%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP135^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.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 08:55:49 AM UTC 2026
% Result : Theorem 0.31s 1.68s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 19 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 114 ( 7 ~; 0 |; 0 &; 107 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 23 ( 22 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 146 ( 143 usr; 15 con; 0-3 aty)
% Number of variables : 20 ( 20 ^; 0 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_7,type,
set_nat: $tType ).
thf(type_def_8,type,
paraco1605129243lle_tv: $tType ).
thf(type_def_9,type,
set_Pa1764573435lle_tv: $tType ).
thf(type_def_10,type,
product_prod_nat_nat: $tType ).
thf(type_def_11,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_12,type,
produc270694976lle_tv: $tType ).
thf(type_def_13,type,
set_Pr13445366lle_tv: $tType ).
thf(type_def_14,type,
produc194167194tv_nat: $tType ).
thf(type_def_15,type,
set_Pr1725653840tv_nat: $tType ).
thf(type_def_16,type,
produc1647334210lle_tv: $tType ).
thf(type_def_17,type,
set_Pr2014382200lle_tv: $tType ).
thf(type_def_18,type,
set_Pr2120184979lle_fm: $tType ).
thf(type_def_19,type,
set_Pr560526279lle_tv: $tType ).
thf(type_def_20,type,
set_Pr1723822845lle_tv: $tType ).
thf(type_def_21,type,
set_Pr840833727at_nat: $tType ).
thf(type_def_22,type,
list_char: $tType ).
thf(type_def_23,type,
produc931990033lle_tv: $tType ).
thf(type_def_24,type,
paraco1604210848lle_fm: $tType ).
thf(type_def_25,type,
produc696645085lle_fm: $tType ).
thf(type_def_26,type,
produc1443694919lle_tv: $tType ).
thf(type_def_27,type,
produc596913417at_nat: $tType ).
thf(func_def_0,type,
set_Pr1723822845lle_tv: $tType ).
thf(func_def_1,type,
set_Pr2120184979lle_fm: $tType ).
thf(func_def_2,type,
produc1443694919lle_tv: $tType ).
thf(func_def_3,type,
produc696645085lle_fm: $tType ).
thf(func_def_4,type,
set_Pr2014382200lle_tv: $tType ).
thf(func_def_5,type,
set_Pr840833727at_nat: $tType ).
thf(func_def_6,type,
set_Pr560526279lle_tv: $tType ).
thf(func_def_7,type,
produc1647334210lle_tv: $tType ).
thf(func_def_8,type,
produc596913417at_nat: $tType ).
thf(func_def_9,type,
produc931990033lle_tv: $tType ).
thf(func_def_10,type,
set_Pr1725653840tv_nat: $tType ).
thf(func_def_11,type,
set_Pr13445366lle_tv: $tType ).
thf(func_def_12,type,
produc194167194tv_nat: $tType ).
thf(func_def_13,type,
produc270694976lle_tv: $tType ).
thf(func_def_14,type,
set_Pr1986765409at_nat: $tType ).
thf(func_def_15,type,
set_Pa1764573435lle_tv: $tType ).
thf(func_def_16,type,
product_prod_nat_nat: $tType ).
thf(func_def_17,type,
paraco1605129243lle_tv: $tType ).
thf(func_def_18,type,
paraco1604210848lle_fm: $tType ).
thf(func_def_19,type,
list_char: $tType ).
thf(func_def_20,type,
set_nat: $tType ).
thf(func_def_21,type,
nat: $tType ).
thf(func_def_22,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(func_def_23,type,
inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
thf(func_def_24,type,
inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
thf(func_def_25,type,
inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
thf(func_def_26,type,
inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
thf(func_def_27,type,
inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
thf(func_def_28,type,
inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
thf(func_def_29,type,
inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
thf(func_def_30,type,
the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
thf(func_def_31,type,
the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_32,type,
if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_33,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_34,type,
ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
thf(func_def_35,type,
ord_le1007985907lle_fm: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > $o ).
thf(func_def_36,type,
ord_le1784136743lle_tv: set_Pr560526279lle_tv > set_Pr560526279lle_tv > $o ).
thf(func_def_37,type,
top_top_nat_o: nat > $o ).
thf(func_def_38,type,
top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
thf(func_def_39,type,
top_to632227436_nat_o: product_prod_nat_nat > $o ).
thf(func_def_40,type,
top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
thf(func_def_41,type,
top_to900819589_nat_o: produc194167194tv_nat > $o ).
