ A )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X ) @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subset_iff
% 0.28/0.47 thf(fact_221_image__subset__iff,axiom,
% 0.28/0.47 ! [F: $o > $o,A: set_o,B: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ B )
% 0.28/0.47 = ( ! [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ A )
% 0.28/0.47 => ( member_o @ ( F @ X ) @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subset_iff
% 0.28/0.47 thf(fact_222_subset__imageE,axiom,
% 0.28/0.47 ! [B: set_Pa1764573435lle_tv,F: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B @ ( image_1187894195lle_tv @ F @ A ) )
% 0.28/0.47 => ~ ! [C3: set_list_char] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ C3 @ A )
% 0.28/0.47 => ( B
% 0.28/0.47 != ( image_1187894195lle_tv @ F @ C3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_imageE
% 0.28/0.47 thf(fact_223_subset__imageE,axiom,
% 0.28/0.47 ! [B: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B @ ( image_335818702lle_tv @ F @ A ) )
% 0.28/0.47 => ~ ! [C3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ C3 @ A )
% 0.28/0.47 => ( B
% 0.28/0.47 != ( image_335818702lle_tv @ F @ C3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_imageE
% 0.28/0.47 thf(fact_224_subset__imageE,axiom,
% 0.28/0.47 ! [B: set_Pa1764573435lle_tv,F: $o > paraco1605129243lle_tv,A: set_o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B @ ( image_1491822472lle_tv @ F @ A ) )
% 0.28/0.47 => ~ ! [C3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ C3 @ A )
% 0.28/0.47 => ( B
% 0.28/0.47 != ( image_1491822472lle_tv @ F @ C3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_imageE
% 0.28/0.47 thf(fact_225_subset__imageE,axiom,
% 0.28/0.47 ! [B: set_o,F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B @ ( image_991799618e_tv_o @ F @ A ) )
% 0.28/0.47 => ~ ! [C3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ C3 @ A )
% 0.28/0.47 => ( B
% 0.28/0.47 != ( image_991799618e_tv_o @ F @ C3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_imageE
% 0.28/0.47 thf(fact_226_subset__imageE,axiom,
% 0.28/0.47 ! [B: set_o,F: $o > $o,A: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B @ ( image_o_o @ F @ A ) )
% 0.28/0.47 => ~ ! [C3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ C3 @ A )
% 0.28/0.47 => ( B
% 0.28/0.47 != ( image_o_o @ F @ C3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_imageE
% 0.28/0.47 thf(fact_227_image__subsetI,axiom,
% 0.28/0.47 ! [A: set_o,F: $o > list_char,B: set_list_char] :
% 0.28/0.47 ( ! [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ A )
% 0.28/0.47 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le1836582007t_char @ ( image_o_list_char @ F @ A ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_228_image__subsetI,axiom,
% 0.28/0.47 ! [A: set_list_char,F: list_char > list_char,B: set_list_char] :
% 0.28/0.47 ( ! [X3: list_char] :
% 0.28/0.47 ( ( member_list_char @ X3 @ A )
% 0.28/0.47 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le1836582007t_char @ ( image_890964937t_char @ F @ A ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_229_image__subsetI,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > list_char,B: set_list_char] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X3 @ A )
% 0.28/0.47 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le1836582007t_char @ ( image_1971766583t_char @ F @ A ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_230_image__subsetI,axiom,
% 0.28/0.47 ! [A: set_o,F: $o > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ! [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( image_1491822472lle_tv @ F @ A ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_231_image__subsetI,axiom,
% 0.28/0.47 ! [A: set_list_char,F: list_char > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ! [X3: list_char] :
% 0.28/0.47 ( ( member_list_char @ X3 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_232_image__subsetI,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X3 @ A )
% 0.28/0.47 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ A ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_233_image__subsetI,axiom,
% 0.28/0.47 ! [A: set_o,F: $o > $o,B: set_o] :
% 0.28/0.47 ( ! [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ A )
% 0.28/0.47 => ( member_o @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_234_image__subsetI,axiom,
% 0.28/0.47 ! [A: set_list_char,F: list_char > $o,B: set_o] :
% 0.28/0.47 ( ! [X3: list_char] :
% 0.28/0.47 ( ( member_list_char @ X3 @ A )
% 0.28/0.47 => ( member_o @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( image_list_char_o @ F @ A ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_235_image__subsetI,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > $o,B: set_o] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X3 @ A )
% 0.28/0.47 => ( member_o @ ( F @ X3 ) @ B ) )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ F @ A ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_236_image__mono,axiom,
% 0.28/0.47 ! [A: set_list_char,B: set_list_char,F: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ A @ B )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ ( image_1187894195lle_tv @ F @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_mono
% 0.28/0.47 thf(fact_237_image__mono,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A @ B )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ A ) @ ( image_335818702lle_tv @ F @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_mono
% 0.28/0.47 thf(fact_238_image__mono,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A @ B )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ F @ A ) @ ( image_991799618e_tv_o @ F @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_mono
% 0.28/0.47 thf(fact_239_image__mono,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o,F: $o > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.28/0.47 => ( ord_le241064091lle_tv @ ( image_1491822472lle_tv @ F @ A ) @ ( image_1491822472lle_tv @ F @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_mono
% 0.28/0.47 thf(fact_240_image__mono,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o,F: $o > $o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.28/0.47 => ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ ( image_o_o @ F @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_mono
% 0.28/0.47 thf(fact_241_range__eqI,axiom,
% 0.28/0.47 ! [B2: $o,F: list_char > $o,X2: list_char] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_o @ B2 @ ( image_list_char_o @ F @ top_to748628679t_char ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_eqI
% 0.28/0.47 thf(fact_242_range__eqI,axiom,
% 0.28/0.47 ! [B2: list_char,F: list_char > list_char,X2: list_char] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_list_char @ B2 @ ( image_890964937t_char @ F @ top_to748628679t_char ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_eqI
% 0.28/0.47 thf(fact_243_range__eqI,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv,X2: list_char] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ top_to748628679t_char ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_eqI
% 0.28/0.47 thf(fact_244_range__eqI,axiom,
% 0.28/0.47 ! [B2: $o,F: $o > $o,X2: $o] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_o @ B2 @ ( image_o_o @ F @ top_top_set_o ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_eqI
% 0.28/0.47 thf(fact_245_range__eqI,axiom,
% 0.28/0.47 ! [B2: list_char,F: $o > list_char,X2: $o] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member_list_char @ B2 @ ( image_o_list_char @ F @ top_top_set_o ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_eqI
% 0.28/0.47 thf(fact_246_range__eqI,axiom,
% 0.28/0.47 ! [B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv,X2: $o] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ top_top_set_o ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % range_eqI
% 0.28/0.47 thf(fact_247_rangeI,axiom,
% 0.28/0.47 ! [F: list_char > $o,X2: list_char] : ( member_o @ ( F @ X2 ) @ ( image_list_char_o @ F @ top_to748628679t_char ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeI
% 0.28/0.47 thf(fact_248_rangeI,axiom,
% 0.28/0.47 ! [F: list_char > list_char,X2: list_char] : ( member_list_char @ ( F @ X2 ) @ ( image_890964937t_char @ F @ top_to748628679t_char ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeI
% 0.28/0.47 thf(fact_249_rangeI,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,X2: list_char] : ( member266900804lle_tv @ ( F @ X2 ) @ ( image_1187894195lle_tv @ F @ top_to748628679t_char ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeI
% 0.28/0.47 thf(fact_250_rangeI,axiom,
% 0.28/0.47 ! [F: $o > $o,X2: $o] : ( member_o @ ( F @ X2 ) @ ( image_o_o @ F @ top_top_set_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeI
% 0.28/0.47 thf(fact_251_rangeI,axiom,
% 0.28/0.47 ! [F: $o > list_char,X2: $o] : ( member_list_char @ ( F @ X2 ) @ ( image_o_list_char @ F @ top_top_set_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeI
% 0.28/0.47 thf(fact_252_rangeI,axiom,
% 0.28/0.47 ! [F: $o > paraco1605129243lle_tv,X2: $o] : ( member266900804lle_tv @ ( F @ X2 ) @ ( image_1491822472lle_tv @ F @ top_top_set_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % rangeI
% 0.28/0.47 thf(fact_253_subset__UNIV,axiom,
% 0.28/0.47 ! [A: set_list_char] : ( ord_le1836582007t_char @ A @ top_to748628679t_char ) ).
% 0.28/0.47
% 0.28/0.47 % subset_UNIV
% 0.28/0.47 thf(fact_254_subset__UNIV,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ) ).
% 0.28/0.47
% 0.28/0.47 % subset_UNIV
% 0.28/0.47 thf(fact_255_subset__UNIV,axiom,
% 0.28/0.47 ! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ) ).
% 0.28/0.47
% 0.28/0.47 % subset_UNIV
% 0.28/0.47 thf(fact_256_surj__def,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ( image_1187894195lle_tv @ F @ top_to748628679t_char )
% 0.28/0.47 = top_to1057771083lle_tv )
% 0.28/0.47 = ( ! [Y4: paraco1605129243lle_tv] :
% 0.28/0.47 ? [X: list_char] :
% 0.28/0.47 ( Y4
% 0.28/0.47 = ( F @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surj_def
% 0.28/0.47 thf(fact_257_surj__def,axiom,
% 0.28/0.47 ! [F: list_char > list_char] :
% 0.28/0.47 ( ( ( image_890964937t_char @ F @ top_to748628679t_char )
% 0.28/0.47 = top_to748628679t_char )
% 0.28/0.47 = ( ! [Y4: list_char] :
% 0.28/0.47 ? [X: list_char] :
% 0.28/0.47 ( Y4
% 0.28/0.47 = ( F @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surj_def
% 0.28/0.47 thf(fact_258_surj__def,axiom,
% 0.28/0.47 ! [F: list_char > $o] :
% 0.28/0.47 ( ( ( image_list_char_o @ F @ top_to748628679t_char )
% 0.28/0.47 = top_top_set_o )
% 0.28/0.47 = ( ! [Y4: $o] :
% 0.28/0.47 ? [X: list_char] :
% 0.28/0.47 ( Y4
% 0.28/0.47 = ( F @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surj_def
% 0.28/0.47 thf(fact_259_surj__def,axiom,
% 0.28/0.47 ! [F: $o > list_char] :
% 0.28/0.47 ( ( ( image_o_list_char @ F @ top_top_set_o )
% 0.28/0.47 = top_to748628679t_char )
% 0.28/0.47 = ( ! [Y4: list_char] :
% 0.28/0.47 ? [X: $o] :
% 0.28/0.47 ( Y4
% 0.28/0.47 = ( F @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surj_def
% 0.28/0.47 thf(fact_260_surj__def,axiom,
% 0.28/0.47 ! [F: $o > $o] :
% 0.28/0.47 ( ( ( image_o_o @ F @ top_top_set_o )
% 0.28/0.47 = top_top_set_o )
% 0.28/0.47 = ( ! [Y4: $o] :
% 0.28/0.47 ? [X: $o] :
% 0.28/0.47 ( Y4
% 0.28/0.47 = ( F @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surj_def
% 0.28/0.47 thf(fact_261_surjI,axiom,
% 0.28/0.47 ! [G: list_char > paraco1605129243lle_tv,F: paraco1605129243lle_tv > list_char] :
% 0.28/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( G @ ( F @ X3 ) )
% 0.28/0.47 = X3 )
% 0.28/0.47 => ( ( image_1187894195lle_tv @ G @ top_to748628679t_char )
% 0.28/0.47 = top_to1057771083lle_tv ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjI
% 0.28/0.47 thf(fact_262_surjI,axiom,
% 0.28/0.47 ! [G: list_char > list_char,F: list_char > list_char] :
% 0.28/0.47 ( ! [X3: list_char] :
% 0.28/0.47 ( ( G @ ( F @ X3 ) )
% 0.28/0.47 = X3 )
% 0.28/0.47 => ( ( image_890964937t_char @ G @ top_to748628679t_char )
% 0.28/0.47 = top_to748628679t_char ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjI
% 0.28/0.47 thf(fact_263_surjI,axiom,
% 0.28/0.47 ! [G: list_char > $o,F: $o > list_char] :
% 0.28/0.47 ( ! [X3: $o] :
% 0.28/0.47 ( ( G @ ( F @ X3 ) )
% 0.28/0.47 = X3 )
% 0.28/0.47 => ( ( image_list_char_o @ G @ top_to748628679t_char )
% 0.28/0.47 = top_top_set_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjI
% 0.28/0.47 thf(fact_264_surjI,axiom,
% 0.28/0.47 ! [G: $o > list_char,F: list_char > $o] :
% 0.28/0.47 ( ! [X3: list_char] :
% 0.28/0.47 ( ( G @ ( F @ X3 ) )
% 0.28/0.47 = X3 )
% 0.28/0.47 => ( ( image_o_list_char @ G @ top_top_set_o )
% 0.28/0.47 = top_to748628679t_char ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjI
% 0.28/0.47 thf(fact_265_surjI,axiom,
% 0.28/0.47 ! [G: $o > $o,F: $o > $o] :
% 0.28/0.47 ( ! [X3: $o] :
% 0.28/0.47 ( ( G @ ( F @ X3 ) )
% 0.28/0.47 = X3 )
% 0.28/0.47 => ( ( image_o_o @ G @ top_top_set_o )
% 0.28/0.47 = top_top_set_o ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjI
% 0.28/0.47 thf(fact_266_surjE,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,Y3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ( image_1187894195lle_tv @ F @ top_to748628679t_char )
% 0.28/0.47 = top_to1057771083lle_tv )
% 0.28/0.47 => ~ ! [X3: list_char] :
% 0.28/0.47 ( Y3
% 0.28/0.47 != ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjE
% 0.28/0.47 thf(fact_267_surjE,axiom,
% 0.28/0.47 ! [F: list_char > list_char,Y3: list_char] :
% 0.28/0.47 ( ( ( image_890964937t_char @ F @ top_to748628679t_char )
% 0.28/0.47 = top_to748628679t_char )
% 0.28/0.47 => ~ ! [X3: list_char] :
% 0.28/0.47 ( Y3
% 0.28/0.47 != ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjE
% 0.28/0.47 thf(fact_268_surjE,axiom,
% 0.28/0.47 ! [F: list_char > $o,Y3: $o] :
% 0.28/0.47 ( ( ( image_list_char_o @ F @ top_to748628679t_char )
% 0.28/0.47 = top_top_set_o )
% 0.28/0.47 => ~ ! [X3: list_char] :
% 0.28/0.47 ( Y3
% 0.28/0.47 = ( ~ ( F @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjE
% 0.28/0.47 thf(fact_269_surjE,axiom,
% 0.28/0.47 ! [F: $o > list_char,Y3: list_char] :
% 0.28/0.47 ( ( ( image_o_list_char @ F @ top_top_set_o )
% 0.28/0.47 = top_to748628679t_char )
% 0.28/0.47 => ~ ! [X3: $o] :
% 0.28/0.47 ( Y3
% 0.28/0.47 != ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjE
% 0.28/0.47 thf(fact_270_surjE,axiom,
% 0.28/0.47 ! [F: $o > $o,Y3: $o] :
% 0.28/0.47 ( ( ( image_o_o @ F @ top_top_set_o )
% 0.28/0.47 = top_top_set_o )
% 0.28/0.47 => ~ ! [X3: $o] :
% 0.28/0.47 ( Y3
% 0.28/0.47 = ( ~ ( F @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjE
% 0.28/0.47 thf(fact_271_surjD,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,Y3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ( image_1187894195lle_tv @ F @ top_to748628679t_char )
% 0.28/0.47 = top_to1057771083lle_tv )
% 0.28/0.47 => ? [X3: list_char] :
% 0.28/0.47 ( Y3
% 0.28/0.47 = ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjD
% 0.28/0.47 thf(fact_272_surjD,axiom,
% 0.28/0.47 ! [F: list_char > list_char,Y3: list_char] :
% 0.28/0.47 ( ( ( image_890964937t_char @ F @ top_to748628679t_char )
% 0.28/0.47 = top_to748628679t_char )
% 0.28/0.47 => ? [X3: list_char] :
% 0.28/0.47 ( Y3
% 0.28/0.47 = ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjD
% 0.28/0.47 thf(fact_273_surjD,axiom,
% 0.28/0.47 ! [F: list_char > $o,Y3: $o] :
% 0.28/0.47 ( ( ( image_list_char_o @ F @ top_to748628679t_char )
% 0.28/0.47 = top_top_set_o )
% 0.28/0.47 => ? [X3: list_char] :
% 0.28/0.47 ( Y3
% 0.28/0.47 = ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjD
% 0.28/0.47 thf(fact_274_surjD,axiom,
% 0.28/0.47 ! [F: $o > list_char,Y3: list_char] :
% 0.28/0.47 ( ( ( image_o_list_char @ F @ top_top_set_o )
% 0.28/0.47 = top_to748628679t_char )
% 0.28/0.47 => ? [X3: $o] :
% 0.28/0.47 ( Y3
% 0.28/0.47 = ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjD
% 0.28/0.47 thf(fact_275_surjD,axiom,
% 0.28/0.47 ! [F: $o > $o,Y3: $o] :
% 0.28/0.47 ( ( ( image_o_o @ F @ top_top_set_o )
% 0.28/0.47 = top_top_set_o )
% 0.28/0.47 => ? [X3: $o] :
% 0.28/0.47 ( Y3
% 0.28/0.47 = ( F @ X3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % surjD
% 0.28/0.47 thf(fact_276_all__subset__image,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,P2: set_Pa1764573435lle_tv > $o] :
% 0.28/0.47 ( ( ! [B3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B3 @ ( image_1187894195lle_tv @ F @ A ) )
% 0.28/0.47 => ( P2 @ B3 ) ) )
% 0.28/0.47 = ( ! [B3: set_list_char] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ B3 @ A )
% 0.28/0.47 => ( P2 @ ( image_1187894195lle_tv @ F @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_subset_image
% 0.28/0.47 thf(fact_277_all__subset__image,axiom,
% 0.28/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,P2: set_Pa1764573435lle_tv > $o] :
% 0.28/0.47 ( ( ! [B3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B3 @ ( image_335818702lle_tv @ F @ A ) )
% 0.28/0.47 => ( P2 @ B3 ) ) )
% 0.28/0.47 = ( ! [B3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B3 @ A )
% 0.28/0.47 => ( P2 @ ( image_335818702lle_tv @ F @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_subset_image
% 0.28/0.47 thf(fact_278_all__subset__image,axiom,
% 0.28/0.47 ! [F: $o > paraco1605129243lle_tv,A: set_o,P2: set_Pa1764573435lle_tv > $o] :
% 0.28/0.47 ( ( ! [B3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B3 @ ( image_1491822472lle_tv @ F @ A ) )
% 0.28/0.47 => ( P2 @ B3 ) ) )
% 0.28/0.47 = ( ! [B3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B3 @ A )
% 0.28/0.47 => ( P2 @ ( image_1491822472lle_tv @ F @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_subset_image
% 0.28/0.47 thf(fact_279_all__subset__image,axiom,
% 0.28/0.47 ! [F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv,P2: set_o > $o] :
% 0.28/0.47 ( ( ! [B3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B3 @ ( image_991799618e_tv_o @ F @ A ) )
% 0.28/0.47 => ( P2 @ B3 ) ) )
% 0.28/0.47 = ( ! [B3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B3 @ A )
% 0.28/0.47 => ( P2 @ ( image_991799618e_tv_o @ F @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_subset_image
% 0.28/0.47 thf(fact_280_all__subset__image,axiom,
% 0.28/0.47 ! [F: $o > $o,A: set_o,P2: set_o > $o] :
% 0.28/0.47 ( ( ! [B3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B3 @ ( image_o_o @ F @ A ) )
% 0.28/0.47 => ( P2 @ B3 ) ) )
% 0.28/0.47 = ( ! [B3: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B3 @ A )
% 0.28/0.47 => ( P2 @ ( image_o_o @ F @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_subset_image
% 0.28/0.47 thf(fact_281_valid__def,axiom,
% 0.28/0.47 ( paraco327635598_valid
% 0.28/0.47 = ( ^ [P: paraco1604210848lle_fm] :
% 0.28/0.47 ! [I: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( paraco1325918602e_eval @ I @ P )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % valid_def
% 0.28/0.47 thf(fact_282_pred__subset__eq,axiom,
% 0.28/0.47 ! [R: set_list_char,S: set_list_char] :
% 0.28/0.47 ( ( ord_le1945897678char_o
% 0.28/0.47 @ ^ [X: list_char] : ( member_list_char @ X @ R )
% 0.28/0.47 @ ^ [X: list_char] : ( member_list_char @ X @ S ) )
% 0.28/0.47 = ( ord_le1836582007t_char @ R @ S ) ) ).
% 0.28/0.47
% 0.28/0.47 % pred_subset_eq
% 0.28/0.47 thf(fact_283_pred__subset__eq,axiom,
% 0.28/0.47 ! [R: set_Pa1764573435lle_tv,S: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le1632188418e_tv_o
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ R )
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ S ) )
% 0.28/0.47 = ( ord_le241064091lle_tv @ R @ S ) ) ).
% 0.28/0.47
% 0.28/0.47 % pred_subset_eq
% 0.28/0.47 thf(fact_284_pred__subset__eq,axiom,
% 0.28/0.47 ! [R: set_o,S: set_o] :
% 0.28/0.47 ( ( ord_less_eq_o_o
% 0.28/0.47 @ ^ [X: $o] : ( member_o @ X @ R )
% 0.28/0.47 @ ^ [X: $o] : ( member_o @ X @ S ) )
% 0.28/0.47 = ( ord_less_eq_set_o @ R @ S ) ) ).
% 0.28/0.47
% 0.28/0.47 % pred_subset_eq
% 0.28/0.47 thf(fact_285_subset__Collect__iff,axiom,
% 0.28/0.47 ! [B: set_list_char,A: set_list_char,P2: list_char > $o] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ B @ A )
% 0.28/0.47 => ( ( ord_le1836582007t_char @ B
% 0.28/0.47 @ ( collect_list_char
% 0.28/0.47 @ ^ [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) ) )
% 0.28/0.47 = ( ! [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ B )
% 0.28/0.47 => ( P2 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_Collect_iff
% 0.28/0.47 thf(fact_286_subset__Collect__iff,axiom,
% 0.28/0.47 ! [B: set_nat,A: set_nat,P2: nat > $o] :
% 0.28/0.47 ( ( ord_less_eq_set_nat @ B @ A )
% 0.28/0.47 => ( ( ord_less_eq_set_nat @ B
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) ) )
% 0.28/0.47 = ( ! [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ B )
% 0.28/0.47 => ( P2 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_Collect_iff
% 0.28/0.47 thf(fact_287_subset__Collect__iff,axiom,
% 0.28/0.47 ! [B: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B @ A )
% 0.28/0.47 => ( ( ord_le241064091lle_tv @ B
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) ) )
% 0.28/0.47 = ( ! [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ B )
% 0.28/0.47 => ( P2 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_Collect_iff
% 0.28/0.47 thf(fact_288_subset__Collect__iff,axiom,
% 0.28/0.47 ! [B: set_o,A: set_o,P2: $o > $o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B @ A )
% 0.28/0.47 => ( ( ord_less_eq_set_o @ B
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) ) )
% 0.28/0.47 = ( ! [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ B )
% 0.28/0.47 => ( P2 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_Collect_iff
% 0.28/0.47 thf(fact_289_subset__CollectI,axiom,
% 0.28/0.47 ! [B: set_list_char,A: set_list_char,Q: list_char > $o,P2: list_char > $o] :
% 0.28/0.47 ( ( ord_le1836582007t_char @ B @ A )
% 0.28/0.47 => ( ! [X3: list_char] :
% 0.28/0.47 ( ( member_list_char @ X3 @ B )
% 0.28/0.47 => ( ( Q @ X3 )
% 0.28/0.47 => ( P2 @ X3 ) ) )
% 0.28/0.47 => ( ord_le1836582007t_char
% 0.28/0.47 @ ( collect_list_char
% 0.28/0.47 @ ^ [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ B )
% 0.28/0.47 & ( Q @ X ) ) )
% 0.28/0.47 @ ( collect_list_char
% 0.28/0.47 @ ^ [X: list_char] :
% 0.28/0.47 ( ( member_list_char @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_CollectI
% 0.28/0.47 thf(fact_290_subset__CollectI,axiom,
% 0.28/0.47 ! [B: set_nat,A: set_nat,Q: nat > $o,P2: nat > $o] :
% 0.28/0.47 ( ( ord_less_eq_set_nat @ B @ A )
% 0.28/0.47 => ( ! [X3: nat] :
% 0.28/0.47 ( ( member_nat @ X3 @ B )
% 0.28/0.47 => ( ( Q @ X3 )
% 0.28/0.47 => ( P2 @ X3 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_nat
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ B )
% 0.28/0.47 & ( Q @ X ) ) )
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( member_nat @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_CollectI
% 0.28/0.47 thf(fact_291_subset__CollectI,axiom,
% 0.28/0.47 ! [B: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv,Q: paraco1605129243lle_tv > $o,P2: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ B @ A )
% 0.28/0.47 => ( ! [X3: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X3 @ B )
% 0.28/0.47 => ( ( Q @ X3 )
% 0.28/0.47 => ( P2 @ X3 ) ) )
% 0.28/0.47 => ( ord_le241064091lle_tv
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ B )
% 0.28/0.47 & ( Q @ X ) ) )
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( member266900804lle_tv @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_CollectI
% 0.28/0.47 thf(fact_292_subset__CollectI,axiom,
% 0.28/0.47 ! [B: set_o,A: set_o,Q: $o > $o,P2: $o > $o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ B @ A )
% 0.28/0.47 => ( ! [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ B )
% 0.28/0.47 => ( ( Q @ X3 )
% 0.28/0.47 => ( P2 @ X3 ) ) )
% 0.28/0.47 => ( ord_less_eq_set_o
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ B )
% 0.28/0.47 & ( Q @ X ) ) )
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( member_o @ X @ A )
% 0.28/0.47 & ( P2 @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_CollectI
% 0.28/0.47 thf(fact_293_conj__subset__def,axiom,
% 0.28/0.47 ! [A: set_nat,P2: nat > $o,Q: nat > $o] :
% 0.28/0.47 ( ( ord_less_eq_set_nat @ A
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [X: nat] :
% 0.28/0.47 ( ( P2 @ X )
% 0.28/0.47 & ( Q @ X ) ) ) )
% 0.28/0.47 = ( ( ord_less_eq_set_nat @ A @ ( collect_nat @ P2 ) )
% 0.28/0.47 & ( ord_less_eq_set_nat @ A @ ( collect_nat @ Q ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % conj_subset_def
% 0.28/0.47 thf(fact_294_conj__subset__def,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A
% 0.28/0.47 @ ( collec1111687558lle_tv
% 0.28/0.47 @ ^ [X: paraco1605129243lle_tv] :
% 0.28/0.47 ( ( P2 @ X )
% 0.28/0.47 & ( Q @ X ) ) ) )
% 0.28/0.47 = ( ( ord_le241064091lle_tv @ A @ ( collec1111687558lle_tv @ P2 ) )
% 0.28/0.47 & ( ord_le241064091lle_tv @ A @ ( collec1111687558lle_tv @ Q ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % conj_subset_def
% 0.28/0.47 thf(fact_295_conj__subset__def,axiom,
% 0.28/0.47 ! [A: set_o,P2: $o > $o,Q: $o > $o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A
% 0.28/0.47 @ ( collect_o
% 0.28/0.47 @ ^ [X: $o] :
% 0.28/0.47 ( ( P2 @ X )
% 0.28/0.47 & ( Q @ X ) ) ) )
% 0.28/0.47 = ( ( ord_less_eq_set_o @ A @ ( collect_o @ P2 ) )
% 0.28/0.47 & ( ord_less_eq_set_o @ A @ ( collect_o @ Q ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % conj_subset_def
% 0.28/0.47 thf(fact_296_Sup_OSUP__identity__eq,axiom,
% 0.28/0.47 ! [Sup: set_o > $o,A: set_o] :
% 0.28/0.47 ( ( Sup
% 0.28/0.47 @ ( image_o_o
% 0.28/0.47 @ ^ [X: $o] : X
% 0.28/0.47 @ A ) )
% 0.28/0.47 = ( Sup @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % Sup.SUP_identity_eq
% 0.28/0.47 thf(fact_297_Inf_OINF__cong,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o,C2: $o > $o,D: $o > $o,Inf: set_o > $o] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ! [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ B )
% 0.28/0.47 => ( ( C2 @ X3 )
% 0.28/0.47 = ( D @ X3 ) ) )
% 0.28/0.47 => ( ( Inf @ ( image_o_o @ C2 @ A ) )
% 0.28/0.47 = ( Inf @ ( image_o_o @ D @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Inf.INF_cong
% 0.28/0.47 thf(fact_298_Inf_OINF__cong,axiom,
% 0.28/0.47 ! [A: set_list_char,B: set_list_char,C2: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv,Inf: set_Pa1764573435lle_tv > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ! [X3: list_char] :
% 0.28/0.47 ( ( member_list_char @ X3 @ B )
% 0.28/0.47 => ( ( C2 @ X3 )
% 0.28/0.47 = ( D @ X3 ) ) )
% 0.28/0.47 => ( ( Inf @ ( image_1187894195lle_tv @ C2 @ A ) )
% 0.28/0.47 = ( Inf @ ( image_1187894195lle_tv @ D @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Inf.INF_cong
% 0.28/0.47 thf(fact_299_Sup_OSUP__cong,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o,C2: $o > $o,D: $o > $o,Sup: set_o > $o] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ! [X3: $o] :
% 0.28/0.47 ( ( member_o @ X3 @ B )
% 0.28/0.47 => ( ( C2 @ X3 )
% 0.28/0.47 = ( D @ X3 ) ) )
% 0.28/0.47 => ( ( Sup @ ( image_o_o @ C2 @ A ) )
% 0.28/0.47 = ( Sup @ ( image_o_o @ D @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Sup.SUP_cong
% 0.28/0.47 thf(fact_300_Sup_OSUP__cong,axiom,
% 0.28/0.47 ! [A: set_list_char,B: set_list_char,C2: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv,Sup: set_Pa1764573435lle_tv > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ! [X3: list_char] :
% 0.28/0.47 ( ( member_list_char @ X3 @ B )
% 0.28/0.47 => ( ( C2 @ X3 )
% 0.28/0.47 = ( D @ X3 ) ) )
% 0.28/0.47 => ( ( Sup @ ( image_1187894195lle_tv @ C2 @ A ) )
% 0.28/0.47 = ( Sup @ ( image_1187894195lle_tv @ D @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Sup.SUP_cong
% 0.28/0.47 thf(fact_301_top__empty__eq,axiom,
% 0.28/0.47 ( top_to1299250770e_tv_o
% 0.28/0.47 = ( ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % top_empty_eq
% 0.28/0.47 thf(fact_302_top__empty__eq,axiom,
% 0.28/0.47 ( top_top_list_char_o
% 0.28/0.47 = ( ^ [X: list_char] : ( member_list_char @ X @ top_to748628679t_char ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % top_empty_eq
% 0.28/0.47 thf(fact_303_top__empty__eq,axiom,
% 0.28/0.47 ( top_top_o_o
% 0.28/0.47 = ( ^ [X: $o] : ( member_o @ X @ top_top_set_o ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % top_empty_eq
% 0.28/0.47 thf(fact_304_Inf_OINF__identity__eq,axiom,
% 0.28/0.47 ! [Inf: set_o > $o,A: set_o] :
% 0.28/0.47 ( ( Inf
% 0.28/0.47 @ ( image_o_o
% 0.28/0.47 @ ^ [X: $o] : X
% 0.28/0.47 @ A ) )
% 0.28/0.47 = ( Inf @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % Inf.INF_identity_eq
% 0.28/0.47 thf(fact_305_eval_Osimps_I2_J,axiom,
% 0.28/0.47 ! [I2: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( paraco1325918602e_eval @ I2 @ paraco367965286_Truth )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) ) ).
% 0.28/0.47
% 0.28/0.47 % eval.simps(2)
% 0.28/0.47 thf(fact_306_image__Fpow__mono,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ B )
% 0.28/0.47 => ( ord_le263913851lle_tv @ ( image_30320477lle_tv @ ( image_1187894195lle_tv @ F ) @ ( finite1803457147t_char @ A ) ) @ ( finite2011762305lle_tv @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Fpow_mono
% 0.28/0.47 thf(fact_307_image__Fpow__mono,axiom,
% 0.28/0.47 ! [F: $o > $o,A: set_o,B: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ B )
% 0.28/0.47 => ( ord_le2085948664_set_o @ ( image_set_o_set_o @ ( image_o_o @ F ) @ ( finite_Fpow_o @ A ) ) @ ( finite_Fpow_o @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Fpow_mono
% 0.28/0.47 thf(fact_308_eval_Osimps_I5_J,axiom,
% 0.28/0.47 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 != ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1344940915le_Det @ $false ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eval.simps(5)
% 0.28/0.47 thf(fact_309_fm_Oinject_I4_J,axiom,
% 0.28/0.47 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,Y51: paraco1604210848lle_fm,Y52: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.28/0.47 = ( paraco1389086619le_Eql @ Y51 @ Y52 ) )
% 0.28/0.47 = ( ( X51 = Y51 )
% 0.28/0.47 & ( X52 = Y52 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.inject(4)
% 0.28/0.47 thf(fact_310_fm_Odistinct_I15_J,axiom,
% 0.28/0.47 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.28/0.47 ( paraco367965286_Truth
% 0.28/0.47 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(15)
% 0.28/0.47 thf(fact_311_Fpow__mono,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A @ B )
% 0.28/0.47 => ( ord_le263913851lle_tv @ ( finite2011762305lle_tv @ A ) @ ( finite2011762305lle_tv @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Fpow_mono
% 0.28/0.47 thf(fact_312_Fpow__mono,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.28/0.47 => ( ord_le2085948664_set_o @ ( finite_Fpow_o @ A ) @ ( finite_Fpow_o @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Fpow_mono
% 0.28/0.47 thf(fact_313_eval__equality__simplify,axiom,
% 0.28/0.47 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1344940915le_Det
% 0.28/0.47 @ ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ Q2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eval_equality_simplify
% 0.28/0.47 thf(fact_314_image__Pow__mono,axiom,
% 0.28/0.47 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ B )
% 0.28/0.47 => ( ord_le263913851lle_tv @ ( image_30320477lle_tv @ ( image_1187894195lle_tv @ F ) @ ( pow_list_char @ A ) ) @ ( pow_Pa475453624lle_tv @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Pow_mono
% 0.28/0.47 thf(fact_315_image__Pow__mono,axiom,
% 0.28/0.47 ! [F: $o > $o,A: set_o,B: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ B )
% 0.28/0.47 => ( ord_le2085948664_set_o @ ( image_set_o_set_o @ ( image_o_o @ F ) @ ( pow_o @ A ) ) @ ( pow_o @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_Pow_mono
% 0.28/0.47 thf(fact_316_eval_Osimps_I4_J,axiom,
% 0.28/0.47 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ P3 ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 != ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 0.28/0.47 => ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ Q2 ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 != ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ P3 ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 0.28/0.47 != ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eval.simps(4)
% 0.28/0.47 thf(fact_317_Greatest__equality,axiom,
% 0.28/0.47 ! [P2: set_Pa1764573435lle_tv > $o,X2: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( P2 @ X2 )
% 0.28/0.47 => ( ! [Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( P2 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ Y5 @ X2 ) )
% 0.28/0.47 => ( ( order_350719188lle_tv @ P2 )
% 0.28/0.47 = X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Greatest_equality
% 0.28/0.47 thf(fact_318_Greatest__equality,axiom,
% 0.28/0.47 ! [P2: set_o > $o,X2: set_o] :
% 0.28/0.47 ( ( P2 @ X2 )
% 0.28/0.47 => ( ! [Y5: set_o] :
% 0.28/0.47 ( ( P2 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ Y5 @ X2 ) )
% 0.28/0.47 => ( ( order_Greatest_set_o @ P2 )
% 0.28/0.47 = X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Greatest_equality
% 0.28/0.47 thf(fact_319_GreatestI2__order,axiom,
% 0.28/0.47 ! [P2: set_Pa1764573435lle_tv > $o,X2: set_Pa1764573435lle_tv,Q: set_Pa1764573435lle_tv > $o] :
% 0.28/0.47 ( ( P2 @ X2 )
% 0.28/0.47 => ( ! [Y5: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( P2 @ Y5 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ Y5 @ X2 ) )
% 0.28/0.47 => ( ! [X3: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( ! [Y6: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( P2 @ Y6 )
% 0.28/0.47 => ( ord_le241064091lle_tv @ Y6 @ X3 ) )
% 0.28/0.47 => ( Q @ X3 ) ) )
% 0.28/0.47 => ( Q @ ( order_350719188lle_tv @ P2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % GreatestI2_order
% 0.28/0.47 thf(fact_320_GreatestI2__order,axiom,
% 0.28/0.47 ! [P2: set_o > $o,X2: set_o,Q: set_o > $o] :
% 0.28/0.47 ( ( P2 @ X2 )
% 0.28/0.47 => ( ! [Y5: set_o] :
% 0.28/0.47 ( ( P2 @ Y5 )
% 0.28/0.47 => ( ord_less_eq_set_o @ Y5 @ X2 ) )
% 0.28/0.47 => ( ! [X3: set_o] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( ! [Y6: set_o] :
% 0.28/0.47 ( ( P2 @ Y6 )
% 0.28/0.47 => ( ord_less_eq_set_o @ Y6 @ X3 ) )
% 0.28/0.47 => ( Q @ X3 ) ) )
% 0.28/0.47 => ( Q @ ( order_Greatest_set_o @ P2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % GreatestI2_order
% 0.28/0.47 thf(fact_321_fm_Oinject_I3_J,axiom,
% 0.28/0.47 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,Y41: paraco1604210848lle_fm,Y42: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.28/0.47 = ( paraco69239110le_Con @ Y41 @ Y42 ) )
% 0.28/0.47 = ( ( X41 = Y41 )
% 0.28/0.47 & ( X42 = Y42 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.inject(3)
% 0.28/0.47 thf(fact_322_PowI,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ A @ B )
% 0.28/0.47 => ( member1875402276lle_tv @ A @ ( pow_Pa475453624lle_tv @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % PowI
% 0.28/0.47 thf(fact_323_PowI,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o] :
% 0.28/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.28/0.47 => ( member_set_o @ A @ ( pow_o @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % PowI
% 0.28/0.47 thf(fact_324_Pow__iff,axiom,
% 0.28/0.47 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.28/0.47 ( ( member1875402276lle_tv @ A @ ( pow_Pa475453624lle_tv @ B ) )
% 0.28/0.47 = ( ord_le241064091lle_tv @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % Pow_iff
% 0.28/0.47 thf(fact_325_Pow__iff,axiom,
% 0.28/0.47 ! [A: set_o,B: set_o] :
% 0.28/0.47 ( ( member_set_o @ A @ ( pow_o @ B ) )
% 0.28/0.47 = ( ord_less_eq_set_o @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % Pow_iff
% 0.28/0.47 thf(fact_326_Pow__UNIV,axiom,
% 0.28/0.47 ( ( pow_list_char @ top_to748628679t_char )
% 0.28/0.47 = top_to697846397t_char ) ).
% 0.28/0.47
% 0.28/0.47 % Pow_UNIV
% 0.28/0.47 thf(fact_327_Pow__UNIV,axiom,
% 0.28/0.47 ( ( pow_o @ top_top_set_o )
% 0.28/0.47 = top_top_set_set_o ) ).
% 0.28/0.47
% 0.28/0.47 % Pow_UNIV
% 0.28/0.47 thf(fact_328_fm_Odistinct_I25_J,axiom,
% 0.28/0.47 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.28/0.47 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(25)
% 0.28/0.47 thf(fact_329_fm_Odistinct_I13_J,axiom,
% 0.28/0.47 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.28/0.47 ( paraco367965286_Truth
% 0.28/0.47 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(13)
% 0.28/0.47 thf(fact_330_conjunction,axiom,
% 0.28/0.47 ! [P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco327635598_valid @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 0.28/0.47 = ( ( paraco327635598_valid @ P3 )
% 0.28/0.47 & ( paraco327635598_valid @ Q2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % conjunction
% 0.28/0.47 thf(fact_331_eval__negation,axiom,
% 0.28/0.47 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 = ( paraco1344940915le_Det @ $false ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P3 ) )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 != ( paraco1344940915le_Det @ $false ) )
% 0.28/0.47 => ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P3 ) )
% 0.28/0.47 = ( paraco1344940915le_Det @ $false ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 != ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P3 ) )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ P3 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eval_negation
% 0.28/0.47 thf(fact_332_fm_Oinject_I2_J,axiom,
% 0.28/0.47 ! [X32: paraco1604210848lle_fm,Y32: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( ( paraco445776468le_Neg @ X32 )
% 0.28/0.47 = ( paraco445776468le_Neg @ Y32 ) )
% 0.28/0.47 = ( X32 = Y32 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.inject(2)
% 0.28/0.47 thf(fact_333_double__negation,axiom,
% 0.28/0.47 ( paraco1325918602e_eval
% 0.28/0.47 = ( ^ [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ P ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % double_negation
% 0.28/0.47 thf(fact_334_fm_Odistinct_I21_J,axiom,
% 0.28/0.47 ! [X32: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco445776468le_Neg @ X32 )
% 0.28/0.47 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(21)
% 0.28/0.47 thf(fact_335_fm_Odistinct_I19_J,axiom,
% 0.28/0.47 ! [X32: paraco1604210848lle_fm,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco445776468le_Neg @ X32 )
% 0.28/0.47 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(19)
% 0.28/0.47 thf(fact_336_fm_Odistinct_I11_J,axiom,
% 0.28/0.47 ! [X32: paraco1604210848lle_fm] :
% 0.28/0.47 ( paraco367965286_Truth
% 0.28/0.47 != ( paraco445776468le_Neg @ X32 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(11)
% 0.28/0.47 thf(fact_337_eval__equality,axiom,
% 0.28/0.47 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 != ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 0.28/0.47 => ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ Q2 ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 != ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ P3 ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 0.28/0.47 != ( paraco1344940915le_Det @ $true ) )
% 0.28/0.47 => ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 = ( paraco1344940915le_Det @ $false ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ Q2 ) ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 0.28/0.47 != ( paraco1344940915le_Det @ $false ) )
% 0.28/0.47 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 0.28/0.47 = ( paraco1344940915le_Det @ $false ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P3 ) ) ) )
% 0.28/0.47 & ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 0.28/0.47 != ( paraco1344940915le_Det @ $false ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 0.28/0.47 = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eval_equality
% 0.28/0.47 thf(fact_338_fm_Oexhaust,axiom,
% 0.28/0.47 ! [Y3: paraco1604210848lle_fm] :
% 0.28/0.47 ( ! [X12: list_char] :
% 0.28/0.47 ( Y3
% 0.28/0.47 != ( paraco1480028776le_Pro @ X12 ) )
% 0.28/0.47 => ( ( Y3 != paraco367965286_Truth )
% 0.28/0.47 => ( ! [X33: paraco1604210848lle_fm] :
% 0.28/0.47 ( Y3
% 0.28/0.47 != ( paraco445776468le_Neg @ X33 ) )
% 0.28/0.47 => ( ! [X412: paraco1604210848lle_fm,X422: paraco1604210848lle_fm] :
% 0.28/0.47 ( Y3
% 0.28/0.47 != ( paraco69239110le_Con @ X412 @ X422 ) )
% 0.28/0.47 => ( ! [X512: paraco1604210848lle_fm,X522: paraco1604210848lle_fm] :
% 0.28/0.47 ( Y3
% 0.28/0.47 != ( paraco1389086619le_Eql @ X512 @ X522 ) )
% 0.28/0.47 => ~ ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.28/0.47 ( Y3
% 0.28/0.47 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.exhaust
% 0.28/0.47 thf(fact_339_fm_Oinduct,axiom,
% 0.28/0.47 ! [P2: paraco1604210848lle_fm > $o,Fm: paraco1604210848lle_fm] :
% 0.28/0.47 ( ! [X3: list_char] : ( P2 @ ( paraco1480028776le_Pro @ X3 ) )
% 0.28/0.47 => ( ( P2 @ paraco367965286_Truth )
% 0.28/0.47 => ( ! [X3: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( P2 @ ( paraco445776468le_Neg @ X3 ) ) )
% 0.28/0.47 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( P2 @ X1a )
% 0.28/0.47 => ( ( P2 @ X22 )
% 0.28/0.47 => ( P2 @ ( paraco69239110le_Con @ X1a @ X22 ) ) ) )
% 0.28/0.47 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( P2 @ X1a )
% 0.28/0.47 => ( ( P2 @ X22 )
% 0.28/0.47 => ( P2 @ ( paraco1389086619le_Eql @ X1a @ X22 ) ) ) )
% 0.28/0.47 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( P2 @ X1a )
% 0.28/0.47 => ( ( P2 @ X22 )
% 0.28/0.47 => ( P2 @ ( paraco1745535428le_Eql @ X1a @ X22 ) ) ) )
% 0.28/0.47 => ( P2 @ Fm ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.induct
% 0.28/0.47 thf(fact_340_fm_Oinject_I5_J,axiom,
% 0.28/0.47 ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm,Y61: paraco1604210848lle_fm,Y62: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( ( paraco1745535428le_Eql @ X612 @ X622 )
% 0.28/0.47 = ( paraco1745535428le_Eql @ Y61 @ Y62 ) )
% 0.28/0.47 = ( ( X612 = Y61 )
% 0.28/0.47 & ( X622 = Y62 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.inject(5)
% 0.28/0.47 thf(fact_341_fm_Oinject_I1_J,axiom,
% 0.28/0.47 ! [X1: list_char,Y1: list_char] :
% 0.28/0.47 ( ( ( paraco1480028776le_Pro @ X1 )
% 0.28/0.47 = ( paraco1480028776le_Pro @ Y1 ) )
% 0.28/0.47 = ( X1 = Y1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.inject(1)
% 0.28/0.47 thf(fact_342_fm_Odistinct_I9_J,axiom,
% 0.28/0.47 ! [X1: list_char,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.28/0.47 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(9)
% 0.28/0.47 thf(fact_343_eval_Osimps_I1_J,axiom,
% 0.28/0.47 ! [I2: list_char > paraco1605129243lle_tv,S2: list_char] :
% 0.28/0.47 ( ( paraco1325918602e_eval @ I2 @ ( paraco1480028776le_Pro @ S2 ) )
% 0.28/0.47 = ( I2 @ S2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % eval.simps(1)
% 0.28/0.47 thf(fact_344_fm_Odistinct_I23_J,axiom,
% 0.28/0.47 ! [X32: paraco1604210848lle_fm,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco445776468le_Neg @ X32 )
% 0.28/0.47 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(23)
% 0.28/0.47 thf(fact_345_fm_Odistinct_I3_J,axiom,
% 0.28/0.47 ! [X1: list_char,X32: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.28/0.47 != ( paraco445776468le_Neg @ X32 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(3)
% 0.28/0.47 thf(fact_346_fm_Odistinct_I27_J,axiom,
% 0.28/0.47 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.28/0.47 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(27)
% 0.28/0.47 thf(fact_347_fm_Odistinct_I29_J,axiom,
% 0.28/0.47 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.28/0.47 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(29)
% 0.28/0.47 thf(fact_348_fm_Odistinct_I5_J,axiom,
% 0.28/0.47 ! [X1: list_char,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.28/0.47 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(5)
% 0.28/0.47 thf(fact_349_fm_Odistinct_I7_J,axiom,
% 0.28/0.47 ! [X1: list_char,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.28/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.28/0.47 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(7)
% 0.28/0.47 thf(fact_350_fm_Odistinct_I17_J,axiom,
% 0.28/0.47 ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 0.28/0.47 ( paraco367965286_Truth
% 0.28/0.47 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(17)
% 0.28/0.47 thf(fact_351_fm_Odistinct_I1_J,axiom,
% 0.28/0.47 ! [X1: list_char] :
% 0.28/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.28/0.47 != paraco367965286_Truth ) ).
% 0.28/0.47
% 0.28/0.47 % fm.distinct(1)
% 0.28/0.47 thf(fact_352_eval_Ocases,axiom,
% 0.28/0.47 ! [X2: produc696645085lle_fm] :
% 0.28/0.47 ( ! [I3: list_char > paraco1605129243lle_tv,S3: list_char] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco1480028776le_Pro @ S3 ) ) )
% 0.28/0.47 => ( ! [I3: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( produc1710735575lle_fm @ I3 @ paraco367965286_Truth ) )
% 0.28/0.47 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 0.28/0.47 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) )
% 0.28/0.47 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) )
% 0.28/0.47 => ~ ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eval.cases
% 0.28/0.47 thf(fact_353_Sup__bool__def,axiom,
% 0.28/0.47 ( complete_Sup_Sup_o
% 0.28/0.47 = ( member_o @ $true ) ) ).
% 0.28/0.47
% 0.28/0.47 % Sup_bool_def
% 0.28/0.47
% 0.28/0.47 % Conjectures (1)
% 0.28/0.47 thf(conj_0,conjecture,
% 0.28/0.47 ( ( ! [I: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( paraco1325918602e_eval @ I @ p )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) ) )
% 0.28/0.47 != ( ~ ! [I: list_char > paraco1605129243lle_tv] :
% 0.28/0.47 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ I @ top_to748628679t_char )
% 0.28/0.47 @ ( paraco1933902578domain
% 0.28/0.47 @ ( collect_nat
% 0.28/0.47 @ ^ [N: nat] : $true ) ) )
% 0.28/0.47 => ( ( paraco1325918602e_eval @ I @ p )
% 0.28/0.47 = ( paraco1344940915le_Det @ $true ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.70/1.52 ---- Embedded in THF ---
% 2.70/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.70/1.52 %%% Generated on Tue Feb 24 08:27:04 EST 2026
% 2.70/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.70/1.52 %%% Logic specification used:
% 2.70/1.52 %%% thf(spec, logic, $$dhol).