thf(func_def_43,type,
top_top_set_nat: set_nat ).
thf(func_def_44,type,
top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
thf(func_def_45,type,
top_to775056195lle_fm: set_Pr2120184979lle_fm ).
thf(func_def_46,type,
top_to449985143lle_tv: set_Pr560526279lle_tv ).
thf(func_def_47,type,
top_to1555900337at_nat: set_Pr1986765409at_nat ).
thf(func_def_48,type,
top_to1411004326lle_tv: set_Pr13445366lle_tv ).
thf(func_def_49,type,
top_to378694061lle_tv: set_Pr1723822845lle_tv ).
thf(func_def_50,type,
top_to730292591at_nat: set_Pr840833727at_nat ).
thf(func_def_51,type,
top_to975729152tv_nat: set_Pr1725653840tv_nat ).
thf(func_def_52,type,
top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
thf(func_def_53,type,
paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).
thf(func_def_54,type,
paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_55,type,
paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).
thf(func_def_56,type,
paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
thf(func_def_57,type,
paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_58,type,
paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_59,type,
paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_60,type,
paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(func_def_61,type,
paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
thf(func_def_62,type,
paraco367965286_Truth: paraco1604210848lle_fm ).
thf(func_def_63,type,
paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
thf(func_def_64,type,
paraco793048302_Indet: nat > paraco1605129243lle_tv ).
thf(func_def_65,type,
paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_66,type,
paraco327635598_valid: paraco1604210848lle_fm > $o ).
thf(func_def_67,type,
paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
thf(func_def_68,type,
produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
thf(func_def_69,type,
produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).
thf(func_def_70,type,
produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).
thf(func_def_71,type,
produc1633679363at_nat: paraco1605129243lle_tv > ( nat > nat ) > produc596913417at_nat ).
thf(func_def_72,type,
produc1942165868lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > produc696645085lle_fm ).
thf(func_def_73,type,
produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).
thf(func_def_74,type,
produc1807466521lle_tv: ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
thf(func_def_75,type,
produc109093078at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
thf(func_def_76,type,
produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).
thf(func_def_77,type,
produc275353523e_fm_o: ( produc696645085lle_fm > $o ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ).
thf(func_def_78,type,
produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).
thf(func_def_79,type,
produc1900967599lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
thf(func_def_80,type,
produc1566550641lle_tv: ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > produc696645085lle_fm > produc931990033lle_tv ).
thf(func_def_81,type,
produc951033137lle_fm: ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc931990033lle_tv > produc696645085lle_fm ).
thf(func_def_82,type,
produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
thf(func_def_83,type,
produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_84,type,
produc313957681lle_tv: ( nat > nat ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
thf(func_def_85,type,
produc1685803475tv_nat: ( nat > nat ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > product_prod_nat_nat ).
thf(func_def_86,type,
produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
thf(func_def_87,type,
produc1250721397at_nat: ( nat > paraco1605129243lle_tv ) > ( nat > nat ) > product_prod_nat_nat > produc194167194tv_nat ).
thf(func_def_88,type,
produc210389789lle_tv: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc1647334210lle_tv ).
thf(func_def_89,type,
produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
thf(func_def_90,type,
produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
thf(func_def_91,type,
produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
thf(func_def_92,type,
produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
thf(func_def_93,type,
produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
thf(func_def_94,type,
produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
thf(func_def_95,type,
produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(func_def_96,type,
produc1636169559lle_tv: produc931990033lle_tv > nat > nat ).
thf(func_def_97,type,
produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).
thf(func_def_98,type,
produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).
thf(func_def_99,type,
produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).
thf(func_def_100,type,
produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv ).
thf(func_def_101,type,
produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).
thf(func_def_102,type,
produc500618325at_nat: produc596913417at_nat > nat > nat ).
thf(func_def_103,type,
produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).
thf(func_def_104,type,
produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat ).
thf(func_def_105,type,
produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).
thf(func_def_106,type,
produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).
thf(func_def_107,type,
inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_108,type,
inv_im1292588663lle_tv: set_Pr1986765409at_nat > ( paraco1605129243lle_tv > nat ) > set_Pr2014382200lle_tv ).
thf(func_def_109,type,
inv_im516950809tv_nat: set_Pr2014382200lle_tv > ( nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat ).
thf(func_def_110,type,
inv_im719552961lle_tv: set_Pr2014382200lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv ).
thf(func_def_111,type,
total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_112,type,
total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o ).
thf(func_def_113,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_114,type,
collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(func_def_115,type,
collec835549234lle_fm: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm ).
thf(func_def_116,type,
collec1624074086lle_tv: ( produc931990033lle_tv > $o ) > set_Pr560526279lle_tv ).
thf(func_def_117,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_118,type,
collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
thf(func_def_119,type,
collec1582599068lle_tv: ( produc1443694919lle_tv > $o ) > set_Pr1723822845lle_tv ).
thf(func_def_120,type,
collec1288997470at_nat: ( produc596913417at_nat > $o ) > set_Pr840833727at_nat ).
thf(func_def_121,type,
collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
thf(func_def_122,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_123,type,
image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
thf(func_def_124,type,
image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
thf(func_def_125,type,
image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(func_def_126,type,
image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).
thf(func_def_127,type,
image_1154804148lle_tv: ( produc696645085lle_fm > produc931990033lle_tv ) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv ).
thf(func_def_128,type,
image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).
thf(func_def_129,type,
image_1585092542lle_fm: ( produc931990033lle_tv > produc696645085lle_fm ) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm ).
thf(func_def_130,type,
image_1751508608lle_tv: ( produc931990033lle_tv > produc931990033lle_tv ) > set_Pr560526279lle_tv > set_Pr560526279lle_tv ).
thf(func_def_131,type,
image_1724396928at_nat: ( produc931990033lle_tv > produc596913417at_nat ) > set_Pr560526279lle_tv > set_Pr840833727at_nat ).
thf(func_def_132,type,
image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_133,type,
image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
thf(func_def_134,type,
image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
thf(func_def_135,type,
image_1507992062lle_tv: ( product_prod_nat_nat > produc1647334210lle_tv ) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv ).
thf(func_def_136,type,
image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
thf(func_def_137,type,
image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
thf(func_def_138,type,
image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
thf(func_def_139,type,
image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
thf(func_def_140,type,
image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).
thf(func_def_141,type,
image_769496456lle_tv: ( produc596913417at_nat > produc931990033lle_tv ) > set_Pr840833727at_nat > set_Pr560526279lle_tv ).
thf(func_def_142,type,
image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
thf(func_def_143,type,
image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
thf(func_def_144,type,
accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).
thf(func_def_145,type,
member_nat: nat > set_nat > $o ).
thf(func_def_146,type,
member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
thf(func_def_147,type,
member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).
thf(func_def_148,type,
member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o ).
thf(func_def_149,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_150,type,
member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
thf(func_def_151,type,
member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).
thf(func_def_152,type,
member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).
thf(func_def_153,type,
member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
thf(func_def_154,type,
member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
thf(func_def_155,type,
f: nat > nat ).
thf(func_def_156,type,
i: list_char > paraco1605129243lle_tv ).
thf(func_def_157,type,
p1: paraco1604210848lle_fm ).
thf(func_def_158,type,
p2: paraco1604210848lle_fm ).
thf(func_def_170,type,
sK0: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv > nat ).
thf(func_def_171,type,
sK1: paraco1605129243lle_tv > paraco1605129243lle_tv > $o ).
thf(func_def_172,type,
sK2: ( nat > nat ) > nat ).
thf(func_def_173,type,
sK3: ( nat > nat ) > nat ).
thf(func_def_174,type,
sK4: ( nat > nat ) > nat ).
thf(func_def_175,type,
sK5: ( nat > nat ) > nat ).
thf(func_def_177,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f938,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f937,f915]) ).
thf(f915,plain,
( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
= ( paraco1344940915le_Det @ $true ) ),
inference(cnf_transformation,[status(thm)],[f378]) ).
thf(f378,plain,
( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
= ( paraco1344940915le_Det @ $true ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( paraco1344940915le_Det @ $true )
= ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.cKDKiLlZzx/DTF2THF_30016.p',fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062) ).
thf(f937,plain,
( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
!= ( paraco1344940915le_Det @ $true ) ),
inference(superposition,[status(thm)],[f936,f935]) ).
thf(f935,plain,
( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
= ( paraco1325918602e_eval
@ ^ [Y0: list_char] : ( paraco1147068288nge_tv @ f @ ( i @ Y0 ) )
@ p2 ) ),
inference(beta_eta_normalization,[status(thm)],[f925]) ).