% 2.70/1.52
% 2.70/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PTGbAxFx6h/DTF2DTF21650.p
% See solution above
% 2.70/1.52 ------------------------
% 2.70/1.58 ---- Cleaned THF ---
% 2.70/1.58 thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 2.70/1.58 produc696645085lle_fm: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 2.70/1.58 set_se800614875lle_tv: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J,type,
% 2.70/1.58 set_set_list_char: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.70/1.58 set_Pa1764573435lle_tv: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
% 2.70/1.58 set_list_char: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.70/1.58 paraco1605129243lle_tv: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 2.70/1.58 paraco1604210848lle_fm: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 2.70/1.58 set_set_o: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 2.70/1.58 list_char: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.70/1.58 set_nat: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 2.70/1.58 set_o: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(ty_n_t__Nat__Onat,type,
% 2.70/1.58 nat: $tType ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Complete__Lattices_OSup__class_OSup_001_Eo,type,
% 2.70/1.58 complete_Sup_Sup_o: set_o > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Finite__Set_OFpow_001_Eo,type,
% 2.70/1.58 finite_Fpow_o: set_o > set_set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Finite__Set_OFpow_001t__List__Olist_It__String__Ochar_J,type,
% 2.70/1.58 finite1803457147t_char: set_list_char > set_set_list_char ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Finite__Set_OFpow_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.70/1.58 finite2011762305lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_Eo_J,type,
% 2.70/1.58 ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 2.70/1.58 ord_le1945897678char_o: ( list_char > $o ) > ( list_char > $o ) > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 2.70/1.58 ord_le1632188418e_tv_o: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
% 2.70/1.58 ord_less_eq_set_o: set_o > set_o > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
% 2.70/1.58 ord_le1836582007t_char: set_list_char > set_list_char > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.70/1.58 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.70/1.58 ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 2.70/1.58 ord_le2085948664_set_o: set_set_o > set_set_o > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 2.70/1.58 ord_le263913851lle_tv: set_se800614875lle_tv > set_se800614875lle_tv > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_I_Eo_J,type,
% 2.70/1.58 order_Greatest_set_o: ( set_o > $o ) > set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.70/1.58 order_350719188lle_tv: ( set_Pa1764573435lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_M_Eo_J,type,
% 2.70/1.58 top_top_o_o: $o > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 2.70/1.58 top_top_list_char_o: list_char > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
% 2.70/1.58 top_top_nat_o: nat > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 2.70/1.58 top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 2.70/1.58 top_top_set_o: set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
% 2.70/1.58 top_to748628679t_char: set_list_char ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.70/1.58 top_top_set_nat: set_nat ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.70/1.58 top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 2.70/1.58 top_top_set_set_o: set_set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J,type,
% 2.70/1.58 top_to697846397t_char: set_set_list_char ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Odomain,type,
% 2.70/1.58 paraco1933902578domain: set_nat > set_Pa1764573435lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Oeval,type,
% 2.70/1.58 paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OCon_H,type,
% 2.70/1.58 paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql,type,
% 2.70/1.58 paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql_H,type,
% 2.70/1.58 paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_ONeg_H,type,
% 2.70/1.58 paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OPro,type,
% 2.70/1.58 paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OTruth,type,
% 2.70/1.58 paraco367965286_Truth: paraco1604210848lle_fm ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_ODet,type,
% 2.70/1.58 paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid,type,
% 2.70/1.58 paraco327635598_valid: paraco1604210848lle_fm > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid__in,type,
% 2.70/1.58 paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 2.70/1.58 produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_OCollect_001_Eo,type,
% 2.70/1.58 collect_o: ( $o > $o ) > set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_OCollect_001t__List__Olist_It__String__Ochar_J,type,
% 2.70/1.58 collect_list_char: ( list_char > $o ) > set_list_char ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 2.70/1.58 collect_nat: ( nat > $o ) > set_nat ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_OCollect_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.70/1.58 collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_OPow_001_Eo,type,
% 2.70/1.58 pow_o: set_o > set_set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_OPow_001t__List__Olist_It__String__Ochar_J,type,
% 2.70/1.58 pow_list_char: set_list_char > set_set_list_char ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_OPow_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.70/1.58 pow_Pa475453624lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001_Eo_001_Eo,type,
% 2.70/1.58 image_o_o: ( $o > $o ) > set_o > set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001_Eo_001t__List__Olist_It__String__Ochar_J,type,
% 2.70/1.58 image_o_list_char: ( $o > list_char ) > set_o > set_list_char ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001_Eo_001t__Nat__Onat,type,
% 2.70/1.58 image_o_nat: ( $o > nat ) > set_o > set_nat ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001_Eo_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.70/1.58 image_1491822472lle_tv: ( $o > paraco1605129243lle_tv ) > set_o > set_Pa1764573435lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__List__Olist_It__String__Ochar_J_001_Eo,type,
% 2.70/1.58 image_list_char_o: ( list_char > $o ) > set_list_char > set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
% 2.70/1.58 image_890964937t_char: ( list_char > list_char ) > set_list_char > set_list_char ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__List__Olist_It__String__Ochar_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.70/1.58 image_1187894195lle_tv: ( list_char > paraco1605129243lle_tv ) > set_list_char > set_Pa1764573435lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Nat__Onat_001_Eo,type,
% 2.70/1.58 image_nat_o: ( nat > $o ) > set_nat > set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
% 2.70/1.58 image_nat_list_char: ( nat > list_char ) > set_nat > set_list_char ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.70/1.58 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.70/1.58 image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_Eo,type,
% 2.70/1.58 image_991799618e_tv_o: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv > set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__List__Olist_It__String__Ochar_J,type,
% 2.70/1.58 image_1971766583t_char: ( paraco1605129243lle_tv > list_char ) > set_Pa1764573435lle_tv > set_list_char ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 2.70/1.58 image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.70/1.58 image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
% 2.70/1.58 image_set_o_set_o: ( set_o > set_o ) > set_set_o > set_set_o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_Set_Oimage_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.70/1.58 image_30320477lle_tv: ( set_list_char > set_Pa1764573435lle_tv ) > set_set_list_char > set_se800614875lle_tv ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_member_001_Eo,type,
% 2.70/1.58 member_o: $o > set_o > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_member_001t__List__Olist_It__String__Ochar_J,type,
% 2.70/1.58 member_list_char: list_char > set_list_char > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_member_001t__Nat__Onat,type,
% 2.70/1.58 member_nat: nat > set_nat > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.70/1.58 member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_member_001t__Set__Oset_I_Eo_J,type,
% 2.70/1.58 member_set_o: set_o > set_set_o > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_c_member_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.70/1.58 member1875402276lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv > $o ).
% 2.70/1.58
% 2.70/1.58 thf(sy_v_p,type,
% 2.70/1.58 p: paraco1604210848lle_fm ).
% 2.70/1.58
% 2.70/1.58 thf(fact_0_universal__domain,axiom,
% 2.70/1.58 ( ( paraco1933902578domain
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [N: nat] : $true ) )
% 2.70/1.58 = ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] : $true ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_1_tv_Oinject_I1_J,axiom,
% 2.70/1.58 ! [X1: $o,Y1: $o] :
% 2.70/1.58 ( ( ( paraco1344940915le_Det @ X1 )
% 2.70/1.58 = ( paraco1344940915le_Det @ Y1 ) )
% 2.70/1.58 = ( X1 = Y1 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_2_valid__in__def,axiom,
% 2.70/1.58 ( paraco55203475lid_in
% 2.70/1.58 = ( ^ [U: set_nat,P: paraco1604210848lle_fm] :
% 2.70/1.58 ! [I: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ I @ top_to748628679t_char ) @ ( paraco1933902578domain @ U ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I @ P )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_3_image__ident,axiom,
% 2.70/1.58 ! [Y: set_o] :
% 2.70/1.58 ( ( image_o_o
% 2.70/1.58 @ ^ [X: $o] : X
% 2.70/1.58 @ Y )
% 2.70/1.58 = Y ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_4_UNIV__I,axiom,
% 2.70/1.58 ! [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_5_UNIV__I,axiom,
% 2.70/1.58 ! [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_6_UNIV__I,axiom,
% 2.70/1.58 ! [X2: list_char] : ( member_list_char @ X2 @ top_to748628679t_char ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_7_iso__tuple__UNIV__I,axiom,
% 2.70/1.58 ! [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_8_iso__tuple__UNIV__I,axiom,
% 2.70/1.58 ! [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_9_iso__tuple__UNIV__I,axiom,
% 2.70/1.58 ! [X2: list_char] : ( member_list_char @ X2 @ top_to748628679t_char ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_10_subsetI,axiom,
% 2.70/1.58 ! [A: set_list_char,B: set_list_char] :
% 2.70/1.58 ( ! [X3: list_char] :
% 2.70/1.58 ( ( member_list_char @ X3 @ A )
% 2.70/1.58 => ( member_list_char @ X3 @ B ) )
% 2.70/1.58 => ( ord_le1836582007t_char @ A @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_11_subsetI,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o] :
% 2.70/1.58 ( ! [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ A )
% 2.70/1.58 => ( member_o @ X3 @ B ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ A @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_12_subsetI,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X3 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ X3 @ B ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_13_subset__antisym,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A @ B )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B @ A )
% 2.70/1.58 => ( A = B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_14_subset__antisym,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A @ B )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B @ A )
% 2.70/1.58 => ( A = B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_15_image__eqI,axiom,
% 2.70/1.58 ! [B2: list_char,F: $o > list_char,X2: $o,A: set_o] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( member_list_char @ B2 @ ( image_o_list_char @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_16_image__eqI,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv,X2: $o,A: set_o] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_17_image__eqI,axiom,
% 2.70/1.58 ! [B2: $o,F: list_char > $o,X2: list_char,A: set_list_char] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( member_o @ B2 @ ( image_list_char_o @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_18_image__eqI,axiom,
% 2.70/1.58 ! [B2: list_char,F: list_char > list_char,X2: list_char,A: set_list_char] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( member_list_char @ B2 @ ( image_890964937t_char @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_19_image__eqI,axiom,
% 2.70/1.58 ! [B2: $o,F: paraco1605129243lle_tv > $o,X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( member_o @ B2 @ ( image_991799618e_tv_o @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_20_image__eqI,axiom,
% 2.70/1.58 ! [B2: list_char,F: paraco1605129243lle_tv > list_char,X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( member_list_char @ B2 @ ( image_1971766583t_char @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_21_image__eqI,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_22_image__eqI,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv,X2: list_char,A: set_list_char] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_23_image__eqI,axiom,
% 2.70/1.58 ! [B2: $o,F: $o > $o,X2: $o,A: set_o] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( member_o @ B2 @ ( image_o_o @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_24_order__refl,axiom,
% 2.70/1.58 ! [X2: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ X2 @ X2 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_25_order__refl,axiom,
% 2.70/1.58 ! [X2: set_o] : ( ord_less_eq_set_o @ X2 @ X2 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_26_rangeE,axiom,
% 2.70/1.58 ! [B2: $o,F: list_char > $o] :
% 2.70/1.58 ( ( member_o @ B2 @ ( image_list_char_o @ F @ top_to748628679t_char ) )
% 2.70/1.58 => ~ ! [X3: list_char] :
% 2.70/1.58 ( B2
% 2.70/1.58 = ( ~ ( F @ X3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_27_rangeE,axiom,
% 2.70/1.58 ! [B2: list_char,F: list_char > list_char] :
% 2.70/1.58 ( ( member_list_char @ B2 @ ( image_890964937t_char @ F @ top_to748628679t_char ) )
% 2.70/1.58 => ~ ! [X3: list_char] :
% 2.70/1.58 ( B2
% 2.70/1.58 != ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_28_rangeE,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ top_to748628679t_char ) )
% 2.70/1.58 => ~ ! [X3: list_char] :
% 2.70/1.58 ( B2
% 2.70/1.58 != ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_29_rangeE,axiom,
% 2.70/1.58 ! [B2: $o,F: $o > $o] :
% 2.70/1.58 ( ( member_o @ B2 @ ( image_o_o @ F @ top_top_set_o ) )
% 2.70/1.58 => ~ ! [X3: $o] :
% 2.70/1.58 ( B2
% 2.70/1.58 = ( ~ ( F @ X3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_30_rangeE,axiom,
% 2.70/1.58 ! [B2: list_char,F: $o > list_char] :
% 2.70/1.58 ( ( member_list_char @ B2 @ ( image_o_list_char @ F @ top_top_set_o ) )
% 2.70/1.58 => ~ ! [X3: $o] :
% 2.70/1.58 ( B2
% 2.70/1.58 != ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_31_rangeE,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ top_top_set_o ) )
% 2.70/1.58 => ~ ! [X3: $o] :
% 2.70/1.58 ( B2
% 2.70/1.58 != ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_32_range__composition,axiom,
% 2.70/1.58 ! [F: $o > $o,G: list_char > $o] :
% 2.70/1.58 ( ( image_list_char_o
% 2.70/1.58 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 2.70/1.58 @ top_to748628679t_char )
% 2.70/1.58 = ( image_o_o @ F @ ( image_list_char_o @ G @ top_to748628679t_char ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_33_range__composition,axiom,
% 2.70/1.58 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( image_1187894195lle_tv
% 2.70/1.58 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 2.70/1.58 @ top_to748628679t_char )
% 2.70/1.58 = ( image_335818702lle_tv @ F @ ( image_1187894195lle_tv @ G @ top_to748628679t_char ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_34_range__composition,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,G: list_char > list_char] :
% 2.70/1.58 ( ( image_1187894195lle_tv
% 2.70/1.58 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 2.70/1.58 @ top_to748628679t_char )
% 2.70/1.58 = ( image_1187894195lle_tv @ F @ ( image_890964937t_char @ G @ top_to748628679t_char ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_35_range__composition,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,G: $o > list_char] :
% 2.70/1.58 ( ( image_1491822472lle_tv
% 2.70/1.58 @ ^ [X: $o] : ( F @ ( G @ X ) )
% 2.70/1.58 @ top_top_set_o )
% 2.70/1.58 = ( image_1187894195lle_tv @ F @ ( image_o_list_char @ G @ top_top_set_o ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_36_range__composition,axiom,
% 2.70/1.58 ! [F: $o > $o,G: $o > $o] :
% 2.70/1.58 ( ( image_o_o
% 2.70/1.58 @ ^ [X: $o] : ( F @ ( G @ X ) )
% 2.70/1.58 @ top_top_set_o )
% 2.70/1.58 = ( image_o_o @ F @ ( image_o_o @ G @ top_top_set_o ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_37_image__Collect__subsetI,axiom,
% 2.70/1.58 ! [P2: nat > $o,F: nat > list_char,B: set_list_char] :
% 2.70/1.58 ( ! [X3: nat] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le1836582007t_char @ ( image_nat_list_char @ F @ ( collect_nat @ P2 ) ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_38_image__Collect__subsetI,axiom,
% 2.70/1.58 ! [P2: paraco1605129243lle_tv > $o,F: paraco1605129243lle_tv > list_char,B: set_list_char] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le1836582007t_char @ ( image_1971766583t_char @ F @ ( collec1111687558lle_tv @ P2 ) ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_39_image__Collect__subsetI,axiom,
% 2.70/1.58 ! [P2: list_char > $o,F: list_char > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ! [X3: list_char] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ ( collect_list_char @ P2 ) ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_40_image__Collect__subsetI,axiom,
% 2.70/1.58 ! [P2: nat > $o,F: nat > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ! [X3: nat] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( image_1151963140lle_tv @ F @ ( collect_nat @ P2 ) ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_41_image__Collect__subsetI,axiom,
% 2.70/1.58 ! [P2: paraco1605129243lle_tv > $o,F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ ( collec1111687558lle_tv @ P2 ) ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_42_image__Collect__subsetI,axiom,
% 2.70/1.58 ! [P2: $o > $o,F: $o > $o,B: set_o] :
% 2.70/1.58 ( ! [X3: $o] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( member_o @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( image_o_o @ F @ ( collect_o @ P2 ) ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_43_image__Collect__subsetI,axiom,
% 2.70/1.58 ! [P2: nat > $o,F: nat > $o,B: set_o] :
% 2.70/1.58 ( ! [X3: nat] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( member_o @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( image_nat_o @ F @ ( collect_nat @ P2 ) ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_44_image__Collect__subsetI,axiom,
% 2.70/1.58 ! [P2: paraco1605129243lle_tv > $o,F: paraco1605129243lle_tv > $o,B: set_o] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( member_o @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ F @ ( collec1111687558lle_tv @ P2 ) ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_45_top__set__def,axiom,
% 2.70/1.58 ( top_top_set_nat
% 2.70/1.58 = ( collect_nat @ top_top_nat_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_46_top__set__def,axiom,
% 2.70/1.58 ( top_to1057771083lle_tv
% 2.70/1.58 = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_47_top__set__def,axiom,
% 2.70/1.58 ( top_to748628679t_char
% 2.70/1.58 = ( collect_list_char @ top_top_list_char_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_48_top__set__def,axiom,
% 2.70/1.58 ( top_top_set_o
% 2.70/1.58 = ( collect_o @ top_top_o_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_49_less__eq__set__def,axiom,
% 2.70/1.58 ( ord_le1836582007t_char
% 2.70/1.58 = ( ^ [A2: set_list_char,B3: set_list_char] :
% 2.70/1.58 ( ord_le1945897678char_o
% 2.70/1.58 @ ^ [X: list_char] : ( member_list_char @ X @ A2 )
% 2.70/1.58 @ ^ [X: list_char] : ( member_list_char @ X @ B3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_50_less__eq__set__def,axiom,
% 2.70/1.58 ( ord_le241064091lle_tv
% 2.70/1.58 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ord_le1632188418e_tv_o
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ A2 )
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ B3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_51_less__eq__set__def,axiom,
% 2.70/1.58 ( ord_less_eq_set_o
% 2.70/1.58 = ( ^ [A2: set_o,B3: set_o] :
% 2.70/1.58 ( ord_less_eq_o_o
% 2.70/1.58 @ ^ [X: $o] : ( member_o @ X @ A2 )
% 2.70/1.58 @ ^ [X: $o] : ( member_o @ X @ B3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_52_dual__order_Oantisym,axiom,
% 2.70/1.58 ! [B2: set_Pa1764573435lle_tv,A3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B2 @ A3 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 2.70/1.58 => ( A3 = B2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_53_dual__order_Oantisym,axiom,
% 2.70/1.58 ! [B2: set_o,A3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B2 @ A3 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ A3 @ B2 )
% 2.70/1.58 => ( A3 = B2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_54_dual__order_Oeq__iff,axiom,
% 2.70/1.58 ( ( ^ [Y2: set_Pa1764573435lle_tv,Z: set_Pa1764573435lle_tv] : ( Y2 = Z ) )
% 2.70/1.58 = ( ^ [A4: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B4 @ A4 )
% 2.70/1.58 & ( ord_le241064091lle_tv @ A4 @ B4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_55_dual__order_Oeq__iff,axiom,
% 2.70/1.58 ( ( ^ [Y2: set_o,Z: set_o] : ( Y2 = Z ) )
% 2.70/1.58 = ( ^ [A4: set_o,B4: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B4 @ A4 )
% 2.70/1.58 & ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_56_dual__order_Otrans,axiom,
% 2.70/1.58 ! [B2: set_Pa1764573435lle_tv,A3: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B2 @ A3 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ C @ B2 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ C @ A3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_57_dual__order_Otrans,axiom,
% 2.70/1.58 ! [B2: set_o,A3: set_o,C: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B2 @ A3 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ C @ B2 )
% 2.70/1.58 => ( ord_less_eq_set_o @ C @ A3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_58_dual__order_Orefl,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A3 @ A3 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_59_dual__order_Orefl,axiom,
% 2.70/1.58 ! [A3: set_o] : ( ord_less_eq_set_o @ A3 @ A3 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_60_order__trans,axiom,
% 2.70/1.58 ! [X2: set_Pa1764573435lle_tv,Y3: set_Pa1764573435lle_tv,Z2: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X2 @ Y3 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ Y3 @ Z2 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ X2 @ Z2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_61_order__trans,axiom,
% 2.70/1.58 ! [X2: set_o,Y3: set_o,Z2: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X2 @ Y3 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ Y3 @ Z2 )
% 2.70/1.58 => ( ord_less_eq_set_o @ X2 @ Z2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_62_order__class_Oorder_Oantisym,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B2 @ A3 )
% 2.70/1.58 => ( A3 = B2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_63_order__class_Oorder_Oantisym,axiom,
% 2.70/1.58 ! [A3: set_o,B2: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B2 @ A3 )
% 2.70/1.58 => ( A3 = B2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_64_ord__le__eq__trans,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 2.70/1.58 => ( ( B2 = C )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A3 @ C ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_65_ord__le__eq__trans,axiom,
% 2.70/1.58 ! [A3: set_o,B2: set_o,C: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 2.70/1.58 => ( ( B2 = C )
% 2.70/1.58 => ( ord_less_eq_set_o @ A3 @ C ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_66_ord__eq__le__trans,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( A3 = B2 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A3 @ C ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_67_ord__eq__le__trans,axiom,
% 2.70/1.58 ! [A3: set_o,B2: set_o,C: set_o] :
% 2.70/1.58 ( ( A3 = B2 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B2 @ C )
% 2.70/1.58 => ( ord_less_eq_set_o @ A3 @ C ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_68_order__class_Oorder_Oeq__iff,axiom,
% 2.70/1.58 ( ( ^ [Y2: set_Pa1764573435lle_tv,Z: set_Pa1764573435lle_tv] : ( Y2 = Z ) )
% 2.70/1.58 = ( ^ [A4: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A4 @ B4 )
% 2.70/1.58 & ( ord_le241064091lle_tv @ B4 @ A4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_69_order__class_Oorder_Oeq__iff,axiom,
% 2.70/1.58 ( ( ^ [Y2: set_o,Z: set_o] : ( Y2 = Z ) )
% 2.70/1.58 = ( ^ [A4: set_o,B4: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 2.70/1.58 & ( ord_less_eq_set_o @ B4 @ A4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_70_antisym__conv,axiom,
% 2.70/1.58 ! [Y3: set_Pa1764573435lle_tv,X2: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ Y3 @ X2 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ X2 @ Y3 )
% 2.70/1.58 = ( X2 = Y3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_71_antisym__conv,axiom,
% 2.70/1.58 ! [Y3: set_o,X2: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ Y3 @ X2 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ X2 @ Y3 )
% 2.70/1.58 = ( X2 = Y3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_72_order_Otrans,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A3 @ C ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_73_order_Otrans,axiom,
% 2.70/1.58 ! [A3: set_o,B2: set_o,C: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B2 @ C )
% 2.70/1.58 => ( ord_less_eq_set_o @ A3 @ C ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_74_eq__refl,axiom,
% 2.70/1.58 ! [X2: set_Pa1764573435lle_tv,Y3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( X2 = Y3 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ X2 @ Y3 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_75_eq__refl,axiom,
% 2.70/1.58 ! [X2: set_o,Y3: set_o] :
% 2.70/1.58 ( ( X2 = Y3 )
% 2.70/1.58 => ( ord_less_eq_set_o @ X2 @ Y3 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_76_antisym,axiom,
% 2.70/1.58 ! [X2: set_Pa1764573435lle_tv,Y3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X2 @ Y3 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ Y3 @ X2 )
% 2.70/1.58 => ( X2 = Y3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_77_antisym,axiom,
% 2.70/1.58 ! [X2: set_o,Y3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X2 @ Y3 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ Y3 @ X2 )
% 2.70/1.58 => ( X2 = Y3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_78_eq__iff,axiom,
% 2.70/1.58 ( ( ^ [Y2: set_Pa1764573435lle_tv,Z: set_Pa1764573435lle_tv] : ( Y2 = Z ) )
% 2.70/1.58 = ( ^ [X: set_Pa1764573435lle_tv,Y4: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X @ Y4 )
% 2.70/1.58 & ( ord_le241064091lle_tv @ Y4 @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_79_eq__iff,axiom,
% 2.70/1.58 ( ( ^ [Y2: set_o,Z: set_o] : ( Y2 = Z ) )
% 2.70/1.58 = ( ^ [X: set_o,Y4: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X @ Y4 )
% 2.70/1.58 & ( ord_less_eq_set_o @ Y4 @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_80_ord__le__eq__subst,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 2.70/1.58 => ( ( ( F @ B2 )
% 2.70/1.58 = C )
% 2.70/1.58 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ A3 ) @ C ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_81_ord__le__eq__subst,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_o,C: set_o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 2.70/1.58 => ( ( ( F @ B2 )
% 2.70/1.58 = C )
% 2.70/1.58 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ A3 ) @ C ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_82_ord__le__eq__subst,axiom,
% 2.70/1.58 ! [A3: set_o,B2: set_o,F: set_o > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 2.70/1.58 => ( ( ( F @ B2 )
% 2.70/1.58 = C )
% 2.70/1.58 => ( ! [X3: set_o,Y5: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ A3 ) @ C ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_83_ord__le__eq__subst,axiom,
% 2.70/1.58 ! [A3: set_o,B2: set_o,F: set_o > set_o,C: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 2.70/1.58 => ( ( ( F @ B2 )
% 2.70/1.58 = C )
% 2.70/1.58 => ( ! [X3: set_o,Y5: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ A3 ) @ C ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_84_ord__eq__le__subst,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( A3
% 2.70/1.58 = ( F @ B2 ) )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 2.70/1.58 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A3 @ ( F @ C ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_85_ord__eq__le__subst,axiom,
% 2.70/1.58 ! [A3: set_o,F: set_Pa1764573435lle_tv > set_o,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( A3
% 2.70/1.58 = ( F @ B2 ) )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 2.70/1.58 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ A3 @ ( F @ C ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_86_ord__eq__le__subst,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,F: set_o > set_Pa1764573435lle_tv,B2: set_o,C: set_o] :
% 2.70/1.58 ( ( A3
% 2.70/1.58 = ( F @ B2 ) )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B2 @ C )
% 2.70/1.58 => ( ! [X3: set_o,Y5: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A3 @ ( F @ C ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_87_ord__eq__le__subst,axiom,
% 2.70/1.58 ! [A3: set_o,F: set_o > set_o,B2: set_o,C: set_o] :
% 2.70/1.58 ( ( A3
% 2.70/1.58 = ( F @ B2 ) )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B2 @ C )
% 2.70/1.58 => ( ! [X3: set_o,Y5: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ A3 @ ( F @ C ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_88_order__subst2,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ ( F @ B2 ) @ C )
% 2.70/1.58 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ A3 ) @ C ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_89_order__subst2,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_o,C: set_o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A3 @ B2 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ ( F @ B2 ) @ C )
% 2.70/1.58 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ A3 ) @ C ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_90_order__subst2,axiom,
% 2.70/1.58 ! [A3: set_o,B2: set_o,F: set_o > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ ( F @ B2 ) @ C )
% 2.70/1.58 => ( ! [X3: set_o,Y5: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ A3 ) @ C ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_91_order__subst2,axiom,
% 2.70/1.58 ! [A3: set_o,B2: set_o,F: set_o > set_o,C: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ ( F @ B2 ) @ C )
% 2.70/1.58 => ( ! [X3: set_o,Y5: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ A3 ) @ C ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_92_order__subst1,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A3 @ ( F @ B2 ) )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 2.70/1.58 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A3 @ ( F @ C ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_93_order__subst1,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv,F: set_o > set_Pa1764573435lle_tv,B2: set_o,C: set_o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A3 @ ( F @ B2 ) )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B2 @ C )
% 2.70/1.58 => ( ! [X3: set_o,Y5: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A3 @ ( F @ C ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_94_order__subst1,axiom,
% 2.70/1.58 ! [A3: set_o,F: set_Pa1764573435lle_tv > set_o,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A3 @ ( F @ B2 ) )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B2 @ C )
% 2.70/1.58 => ( ! [X3: set_Pa1764573435lle_tv,Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ X3 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ A3 @ ( F @ C ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_95_order__subst1,axiom,
% 2.70/1.58 ! [A3: set_o,F: set_o > set_o,B2: set_o,C: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A3 @ ( F @ B2 ) )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B2 @ C )
% 2.70/1.58 => ( ! [X3: set_o,Y5: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ X3 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ A3 @ ( F @ C ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_96_rev__image__eqI,axiom,
% 2.70/1.58 ! [X2: $o,A: set_o,B2: $o,F: $o > $o] :
% 2.70/1.58 ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_o @ B2 @ ( image_o_o @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_97_rev__image__eqI,axiom,
% 2.70/1.58 ! [X2: $o,A: set_o,B2: list_char,F: $o > list_char] :
% 2.70/1.58 ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_list_char @ B2 @ ( image_o_list_char @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_98_rev__image__eqI,axiom,
% 2.70/1.58 ! [X2: $o,A: set_o,B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_99_rev__image__eqI,axiom,
% 2.70/1.58 ! [X2: list_char,A: set_list_char,B2: $o,F: list_char > $o] :
% 2.70/1.58 ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_o @ B2 @ ( image_list_char_o @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_100_rev__image__eqI,axiom,
% 2.70/1.58 ! [X2: list_char,A: set_list_char,B2: list_char,F: list_char > list_char] :
% 2.70/1.58 ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_list_char @ B2 @ ( image_890964937t_char @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_101_rev__image__eqI,axiom,
% 2.70/1.58 ! [X2: list_char,A: set_list_char,B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_102_rev__image__eqI,axiom,
% 2.70/1.58 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: $o,F: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_o @ B2 @ ( image_991799618e_tv_o @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_103_rev__image__eqI,axiom,
% 2.70/1.58 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: list_char,F: paraco1605129243lle_tv > list_char] :
% 2.70/1.58 ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_list_char @ B2 @ ( image_1971766583t_char @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_104_rev__image__eqI,axiom,
% 2.70/1.58 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_105_ball__imageD,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X3 @ ( image_1187894195lle_tv @ F @ A ) )
% 2.70/1.58 => ( P2 @ X3 ) )
% 2.70/1.58 => ! [X4: list_char] :
% 2.70/1.58 ( ( member_list_char @ X4 @ A )
% 2.70/1.58 => ( P2 @ ( F @ X4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_106_ball__imageD,axiom,
% 2.70/1.58 ! [F: $o > $o,A: set_o,P2: $o > $o] :
% 2.70/1.58 ( ! [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ ( image_o_o @ F @ A ) )
% 2.70/1.58 => ( P2 @ X3 ) )
% 2.70/1.58 => ! [X4: $o] :
% 2.70/1.58 ( ( member_o @ X4 @ A )
% 2.70/1.58 => ( P2 @ ( F @ X4 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_107_image__cong,axiom,
% 2.70/1.58 ! [M: set_o,N2: set_o,F: $o > $o,G: $o > $o] :
% 2.70/1.58 ( ( M = N2 )
% 2.70/1.58 => ( ! [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ N2 )
% 2.70/1.58 => ( ( F @ X3 )
% 2.70/1.58 = ( G @ X3 ) ) )
% 2.70/1.58 => ( ( image_o_o @ F @ M )
% 2.70/1.58 = ( image_o_o @ G @ N2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_108_image__cong,axiom,
% 2.70/1.58 ! [M: set_list_char,N2: set_list_char,F: list_char > paraco1605129243lle_tv,G: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( M = N2 )
% 2.70/1.58 => ( ! [X3: list_char] :
% 2.70/1.58 ( ( member_list_char @ X3 @ N2 )
% 2.70/1.58 => ( ( F @ X3 )
% 2.70/1.58 = ( G @ X3 ) ) )
% 2.70/1.58 => ( ( image_1187894195lle_tv @ F @ M )
% 2.70/1.58 = ( image_1187894195lle_tv @ G @ N2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_109_mem__Collect__eq,axiom,
% 2.70/1.58 ! [A3: $o,P2: $o > $o] :
% 2.70/1.58 ( ( member_o @ A3 @ ( collect_o @ P2 ) )
% 2.70/1.58 = ( P2 @ A3 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_110_mem__Collect__eq,axiom,
% 2.70/1.58 ! [A3: list_char,P2: list_char > $o] :
% 2.70/1.58 ( ( member_list_char @ A3 @ ( collect_list_char @ P2 ) )
% 2.70/1.58 = ( P2 @ A3 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_111_mem__Collect__eq,axiom,
% 2.70/1.58 ! [A3: nat,P2: nat > $o] :
% 2.70/1.58 ( ( member_nat @ A3 @ ( collect_nat @ P2 ) )
% 2.70/1.58 = ( P2 @ A3 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_112_mem__Collect__eq,axiom,
% 2.70/1.58 ! [A3: paraco1605129243lle_tv,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( member266900804lle_tv @ A3 @ ( collec1111687558lle_tv @ P2 ) )
% 2.70/1.58 = ( P2 @ A3 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_113_Collect__mem__eq,axiom,
% 2.70/1.58 ! [A: set_o] :
% 2.70/1.58 ( ( collect_o
% 2.70/1.58 @ ^ [X: $o] : ( member_o @ X @ A ) )
% 2.70/1.58 = A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_114_Collect__mem__eq,axiom,
% 2.70/1.58 ! [A: set_list_char] :
% 2.70/1.58 ( ( collect_list_char
% 2.70/1.58 @ ^ [X: list_char] : ( member_list_char @ X @ A ) )
% 2.70/1.58 = A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_115_Collect__mem__eq,axiom,
% 2.70/1.58 ! [A: set_nat] :
% 2.70/1.58 ( ( collect_nat
% 2.70/1.58 @ ^ [X: nat] : ( member_nat @ X @ A ) )
% 2.70/1.58 = A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_116_Collect__mem__eq,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ A ) )
% 2.70/1.58 = A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_117_Collect__cong,axiom,
% 2.70/1.58 ! [P2: nat > $o,Q: nat > $o] :
% 2.70/1.58 ( ! [X3: nat] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 = ( Q @ X3 ) )
% 2.70/1.58 => ( ( collect_nat @ P2 )
% 2.70/1.58 = ( collect_nat @ Q ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_118_Collect__cong,axiom,
% 2.70/1.58 ! [P2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 = ( Q @ X3 ) )
% 2.70/1.58 => ( ( collec1111687558lle_tv @ P2 )
% 2.70/1.58 = ( collec1111687558lle_tv @ Q ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_119_bex__imageD,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ? [X4: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X4 @ ( image_1187894195lle_tv @ F @ A ) )
% 2.70/1.58 & ( P2 @ X4 ) )
% 2.70/1.58 => ? [X3: list_char] :
% 2.70/1.58 ( ( member_list_char @ X3 @ A )
% 2.70/1.58 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_120_bex__imageD,axiom,
% 2.70/1.58 ! [F: $o > $o,A: set_o,P2: $o > $o] :
% 2.70/1.58 ( ? [X4: $o] :
% 2.70/1.58 ( ( member_o @ X4 @ ( image_o_o @ F @ A ) )
% 2.70/1.58 & ( P2 @ X4 ) )
% 2.70/1.58 => ? [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ A )
% 2.70/1.58 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_121_image__iff,axiom,
% 2.70/1.58 ! [Z2: $o,F: $o > $o,A: set_o] :
% 2.70/1.58 ( ( member_o @ Z2 @ ( image_o_o @ F @ A ) )
% 2.70/1.58 = ( ? [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ A )
% 2.70/1.58 & ( Z2
% 2.70/1.58 = ( F @ X ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_122_image__iff,axiom,
% 2.70/1.58 ! [Z2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 2.70/1.58 ( ( member266900804lle_tv @ Z2 @ ( image_1187894195lle_tv @ F @ A ) )
% 2.70/1.58 = ( ? [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ A )
% 2.70/1.58 & ( Z2
% 2.70/1.58 = ( F @ X ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_123_imageI,axiom,
% 2.70/1.58 ! [X2: $o,A: set_o,F: $o > $o] :
% 2.70/1.58 ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( member_o @ ( F @ X2 ) @ ( image_o_o @ F @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_124_imageI,axiom,
% 2.70/1.58 ! [X2: $o,A: set_o,F: $o > list_char] :
% 2.70/1.58 ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( member_list_char @ ( F @ X2 ) @ ( image_o_list_char @ F @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_125_imageI,axiom,
% 2.70/1.58 ! [X2: $o,A: set_o,F: $o > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X2 ) @ ( image_1491822472lle_tv @ F @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_126_imageI,axiom,
% 2.70/1.58 ! [X2: list_char,A: set_list_char,F: list_char > $o] :
% 2.70/1.58 ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( member_o @ ( F @ X2 ) @ ( image_list_char_o @ F @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_127_imageI,axiom,
% 2.70/1.58 ! [X2: list_char,A: set_list_char,F: list_char > list_char] :
% 2.70/1.58 ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( member_list_char @ ( F @ X2 ) @ ( image_890964937t_char @ F @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_128_imageI,axiom,
% 2.70/1.58 ! [X2: list_char,A: set_list_char,F: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X2 ) @ ( image_1187894195lle_tv @ F @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_129_imageI,axiom,
% 2.70/1.58 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( member_o @ ( F @ X2 ) @ ( image_991799618e_tv_o @ F @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_130_imageI,axiom,
% 2.70/1.58 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > list_char] :
% 2.70/1.58 ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( member_list_char @ ( F @ X2 ) @ ( image_1971766583t_char @ F @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_131_imageI,axiom,
% 2.70/1.58 ! [X2: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X2 ) @ ( image_335818702lle_tv @ F @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_132_Collect__mono__iff,axiom,
% 2.70/1.58 ! [P2: nat > $o,Q: nat > $o] :
% 2.70/1.58 ( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) )
% 2.70/1.58 = ( ! [X: nat] :
% 2.70/1.58 ( ( P2 @ X )
% 2.70/1.58 => ( Q @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_133_Collect__mono__iff,axiom,
% 2.70/1.58 ! [P2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ ( collec1111687558lle_tv @ P2 ) @ ( collec1111687558lle_tv @ Q ) )
% 2.70/1.58 = ( ! [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( P2 @ X )
% 2.70/1.58 => ( Q @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_134_Collect__mono__iff,axiom,
% 2.70/1.58 ! [P2: $o > $o,Q: $o > $o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q ) )
% 2.70/1.58 = ( ! [X: $o] :
% 2.70/1.58 ( ( P2 @ X )
% 2.70/1.58 => ( Q @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_135_set__eq__subset,axiom,
% 2.70/1.58 ( ( ^ [Y2: set_Pa1764573435lle_tv,Z: set_Pa1764573435lle_tv] : ( Y2 = Z ) )
% 2.70/1.58 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A2 @ B3 )
% 2.70/1.58 & ( ord_le241064091lle_tv @ B3 @ A2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_136_set__eq__subset,axiom,
% 2.70/1.58 ( ( ^ [Y2: set_o,Z: set_o] : ( Y2 = Z ) )
% 2.70/1.58 = ( ^ [A2: set_o,B3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A2 @ B3 )
% 2.70/1.58 & ( ord_less_eq_set_o @ B3 @ A2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_137_subset__trans,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C2: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A @ B )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B @ C2 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A @ C2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_138_subset__trans,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o,C2: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A @ B )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B @ C2 )
% 2.70/1.58 => ( ord_less_eq_set_o @ A @ C2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_139_Collect__mono,axiom,
% 2.70/1.58 ! [P2: nat > $o,Q: nat > $o] :
% 2.70/1.58 ( ! [X3: nat] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( Q @ X3 ) )
% 2.70/1.58 => ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_140_Collect__mono,axiom,
% 2.70/1.58 ! [P2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( Q @ X3 ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( collec1111687558lle_tv @ P2 ) @ ( collec1111687558lle_tv @ Q ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_141_Collect__mono,axiom,
% 2.70/1.58 ! [P2: $o > $o,Q: $o > $o] :
% 2.70/1.58 ( ! [X3: $o] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( Q @ X3 ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_142_subset__refl,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_143_subset__refl,axiom,
% 2.70/1.58 ! [A: set_o] : ( ord_less_eq_set_o @ A @ A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_144_subset__iff,axiom,
% 2.70/1.58 ( ord_le1836582007t_char
% 2.70/1.58 = ( ^ [A2: set_list_char,B3: set_list_char] :
% 2.70/1.58 ! [T: list_char] :
% 2.70/1.58 ( ( member_list_char @ T @ A2 )
% 2.70/1.58 => ( member_list_char @ T @ B3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_145_subset__iff,axiom,
% 2.70/1.58 ( ord_le241064091lle_tv
% 2.70/1.58 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ! [T: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ T @ A2 )
% 2.70/1.58 => ( member266900804lle_tv @ T @ B3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_146_subset__iff,axiom,
% 2.70/1.58 ( ord_less_eq_set_o
% 2.70/1.58 = ( ^ [A2: set_o,B3: set_o] :
% 2.70/1.58 ! [T: $o] :
% 2.70/1.58 ( ( member_o @ T @ A2 )
% 2.70/1.58 => ( member_o @ T @ B3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_147_equalityD2,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ( ord_le241064091lle_tv @ B @ A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_148_equalityD2,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ( ord_less_eq_set_o @ B @ A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_149_equalityD1,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ( ord_le241064091lle_tv @ A @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_150_equalityD1,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ( ord_less_eq_set_o @ A @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_151_subset__eq,axiom,
% 2.70/1.58 ( ord_le1836582007t_char
% 2.70/1.58 = ( ^ [A2: set_list_char,B3: set_list_char] :
% 2.70/1.58 ! [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ A2 )
% 2.70/1.58 => ( member_list_char @ X @ B3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_152_subset__eq,axiom,
% 2.70/1.58 ( ord_le241064091lle_tv
% 2.70/1.58 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ! [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ A2 )
% 2.70/1.58 => ( member266900804lle_tv @ X @ B3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_153_subset__eq,axiom,
% 2.70/1.58 ( ord_less_eq_set_o
% 2.70/1.58 = ( ^ [A2: set_o,B3: set_o] :
% 2.70/1.58 ! [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ A2 )
% 2.70/1.58 => ( member_o @ X @ B3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_154_equalityE,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ~ ( ( ord_le241064091lle_tv @ A @ B )
% 2.70/1.58 => ~ ( ord_le241064091lle_tv @ B @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_155_equalityE,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ~ ( ( ord_less_eq_set_o @ A @ B )
% 2.70/1.58 => ~ ( ord_less_eq_set_o @ B @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_156_subsetD,axiom,
% 2.70/1.58 ! [A: set_list_char,B: set_list_char,C: list_char] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ A @ B )
% 2.70/1.58 => ( ( member_list_char @ C @ A )
% 2.70/1.58 => ( member_list_char @ C @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_157_subsetD,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A @ B )
% 2.70/1.58 => ( ( member266900804lle_tv @ C @ A )
% 2.70/1.58 => ( member266900804lle_tv @ C @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_158_subsetD,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o,C: $o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A @ B )
% 2.70/1.58 => ( ( member_o @ C @ A )
% 2.70/1.58 => ( member_o @ C @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_159_in__mono,axiom,
% 2.70/1.58 ! [A: set_list_char,B: set_list_char,X2: list_char] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ A @ B )
% 2.70/1.58 => ( ( member_list_char @ X2 @ A )
% 2.70/1.58 => ( member_list_char @ X2 @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_160_in__mono,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,X2: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A @ B )
% 2.70/1.58 => ( ( member266900804lle_tv @ X2 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ X2 @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_161_in__mono,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o,X2: $o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A @ B )
% 2.70/1.58 => ( ( member_o @ X2 @ A )
% 2.70/1.58 => ( member_o @ X2 @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_162_UNIV__witness,axiom,
% 2.70/1.58 ? [X3: paraco1605129243lle_tv] : ( member266900804lle_tv @ X3 @ top_to1057771083lle_tv ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_163_UNIV__witness,axiom,
% 2.70/1.58 ? [X3: list_char] : ( member_list_char @ X3 @ top_to748628679t_char ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_164_UNIV__witness,axiom,
% 2.70/1.58 ? [X3: $o] : ( member_o @ X3 @ top_top_set_o ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_165_UNIV__eq__I,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] : ( member266900804lle_tv @ X3 @ A )
% 2.70/1.58 => ( top_to1057771083lle_tv = A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_166_UNIV__eq__I,axiom,
% 2.70/1.58 ! [A: set_list_char] :
% 2.70/1.58 ( ! [X3: list_char] : ( member_list_char @ X3 @ A )
% 2.70/1.58 => ( top_to748628679t_char = A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_167_UNIV__eq__I,axiom,
% 2.70/1.58 ! [A: set_o] :
% 2.70/1.58 ( ! [X3: $o] : ( member_o @ X3 @ A )
% 2.70/1.58 => ( top_top_set_o = A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_168_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: $o > $o,A: set_o,P2: $o > $o] :
% 2.70/1.58 ( ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ ( image_o_o @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_o_o @ F
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_169_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: nat > $o,A: set_nat,P2: $o > $o] :
% 2.70/1.58 ( ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ ( image_nat_o @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_nat_o @ F
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_170_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv,P2: $o > $o] :
% 2.70/1.58 ( ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ ( image_991799618e_tv_o @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_991799618e_tv_o @ F
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_171_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: $o > nat,A: set_o,P2: nat > $o] :
% 2.70/1.58 ( ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ ( image_o_nat @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_o_nat @ F
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_172_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: nat > nat,A: set_nat,P2: nat > $o] :
% 2.70/1.58 ( ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ ( image_nat_nat @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_nat_nat @ F
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_173_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: paraco1605129243lle_tv > nat,A: set_Pa1764573435lle_tv,P2: nat > $o] :
% 2.70/1.58 ( ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ ( image_376325286tv_nat @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_376325286tv_nat @ F
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_174_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: $o > paraco1605129243lle_tv,A: set_o,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ ( image_1491822472lle_tv @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_1491822472lle_tv @ F
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_175_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: nat > paraco1605129243lle_tv,A: set_nat,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ ( image_1151963140lle_tv @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_1151963140lle_tv @ F
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_176_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_335818702lle_tv @ F
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_177_Compr__image__eq,axiom,
% 2.70/1.58 ! [F: list_char > $o,A: set_list_char,P2: $o > $o] :
% 2.70/1.58 ( ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ ( image_list_char_o @ F @ A ) )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 = ( image_list_char_o @ F
% 2.70/1.58 @ ( collect_list_char
% 2.70/1.58 @ ^ [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ A )
% 2.70/1.58 & ( P2 @ ( F @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_178_image__image,axiom,
% 2.70/1.58 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 2.70/1.58 ( ( image_335818702lle_tv @ F @ ( image_1187894195lle_tv @ G @ A ) )
% 2.70/1.58 = ( image_1187894195lle_tv
% 2.70/1.58 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 2.70/1.58 @ A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_179_image__image,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,G: list_char > list_char,A: set_list_char] :
% 2.70/1.58 ( ( image_1187894195lle_tv @ F @ ( image_890964937t_char @ G @ A ) )
% 2.70/1.58 = ( image_1187894195lle_tv
% 2.70/1.58 @ ^ [X: list_char] : ( F @ ( G @ X ) )
% 2.70/1.58 @ A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_180_image__image,axiom,
% 2.70/1.58 ! [F: $o > $o,G: $o > $o,A: set_o] :
% 2.70/1.58 ( ( image_o_o @ F @ ( image_o_o @ G @ A ) )
% 2.70/1.58 = ( image_o_o
% 2.70/1.58 @ ^ [X: $o] : ( F @ ( G @ X ) )
% 2.70/1.58 @ A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_181_imageE,axiom,
% 2.70/1.58 ! [B2: $o,F: $o > $o,A: set_o] :
% 2.70/1.58 ( ( member_o @ B2 @ ( image_o_o @ F @ A ) )
% 2.70/1.58 => ~ ! [X3: $o] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X3 ) )
% 2.70/1.58 => ~ ( member_o @ X3 @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_182_imageE,axiom,
% 2.70/1.58 ! [B2: $o,F: list_char > $o,A: set_list_char] :
% 2.70/1.58 ( ( member_o @ B2 @ ( image_list_char_o @ F @ A ) )
% 2.70/1.58 => ~ ! [X3: list_char] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X3 ) )
% 2.70/1.58 => ~ ( member_list_char @ X3 @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_183_imageE,axiom,
% 2.70/1.58 ! [B2: $o,F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( member_o @ B2 @ ( image_991799618e_tv_o @ F @ A ) )
% 2.70/1.58 => ~ ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X3 ) )
% 2.70/1.58 => ~ ( member266900804lle_tv @ X3 @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_184_imageE,axiom,
% 2.70/1.58 ! [B2: list_char,F: $o > list_char,A: set_o] :
% 2.70/1.58 ( ( member_list_char @ B2 @ ( image_o_list_char @ F @ A ) )
% 2.70/1.58 => ~ ! [X3: $o] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X3 ) )
% 2.70/1.58 => ~ ( member_o @ X3 @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_185_imageE,axiom,
% 2.70/1.58 ! [B2: list_char,F: list_char > list_char,A: set_list_char] :
% 2.70/1.58 ( ( member_list_char @ B2 @ ( image_890964937t_char @ F @ A ) )
% 2.70/1.58 => ~ ! [X3: list_char] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X3 ) )
% 2.70/1.58 => ~ ( member_list_char @ X3 @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_186_imageE,axiom,
% 2.70/1.58 ! [B2: list_char,F: paraco1605129243lle_tv > list_char,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( member_list_char @ B2 @ ( image_1971766583t_char @ F @ A ) )
% 2.70/1.58 => ~ ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X3 ) )
% 2.70/1.58 => ~ ( member266900804lle_tv @ X3 @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_187_imageE,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv,A: set_o] :
% 2.70/1.58 ( ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ A ) )
% 2.70/1.58 => ~ ! [X3: $o] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X3 ) )
% 2.70/1.58 => ~ ( member_o @ X3 @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_188_imageE,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 2.70/1.58 ( ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ A ) )
% 2.70/1.58 => ~ ! [X3: list_char] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X3 ) )
% 2.70/1.58 => ~ ( member_list_char @ X3 @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_189_imageE,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) )
% 2.70/1.58 => ~ ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X3 ) )