thf(f925,plain,
( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
= ( paraco1325918602e_eval
@ ( ^ [Y0: nat > nat,Y1: list_char > paraco1605129243lle_tv,Y2: list_char] : ( paraco1147068288nge_tv @ Y0 @ ( Y1 @ Y2 ) )
@ f
@ i )
@ p2 ) ),
inference(definition_unfolding,[status(thm)],[f904,f901]) ).
thf(f901,plain,
( paraco761681009ge_int
= ( ^ [Y0: nat > nat,Y1: list_char > paraco1605129243lle_tv,Y2: list_char] : ( paraco1147068288nge_tv @ Y0 @ ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f675]) ).
thf(f675,plain,
( paraco761681009ge_int
= ( ^ [Y0: nat > nat,Y1: list_char > paraco1605129243lle_tv,Y2: list_char] : ( paraco1147068288nge_tv @ Y0 @ ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f674]) ).
thf(f674,plain,
( paraco761681009ge_int
= ( ^ [X0: nat > nat,X1: list_char > paraco1605129243lle_tv,X2: list_char] : ( paraco1147068288nge_tv @ X0 @ ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( paraco761681009ge_int
= ( ^ [X2: nat > nat,X3: list_char > paraco1605129243lle_tv,X4: list_char] : ( paraco1147068288nge_tv @ X2 @ ( X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.cKDKiLlZzx/DTF2THF_30016.p',fact_7_change__int__def) ).
thf(f904,plain,
( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
= ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
= ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.cKDKiLlZzx/DTF2THF_30016.p',fact_2_ih2) ).
thf(f936,plain,
( ( paraco1325918602e_eval
@ ^ [Y0: list_char] : ( paraco1147068288nge_tv @ f @ ( i @ Y0 ) )
@ p2 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(beta_eta_normalization,[status(thm)],[f926]) ).
thf(f926,plain,
( ( paraco1344940915le_Det @ $true )
!= ( paraco1325918602e_eval
@ ( ^ [Y0: nat > nat,Y1: list_char > paraco1605129243lle_tv,Y2: list_char] : ( paraco1147068288nge_tv @ Y0 @ ( Y1 @ Y2 ) )
@ f
@ i )
@ p2 ) ),
inference(definition_unfolding,[status(thm)],[f909,f901]) ).
thf(f909,plain,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(cnf_transformation,[status(thm)],[f869]) ).
thf(f869,plain,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(flattening,[status(thm)],[f657]) ).
thf(f657,plain,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(fool_elimination,[status(thm)],[f360]) ).
thf(f360,negated_conjecture,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
!= ( paraco1344940915le_Det @ $true ) ),
inference(negated_conjecture,[status(cth)],[f359]) ).
thf(f359,conjecture,
( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
= ( paraco1344940915le_Det @ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.cKDKiLlZzx/DTF2THF_30016.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP135^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:28:33 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : ITP135^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.46 % Domain : Interactive Theorem Proving
% 0.20/0.46 % Problem : Sledgehammer Paraconsistency problem prob_1041__3275778_1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Des21]
% 0.20/0.46 % Names : Paraconsistency/prob_1041__3275778_1 [Des21]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.20/0.46 % Syntax : Number of formulae : 518 ( 174 unt; 159 typ; 0 def)
% 0.20/0.46 % Number of atoms : 1007 ( 549 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 16 ( 2 avg)
% 0.20/0.46 % Number of connectives : 2726 ( 111 ~; 2 |; 31 &;2123 @)
% 0.20/0.46 % ( 0 <=>; 459 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 16 ( 6 avg)
% 0.20/0.46 % Number of types : 23 ( 22 usr)
% 0.20/0.46 % Number of type conns : 735 ( 735 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 140 ( 137 usr; 16 con; 0-3 aty)
% 0.20/0.46 % Number of variables : 1013 ( 38 ^; 950 !; 25 ?;1013 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:40:05.471
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (22)
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 0.20/0.46 set_Pr1723822845lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.20/0.46 set_Pr2120184979lle_fm: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.20/0.46 produc1443694919lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 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,
% 0.20/0.46 produc696645085lle_fm: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.20/0.46 set_Pr2014382200lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 set_Pr840833727at_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.20/0.46 set_Pr560526279lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 produc1647334210lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 produc596913417at_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 produc931990033lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 set_Pr1725653840tv_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.20/0.46 set_Pr13445366lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.20/0.46 produc194167194tv_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 produc270694976lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 set_Pr1986765409at_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 set_Pa1764573435lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.20/0.46 product_prod_nat_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.20/0.46 paraco1605129243lle_tv: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.20/0.46 paraco1604210848lle_fm: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 0.20/0.46 list_char: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.20/0.46 set_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.20/0.46 nat: $tType ).