% 2.70/1.58 => ~ ( member266900804lle_tv @ X3 @ A ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_190_Collect__restrict,axiom,
% 2.70/1.58 ! [X5: set_list_char,P2: list_char > $o] :
% 2.70/1.58 ( ord_le1836582007t_char
% 2.70/1.58 @ ( collect_list_char
% 2.70/1.58 @ ^ [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ X5 )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 @ X5 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_191_Collect__restrict,axiom,
% 2.70/1.58 ! [X5: set_nat,P2: nat > $o] :
% 2.70/1.58 ( ord_less_eq_set_nat
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ X5 )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 @ X5 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_192_Collect__restrict,axiom,
% 2.70/1.58 ! [X5: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ord_le241064091lle_tv
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ X5 )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 @ X5 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_193_Collect__restrict,axiom,
% 2.70/1.58 ! [X5: set_o,P2: $o > $o] :
% 2.70/1.58 ( ord_less_eq_set_o
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ X5 )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 @ X5 ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_194_prop__restrict,axiom,
% 2.70/1.58 ! [X2: list_char,Z3: set_list_char,X5: set_list_char,P2: list_char > $o] :
% 2.70/1.58 ( ( member_list_char @ X2 @ Z3 )
% 2.70/1.58 => ( ( ord_le1836582007t_char @ Z3
% 2.70/1.58 @ ( collect_list_char
% 2.70/1.58 @ ^ [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ X5 )
% 2.70/1.58 & ( P2 @ X ) ) ) )
% 2.70/1.58 => ( P2 @ X2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_195_prop__restrict,axiom,
% 2.70/1.58 ! [X2: nat,Z3: set_nat,X5: set_nat,P2: nat > $o] :
% 2.70/1.58 ( ( member_nat @ X2 @ Z3 )
% 2.70/1.58 => ( ( ord_less_eq_set_nat @ Z3
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ X5 )
% 2.70/1.58 & ( P2 @ X ) ) ) )
% 2.70/1.58 => ( P2 @ X2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_196_prop__restrict,axiom,
% 2.70/1.58 ! [X2: paraco1605129243lle_tv,Z3: set_Pa1764573435lle_tv,X5: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( member266900804lle_tv @ X2 @ Z3 )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ Z3
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ X5 )
% 2.70/1.58 & ( P2 @ X ) ) ) )
% 2.70/1.58 => ( P2 @ X2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_197_prop__restrict,axiom,
% 2.70/1.58 ! [X2: $o,Z3: set_o,X5: set_o,P2: $o > $o] :
% 2.70/1.58 ( ( member_o @ X2 @ Z3 )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ Z3
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ X5 )
% 2.70/1.58 & ( P2 @ X ) ) ) )
% 2.70/1.58 => ( P2 @ X2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_198_Collect__subset,axiom,
% 2.70/1.58 ! [A: set_list_char,P2: list_char > $o] :
% 2.70/1.58 ( ord_le1836582007t_char
% 2.70/1.58 @ ( collect_list_char
% 2.70/1.58 @ ^ [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 @ A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_199_Collect__subset,axiom,
% 2.70/1.58 ! [A: set_nat,P2: nat > $o] :
% 2.70/1.58 ( ord_less_eq_set_nat
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 @ A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_200_Collect__subset,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ord_le241064091lle_tv
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 @ A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_201_Collect__subset,axiom,
% 2.70/1.58 ! [A: set_o,P2: $o > $o] :
% 2.70/1.58 ( ord_less_eq_set_o
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) )
% 2.70/1.58 @ A ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_202_UNIV__def,axiom,
% 2.70/1.58 ( top_top_set_nat
% 2.70/1.58 = ( collect_nat
% 2.70/1.58 @ ^ [X: nat] : $true ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_203_UNIV__def,axiom,
% 2.70/1.58 ( top_to1057771083lle_tv
% 2.70/1.58 = ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] : $true ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_204_UNIV__def,axiom,
% 2.70/1.58 ( top_to748628679t_char
% 2.70/1.58 = ( collect_list_char
% 2.70/1.58 @ ^ [X: list_char] : $true ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_205_UNIV__def,axiom,
% 2.70/1.58 ( top_top_set_o
% 2.70/1.58 = ( collect_o
% 2.70/1.58 @ ^ [X: $o] : $true ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_206_top_Oextremum__uniqueI,axiom,
% 2.70/1.58 ! [A3: set_list_char] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ top_to748628679t_char @ A3 )
% 2.70/1.58 => ( A3 = top_to748628679t_char ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_207_top_Oextremum__uniqueI,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A3 )
% 2.70/1.58 => ( A3 = top_to1057771083lle_tv ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_208_top_Oextremum__uniqueI,axiom,
% 2.70/1.58 ! [A3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ top_top_set_o @ A3 )
% 2.70/1.58 => ( A3 = top_top_set_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_209_top_Oextremum__unique,axiom,
% 2.70/1.58 ! [A3: set_list_char] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ top_to748628679t_char @ A3 )
% 2.70/1.58 = ( A3 = top_to748628679t_char ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_210_top_Oextremum__unique,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A3 )
% 2.70/1.58 = ( A3 = top_to1057771083lle_tv ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_211_top_Oextremum__unique,axiom,
% 2.70/1.58 ! [A3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ top_top_set_o @ A3 )
% 2.70/1.58 = ( A3 = top_top_set_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_212_top__greatest,axiom,
% 2.70/1.58 ! [A3: set_list_char] : ( ord_le1836582007t_char @ A3 @ top_to748628679t_char ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_213_top__greatest,axiom,
% 2.70/1.58 ! [A3: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A3 @ top_to1057771083lle_tv ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_214_top__greatest,axiom,
% 2.70/1.58 ! [A3: set_o] : ( ord_less_eq_set_o @ A3 @ top_top_set_o ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_215_subset__image__iff,axiom,
% 2.70/1.58 ! [B: set_Pa1764573435lle_tv,F: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B @ ( image_1187894195lle_tv @ F @ A ) )
% 2.70/1.58 = ( ? [AA: set_list_char] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ AA @ A )
% 2.70/1.58 & ( B
% 2.70/1.58 = ( image_1187894195lle_tv @ F @ AA ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_216_subset__image__iff,axiom,
% 2.70/1.58 ! [B: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B @ ( image_335818702lle_tv @ F @ A ) )
% 2.70/1.58 = ( ? [AA: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ AA @ A )
% 2.70/1.58 & ( B
% 2.70/1.58 = ( image_335818702lle_tv @ F @ AA ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_217_subset__image__iff,axiom,
% 2.70/1.58 ! [B: set_Pa1764573435lle_tv,F: $o > paraco1605129243lle_tv,A: set_o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B @ ( image_1491822472lle_tv @ F @ A ) )
% 2.70/1.58 = ( ? [AA: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ AA @ A )
% 2.70/1.58 & ( B
% 2.70/1.58 = ( image_1491822472lle_tv @ F @ AA ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_218_subset__image__iff,axiom,
% 2.70/1.58 ! [B: set_o,F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B @ ( image_991799618e_tv_o @ F @ A ) )
% 2.70/1.58 = ( ? [AA: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ AA @ A )
% 2.70/1.58 & ( B
% 2.70/1.58 = ( image_991799618e_tv_o @ F @ AA ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_219_subset__image__iff,axiom,
% 2.70/1.58 ! [B: set_o,F: $o > $o,A: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B @ ( image_o_o @ F @ A ) )
% 2.70/1.58 = ( ? [AA: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ AA @ A )
% 2.70/1.58 & ( B
% 2.70/1.58 = ( image_o_o @ F @ AA ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_220_image__subset__iff,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ B )
% 2.70/1.58 = ( ! [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ A )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X ) @ B ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_221_image__subset__iff,axiom,
% 2.70/1.58 ! [F: $o > $o,A: set_o,B: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ B )
% 2.70/1.58 = ( ! [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ A )
% 2.70/1.58 => ( member_o @ ( F @ X ) @ B ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_222_subset__imageE,axiom,
% 2.70/1.58 ! [B: set_Pa1764573435lle_tv,F: list_char > paraco1605129243lle_tv,A: set_list_char] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B @ ( image_1187894195lle_tv @ F @ A ) )
% 2.70/1.58 => ~ ! [C3: set_list_char] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ C3 @ A )
% 2.70/1.58 => ( B
% 2.70/1.58 != ( image_1187894195lle_tv @ F @ C3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_223_subset__imageE,axiom,
% 2.70/1.58 ! [B: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B @ ( image_335818702lle_tv @ F @ A ) )
% 2.70/1.58 => ~ ! [C3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ C3 @ A )
% 2.70/1.58 => ( B
% 2.70/1.58 != ( image_335818702lle_tv @ F @ C3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_224_subset__imageE,axiom,
% 2.70/1.58 ! [B: set_Pa1764573435lle_tv,F: $o > paraco1605129243lle_tv,A: set_o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B @ ( image_1491822472lle_tv @ F @ A ) )
% 2.70/1.58 => ~ ! [C3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ C3 @ A )
% 2.70/1.58 => ( B
% 2.70/1.58 != ( image_1491822472lle_tv @ F @ C3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_225_subset__imageE,axiom,
% 2.70/1.58 ! [B: set_o,F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B @ ( image_991799618e_tv_o @ F @ A ) )
% 2.70/1.58 => ~ ! [C3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ C3 @ A )
% 2.70/1.58 => ( B
% 2.70/1.58 != ( image_991799618e_tv_o @ F @ C3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_226_subset__imageE,axiom,
% 2.70/1.58 ! [B: set_o,F: $o > $o,A: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B @ ( image_o_o @ F @ A ) )
% 2.70/1.58 => ~ ! [C3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ C3 @ A )
% 2.70/1.58 => ( B
% 2.70/1.58 != ( image_o_o @ F @ C3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_227_image__subsetI,axiom,
% 2.70/1.58 ! [A: set_o,F: $o > list_char,B: set_list_char] :
% 2.70/1.58 ( ! [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ A )
% 2.70/1.58 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le1836582007t_char @ ( image_o_list_char @ F @ A ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_228_image__subsetI,axiom,
% 2.70/1.58 ! [A: set_list_char,F: list_char > list_char,B: set_list_char] :
% 2.70/1.58 ( ! [X3: list_char] :
% 2.70/1.58 ( ( member_list_char @ X3 @ A )
% 2.70/1.58 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le1836582007t_char @ ( image_890964937t_char @ F @ A ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_229_image__subsetI,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > list_char,B: set_list_char] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X3 @ A )
% 2.70/1.58 => ( member_list_char @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le1836582007t_char @ ( image_1971766583t_char @ F @ A ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_230_image__subsetI,axiom,
% 2.70/1.58 ! [A: set_o,F: $o > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ! [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( image_1491822472lle_tv @ F @ A ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_231_image__subsetI,axiom,
% 2.70/1.58 ! [A: set_list_char,F: list_char > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ! [X3: list_char] :
% 2.70/1.58 ( ( member_list_char @ X3 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_232_image__subsetI,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X3 @ A )
% 2.70/1.58 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ A ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_233_image__subsetI,axiom,
% 2.70/1.58 ! [A: set_o,F: $o > $o,B: set_o] :
% 2.70/1.58 ( ! [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ A )
% 2.70/1.58 => ( member_o @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_234_image__subsetI,axiom,
% 2.70/1.58 ! [A: set_list_char,F: list_char > $o,B: set_o] :
% 2.70/1.58 ( ! [X3: list_char] :
% 2.70/1.58 ( ( member_list_char @ X3 @ A )
% 2.70/1.58 => ( member_o @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( image_list_char_o @ F @ A ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_235_image__subsetI,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > $o,B: set_o] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X3 @ A )
% 2.70/1.58 => ( member_o @ ( F @ X3 ) @ B ) )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ F @ A ) @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_236_image__mono,axiom,
% 2.70/1.58 ! [A: set_list_char,B: set_list_char,F: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ A @ B )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ ( image_1187894195lle_tv @ F @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_237_image__mono,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A @ B )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ A ) @ ( image_335818702lle_tv @ F @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_238_image__mono,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A @ B )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ F @ A ) @ ( image_991799618e_tv_o @ F @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_239_image__mono,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o,F: $o > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A @ B )
% 2.70/1.58 => ( ord_le241064091lle_tv @ ( image_1491822472lle_tv @ F @ A ) @ ( image_1491822472lle_tv @ F @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_240_image__mono,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o,F: $o > $o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A @ B )
% 2.70/1.58 => ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ ( image_o_o @ F @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_241_range__eqI,axiom,
% 2.70/1.58 ! [B2: $o,F: list_char > $o,X2: list_char] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_o @ B2 @ ( image_list_char_o @ F @ top_to748628679t_char ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_242_range__eqI,axiom,
% 2.70/1.58 ! [B2: list_char,F: list_char > list_char,X2: list_char] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_list_char @ B2 @ ( image_890964937t_char @ F @ top_to748628679t_char ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_243_range__eqI,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: list_char > paraco1605129243lle_tv,X2: list_char] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member266900804lle_tv @ B2 @ ( image_1187894195lle_tv @ F @ top_to748628679t_char ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_244_range__eqI,axiom,
% 2.70/1.58 ! [B2: $o,F: $o > $o,X2: $o] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_o @ B2 @ ( image_o_o @ F @ top_top_set_o ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_245_range__eqI,axiom,
% 2.70/1.58 ! [B2: list_char,F: $o > list_char,X2: $o] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member_list_char @ B2 @ ( image_o_list_char @ F @ top_top_set_o ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_246_range__eqI,axiom,
% 2.70/1.58 ! [B2: paraco1605129243lle_tv,F: $o > paraco1605129243lle_tv,X2: $o] :
% 2.70/1.58 ( ( B2
% 2.70/1.58 = ( F @ X2 ) )
% 2.70/1.58 => ( member266900804lle_tv @ B2 @ ( image_1491822472lle_tv @ F @ top_top_set_o ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_247_rangeI,axiom,
% 2.70/1.58 ! [F: list_char > $o,X2: list_char] : ( member_o @ ( F @ X2 ) @ ( image_list_char_o @ F @ top_to748628679t_char ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_248_rangeI,axiom,
% 2.70/1.58 ! [F: list_char > list_char,X2: list_char] : ( member_list_char @ ( F @ X2 ) @ ( image_890964937t_char @ F @ top_to748628679t_char ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_249_rangeI,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,X2: list_char] : ( member266900804lle_tv @ ( F @ X2 ) @ ( image_1187894195lle_tv @ F @ top_to748628679t_char ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_250_rangeI,axiom,
% 2.70/1.58 ! [F: $o > $o,X2: $o] : ( member_o @ ( F @ X2 ) @ ( image_o_o @ F @ top_top_set_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_251_rangeI,axiom,
% 2.70/1.58 ! [F: $o > list_char,X2: $o] : ( member_list_char @ ( F @ X2 ) @ ( image_o_list_char @ F @ top_top_set_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_252_rangeI,axiom,
% 2.70/1.58 ! [F: $o > paraco1605129243lle_tv,X2: $o] : ( member266900804lle_tv @ ( F @ X2 ) @ ( image_1491822472lle_tv @ F @ top_top_set_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_253_subset__UNIV,axiom,
% 2.70/1.58 ! [A: set_list_char] : ( ord_le1836582007t_char @ A @ top_to748628679t_char ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_254_subset__UNIV,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_255_subset__UNIV,axiom,
% 2.70/1.58 ! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_256_surj__def,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( ( image_1187894195lle_tv @ F @ top_to748628679t_char )
% 2.70/1.58 = top_to1057771083lle_tv )
% 2.70/1.58 = ( ! [Y4: paraco1605129243lle_tv] :
% 2.70/1.58 ? [X: list_char] :
% 2.70/1.58 ( Y4
% 2.70/1.58 = ( F @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_257_surj__def,axiom,
% 2.70/1.58 ! [F: list_char > list_char] :
% 2.70/1.58 ( ( ( image_890964937t_char @ F @ top_to748628679t_char )
% 2.70/1.58 = top_to748628679t_char )
% 2.70/1.58 = ( ! [Y4: list_char] :
% 2.70/1.58 ? [X: list_char] :
% 2.70/1.58 ( Y4
% 2.70/1.58 = ( F @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_258_surj__def,axiom,
% 2.70/1.58 ! [F: list_char > $o] :
% 2.70/1.58 ( ( ( image_list_char_o @ F @ top_to748628679t_char )
% 2.70/1.58 = top_top_set_o )
% 2.70/1.58 = ( ! [Y4: $o] :
% 2.70/1.58 ? [X: list_char] :
% 2.70/1.58 ( Y4
% 2.70/1.58 = ( F @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_259_surj__def,axiom,
% 2.70/1.58 ! [F: $o > list_char] :
% 2.70/1.58 ( ( ( image_o_list_char @ F @ top_top_set_o )
% 2.70/1.58 = top_to748628679t_char )
% 2.70/1.58 = ( ! [Y4: list_char] :
% 2.70/1.58 ? [X: $o] :
% 2.70/1.58 ( Y4
% 2.70/1.58 = ( F @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_260_surj__def,axiom,
% 2.70/1.58 ! [F: $o > $o] :
% 2.70/1.58 ( ( ( image_o_o @ F @ top_top_set_o )
% 2.70/1.58 = top_top_set_o )
% 2.70/1.58 = ( ! [Y4: $o] :
% 2.70/1.58 ? [X: $o] :
% 2.70/1.58 ( Y4
% 2.70/1.58 = ( F @ X ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_261_surjI,axiom,
% 2.70/1.58 ! [G: list_char > paraco1605129243lle_tv,F: paraco1605129243lle_tv > list_char] :
% 2.70/1.58 ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( G @ ( F @ X3 ) )
% 2.70/1.58 = X3 )
% 2.70/1.58 => ( ( image_1187894195lle_tv @ G @ top_to748628679t_char )
% 2.70/1.58 = top_to1057771083lle_tv ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_262_surjI,axiom,
% 2.70/1.58 ! [G: list_char > list_char,F: list_char > list_char] :
% 2.70/1.58 ( ! [X3: list_char] :
% 2.70/1.58 ( ( G @ ( F @ X3 ) )
% 2.70/1.58 = X3 )
% 2.70/1.58 => ( ( image_890964937t_char @ G @ top_to748628679t_char )
% 2.70/1.58 = top_to748628679t_char ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_263_surjI,axiom,
% 2.70/1.58 ! [G: list_char > $o,F: $o > list_char] :
% 2.70/1.58 ( ! [X3: $o] :
% 2.70/1.58 ( ( G @ ( F @ X3 ) )
% 2.70/1.58 = X3 )
% 2.70/1.58 => ( ( image_list_char_o @ G @ top_to748628679t_char )
% 2.70/1.58 = top_top_set_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_264_surjI,axiom,
% 2.70/1.58 ! [G: $o > list_char,F: list_char > $o] :
% 2.70/1.58 ( ! [X3: list_char] :
% 2.70/1.58 ( ( G @ ( F @ X3 ) )
% 2.70/1.58 = X3 )
% 2.70/1.58 => ( ( image_o_list_char @ G @ top_top_set_o )
% 2.70/1.58 = top_to748628679t_char ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_265_surjI,axiom,
% 2.70/1.58 ! [G: $o > $o,F: $o > $o] :
% 2.70/1.58 ( ! [X3: $o] :
% 2.70/1.58 ( ( G @ ( F @ X3 ) )
% 2.70/1.58 = X3 )
% 2.70/1.58 => ( ( image_o_o @ G @ top_top_set_o )
% 2.70/1.58 = top_top_set_o ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_266_surjE,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,Y3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( ( image_1187894195lle_tv @ F @ top_to748628679t_char )
% 2.70/1.58 = top_to1057771083lle_tv )
% 2.70/1.58 => ~ ! [X3: list_char] :
% 2.70/1.58 ( Y3
% 2.70/1.58 != ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_267_surjE,axiom,
% 2.70/1.58 ! [F: list_char > list_char,Y3: list_char] :
% 2.70/1.58 ( ( ( image_890964937t_char @ F @ top_to748628679t_char )
% 2.70/1.58 = top_to748628679t_char )
% 2.70/1.58 => ~ ! [X3: list_char] :
% 2.70/1.58 ( Y3
% 2.70/1.58 != ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_268_surjE,axiom,
% 2.70/1.58 ! [F: list_char > $o,Y3: $o] :
% 2.70/1.58 ( ( ( image_list_char_o @ F @ top_to748628679t_char )
% 2.70/1.58 = top_top_set_o )
% 2.70/1.58 => ~ ! [X3: list_char] :
% 2.70/1.58 ( Y3
% 2.70/1.58 = ( ~ ( F @ X3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_269_surjE,axiom,
% 2.70/1.58 ! [F: $o > list_char,Y3: list_char] :
% 2.70/1.58 ( ( ( image_o_list_char @ F @ top_top_set_o )
% 2.70/1.58 = top_to748628679t_char )
% 2.70/1.58 => ~ ! [X3: $o] :
% 2.70/1.58 ( Y3
% 2.70/1.58 != ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_270_surjE,axiom,
% 2.70/1.58 ! [F: $o > $o,Y3: $o] :
% 2.70/1.58 ( ( ( image_o_o @ F @ top_top_set_o )
% 2.70/1.58 = top_top_set_o )
% 2.70/1.58 => ~ ! [X3: $o] :
% 2.70/1.58 ( Y3
% 2.70/1.58 = ( ~ ( F @ X3 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_271_surjD,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,Y3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( ( image_1187894195lle_tv @ F @ top_to748628679t_char )
% 2.70/1.58 = top_to1057771083lle_tv )
% 2.70/1.58 => ? [X3: list_char] :
% 2.70/1.58 ( Y3
% 2.70/1.58 = ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_272_surjD,axiom,
% 2.70/1.58 ! [F: list_char > list_char,Y3: list_char] :
% 2.70/1.58 ( ( ( image_890964937t_char @ F @ top_to748628679t_char )
% 2.70/1.58 = top_to748628679t_char )
% 2.70/1.58 => ? [X3: list_char] :
% 2.70/1.58 ( Y3
% 2.70/1.58 = ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_273_surjD,axiom,
% 2.70/1.58 ! [F: list_char > $o,Y3: $o] :
% 2.70/1.58 ( ( ( image_list_char_o @ F @ top_to748628679t_char )
% 2.70/1.58 = top_top_set_o )
% 2.70/1.58 => ? [X3: list_char] :
% 2.70/1.58 ( Y3
% 2.70/1.58 = ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_274_surjD,axiom,
% 2.70/1.58 ! [F: $o > list_char,Y3: list_char] :
% 2.70/1.58 ( ( ( image_o_list_char @ F @ top_top_set_o )
% 2.70/1.58 = top_to748628679t_char )
% 2.70/1.58 => ? [X3: $o] :
% 2.70/1.58 ( Y3
% 2.70/1.58 = ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_275_surjD,axiom,
% 2.70/1.58 ! [F: $o > $o,Y3: $o] :
% 2.70/1.58 ( ( ( image_o_o @ F @ top_top_set_o )
% 2.70/1.58 = top_top_set_o )
% 2.70/1.58 => ? [X3: $o] :
% 2.70/1.58 ( Y3
% 2.70/1.58 = ( F @ X3 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_276_all__subset__image,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,P2: set_Pa1764573435lle_tv > $o] :
% 2.70/1.58 ( ( ! [B3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B3 @ ( image_1187894195lle_tv @ F @ A ) )
% 2.70/1.58 => ( P2 @ B3 ) ) )
% 2.70/1.58 = ( ! [B3: set_list_char] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ B3 @ A )
% 2.70/1.58 => ( P2 @ ( image_1187894195lle_tv @ F @ B3 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_277_all__subset__image,axiom,
% 2.70/1.58 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,P2: set_Pa1764573435lle_tv > $o] :
% 2.70/1.58 ( ( ! [B3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B3 @ ( image_335818702lle_tv @ F @ A ) )
% 2.70/1.58 => ( P2 @ B3 ) ) )
% 2.70/1.58 = ( ! [B3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B3 @ A )
% 2.70/1.58 => ( P2 @ ( image_335818702lle_tv @ F @ B3 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_278_all__subset__image,axiom,
% 2.70/1.58 ! [F: $o > paraco1605129243lle_tv,A: set_o,P2: set_Pa1764573435lle_tv > $o] :
% 2.70/1.58 ( ( ! [B3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B3 @ ( image_1491822472lle_tv @ F @ A ) )
% 2.70/1.58 => ( P2 @ B3 ) ) )
% 2.70/1.58 = ( ! [B3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B3 @ A )
% 2.70/1.58 => ( P2 @ ( image_1491822472lle_tv @ F @ B3 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_279_all__subset__image,axiom,
% 2.70/1.58 ! [F: paraco1605129243lle_tv > $o,A: set_Pa1764573435lle_tv,P2: set_o > $o] :
% 2.70/1.58 ( ( ! [B3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B3 @ ( image_991799618e_tv_o @ F @ A ) )
% 2.70/1.58 => ( P2 @ B3 ) ) )
% 2.70/1.58 = ( ! [B3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B3 @ A )
% 2.70/1.58 => ( P2 @ ( image_991799618e_tv_o @ F @ B3 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_280_all__subset__image,axiom,
% 2.70/1.58 ! [F: $o > $o,A: set_o,P2: set_o > $o] :
% 2.70/1.58 ( ( ! [B3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B3 @ ( image_o_o @ F @ A ) )
% 2.70/1.58 => ( P2 @ B3 ) ) )
% 2.70/1.58 = ( ! [B3: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B3 @ A )
% 2.70/1.58 => ( P2 @ ( image_o_o @ F @ B3 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_281_valid__def,axiom,
% 2.70/1.58 ( paraco327635598_valid
% 2.70/1.58 = ( ^ [P: paraco1604210848lle_fm] :
% 2.70/1.58 ! [I: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( paraco1325918602e_eval @ I @ P )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_282_pred__subset__eq,axiom,
% 2.70/1.58 ! [R: set_list_char,S: set_list_char] :
% 2.70/1.58 ( ( ord_le1945897678char_o
% 2.70/1.58 @ ^ [X: list_char] : ( member_list_char @ X @ R )
% 2.70/1.58 @ ^ [X: list_char] : ( member_list_char @ X @ S ) )
% 2.70/1.58 = ( ord_le1836582007t_char @ R @ S ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_283_pred__subset__eq,axiom,
% 2.70/1.58 ! [R: set_Pa1764573435lle_tv,S: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le1632188418e_tv_o
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ R )
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ S ) )
% 2.70/1.58 = ( ord_le241064091lle_tv @ R @ S ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_284_pred__subset__eq,axiom,
% 2.70/1.58 ! [R: set_o,S: set_o] :
% 2.70/1.58 ( ( ord_less_eq_o_o
% 2.70/1.58 @ ^ [X: $o] : ( member_o @ X @ R )
% 2.70/1.58 @ ^ [X: $o] : ( member_o @ X @ S ) )
% 2.70/1.58 = ( ord_less_eq_set_o @ R @ S ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_285_subset__Collect__iff,axiom,
% 2.70/1.58 ! [B: set_list_char,A: set_list_char,P2: list_char > $o] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ B @ A )
% 2.70/1.58 => ( ( ord_le1836582007t_char @ B
% 2.70/1.58 @ ( collect_list_char
% 2.70/1.58 @ ^ [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) ) )
% 2.70/1.58 = ( ! [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ B )
% 2.70/1.58 => ( P2 @ X ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_286_subset__Collect__iff,axiom,
% 2.70/1.58 ! [B: set_nat,A: set_nat,P2: nat > $o] :
% 2.70/1.58 ( ( ord_less_eq_set_nat @ B @ A )
% 2.70/1.58 => ( ( ord_less_eq_set_nat @ B
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) ) )
% 2.70/1.58 = ( ! [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ B )
% 2.70/1.58 => ( P2 @ X ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_287_subset__Collect__iff,axiom,
% 2.70/1.58 ! [B: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B @ A )
% 2.70/1.58 => ( ( ord_le241064091lle_tv @ B
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) ) )
% 2.70/1.58 = ( ! [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ B )
% 2.70/1.58 => ( P2 @ X ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_288_subset__Collect__iff,axiom,
% 2.70/1.58 ! [B: set_o,A: set_o,P2: $o > $o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B @ A )
% 2.70/1.58 => ( ( ord_less_eq_set_o @ B
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) ) )
% 2.70/1.58 = ( ! [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ B )
% 2.70/1.58 => ( P2 @ X ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_289_subset__CollectI,axiom,
% 2.70/1.58 ! [B: set_list_char,A: set_list_char,Q: list_char > $o,P2: list_char > $o] :
% 2.70/1.58 ( ( ord_le1836582007t_char @ B @ A )
% 2.70/1.58 => ( ! [X3: list_char] :
% 2.70/1.58 ( ( member_list_char @ X3 @ B )
% 2.70/1.58 => ( ( Q @ X3 )
% 2.70/1.58 => ( P2 @ X3 ) ) )
% 2.70/1.58 => ( ord_le1836582007t_char
% 2.70/1.58 @ ( collect_list_char
% 2.70/1.58 @ ^ [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ B )
% 2.70/1.58 & ( Q @ X ) ) )
% 2.70/1.58 @ ( collect_list_char
% 2.70/1.58 @ ^ [X: list_char] :
% 2.70/1.58 ( ( member_list_char @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_290_subset__CollectI,axiom,
% 2.70/1.58 ! [B: set_nat,A: set_nat,Q: nat > $o,P2: nat > $o] :
% 2.70/1.58 ( ( ord_less_eq_set_nat @ B @ A )
% 2.70/1.58 => ( ! [X3: nat] :
% 2.70/1.58 ( ( member_nat @ X3 @ B )
% 2.70/1.58 => ( ( Q @ X3 )
% 2.70/1.58 => ( P2 @ X3 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_nat
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ B )
% 2.70/1.58 & ( Q @ X ) ) )
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( member_nat @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_291_subset__CollectI,axiom,
% 2.70/1.58 ! [B: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv,Q: paraco1605129243lle_tv > $o,P2: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ B @ A )
% 2.70/1.58 => ( ! [X3: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X3 @ B )
% 2.70/1.58 => ( ( Q @ X3 )
% 2.70/1.58 => ( P2 @ X3 ) ) )
% 2.70/1.58 => ( ord_le241064091lle_tv
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ B )
% 2.70/1.58 & ( Q @ X ) ) )
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( member266900804lle_tv @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_292_subset__CollectI,axiom,
% 2.70/1.58 ! [B: set_o,A: set_o,Q: $o > $o,P2: $o > $o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ B @ A )
% 2.70/1.58 => ( ! [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ B )
% 2.70/1.58 => ( ( Q @ X3 )
% 2.70/1.58 => ( P2 @ X3 ) ) )
% 2.70/1.58 => ( ord_less_eq_set_o
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ B )
% 2.70/1.58 & ( Q @ X ) ) )
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( member_o @ X @ A )
% 2.70/1.58 & ( P2 @ X ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_293_conj__subset__def,axiom,
% 2.70/1.58 ! [A: set_nat,P2: nat > $o,Q: nat > $o] :
% 2.70/1.58 ( ( ord_less_eq_set_nat @ A
% 2.70/1.58 @ ( collect_nat
% 2.70/1.58 @ ^ [X: nat] :
% 2.70/1.58 ( ( P2 @ X )
% 2.70/1.58 & ( Q @ X ) ) ) )
% 2.70/1.58 = ( ( ord_less_eq_set_nat @ A @ ( collect_nat @ P2 ) )
% 2.70/1.58 & ( ord_less_eq_set_nat @ A @ ( collect_nat @ Q ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_294_conj__subset__def,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,P2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A
% 2.70/1.58 @ ( collec1111687558lle_tv
% 2.70/1.58 @ ^ [X: paraco1605129243lle_tv] :
% 2.70/1.58 ( ( P2 @ X )
% 2.70/1.58 & ( Q @ X ) ) ) )
% 2.70/1.58 = ( ( ord_le241064091lle_tv @ A @ ( collec1111687558lle_tv @ P2 ) )
% 2.70/1.58 & ( ord_le241064091lle_tv @ A @ ( collec1111687558lle_tv @ Q ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_295_conj__subset__def,axiom,
% 2.70/1.58 ! [A: set_o,P2: $o > $o,Q: $o > $o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A
% 2.70/1.58 @ ( collect_o
% 2.70/1.58 @ ^ [X: $o] :
% 2.70/1.58 ( ( P2 @ X )
% 2.70/1.58 & ( Q @ X ) ) ) )
% 2.70/1.58 = ( ( ord_less_eq_set_o @ A @ ( collect_o @ P2 ) )
% 2.70/1.58 & ( ord_less_eq_set_o @ A @ ( collect_o @ Q ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_296_Sup_OSUP__identity__eq,axiom,
% 2.70/1.58 ! [Sup: set_o > $o,A: set_o] :
% 2.70/1.58 ( ( Sup
% 2.70/1.58 @ ( image_o_o
% 2.70/1.58 @ ^ [X: $o] : X
% 2.70/1.58 @ A ) )
% 2.70/1.58 = ( Sup @ A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_297_Inf_OINF__cong,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o,C2: $o > $o,D: $o > $o,Inf: set_o > $o] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ( ! [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ B )
% 2.70/1.58 => ( ( C2 @ X3 )
% 2.70/1.58 = ( D @ X3 ) ) )
% 2.70/1.58 => ( ( Inf @ ( image_o_o @ C2 @ A ) )
% 2.70/1.58 = ( Inf @ ( image_o_o @ D @ B ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_298_Inf_OINF__cong,axiom,
% 2.70/1.58 ! [A: set_list_char,B: set_list_char,C2: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv,Inf: set_Pa1764573435lle_tv > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ( ! [X3: list_char] :
% 2.70/1.58 ( ( member_list_char @ X3 @ B )
% 2.70/1.58 => ( ( C2 @ X3 )
% 2.70/1.58 = ( D @ X3 ) ) )
% 2.70/1.58 => ( ( Inf @ ( image_1187894195lle_tv @ C2 @ A ) )
% 2.70/1.58 = ( Inf @ ( image_1187894195lle_tv @ D @ B ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_299_Sup_OSUP__cong,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o,C2: $o > $o,D: $o > $o,Sup: set_o > $o] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ( ! [X3: $o] :
% 2.70/1.58 ( ( member_o @ X3 @ B )
% 2.70/1.58 => ( ( C2 @ X3 )
% 2.70/1.58 = ( D @ X3 ) ) )
% 2.70/1.58 => ( ( Sup @ ( image_o_o @ C2 @ A ) )
% 2.70/1.58 = ( Sup @ ( image_o_o @ D @ B ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_300_Sup_OSUP__cong,axiom,
% 2.70/1.58 ! [A: set_list_char,B: set_list_char,C2: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv,Sup: set_Pa1764573435lle_tv > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( A = B )
% 2.70/1.58 => ( ! [X3: list_char] :
% 2.70/1.58 ( ( member_list_char @ X3 @ B )
% 2.70/1.58 => ( ( C2 @ X3 )
% 2.70/1.58 = ( D @ X3 ) ) )
% 2.70/1.58 => ( ( Sup @ ( image_1187894195lle_tv @ C2 @ A ) )
% 2.70/1.58 = ( Sup @ ( image_1187894195lle_tv @ D @ B ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_301_top__empty__eq,axiom,
% 2.70/1.58 ( top_to1299250770e_tv_o
% 2.70/1.58 = ( ^ [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_302_top__empty__eq,axiom,
% 2.70/1.58 ( top_top_list_char_o
% 2.70/1.58 = ( ^ [X: list_char] : ( member_list_char @ X @ top_to748628679t_char ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_303_top__empty__eq,axiom,
% 2.70/1.58 ( top_top_o_o
% 2.70/1.58 = ( ^ [X: $o] : ( member_o @ X @ top_top_set_o ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_304_Inf_OINF__identity__eq,axiom,
% 2.70/1.58 ! [Inf: set_o > $o,A: set_o] :
% 2.70/1.58 ( ( Inf
% 2.70/1.58 @ ( image_o_o
% 2.70/1.58 @ ^ [X: $o] : X
% 2.70/1.58 @ A ) )
% 2.70/1.58 = ( Inf @ A ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_305_eval_Osimps_I2_J,axiom,
% 2.70/1.58 ! [I2: list_char > paraco1605129243lle_tv] :
% 2.70/1.58 ( ( paraco1325918602e_eval @ I2 @ paraco367965286_Truth )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_306_image__Fpow__mono,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ B )
% 2.70/1.58 => ( ord_le263913851lle_tv @ ( image_30320477lle_tv @ ( image_1187894195lle_tv @ F ) @ ( finite1803457147t_char @ A ) ) @ ( finite2011762305lle_tv @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_307_image__Fpow__mono,axiom,
% 2.70/1.58 ! [F: $o > $o,A: set_o,B: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ B )
% 2.70/1.58 => ( ord_le2085948664_set_o @ ( image_set_o_set_o @ ( image_o_o @ F ) @ ( finite_Fpow_o @ A ) ) @ ( finite_Fpow_o @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_308_eval_Osimps_I5_J,axiom,
% 2.70/1.58 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 != ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1344940915le_Det @ $false ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_309_fm_Oinject_I4_J,axiom,
% 2.70/1.58 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,Y51: paraco1604210848lle_fm,Y52: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 2.70/1.58 = ( paraco1389086619le_Eql @ Y51 @ Y52 ) )
% 2.70/1.58 = ( ( X51 = Y51 )
% 2.70/1.58 & ( X52 = Y52 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_310_fm_Odistinct_I15_J,axiom,
% 2.70/1.58 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 2.70/1.58 ( paraco367965286_Truth
% 2.70/1.58 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_311_Fpow__mono,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A @ B )
% 2.70/1.58 => ( ord_le263913851lle_tv @ ( finite2011762305lle_tv @ A ) @ ( finite2011762305lle_tv @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_312_Fpow__mono,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A @ B )
% 2.70/1.58 => ( ord_le2085948664_set_o @ ( finite_Fpow_o @ A ) @ ( finite_Fpow_o @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_313_eval__equality__simplify,axiom,
% 2.70/1.58 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1344940915le_Det
% 2.70/1.58 @ ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ Q2 ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_314_image__Pow__mono,axiom,
% 2.70/1.58 ! [F: list_char > paraco1605129243lle_tv,A: set_list_char,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ F @ A ) @ B )
% 2.70/1.58 => ( ord_le263913851lle_tv @ ( image_30320477lle_tv @ ( image_1187894195lle_tv @ F ) @ ( pow_list_char @ A ) ) @ ( pow_Pa475453624lle_tv @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_315_image__Pow__mono,axiom,
% 2.70/1.58 ! [F: $o > $o,A: set_o,B: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ ( image_o_o @ F @ A ) @ B )
% 2.70/1.58 => ( ord_le2085948664_set_o @ ( image_set_o_set_o @ ( image_o_o @ F ) @ ( pow_o @ A ) ) @ ( pow_o @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_316_eval_Osimps_I4_J,axiom,
% 2.70/1.58 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ P3 ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 != ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 2.70/1.58 => ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ Q2 ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 != ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ P3 ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 2.70/1.58 != ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_317_Greatest__equality,axiom,
% 2.70/1.58 ! [P2: set_Pa1764573435lle_tv > $o,X2: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( P2 @ X2 )
% 2.70/1.58 => ( ! [Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( P2 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ Y5 @ X2 ) )
% 2.70/1.58 => ( ( order_350719188lle_tv @ P2 )
% 2.70/1.58 = X2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_318_Greatest__equality,axiom,
% 2.70/1.58 ! [P2: set_o > $o,X2: set_o] :
% 2.70/1.58 ( ( P2 @ X2 )
% 2.70/1.58 => ( ! [Y5: set_o] :
% 2.70/1.58 ( ( P2 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ Y5 @ X2 ) )
% 2.70/1.58 => ( ( order_Greatest_set_o @ P2 )
% 2.70/1.58 = X2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_319_GreatestI2__order,axiom,
% 2.70/1.58 ! [P2: set_Pa1764573435lle_tv > $o,X2: set_Pa1764573435lle_tv,Q: set_Pa1764573435lle_tv > $o] :
% 2.70/1.58 ( ( P2 @ X2 )
% 2.70/1.58 => ( ! [Y5: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( P2 @ Y5 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ Y5 @ X2 ) )
% 2.70/1.58 => ( ! [X3: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( ! [Y6: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( P2 @ Y6 )
% 2.70/1.58 => ( ord_le241064091lle_tv @ Y6 @ X3 ) )
% 2.70/1.58 => ( Q @ X3 ) ) )
% 2.70/1.58 => ( Q @ ( order_350719188lle_tv @ P2 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_320_GreatestI2__order,axiom,
% 2.70/1.58 ! [P2: set_o > $o,X2: set_o,Q: set_o > $o] :
% 2.70/1.58 ( ( P2 @ X2 )
% 2.70/1.58 => ( ! [Y5: set_o] :
% 2.70/1.58 ( ( P2 @ Y5 )
% 2.70/1.58 => ( ord_less_eq_set_o @ Y5 @ X2 ) )
% 2.70/1.58 => ( ! [X3: set_o] :
% 2.70/1.58 ( ( P2 @ X3 )
% 2.70/1.58 => ( ! [Y6: set_o] :
% 2.70/1.58 ( ( P2 @ Y6 )
% 2.70/1.58 => ( ord_less_eq_set_o @ Y6 @ X3 ) )
% 2.70/1.58 => ( Q @ X3 ) ) )
% 2.70/1.58 => ( Q @ ( order_Greatest_set_o @ P2 ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_321_fm_Oinject_I3_J,axiom,
% 2.70/1.58 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,Y41: paraco1604210848lle_fm,Y42: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( ( paraco69239110le_Con @ X41 @ X42 )
% 2.70/1.58 = ( paraco69239110le_Con @ Y41 @ Y42 ) )
% 2.70/1.58 = ( ( X41 = Y41 )
% 2.70/1.58 & ( X42 = Y42 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_322_PowI,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( ord_le241064091lle_tv @ A @ B )
% 2.70/1.58 => ( member1875402276lle_tv @ A @ ( pow_Pa475453624lle_tv @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_323_PowI,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o] :
% 2.70/1.58 ( ( ord_less_eq_set_o @ A @ B )
% 2.70/1.58 => ( member_set_o @ A @ ( pow_o @ B ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_324_Pow__iff,axiom,
% 2.70/1.58 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 2.70/1.58 ( ( member1875402276lle_tv @ A @ ( pow_Pa475453624lle_tv @ B ) )
% 2.70/1.58 = ( ord_le241064091lle_tv @ A @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_325_Pow__iff,axiom,
% 2.70/1.58 ! [A: set_o,B: set_o] :
% 2.70/1.58 ( ( member_set_o @ A @ ( pow_o @ B ) )
% 2.70/1.58 = ( ord_less_eq_set_o @ A @ B ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_326_Pow__UNIV,axiom,
% 2.70/1.58 ( ( pow_list_char @ top_to748628679t_char )
% 2.70/1.58 = top_to697846397t_char ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_327_Pow__UNIV,axiom,
% 2.70/1.58 ( ( pow_o @ top_top_set_o )
% 2.70/1.58 = top_top_set_set_o ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_328_fm_Odistinct_I25_J,axiom,
% 2.70/1.58 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( paraco69239110le_Con @ X41 @ X42 )
% 2.70/1.58 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_329_fm_Odistinct_I13_J,axiom,
% 2.70/1.58 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 2.70/1.58 ( paraco367965286_Truth
% 2.70/1.58 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_330_conjunction,axiom,
% 2.70/1.58 ! [P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( paraco327635598_valid @ ( paraco69239110le_Con @ P3 @ Q2 ) )
% 2.70/1.58 = ( ( paraco327635598_valid @ P3 )
% 2.70/1.58 & ( paraco327635598_valid @ Q2 ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_331_eval__negation,axiom,
% 2.70/1.58 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 = ( paraco1344940915le_Det @ $false ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P3 ) )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 != ( paraco1344940915le_Det @ $false ) )
% 2.70/1.58 => ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P3 ) )
% 2.70/1.58 = ( paraco1344940915le_Det @ $false ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 != ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P3 ) )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ P3 ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_332_fm_Oinject_I2_J,axiom,
% 2.70/1.58 ! [X32: paraco1604210848lle_fm,Y32: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( ( paraco445776468le_Neg @ X32 )
% 2.70/1.58 = ( paraco445776468le_Neg @ Y32 ) )
% 2.70/1.58 = ( X32 = Y32 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_333_double__negation,axiom,
% 2.70/1.58 ( paraco1325918602e_eval
% 2.70/1.58 = ( ^ [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ P ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_334_fm_Odistinct_I21_J,axiom,
% 2.70/1.58 ! [X32: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( paraco445776468le_Neg @ X32 )
% 2.70/1.58 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_335_fm_Odistinct_I19_J,axiom,
% 2.70/1.58 ! [X32: paraco1604210848lle_fm,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( paraco445776468le_Neg @ X32 )
% 2.70/1.58 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_336_fm_Odistinct_I11_J,axiom,
% 2.70/1.58 ! [X32: paraco1604210848lle_fm] :
% 2.70/1.58 ( paraco367965286_Truth
% 2.70/1.58 != ( paraco445776468le_Neg @ X32 ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_337_eval__equality,axiom,
% 2.70/1.58 ! [I2: list_char > paraco1605129243lle_tv,P3: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
% 2.70/1.58 ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 != ( paraco1325918602e_eval @ I2 @ Q2 ) )
% 2.70/1.58 => ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ Q2 ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 != ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 2.70/1.58 = ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ P3 ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 2.70/1.58 != ( paraco1344940915le_Det @ $true ) )
% 2.70/1.58 => ( ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 = ( paraco1344940915le_Det @ $false ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ Q2 ) ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ P3 )
% 2.70/1.58 != ( paraco1344940915le_Det @ $false ) )
% 2.70/1.58 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 2.70/1.58 = ( paraco1344940915le_Det @ $false ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P3 ) ) ) )
% 2.70/1.58 & ( ( ( paraco1325918602e_eval @ I2 @ Q2 )
% 2.70/1.58 != ( paraco1344940915le_Det @ $false ) )
% 2.70/1.58 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P3 @ Q2 ) )
% 2.70/1.58 = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_338_fm_Oexhaust,axiom,
% 2.70/1.58 ! [Y3: paraco1604210848lle_fm] :
% 2.70/1.58 ( ! [X12: list_char] :
% 2.70/1.58 ( Y3
% 2.70/1.58 != ( paraco1480028776le_Pro @ X12 ) )
% 2.70/1.58 => ( ( Y3 != paraco367965286_Truth )
% 2.70/1.58 => ( ! [X33: paraco1604210848lle_fm] :
% 2.70/1.58 ( Y3
% 2.70/1.58 != ( paraco445776468le_Neg @ X33 ) )
% 2.70/1.58 => ( ! [X412: paraco1604210848lle_fm,X422: paraco1604210848lle_fm] :
% 2.70/1.58 ( Y3
% 2.70/1.58 != ( paraco69239110le_Con @ X412 @ X422 ) )
% 2.70/1.58 => ( ! [X512: paraco1604210848lle_fm,X522: paraco1604210848lle_fm] :
% 2.70/1.58 ( Y3
% 2.70/1.58 != ( paraco1389086619le_Eql @ X512 @ X522 ) )
% 2.70/1.58 => ~ ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 2.70/1.58 ( Y3
% 2.70/1.58 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ) ) ) ) ) ).
% 2.70/1.58
% 2.70/1.58 thf(fact_339_fm_Oinduct,axiom,
% 2.70/1.58 ! [P2: paraco1604210848lle_fm > $o,Fm: paraco1604210848lle_fm] :
% 2.70/1.59 ( ! [X3: list_char] : ( P2 @ ( paraco1480028776le_Pro @ X3 ) )
% 2.70/1.59 => ( ( P2 @ paraco367965286_Truth )
% 2.70/1.59 => ( ! [X3: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( P2 @ X3 )
% 2.70/1.59 => ( P2 @ ( paraco445776468le_Neg @ X3 ) ) )
% 2.70/1.59 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( P2 @ X1a )
% 2.70/1.59 => ( ( P2 @ X22 )
% 2.70/1.59 => ( P2 @ ( paraco69239110le_Con @ X1a @ X22 ) ) ) )
% 2.70/1.59 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( P2 @ X1a )
% 2.70/1.59 => ( ( P2 @ X22 )
% 2.70/1.59 => ( P2 @ ( paraco1389086619le_Eql @ X1a @ X22 ) ) ) )
% 2.70/1.59 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( P2 @ X1a )
% 2.70/1.59 => ( ( P2 @ X22 )
% 2.70/1.59 => ( P2 @ ( paraco1745535428le_Eql @ X1a @ X22 ) ) ) )
% 2.70/1.59 => ( P2 @ Fm ) ) ) ) ) ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_340_fm_Oinject_I5_J,axiom,
% 2.70/1.59 ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm,Y61: paraco1604210848lle_fm,Y62: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( ( paraco1745535428le_Eql @ X612 @ X622 )
% 2.70/1.59 = ( paraco1745535428le_Eql @ Y61 @ Y62 ) )
% 2.70/1.59 = ( ( X612 = Y61 )
% 2.70/1.59 & ( X622 = Y62 ) ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_341_fm_Oinject_I1_J,axiom,
% 2.70/1.59 ! [X1: list_char,Y1: list_char] :
% 2.70/1.59 ( ( ( paraco1480028776le_Pro @ X1 )
% 2.70/1.59 = ( paraco1480028776le_Pro @ Y1 ) )
% 2.70/1.59 = ( X1 = Y1 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_342_fm_Odistinct_I9_J,axiom,
% 2.70/1.59 ! [X1: list_char,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( paraco1480028776le_Pro @ X1 )
% 2.70/1.59 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_343_eval_Osimps_I1_J,axiom,
% 2.70/1.59 ! [I2: list_char > paraco1605129243lle_tv,S2: list_char] :
% 2.70/1.59 ( ( paraco1325918602e_eval @ I2 @ ( paraco1480028776le_Pro @ S2 ) )
% 2.70/1.59 = ( I2 @ S2 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_344_fm_Odistinct_I23_J,axiom,
% 2.70/1.59 ! [X32: paraco1604210848lle_fm,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( paraco445776468le_Neg @ X32 )
% 2.70/1.59 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_345_fm_Odistinct_I3_J,axiom,
% 2.70/1.59 ! [X1: list_char,X32: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( paraco1480028776le_Pro @ X1 )
% 2.70/1.59 != ( paraco445776468le_Neg @ X32 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_346_fm_Odistinct_I27_J,axiom,
% 2.70/1.59 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( paraco69239110le_Con @ X41 @ X42 )
% 2.70/1.59 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_347_fm_Odistinct_I29_J,axiom,
% 2.70/1.59 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 2.70/1.59 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_348_fm_Odistinct_I5_J,axiom,
% 2.70/1.59 ! [X1: list_char,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( paraco1480028776le_Pro @ X1 )
% 2.70/1.59 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_349_fm_Odistinct_I7_J,axiom,
% 2.70/1.59 ! [X1: list_char,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 2.70/1.59 ( ( paraco1480028776le_Pro @ X1 )
% 2.70/1.59 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_350_fm_Odistinct_I17_J,axiom,
% 2.70/1.59 ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 2.70/1.59 ( paraco367965286_Truth
% 2.70/1.59 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_351_fm_Odistinct_I1_J,axiom,
% 2.70/1.59 ! [X1: list_char] :
% 2.70/1.59 ( ( paraco1480028776le_Pro @ X1 )
% 2.70/1.59 != paraco367965286_Truth ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_352_eval_Ocases,axiom,
% 2.70/1.59 ! [X2: produc696645085lle_fm] :
% 2.70/1.59 ( ! [I3: list_char > paraco1605129243lle_tv,S3: list_char] :
% 2.70/1.59 ( X2
% 2.70/1.59 != ( produc1710735575lle_fm @ I3 @ ( paraco1480028776le_Pro @ S3 ) ) )
% 2.70/1.59 => ( ! [I3: list_char > paraco1605129243lle_tv] :
% 2.70/1.59 ( X2
% 2.70/1.59 != ( produc1710735575lle_fm @ I3 @ paraco367965286_Truth ) )
% 2.70/1.59 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm] :
% 2.70/1.59 ( X2
% 2.70/1.59 != ( produc1710735575lle_fm @ I3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 2.70/1.59 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.70/1.59 ( X2
% 2.70/1.59 != ( produc1710735575lle_fm @ I3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) )
% 2.70/1.59 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.70/1.59 ( X2
% 2.70/1.59 != ( produc1710735575lle_fm @ I3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) )
% 2.70/1.59 => ~ ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.70/1.59 ( X2
% 2.70/1.59 != ( produc1710735575lle_fm @ I3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(fact_353_Sup__bool__def,axiom,
% 2.70/1.59 ( complete_Sup_Sup_o
% 2.70/1.59 = ( member_o @ $true ) ) ).
% 2.70/1.59
% 2.70/1.59 thf(conj_0,conjecture,
% 2.70/1.59 ( ( ! [I: list_char > paraco1605129243lle_tv] :
% 2.70/1.59 ( ( paraco1325918602e_eval @ I @ p )
% 2.70/1.59 = ( paraco1344940915le_Det @ $true ) ) )
% 2.70/1.59 != ( ~ ! [I: list_char > paraco1605129243lle_tv] :
% 2.70/1.59 ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ I @ top_to748628679t_char )
% 2.70/1.59 @ ( paraco1933902578domain
% 2.70/1.59 @ ( collect_nat
% 2.70/1.59 @ ^ [N: nat] : $true ) ) )
% 2.70/1.59 => ( ( paraco1325918602e_eval @ I @ p )
% 2.70/1.59 = ( paraco1344940915le_Det @ $true ) ) ) ) ) ).
% 2.70/1.59 ------------------------
% 2.81/1.61 % (21931)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_21650 for (2999ds/2Mi)
% 2.81/1.61 % (21931)Instruction limit reached!
% 2.81/1.61 % (21931)------------------------------
% 2.81/1.61 % (21931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.61 % (21931)Termination reason: Unknown
% 2.81/1.61 % (21931)Termination phase: shuffling
% 2.81/1.61
% 2.81/1.61 % (21931)Memory used [KB]: 1407
% 2.81/1.61 % (21931)Time elapsed: 0.002 s
% 2.81/1.61 % (21931)Instructions burned: 3 (million)
% 2.81/1.61 % (21931)------------------------------
% 2.81/1.61 % (21931)------------------------------
% 2.81/1.61 % (21927)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/183Mi)
% 2.81/1.61 % (21928)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_21650 for (2999ds/4Mi)
% 2.81/1.62 % (21929)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_21650 for (2999ds/27Mi)
% 2.81/1.62 % (21930)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/2Mi)
% 2.81/1.62 % (21932)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_21650 for (2999ds/275Mi)
% 2.81/1.62 % (21933)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/18Mi)
% 2.81/1.62 % (21930)Instruction limit reached!
% 2.81/1.62 % (21930)------------------------------
% 2.81/1.62 % (21930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.62 % (21930)Termination reason: Unknown
% 2.81/1.62 % (21930)Termination phase: shuffling
% 2.81/1.62
% 2.81/1.62 % (21930)Memory used [KB]: 1407
% 2.81/1.62 % (21930)Time elapsed: 0.004 s
% 2.81/1.62 % (21930)Instructions burned: 2 (million)
% 2.81/1.62 % (21930)------------------------------
% 2.81/1.62 % (21930)------------------------------
% 2.81/1.62 % (21928)Instruction limit reached!
% 2.81/1.62 % (21928)------------------------------
% 2.81/1.62 % (21928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.62 % (21928)Termination reason: Unknown
% 2.81/1.62 % (21928)Termination phase: shuffling
% 2.81/1.62
% 2.81/1.62 % (21928)Memory used [KB]: 1535
% 2.81/1.62 % (21928)Time elapsed: 0.005 s
% 2.81/1.62 % (21928)Instructions burned: 5 (million)
% 2.81/1.62 % (21928)------------------------------
% 2.81/1.62 % (21928)------------------------------
% 2.81/1.62 % (21934)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/3Mi)
% 2.81/1.62 % (21934)Instruction limit reached!
% 2.81/1.62 % (21934)------------------------------
% 2.81/1.62 % (21934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.62 % (21934)Termination reason: Unknown
% 2.81/1.62 % (21934)Termination phase: shuffling
% 2.81/1.62
% 2.81/1.62 % (21934)Memory used [KB]: 1407
% 2.81/1.62 % (21934)Time elapsed: 0.002 s
% 2.81/1.62 % (21934)Instructions burned: 3 (million)
% 2.81/1.62 % (21934)------------------------------
% 2.81/1.62 % (21934)------------------------------
% 2.81/1.63 % (21933)Instruction limit reached!
% 2.81/1.63 % (21933)------------------------------
% 2.81/1.63 % (21933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.63 % (21933)Termination reason: Unknown
% 2.81/1.63 % (21933)Termination phase: shuffling
% 2.81/1.63
% 2.81/1.63 % (21933)Memory used [KB]: 1791
% 2.81/1.63 % (21933)Time elapsed: 0.014 s
% 2.81/1.63 % (21933)Instructions burned: 19 (million)
% 2.81/1.63 % (21933)------------------------------
% 2.81/1.63 % (21933)------------------------------
% 2.81/1.63 % (21938)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_21650 for (2999ds/3Mi)
% 2.81/1.63 % (21938)Instruction limit reached!
% 2.81/1.63 % (21938)------------------------------
% 2.81/1.63 % (21938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.63 % (21938)Termination reason: Unknown
% 2.81/1.63 % (21938)Termination phase: shuffling
% 2.81/1.63
% 2.81/1.63 % (21938)Memory used [KB]: 1407
% 2.81/1.63 % (21938)Time elapsed: 0.002 s
% 2.81/1.63 % (21938)Instructions burned: 3 (million)
% 2.81/1.63 % (21938)------------------------------
% 2.81/1.63 % (21938)------------------------------
% 2.81/1.63 % (21929)Instruction limit reached!
% 2.81/1.63 % (21929)------------------------------
% 2.81/1.63 % (21929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.63 % (21929)Termination reason: Unknown
% 2.81/1.63 % (21929)Termination phase: shuffling
% 2.81/1.63
% 2.81/1.63 % (21929)Memory used [KB]: 1918
% 2.81/1.63 % (21929)Time elapsed: 0.019 s
% 2.81/1.63 % (21929)Instructions burned: 27 (million)
% 2.81/1.63 % (21929)------------------------------
% 2.81/1.63 % (21929)------------------------------
% 2.81/1.63 % (21936)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_21650 for (2999ds/15Mi)
% 2.81/1.63 % (21935)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_21650 for (2999ds/37Mi)
% 2.81/1.64 % (21940)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/7Mi)
% 2.81/1.64 % (21936)Instruction limit reached!
% 2.81/1.64 % (21936)------------------------------
% 2.81/1.64 % (21936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.64 % (21936)Termination reason: Unknown
% 2.81/1.64 % (21936)Termination phase: shuffling
% 2.81/1.64
% 2.81/1.64 % (21936)Memory used [KB]: 1791
% 2.81/1.64 % (21936)Time elapsed: 0.008 s
% 2.81/1.64 % (21936)Instructions burned: 17 (million)
% 2.81/1.64 % (21936)------------------------------
% 2.81/1.64 % (21936)------------------------------
% 2.81/1.64 % (21940)Instruction limit reached!
% 2.81/1.64 % (21940)------------------------------
% 2.81/1.64 % (21940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.64 % (21940)Termination reason: Unknown
% 2.81/1.64 % (21940)Termination phase: shuffling
% 2.81/1.64
% 2.81/1.64 % (21940)Memory used [KB]: 1535
% 2.81/1.64 % (21940)Time elapsed: 0.004 s
% 2.81/1.64 % (21940)Instructions burned: 9 (million)
% 2.81/1.64 % (21940)------------------------------
% 2.81/1.64 % (21940)------------------------------
% 2.81/1.64 % (21939)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_21650 for (2999ds/1041Mi)
% 2.81/1.65 % (21941)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/16Mi)
% 2.81/1.65 % (21942)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_21650 for (2999ds/3Mi)
% 2.81/1.65 % (21943)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_21650 for (2999ds/3Mi)
% 2.81/1.65 % (21942)Instruction limit reached!
% 2.81/1.65 % (21942)------------------------------
% 2.81/1.65 % (21942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.65 % (21942)Termination reason: Unknown
% 2.81/1.65 % (21942)Termination phase: shuffling
% 2.81/1.65
% 2.81/1.65 % (21942)Memory used [KB]: 1535
% 2.81/1.65 % (21942)Time elapsed: 0.003 s
% 2.81/1.65 % (21942)Instructions burned: 3 (million)
% 2.81/1.65 % (21942)------------------------------
% 2.81/1.65 % (21942)------------------------------
% 2.81/1.65 % (21943)Instruction limit reached!
% 2.81/1.65 % (21943)------------------------------
% 2.81/1.65 % (21943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.65 % (21943)Termination reason: Unknown
% 2.81/1.65 % (21943)Termination phase: shuffling
% 2.81/1.65
% 2.81/1.65 % (21943)Memory used [KB]: 1407
% 2.81/1.65 % (21943)Time elapsed: 0.002 s
% 2.81/1.65 % (21943)Instructions burned: 3 (million)
% 2.81/1.65 % (21943)------------------------------
% 2.81/1.65 % (21943)------------------------------
% 2.81/1.65 % (21935)Instruction limit reached!
% 2.81/1.65 % (21935)------------------------------
% 2.81/1.65 % (21935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.65 % (21935)Termination reason: Unknown
% 2.81/1.65 % (21935)Termination phase: shuffling
% 2.81/1.65
% 2.81/1.65 % (21935)Memory used [KB]: 2302
% 2.81/1.65 % (21935)Time elapsed: 0.021 s
% 2.81/1.65 % (21935)Instructions burned: 37 (million)
% 2.81/1.65 % (21935)------------------------------
% 2.81/1.65 % (21935)------------------------------
% 2.81/1.66 % (21941)Instruction limit reached!
% 2.81/1.66 % (21941)------------------------------
% 2.81/1.66 % (21941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.66 % (21941)Termination reason: Unknown
% 2.81/1.66 % (21941)Termination phase: shuffling
% 2.81/1.66
% 2.81/1.66 % (21941)Memory used [KB]: 1791
% 2.81/1.66 % (21941)Time elapsed: 0.012 s
% 2.81/1.66 % (21941)Instructions burned: 17 (million)
% 2.81/1.66 % (21941)------------------------------
% 2.81/1.66 % (21941)------------------------------
% 2.81/1.66 % (21944)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/7Mi)
% 2.81/1.66 % (21945)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/3Mi)
% 2.81/1.66 % (21945)Instruction limit reached!
% 2.81/1.66 % (21945)------------------------------
% 2.81/1.66 % (21945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.66 % (21945)Termination reason: Unknown
% 2.81/1.66 % (21945)Termination phase: shuffling
% 2.81/1.66
% 2.81/1.66 % (21945)Memory used [KB]: 1407
% 2.81/1.66 % (21945)Time elapsed: 0.002 s
% 2.81/1.66 % (21945)Instructions burned: 3 (million)
% 2.81/1.66 % (21945)------------------------------
% 2.81/1.66 % (21945)------------------------------
% 2.81/1.66 % (21944)Instruction limit reached!
% 2.81/1.66 % (21944)------------------------------
% 2.81/1.66 % (21944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.66 % (21944)Termination reason: Unknown
% 2.81/1.66 % (21944)Termination phase: shuffling
% 2.81/1.66
% 2.81/1.66 % (21944)Memory used [KB]: 1535
% 2.81/1.66 % (21944)Time elapsed: 0.005 s
% 2.81/1.66 % (21944)Instructions burned: 10 (million)
% 2.81/1.66 % (21944)------------------------------
% 2.81/1.66 % (21944)------------------------------
% 2.81/1.67 % (21946)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/4Mi)
% 2.81/1.67 % (21948)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/710Mi)
% 2.81/1.67 % (21946)Instruction limit reached!
% 2.81/1.67 % (21946)------------------------------
% 2.81/1.67 % (21946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.67 % (21946)Termination reason: Unknown
% 2.81/1.67 % (21946)Termination phase: shuffling
% 2.81/1.67
% 2.81/1.67 % (21946)Memory used [KB]: 1535
% 2.81/1.67 % (21946)Time elapsed: 0.004 s
% 2.81/1.67 % (21946)Instructions burned: 5 (million)
% 2.81/1.67 % (21946)------------------------------
% 2.81/1.67 % (21946)------------------------------
% 2.81/1.67 % (21949)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/6Mi)
% 2.81/1.68 % (21947)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/18Mi)
% 2.81/1.68 % (21949)Instruction limit reached!
% 2.81/1.68 % (21949)------------------------------
% 2.81/1.68 % (21949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.68 % (21949)Termination reason: Unknown
% 2.81/1.68 % (21949)Termination phase: shuffling
% 2.81/1.68
% 2.81/1.68 % (21949)Memory used [KB]: 1535
% 2.81/1.68 % (21949)Time elapsed: 0.004 s
% 2.81/1.68 % (21949)Instructions burned: 7 (million)
% 2.81/1.68 % (21949)------------------------------
% 2.81/1.68 % (21949)------------------------------
% 2.81/1.69 % (21950)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_21650 for (2999ds/902Mi)
% 2.81/1.69 % (21951)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_21650 for (2999ds/21Mi)
% 2.81/1.69 % (21947)Instruction limit reached!
% 2.81/1.69 % (21947)------------------------------
% 2.81/1.69 % (21947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.69 % (21947)Termination reason: Unknown
% 2.81/1.69 % (21947)Termination phase: shuffling
% 2.81/1.69
% 2.81/1.69 % (21947)Memory used [KB]: 1791
% 2.81/1.69 % (21947)Time elapsed: 0.013 s
% 2.81/1.69 % (21947)Instructions burned: 19 (million)
% 2.81/1.69 % (21947)------------------------------
% 2.81/1.69 % (21947)------------------------------
% 2.81/1.69 % (21951)Instruction limit reached!
% 2.81/1.69 % (21951)------------------------------
% 2.81/1.69 % (21951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.69 % (21951)Termination reason: Unknown
% 2.81/1.69 % (21951)Termination phase: shuffling
% 2.81/1.69
% 2.81/1.69 % (21951)Memory used [KB]: 1918
% 2.81/1.69 % (21951)Time elapsed: 0.009 s
% 2.81/1.69 % (21951)Instructions burned: 21 (million)
% 2.81/1.69 % (21951)------------------------------
% 2.81/1.69 % (21951)------------------------------
% 2.81/1.70 % (21927)Instruction limit reached!
% 2.81/1.70 % (21927)------------------------------
% 2.81/1.70 % (21927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.70 % (21927)Termination reason: Unknown
% 2.81/1.70 % (21927)Termination phase: Saturation
% 2.81/1.70
% 2.81/1.70 % (21927)Memory used [KB]: 7547
% 2.81/1.70 % (21927)Time elapsed: 0.085 s
% 2.81/1.70 % (21927)Instructions burned: 184 (million)
% 2.81/1.70 % (21927)------------------------------
% 2.81/1.70 % (21927)------------------------------
% 2.81/1.70 % (21953)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_21650 for (2999ds/6Mi)
% 2.81/1.71 % (21952)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21650 for (2999ds/5Mi)
% 2.81/1.71 % (21953)Instruction limit reached!
% 2.81/1.71 % (21953)------------------------------
% 2.81/1.71 % (21953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.71 % (21953)Termination reason: Unknown
% 2.81/1.71 % (21953)Termination phase: shuffling
% 2.81/1.71
% 2.81/1.71 % (21953)Memory used [KB]: 1663
% 2.81/1.71 % (21953)Time elapsed: 0.004 s
% 2.81/1.71 % (21953)Instructions burned: 7 (million)
% 2.81/1.71 % (21953)------------------------------
% 2.81/1.71 % (21953)------------------------------
% 2.81/1.71 % (21954)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21650 for (2998ds/377Mi)
% 2.81/1.71 % (21952)Instruction limit reached!
% 2.81/1.71 % (21952)------------------------------
% 2.81/1.71 % (21952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.71 % (21952)Termination reason: Unknown
% 2.81/1.71 % (21952)Termination phase: shuffling
% 2.81/1.71
% 2.81/1.71 % (21952)Memory used [KB]: 1535
% 2.81/1.71 % (21952)Time elapsed: 0.005 s
% 2.81/1.71 % (21952)Instructions burned: 6 (million)
% 2.81/1.71 % (21952)------------------------------
% 2.81/1.71 % (21952)------------------------------
% 2.81/1.72 % (21955)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_21650 for (2998ds/779Mi)
% 2.81/1.73 % (21956)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_21650 for (2998ds/19Mi)
% 2.81/1.74 % (21932)Instruction limit reached!
% 2.81/1.74 % (21932)------------------------------
% 2.81/1.74 % (21932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.74 % (21932)Termination reason: Unknown
% 2.81/1.74 % (21932)Termination phase: Saturation
% 2.81/1.74
% 2.81/1.74 % (21932)Memory used [KB]: 7291
% 2.81/1.74 % (21932)Time elapsed: 0.123 s
% 2.81/1.74 % (21932)Instructions burned: 275 (million)
% 2.81/1.74 % (21932)------------------------------
% 2.81/1.74 % (21932)------------------------------
% 2.81/1.74 % (21956)Instruction limit reached!
% 2.81/1.74 % (21956)------------------------------
% 2.81/1.74 % (21956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.74 % (21956)Termination reason: Unknown
% 2.81/1.74 % (21956)Termination phase: shuffling
% 2.81/1.74
% 2.81/1.74 % (21956)Memory used [KB]: 1918
% 2.81/1.74 % (21956)Time elapsed: 0.012 s
% 2.81/1.74 % (21956)Instructions burned: 20 (million)
% 2.81/1.74 % (21956)------------------------------
% 2.81/1.74 % (21956)------------------------------
% 2.81/1.74 % (21950)First to succeed.
% 2.81/1.74 % (21950)Refutation found. Thanks to Tanya!
% 2.81/1.74 % SZS status Theorem for DTF2THF_21650
% 2.81/1.74 % SZS output start Proof for DTF2THF_21650
% 2.81/1.74 thf(type_def_5, type, set_o: $tType).
% 2.81/1.74 thf(type_def_7, type, set_set_o: $tType).
% 2.81/1.74 thf(type_def_8, type, set_list_char: $tType).
% 2.81/1.74 thf(type_def_9, type, set_set_list_char: $tType).
% 2.81/1.74 thf(type_def_10, type, set_Pa1764573435lle_tv: $tType).
% 2.81/1.74 thf(type_def_11, type, set_se800614875lle_tv: $tType).
% 2.81/1.74 thf(type_def_12, type, list_char: $tType).
% 2.81/1.74 thf(type_def_13, type, paraco1605129243lle_tv: $tType).
% 2.81/1.74 thf(type_def_14, type, set_nat: $tType).
% 2.81/1.74 thf(type_def_15, type, nat: $tType).
% 2.81/1.74 thf(type_def_16, type, paraco1604210848lle_fm: $tType).
% 2.81/1.74 thf(type_def_17, type, produc696645085lle_fm: $tType).
% 2.81/1.74 thf(func_def_0, type, produc696645085lle_fm: $tType).
% 2.81/1.74 thf(func_def_1, type, set_se800614875lle_tv: $tType).
% 2.81/1.74 thf(func_def_2, type, set_set_list_char: $tType).
% 2.81/1.74 thf(func_def_3, type, set_Pa1764573435lle_tv: $tType).
% 2.81/1.74 thf(func_def_4, type, set_list_char: $tType).
% 2.81/1.74 thf(func_def_5, type, paraco1605129243lle_tv: $tType).
% 2.81/1.74 thf(func_def_6, type, paraco1604210848lle_fm: $tType).
% 2.81/1.74 thf(func_def_7, type, set_set_o: $tType).
% 2.81/1.74 thf(func_def_8, type, list_char: $tType).
% 2.81/1.74 thf(func_def_9, type, set_nat: $tType).
% 2.81/1.74 thf(func_def_10, type, set_o: $tType).
% 2.81/1.74 thf(func_def_11, type, nat: $tType).
% 2.81/1.74 thf(func_def_12, type, complete_Sup_Sup_o: set_o > $o).
% 2.81/1.74 thf(func_def_13, type, finite_Fpow_o: set_o > set_set_o).
% 2.81/1.74 thf(func_def_14, type, finite1803457147t_char: set_list_char > set_set_list_char).
% 2.81/1.74 thf(func_def_15, type, finite2011762305lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv).
% 2.81/1.74 thf(func_def_16, type, ord_less_eq_o_o: ($o > $o) > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_17, type, ord_le1945897678char_o: (list_char > $o) > (list_char > $o) > $o).
% 2.81/1.74 thf(func_def_18, type, ord_le1632188418e_tv_o: (paraco1605129243lle_tv > $o) > (paraco1605129243lle_tv > $o) > $o).
% 2.81/1.74 thf(func_def_19, type, ord_less_eq_set_o: set_o > set_o > $o).
% 2.81/1.74 thf(func_def_20, type, ord_le1836582007t_char: set_list_char > set_list_char > $o).
% 2.81/1.74 thf(func_def_21, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 2.81/1.74 thf(func_def_22, type, ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o).
% 2.81/1.74 thf(func_def_23, type, ord_le2085948664_set_o: set_set_o > set_set_o > $o).
% 2.81/1.74 thf(func_def_24, type, ord_le263913851lle_tv: set_se800614875lle_tv > set_se800614875lle_tv > $o).
% 2.81/1.74 thf(func_def_25, type, order_Greatest_set_o: (set_o > $o) > set_o).
% 2.81/1.74 thf(func_def_26, type, order_350719188lle_tv: (set_Pa1764573435lle_tv > $o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_27, type, top_top_o_o: $o > $o).
% 2.81/1.74 thf(func_def_28, type, top_top_list_char_o: list_char > $o).
% 2.81/1.74 thf(func_def_29, type, top_top_nat_o: nat > $o).
% 2.81/1.74 thf(func_def_30, type, top_to1299250770e_tv_o: paraco1605129243lle_tv > $o).
% 2.81/1.74 thf(func_def_31, type, top_top_set_o: set_o).
% 2.81/1.74 thf(func_def_32, type, top_to748628679t_char: set_list_char).
% 2.81/1.74 thf(func_def_33, type, top_top_set_nat: set_nat).
% 2.81/1.74 thf(func_def_34, type, top_to1057771083lle_tv: set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_35, type, top_top_set_set_o: set_set_o).
% 2.81/1.74 thf(func_def_36, type, top_to697846397t_char: set_set_list_char).
% 2.81/1.74 thf(func_def_37, type, paraco1933902578domain: set_nat > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_38, type, paraco1325918602e_eval: (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_39, type, paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_40, type, paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_41, type, paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_42, type, paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_43, type, paraco1480028776le_Pro: list_char > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_44, type, paraco367965286_Truth: paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_45, type, paraco1344940915le_Det: $o > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_46, type, paraco327635598_valid: paraco1604210848lle_fm > $o).
% 2.81/1.74 thf(func_def_47, type, paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o).
% 2.81/1.74 thf(func_def_48, type, produc1710735575lle_fm: (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > produc696645085lle_fm).
% 2.81/1.74 thf(func_def_49, type, collect_o: ($o > $o) > set_o).
% 2.81/1.74 thf(func_def_50, type, collect_list_char: (list_char > $o) > set_list_char).
% 2.81/1.74 thf(func_def_51, type, collect_nat: (nat > $o) > set_nat).
% 2.81/1.74 thf(func_def_52, type, collec1111687558lle_tv: (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_53, type, pow_o: set_o > set_set_o).
% 2.81/1.74 thf(func_def_54, type, pow_list_char: set_list_char > set_set_list_char).
% 2.81/1.74 thf(func_def_55, type, pow_Pa475453624lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv).
% 2.81/1.74 thf(func_def_56, type, image_o_o: ($o > $o) > set_o > set_o).
% 2.81/1.74 thf(func_def_57, type, image_o_list_char: ($o > list_char) > set_o > set_list_char).
% 2.81/1.74 thf(func_def_58, type, image_o_nat: ($o > nat) > set_o > set_nat).
% 2.81/1.74 thf(func_def_59, type, image_1491822472lle_tv: ($o > paraco1605129243lle_tv) > set_o > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_60, type, image_list_char_o: (list_char > $o) > set_list_char > set_o).
% 2.81/1.74 thf(func_def_61, type, image_890964937t_char: (list_char > list_char) > set_list_char > set_list_char).
% 2.81/1.74 thf(func_def_62, type, image_1187894195lle_tv: (list_char > paraco1605129243lle_tv) > set_list_char > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_63, type, image_nat_o: (nat > $o) > set_nat > set_o).
% 2.81/1.74 thf(func_def_64, type, image_nat_list_char: (nat > list_char) > set_nat > set_list_char).
% 2.81/1.74 thf(func_def_65, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 2.81/1.74 thf(func_def_66, type, image_1151963140lle_tv: (nat > paraco1605129243lle_tv) > set_nat > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_67, type, image_991799618e_tv_o: (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv > set_o).
% 2.81/1.74 thf(func_def_68, type, image_1971766583t_char: (paraco1605129243lle_tv > list_char) > set_Pa1764573435lle_tv > set_list_char).
% 2.81/1.74 thf(func_def_69, type, image_376325286tv_nat: (paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > set_nat).
% 2.81/1.74 thf(func_def_70, type, image_335818702lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_71, type, image_set_o_set_o: (set_o > set_o) > set_set_o > set_set_o).
% 2.81/1.74 thf(func_def_72, type, image_30320477lle_tv: (set_list_char > set_Pa1764573435lle_tv) > set_set_list_char > set_se800614875lle_tv).
% 2.81/1.74 thf(func_def_73, type, member_o: $o > set_o > $o).
% 2.81/1.74 thf(func_def_74, type, member_list_char: list_char > set_list_char > $o).
% 2.81/1.74 thf(func_def_75, type, member_nat: nat > set_nat > $o).
% 2.81/1.74 thf(func_def_76, type, member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o).
% 2.81/1.74 thf(func_def_77, type, member_set_o: set_o > set_set_o > $o).
% 2.81/1.74 thf(func_def_78, type, member1875402276lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv > $o).
% 2.81/1.74 thf(func_def_79, type, p: paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_91, type, sP0: (paraco1604210848lle_fm > $o) > $o).
% 2.81/1.74 thf(func_def_92, type, sP1: (paraco1604210848lle_fm > $o) > $o).
% 2.81/1.74 thf(func_def_93, type, sK2: (paraco1605129243lle_tv > list_char) > list_char > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_94, type, sK3: (paraco1605129243lle_tv > list_char) > set_list_char > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_95, type, sK4: set_Pa1764573435lle_tv > (list_char > paraco1605129243lle_tv) > set_list_char > set_list_char).
% 2.81/1.74 thf(func_def_96, type, sK5: set_nat > (nat > $o) > (nat > $o) > nat).
% 2.81/1.74 thf(func_def_97, type, sK6: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_98, type, sK7: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_99, type, sK8: (set_Pa1764573435lle_tv > $o) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_100, type, sK9: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_101, type, sK10: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_102, type, sK11: produc696645085lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_103, type, sK12: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_104, type, sK13: produc696645085lle_fm > list_char).
% 2.81/1.74 thf(func_def_105, type, sK14: produc696645085lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_106, type, sK15: produc696645085lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_107, type, sK16: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_108, type, sK17: produc696645085lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_109, type, sK18: produc696645085lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_110, type, sK19: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_111, type, sK20: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_112, type, sK21: produc696645085lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_113, type, sK22: produc696645085lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_114, type, sK23: set_o > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_115, type, sK24: (list_char > $o) > $o > list_char).
% 2.81/1.74 thf(func_def_116, type, sK25: set_list_char > (list_char > paraco1605129243lle_tv) > (list_char > paraco1605129243lle_tv) > list_char).
% 2.81/1.74 thf(func_def_117, type, sK26: set_o > set_o > ($o > $o) > set_o).
% 2.81/1.74 thf(func_def_118, type, sK27: set_list_char > set_Pa1764573435lle_tv > (list_char > paraco1605129243lle_tv) > list_char).
% 2.81/1.74 thf(func_def_119, type, sK28: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_120, type, sK29: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_121, type, sK30: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_122, type, sK31: set_nat > (nat > $o) > nat).
% 2.81/1.74 thf(func_def_123, type, sK32: (list_char > paraco1605129243lle_tv) > set_list_char > (list_char > paraco1605129243lle_tv) > list_char).
% 2.81/1.74 thf(func_def_124, type, sK33: paraco1605129243lle_tv > (list_char > paraco1605129243lle_tv) > set_list_char > list_char).
% 2.81/1.74 thf(func_def_125, type, sK34: ($o > $o) > ($o > $o) > set_o > $o).
% 2.81/1.74 thf(func_def_126, type, sK35: ($o > $o) > ($o > $o) > set_o > $o).
% 2.81/1.74 thf(func_def_127, type, sK36: set_Pa1764573435lle_tv > (set_Pa1764573435lle_tv > $o) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_128, type, sK37: set_Pa1764573435lle_tv > (set_Pa1764573435lle_tv > $o) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_129, type, sK38: set_list_char > set_list_char > list_char).
% 2.81/1.74 thf(func_def_130, type, sK39: set_o > ($o > paraco1605129243lle_tv) > paraco1605129243lle_tv > $o).
% 2.81/1.74 thf(func_def_131, type, sK40: (set_o > set_Pa1764573435lle_tv) > set_o).
% 2.81/1.74 thf(func_def_132, type, sK41: (set_o > set_Pa1764573435lle_tv) > set_o).
% 2.81/1.74 thf(func_def_133, type, sK42: (nat > $o) > (nat > $o) > nat).
% 2.81/1.74 thf(func_def_134, type, sK43: ($o > $o) > ($o > $o) > set_o > $o).
% 2.81/1.74 thf(func_def_135, type, sK44: set_list_char > set_list_char > (list_char > list_char) > list_char).
% 2.81/1.74 thf(func_def_137, type, sK46: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_138, type, sK47: set_list_char > (list_char > paraco1605129243lle_tv) > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_139, type, sK48: ($o > list_char) > list_char > $o).
% 2.81/1.74 thf(func_def_140, type, sK49: set_Pa1764573435lle_tv > set_o > (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_141, type, sK50: (list_char > paraco1605129243lle_tv) > (list_char > paraco1605129243lle_tv) > set_list_char > list_char).
% 2.81/1.74 thf(func_def_142, type, sK51: set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_143, type, sK52: set_Pa1764573435lle_tv > (nat > paraco1605129243lle_tv) > (nat > $o) > nat).
% 2.81/1.74 thf(func_def_144, type, sK53: set_o > $o).
% 2.81/1.74 thf(func_def_145, type, sK54: set_o > set_o > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_146, type, sK55: ($o > $o) > set_o > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_147, type, sK56: (set_Pa1764573435lle_tv > $o) > set_list_char > (list_char > paraco1605129243lle_tv) > set_list_char).
% 2.81/1.74 thf(func_def_148, type, sK57: (set_Pa1764573435lle_tv > $o) > set_list_char > (list_char > paraco1605129243lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_149, type, sK58: set_list_char > (list_char > $o) > list_char).
% 2.81/1.74 thf(func_def_150, type, sK59: list_char > (list_char > list_char) > list_char).
% 2.81/1.74 thf(func_def_151, type, sK60: (list_char > list_char) > list_char).
% 2.81/1.74 thf(func_def_152, type, sK61: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_153, type, sK62: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_154, type, sK63: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_155, type, sK64: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_156, type, sK65: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_157, type, sK66: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_158, type, sK67: (paraco1604210848lle_fm > $o) > list_char).
% 2.81/1.74 thf(func_def_159, type, sK68: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_160, type, sK69: set_list_char > (list_char > list_char) > list_char > list_char).
% 2.81/1.74 thf(func_def_161, type, sK70: (list_char > paraco1605129243lle_tv) > paraco1605129243lle_tv > list_char).
% 2.81/1.74 thf(func_def_162, type, sK71: ($o > $o) > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_163, type, sK72: set_list_char > (paraco1605129243lle_tv > $o) > (paraco1605129243lle_tv > list_char) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_164, type, sK73: (paraco1605129243lle_tv > $o) > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_165, type, sK74: set_list_char > (list_char > $o) > (list_char > $o) > list_char).
% 2.81/1.74 thf(func_def_166, type, sK75: $o > (list_char > $o) > list_char).
% 2.81/1.74 thf(func_def_167, type, sK76: (list_char > $o) > $o).
% 2.81/1.74 thf(func_def_168, type, sK77: list_char > (list_char > list_char) > list_char).
% 2.81/1.74 thf(func_def_169, type, sK78: (list_char > $o) > $o > list_char).
% 2.81/1.74 thf(func_def_170, type, sK79: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_171, type, sK80: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_172, type, sK81: (list_char > paraco1605129243lle_tv) > (paraco1605129243lle_tv > list_char) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_173, type, sK82: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_174, type, sK83: ($o > $o) > $o).
% 2.81/1.74 thf(func_def_175, type, sK84: $o > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_176, type, sK85: ($o > list_char) > list_char).
% 2.81/1.74 thf(func_def_177, type, sK86: list_char > ($o > list_char) > $o).
% 2.81/1.74 thf(func_def_178, type, sK87: (nat > $o) > (nat > $o) > nat).
% 2.81/1.74 thf(func_def_179, type, sK88: (set_Pa1764573435lle_tv > $o) > ($o > paraco1605129243lle_tv) > set_o > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_180, type, sK89: (set_Pa1764573435lle_tv > $o) > ($o > paraco1605129243lle_tv) > set_o > set_o).
% 2.81/1.74 thf(func_def_181, type, sK90: (list_char > $o) > $o > list_char).
% 2.81/1.74 thf(func_def_182, type, sK91: ($o > $o) > set_o > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_183, type, sK92: (paraco1605129243lle_tv > $o) > (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_184, type, sK93: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_185, type, sK94: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_186, type, sK95: ($o > $o) > set_o > $o).
% 2.81/1.74 thf(func_def_187, type, sK96: ($o > $o) > $o > $o).
% 2.81/1.74 thf(func_def_188, type, sK97: (set_o > set_o) > set_o).
% 2.81/1.74 thf(func_def_189, type, sK98: (set_o > set_o) > set_o).
% 2.81/1.74 thf(func_def_190, type, sK99: set_list_char > (paraco1605129243lle_tv > $o) > (list_char > paraco1605129243lle_tv) > list_char).
% 2.81/1.74 thf(func_def_191, type, sK100: (set_o > set_Pa1764573435lle_tv) > set_o).
% 2.81/1.74 thf(func_def_192, type, sK101: (set_o > set_Pa1764573435lle_tv) > set_o).
% 2.81/1.74 thf(func_def_193, type, sK102: ($o > list_char) > list_char > $o).
% 2.81/1.74 thf(func_def_194, type, sK103: (list_char > list_char) > (list_char > list_char) > list_char).
% 2.81/1.74 thf(func_def_195, type, sK104: (set_o > set_Pa1764573435lle_tv) > set_o).
% 2.81/1.74 thf(func_def_196, type, sK105: (set_o > set_Pa1764573435lle_tv) > set_o).
% 2.81/1.74 thf(func_def_197, type, sK106: list_char > ($o > list_char) > $o).
% 2.81/1.74 thf(func_def_198, type, sK107: list_char).
% 2.81/1.74 thf(func_def_199, type, sK108: list_char > (list_char > list_char) > list_char).
% 2.81/1.74 thf(func_def_200, type, sK109: $o > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_201, type, sK110: (list_char > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_202, type, sK111: paraco1605129243lle_tv > (list_char > paraco1605129243lle_tv) > list_char).
% 2.81/1.74 thf(func_def_203, type, sK112: set_list_char > list_char).
% 2.81/1.74 thf(func_def_204, type, sK113: paraco1604210848lle_fm > list_char).
% 2.81/1.74 thf(func_def_205, type, sK114: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_206, type, sK115: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_207, type, sK116: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_208, type, sK117: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_209, type, sK118: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_210, type, sK119: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_211, type, sK120: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 2.81/1.74 thf(func_def_212, type, sK121: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_213, type, sK122: ($o > paraco1605129243lle_tv) > paraco1605129243lle_tv > $o).
% 2.81/1.74 thf(func_def_214, type, sK123: ($o > $o) > ($o > $o) > set_o > $o).
% 2.81/1.74 thf(func_def_215, type, sK124: $o > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_216, type, sK125: (set_o > set_o) > set_o).
% 2.81/1.74 thf(func_def_217, type, sK126: (set_o > set_o) > set_o).
% 2.81/1.74 thf(func_def_218, type, sK127: ($o > list_char) > (list_char > $o) > $o).
% 2.81/1.74 thf(func_def_219, type, sK128: (nat > $o) > set_list_char > (nat > list_char) > nat).
% 2.81/1.74 thf(func_def_220, type, sK129: paraco1605129243lle_tv > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_221, type, sK130: paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_222, type, sK131: (set_o > set_o) > set_o).
% 2.81/1.74 thf(func_def_223, type, sK132: (set_o > set_o) > set_o).
% 2.81/1.74 thf(func_def_224, type, sK133: (list_char > $o) > ($o > list_char) > list_char).
% 2.81/1.74 thf(func_def_225, type, sK134: set_o > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_226, type, sK135: list_char > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_227, type, sK136: list_char > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_228, type, sK137: list_char > ($o > list_char) > set_o > $o).
% 2.81/1.74 thf(func_def_229, type, sK138: (list_char > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_list_char > list_char).
% 2.81/1.74 thf(func_def_230, type, sK139: set_Pa1764573435lle_tv > ($o > paraco1605129243lle_tv) > set_o > $o).
% 2.81/1.74 thf(func_def_231, type, sK140: (set_o > $o) > (set_o > $o) > set_o).
% 2.81/1.74 thf(func_def_232, type, sK141: (set_o > $o) > set_o > set_o).
% 2.81/1.74 thf(func_def_233, type, sK142: set_Pa1764573435lle_tv > (set_Pa1764573435lle_tv > $o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_234, type, sK143: (set_Pa1764573435lle_tv > $o) > (set_Pa1764573435lle_tv > $o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_235, type, sK144: ($o > paraco1605129243lle_tv) > set_o > set_Pa1764573435lle_tv > set_o).
% 2.81/1.74 thf(func_def_236, type, sK145: ($o > $o) > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_237, type, sK146: set_list_char > (list_char > $o) > set_o > list_char).
% 2.81/1.74 thf(func_def_238, type, sK147: (paraco1605129243lle_tv > $o) > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_239, type, sK148: set_o > ($o > $o) > set_o > $o).
% 2.81/1.74 thf(func_def_240, type, sK149: (set_o > set_o) > set_o).
% 2.81/1.74 thf(func_def_241, type, sK150: (set_o > set_o) > set_o).
% 2.81/1.74 thf(func_def_242, type, sK151: (set_Pa1764573435lle_tv > set_o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_243, type, sK152: (set_Pa1764573435lle_tv > set_o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_244, type, sK153: set_Pa1764573435lle_tv > ($o > paraco1605129243lle_tv) > set_o > set_o).
% 2.81/1.74 thf(func_def_245, type, sK154: (nat > $o) > (nat > $o) > set_o > nat).
% 2.81/1.74 thf(func_def_246, type, sK155: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_247, type, sK156: paraco1605129243lle_tv > (list_char > paraco1605129243lle_tv) > list_char).
% 2.81/1.74 thf(func_def_248, type, sK157: paraco1605129243lle_tv > set_list_char > (list_char > paraco1605129243lle_tv) > list_char).
% 2.81/1.74 thf(func_def_249, type, sK158: $o > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_250, type, sK159: (set_Pa1764573435lle_tv > set_o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_251, type, sK160: (set_Pa1764573435lle_tv > set_o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_252, type, sK161: ($o > $o) > set_o > set_o > set_o).
% 2.81/1.74 thf(func_def_253, type, sK162: (set_o > set_Pa1764573435lle_tv) > set_o).
% 2.81/1.74 thf(func_def_254, type, sK163: (set_o > set_Pa1764573435lle_tv) > set_o).
% 2.81/1.74 thf(func_def_255, type, sK164: ($o > $o) > set_o > $o > $o).
% 2.81/1.74 thf(func_def_256, type, sK165: ($o > $o) > set_o > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_257, type, sK166: $o > set_list_char > (list_char > $o) > list_char).
% 2.81/1.74 thf(func_def_258, type, sK167: ($o > list_char) > set_o > set_list_char > $o).
% 2.81/1.74 thf(func_def_259, type, sK168: (set_o > $o) > set_o > set_o).
% 2.81/1.74 thf(func_def_260, type, sK169: set_o > set_o > $o).
% 2.81/1.74 thf(func_def_261, type, sK170: $o > ($o > $o) > set_o > $o).
% 2.81/1.74 thf(func_def_262, type, sK171: (list_char > paraco1605129243lle_tv) > set_list_char > set_Pa1764573435lle_tv > set_list_char).
% 2.81/1.74 thf(func_def_263, type, sK172: (paraco1605129243lle_tv > $o) > (paraco1605129243lle_tv > $o) > set_o > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_264, type, sK173: list_char > (list_char > list_char) > list_char).
% 2.81/1.74 thf(func_def_265, type, sK174: ($o > $o) > ($o > $o) > $o).
% 2.81/1.74 thf(func_def_266, type, sK175: (list_char > paraco1605129243lle_tv) > paraco1605129243lle_tv > list_char).
% 2.81/1.74 thf(func_def_267, type, sK176: set_Pa1764573435lle_tv > (list_char > paraco1605129243lle_tv) > (list_char > $o) > list_char).
% 2.81/1.74 thf(func_def_268, type, sK177: (paraco1605129243lle_tv > $o) > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_269, type, sK178: (set_Pa1764573435lle_tv > set_o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_270, type, sK179: (set_Pa1764573435lle_tv > set_o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_271, type, sK180: (set_Pa1764573435lle_tv > set_o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_272, type, sK181: (set_Pa1764573435lle_tv > set_o) > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_273, type, sK182: (nat > $o) > (nat > $o) > nat).
% 2.81/1.74 thf(func_def_274, type, sK183: (paraco1605129243lle_tv > $o) > (set_o > $o) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv).
% 2.81/1.74 thf(func_def_275, type, sK184: (paraco1605129243lle_tv > $o) > (set_o > $o) > set_Pa1764573435lle_tv > set_o).
% 2.81/1.74 thf(func_def_276, type, sK185: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv).
% 2.81/1.74 thf(func_def_277, type, sK186: ($o > $o) > (set_o > $o) > set_o > set_o).
% 2.81/1.74 thf(func_def_278, type, sK187: ($o > $o) > (set_o > $o) > set_o > set_o).
% 2.81/1.74 thf(func_def_280, type, ph189: !>[X0: $tType]:(X0)).
% 2.81/1.74 thf(f2453,plain,(
% 2.81/1.74 $false),
% 2.81/1.74 inference(avatar_sat_refutation,[status(thm)],[f2352,f2361,f2373,f2376,f2448])).
% 2.81/1.74 thf(f2448,plain,(
% 2.81/1.74 spl188_2 | ~spl188_1),
% 2.81/1.74 inference(avatar_split_clause,[status(thm)],[f2431,f2347,f2350])).
% 2.81/1.74 thf(f2350,definition,(
% 2.81/1.74 spl188_2 <=> ! [X2 : list_char > paraco1605129243lle_tv] : ((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X2 @ p))),
% 2.81/1.74 introduced(definition,[new_symbols(naming,[spl188_2])],[avatar_definition])).
% 2.81/1.74 thf(f2347,definition,(
% 2.81/1.74 spl188_1 <=> ! [X3 : list_char > paraco1605129243lle_tv] : (((paraco1325918602e_eval @ X3 @ p) = (paraco1344940915le_Det @ $true)) | ((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X3 @ top_to748628679t_char) @ top_to1057771083lle_tv) != $true))),
% 2.81/1.74 introduced(definition,[new_symbols(naming,[spl188_1])],[avatar_definition])).
% 2.81/1.74 thf(f2431,plain,(
% 2.81/1.74 ( ! [X0 : list_char > paraco1605129243lle_tv] : (((paraco1325918602e_eval @ X0 @ p) = (paraco1344940915le_Det @ $true))) ) | ~spl188_1),
% 2.81/1.74 inference(trivial_inequality_removal,[status(thm)],[f2424])).
% 2.81/1.74 thf(f2424,plain,(
% 2.81/1.74 ( ! [X0 : list_char > paraco1605129243lle_tv] : (($true != $true) | ((paraco1325918602e_eval @ X0 @ p) = (paraco1344940915le_Det @ $true))) ) | ~spl188_1),
% 2.81/1.74 inference(superposition,[status(thm)],[f2348,f2152])).
% 2.81/1.74 thf(f2152,plain,(
% 2.81/1.74 ( ! [X0 : set_Pa1764573435lle_tv] : (((ord_le241064091lle_tv @ X0 @ top_to1057771083lle_tv) = $true)) )),
% 2.81/1.74 inference(cnf_transformation,[status(thm)],[f502])).
% 2.81/1.74 thf(f502,plain,(
% 2.81/1.74 ! [X0 : set_Pa1764573435lle_tv] : ((ord_le241064091lle_tv @ X0 @ top_to1057771083lle_tv) = $true)),
% 2.81/1.74 inference(fool_elimination,[status(thm)],[f501])).
% 2.81/1.74 thf(f501,plain,(
% 2.81/1.74 ! [X0 : set_Pa1764573435lle_tv] : (ord_le241064091lle_tv @ X0 @ top_to1057771083lle_tv)),
% 2.81/1.74 inference(rectify,[status(thm)],[f214])).
% 2.81/1.74 thf(f214,axiom,(
% 2.81/1.74 ! [X18 : set_Pa1764573435lle_tv] : (ord_le241064091lle_tv @ X18 @ top_to1057771083lle_tv)),
% 2.81/1.74 file('/export/starexec/sandbox/tmp/tmp.PTGbAxFx6h/DTF2THF_21650.p',fact_213_top__greatest)).
% 2.81/1.74 thf(f2348,plain,(
% 2.81/1.74 ( ! [X3 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X3 @ top_to748628679t_char) @ top_to1057771083lle_tv) != $true) | ((paraco1325918602e_eval @ X3 @ p) = (paraco1344940915le_Det @ $true))) ) | ~spl188_1),
% 2.81/1.74 inference(avatar_component_clause,[status(thm)],[f2347])).
% 2.81/1.74 thf(f2376,plain,(
% 2.81/1.74 ~spl188_2 | spl188_3),
% 2.81/1.74 inference(avatar_contradiction_clause,[status(thm)],[f2375])).
% 2.81/1.74 thf(f2375,plain,(
% 2.81/1.74 $false | (~spl188_2 | spl188_3)),
% 2.81/1.74 inference(trivial_inequality_removal,[status(thm)],[f2374])).
% 2.81/1.74 thf(f2374,plain,(
% 2.81/1.74 ((paraco1344940915le_Det @ $true) != (paraco1344940915le_Det @ $true)) | (~spl188_2 | spl188_3)),
% 2.81/1.74 inference(superposition,[status(thm)],[f2356,f2351])).
% 2.81/1.74 thf(f2351,plain,(
% 2.81/1.74 ( ! [X2 : list_char > paraco1605129243lle_tv] : (((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X2 @ p))) ) | ~spl188_2),
% 2.81/1.74 inference(avatar_component_clause,[status(thm)],[f2350])).
% 2.81/1.74 thf(f2356,plain,(
% 2.81/1.74 ((paraco1344940915le_Det @ $true) != (paraco1325918602e_eval @ sK135 @ p)) | spl188_3),
% 2.81/1.74 inference(avatar_component_clause,[status(thm)],[f2354])).
% 2.81/1.74 thf(f2354,definition,(
% 2.81/1.74 spl188_3 <=> ((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ sK135 @ p))),
% 2.81/1.74 introduced(definition,[new_symbols(naming,[spl188_3])],[avatar_definition])).
% 2.81/1.74 thf(f2373,plain,(
% 2.81/1.74 ~spl188_2 | spl188_4),
% 2.81/1.74 inference(avatar_contradiction_clause,[status(thm)],[f2372])).
% 2.81/1.74 thf(f2372,plain,(
% 2.81/1.74 $false | (~spl188_2 | spl188_4)),
% 2.81/1.74 inference(trivial_inequality_removal,[status(thm)],[f2371])).
% 2.81/1.74 thf(f2371,plain,(
% 2.81/1.74 ((paraco1344940915le_Det @ $true) != (paraco1344940915le_Det @ $true)) | (~spl188_2 | spl188_4)),
% 2.81/1.74 inference(superposition,[status(thm)],[f2360,f2351])).
% 2.81/1.74 thf(f2360,plain,(
% 2.81/1.74 ((paraco1325918602e_eval @ sK136 @ p) != (paraco1344940915le_Det @ $true)) | spl188_4),
% 2.81/1.74 inference(avatar_component_clause,[status(thm)],[f2358])).
% 2.81/1.74 thf(f2358,definition,(
% 2.81/1.74 spl188_4 <=> ((paraco1325918602e_eval @ sK136 @ p) = (paraco1344940915le_Det @ $true))),
% 2.81/1.74 introduced(definition,[new_symbols(naming,[spl188_4])],[avatar_definition])).
% 2.81/1.74 thf(f2361,plain,(
% 2.81/1.74 ~spl188_3 | ~spl188_4),
% 2.81/1.74 inference(avatar_split_clause,[status(thm)],[f2091,f2358,f2354])).
% 2.81/1.74 thf(f2091,plain,(
% 2.81/1.74 ((paraco1325918602e_eval @ sK136 @ p) != (paraco1344940915le_Det @ $true)) | ((paraco1344940915le_Det @ $true) != (paraco1325918602e_eval @ sK135 @ p))),
% 2.81/1.74 inference(cnf_transformation,[status(thm)],[f1593])).
% 2.81/1.74 thf(f1593,plain,(
% 2.81/1.74 ((((ord_le241064091lle_tv @ (image_1187894195lle_tv @ sK135 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) = $true) & ((paraco1344940915le_Det @ $true) != (paraco1325918602e_eval @ sK135 @ p))) | ((paraco1325918602e_eval @ sK136 @ p) != (paraco1344940915le_Det @ $true))) & (! [X2 : list_char > paraco1605129243lle_tv] : ((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X2 @ p)) | ! [X3 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X3 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) != $true) | ((paraco1325918602e_eval @ X3 @ p) = (paraco1344940915le_Det @ $true))))),
% 2.81/1.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK135,sK136])],[f1590,f1592,f1591])).
% 2.81/1.74 thf(f1591,plain,(
% 2.81/1.74 ? [X0 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X0 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) = $true) & ((paraco1325918602e_eval @ X0 @ p) != (paraco1344940915le_Det @ $true))) => (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ sK135 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) = $true) & ((paraco1344940915le_Det @ $true) != (paraco1325918602e_eval @ sK135 @ p)))),
% 2.81/1.74 introduced(definition,[],[choice_axiom])).
% 2.81/1.74 thf(f1592,plain,(
% 2.81/1.74 ? [X1 : list_char > paraco1605129243lle_tv] : ((paraco1325918602e_eval @ X1 @ p) != (paraco1344940915le_Det @ $true)) => ((paraco1325918602e_eval @ sK136 @ p) != (paraco1344940915le_Det @ $true))),
% 2.81/1.74 introduced(definition,[],[choice_axiom])).
% 2.81/1.74 thf(f1590,plain,(
% 2.81/1.74 (? [X0 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X0 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) = $true) & ((paraco1325918602e_eval @ X0 @ p) != (paraco1344940915le_Det @ $true))) | ? [X1 : list_char > paraco1605129243lle_tv] : ((paraco1325918602e_eval @ X1 @ p) != (paraco1344940915le_Det @ $true))) & (! [X2 : list_char > paraco1605129243lle_tv] : ((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X2 @ p)) | ! [X3 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X3 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) != $true) | ((paraco1325918602e_eval @ X3 @ p) = (paraco1344940915le_Det @ $true))))),
% 2.81/1.74 inference(rectify,[status(thm)],[f1589])).
% 2.81/1.74 thf(f1589,plain,(
% 2.81/1.74 (? [X0 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X0 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) = $true) & ((paraco1325918602e_eval @ X0 @ p) != (paraco1344940915le_Det @ $true))) | ? [X1 : list_char > paraco1605129243lle_tv] : ((paraco1325918602e_eval @ X1 @ p) != (paraco1344940915le_Det @ $true))) & (! [X1 : list_char > paraco1605129243lle_tv] : ((paraco1325918602e_eval @ X1 @ p) = (paraco1344940915le_Det @ $true)) | ! [X0 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X0 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) != $true) | ((paraco1325918602e_eval @ X0 @ p) = (paraco1344940915le_Det @ $true))))),
% 2.81/1.74 inference(nnf_transformation,[status(thm)],[f1183])).
% 2.81/1.74 thf(f1183,plain,(
% 2.81/1.74 ? [X0 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X0 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) = $true) & ((paraco1325918602e_eval @ X0 @ p) != (paraco1344940915le_Det @ $true))) <=> ! [X1 : list_char > paraco1605129243lle_tv] : ((paraco1325918602e_eval @ X1 @ p) = (paraco1344940915le_Det @ $true))),
% 2.81/1.74 inference(ennf_transformation,[status(thm)],[f979])).
% 2.81/1.74 thf(f979,plain,(
% 2.81/1.74 ~(~! [X0 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X0 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) = $true) => ((paraco1325918602e_eval @ X0 @ p) = (paraco1344940915le_Det @ $true))) <~> ! [X1 : list_char > paraco1605129243lle_tv] : ((paraco1325918602e_eval @ X1 @ p) = (paraco1344940915le_Det @ $true)))),
% 2.81/1.74 inference(rectify,[status(thm)],[f414])).
% 2.81/1.74 thf(f414,plain,(
% 2.81/1.74 ~(~! [X0 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X0 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) = $true) => ((paraco1325918602e_eval @ X0 @ p) = (paraco1344940915le_Det @ $true))) <~> ! [X2 : list_char > paraco1605129243lle_tv] : ((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X2 @ p)))),
% 2.81/1.74 inference(fool_elimination,[status(thm)],[f413])).
% 2.81/1.74 thf(f413,plain,(
% 2.81/1.74 ~(~! [X0 : list_char > paraco1605129243lle_tv] : ((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X0 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[X1 : nat] : ($true))))) => ((paraco1325918602e_eval @ X0 @ p) = (paraco1344940915le_Det @ $true))) != ! [X2 : list_char > paraco1605129243lle_tv] : ((paraco1325918602e_eval @ X2 @ p) = (paraco1344940915le_Det @ $true)))),
% 2.81/1.74 inference(rectify,[status(thm)],[f356])).
% 2.81/1.74 thf(f356,negated_conjecture,(
% 2.81/1.74 ~(~! [X6 : list_char > paraco1605129243lle_tv] : ((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X6 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[X0 : nat] : ($true))))) => ((paraco1325918602e_eval @ X6 @ p) = (paraco1344940915le_Det @ $true))) != ! [X6 : list_char > paraco1605129243lle_tv] : ((paraco1325918602e_eval @ X6 @ p) = (paraco1344940915le_Det @ $true)))),
% 2.81/1.74 inference(negated_conjecture,[status(cth)],[f355])).
% 2.81/1.74 thf(f355,conjecture,(
% 2.81/1.74 (~! [X6 : list_char > paraco1605129243lle_tv] : ((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X6 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[X0 : nat] : ($true))))) => ((paraco1325918602e_eval @ X6 @ p) = (paraco1344940915le_Det @ $true))) != ! [X6 : list_char > paraco1605129243lle_tv] : ((paraco1325918602e_eval @ X6 @ p) = (paraco1344940915le_Det @ $true)))),
% 2.81/1.74 file('/export/starexec/sandbox/tmp/tmp.PTGbAxFx6h/DTF2THF_21650.p',conj_0)).
% 2.81/1.74 thf(f2352,plain,(
% 2.81/1.74 spl188_1 | spl188_2),
% 2.81/1.74 inference(avatar_split_clause,[status(thm)],[f2345,f2350,f2347])).
% 2.81/1.74 thf(f2345,plain,(
% 2.81/1.74 ( ! [X2 : list_char > paraco1605129243lle_tv,X3 : list_char > paraco1605129243lle_tv] : (((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X2 @ p)) | ((paraco1325918602e_eval @ X3 @ p) = (paraco1344940915le_Det @ $true)) | ((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X3 @ top_to748628679t_char) @ top_to1057771083lle_tv) != $true)) )),
% 2.81/1.74 inference(forward_demodulation,[status(thm)],[f2344,f1916])).
% 2.81/1.74 thf(f1916,plain,(
% 2.81/1.74 (top_to1057771083lle_tv = (collec1111687558lle_tv @ (^[Y0 : paraco1605129243lle_tv]: ($true))))),
% 2.81/1.74 inference(cnf_transformation,[status(thm)],[f799])).
% 2.81/1.74 thf(f799,plain,(
% 2.81/1.74 (top_to1057771083lle_tv = (collec1111687558lle_tv @ (^[Y0 : paraco1605129243lle_tv]: ($true))))),
% 2.81/1.74 inference(fool_elimination,[status(thm)],[f798])).
% 2.81/1.74 thf(f798,plain,(
% 2.81/1.74 (top_to1057771083lle_tv = (collec1111687558lle_tv @ (^[X0 : paraco1605129243lle_tv] : ($true))))),
% 2.81/1.74 inference(rectify,[status(thm)],[f204])).
% 2.81/1.74 thf(f204,axiom,(
% 2.81/1.74 (top_to1057771083lle_tv = (collec1111687558lle_tv @ (^[X1 : paraco1605129243lle_tv] : ($true))))),
% 2.81/1.74 file('/export/starexec/sandbox/tmp/tmp.PTGbAxFx6h/DTF2THF_21650.p',fact_203_UNIV__def)).
% 2.81/1.74 thf(f2344,plain,(
% 2.81/1.74 ( ! [X2 : list_char > paraco1605129243lle_tv,X3 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X3 @ top_to748628679t_char) @ (collec1111687558lle_tv @ (^[Y0 : paraco1605129243lle_tv]: ($true)))) != $true) | ((paraco1325918602e_eval @ X3 @ p) = (paraco1344940915le_Det @ $true)) | ((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X2 @ p))) )),
% 2.81/1.74 inference(forward_demodulation,[status(thm)],[f2090,f2207])).
% 2.81/1.74 thf(f2207,plain,(
% 2.81/1.74 ((paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true)))) = (collec1111687558lle_tv @ (^[Y0 : paraco1605129243lle_tv]: ($true))))),
% 2.81/1.74 inference(cnf_transformation,[status(thm)],[f531])).
% 2.81/1.74 thf(f531,plain,(
% 2.81/1.74 ((paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true)))) = (collec1111687558lle_tv @ (^[Y0 : paraco1605129243lle_tv]: ($true))))),
% 2.81/1.74 inference(fool_elimination,[status(thm)],[f1])).
% 2.81/1.74 thf(f1,axiom,(
% 2.81/1.74 ((paraco1933902578domain @ (collect_nat @ (^[X0 : nat] : ($true)))) = (collec1111687558lle_tv @ (^[X1 : paraco1605129243lle_tv] : ($true))))),
% 2.81/1.74 file('/export/starexec/sandbox/tmp/tmp.PTGbAxFx6h/DTF2THF_21650.p',fact_0_universal__domain)).
% 2.81/1.74 thf(f2090,plain,(
% 2.81/1.74 ( ! [X2 : list_char > paraco1605129243lle_tv,X3 : list_char > paraco1605129243lle_tv] : (((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X3 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Y0 : nat]: ($true))))) != $true) | ((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X2 @ p)) | ((paraco1325918602e_eval @ X3 @ p) = (paraco1344940915le_Det @ $true))) )),
% 2.81/1.74 inference(cnf_transformation,[status(thm)],[f1593])).
% 2.81/1.74 % SZS output end Proof for DTF2THF_21650
% 2.81/1.74 % (21950)------------------------------
% 2.81/1.74 % (21950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.74 % (21950)Termination reason: Refutation
% 2.81/1.74
% 2.81/1.74 % (21950)Memory used [KB]: 7931
% 2.81/1.74 % (21950)Time elapsed: 0.056 s
% 2.81/1.74 % (21950)Instructions burned: 162 (million)
% 2.81/1.74 % (21950)------------------------------
% 2.81/1.74 % (21950)------------------------------
% 2.81/1.74 % (21926)Success in time 0.144 s
%------------------------------------------------------------------------------