% 0.20/0.46
% 0.20/0.46 % Explicit typings (137)
% 0.20/0.46 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.20/0.46 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.20/0.46 inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.20/0.46 inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.20/0.46 inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.20/0.46 inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.20/0.46 inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.20/0.46 the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.20/0.46 the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.20/0.46 if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.20/0.46 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
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% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_Eo_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_M_Eo_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
% 0.20/0.46 top_top_o: $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
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% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
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% 0.20/0.46
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__int,type,
% 0.20/0.46 paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv,type,
% 0.20/0.46 paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv__rel,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Oeval,type,
% 0.20/0.46 paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OCon_H,type,
% 0.20/0.46 paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql,type,
% 0.20/0.46 paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql_H,type,
% 0.20/0.46 paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_ONeg_H,type,
% 0.20/0.46 paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OPro,type,
% 0.20/0.46 paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OTruth,type,
% 0.20/0.46 paraco367965286_Truth: paraco1604210848lle_fm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_ODet,type,
% 0.20/0.46 paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_OIndet,type,
% 0.20/0.46 paraco793048302_Indet: nat > paraco1605129243lle_tv ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_Ocase__tv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid,type,
% 0.20/0.46 paraco327635598_valid: paraco1604210848lle_fm > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid__in,type,
% 0.20/0.46 paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
% 0.20/0.46
% 0.20/0.46 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,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Oapfst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Oapfst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Obool_Ocase__bool_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Omap__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.20/0.46
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% 0.20/0.46 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
% 0.20/0.46 total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46
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% 0.20/0.46 member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__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,
% 0.20/0.46 member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.20/0.46 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.20/0.46 member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.20/0.46 member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.20/0.46 member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_f,type,
% 0.20/0.46 f: nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_i,type,
% 0.20/0.46 i: list_char > paraco1605129243lle_tv ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_p1____,type,
% 0.20/0.46 p1: paraco1604210848lle_fm ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_p2____,type,
% 0.20/0.46 p2: paraco1604210848lle_fm ).
% 0.20/0.46
% 0.20/0.46 % Relevant facts (355)
% 0.20/0.46 thf(fact_0_a,axiom,
% 0.20/0.46 ( ( paraco1325918602e_eval @ i @ p2 )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) ) ).
% 0.20/0.46
% 0.20/0.46 % a
% 0.20/0.46 thf(fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062,axiom,
% 0.20/0.46 ( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>change_tv f (eval i p2) = Det True\<close>
% 0.20/0.46 thf(fact_2_ih2,axiom,
% 0.20/0.46 ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 0.20/0.46 = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ih2
% 0.20/0.46 thf(fact_3_tv_Oinject_I1_J,axiom,
% 0.20/0.46 ! [X1: $o,Y1: $o] :
% 0.20/0.46 ( ( ( paraco1344940915le_Det @ X1 )
% 0.20/0.46 = ( paraco1344940915le_Det @ Y1 ) )
% 0.20/0.46 = ( X1 = Y1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % tv.inject(1)
% 0.20/0.46 thf(fact_4_a_H_H,axiom,
% 0.20/0.46 ( ( paraco1325918602e_eval @ i @ p1 )
% 0.20/0.46 != ( paraco1344940915le_Det @ $true ) ) ).
% 0.20/0.46
% 0.20/0.46 % a''
% 0.20/0.46 thf(fact_5_a_H,axiom,
% 0.20/0.46 ( ( paraco1325918602e_eval @ i @ p1 )
% 0.20/0.46 != ( paraco1325918602e_eval @ i @ p2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % a'
% 0.20/0.46 thf(fact_6_ih1,axiom,
% 0.20/0.46 ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 0.20/0.46 = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ih1
% 0.20/0.46 thf(fact_7_change__int__def,axiom,
% 0.20/0.46 ( paraco761681009ge_int
% 0.20/0.46 = ( ^ [F: nat > nat,I: list_char > paraco1605129243lle_tv,S: list_char] : ( paraco1147068288nge_tv @ F @ ( I @ S ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % change_int_def
% 0.20/0.46 thf(fact_8_change__tv_Osimps_I1_J,axiom,
% 0.20/0.46 ! [F2: nat > nat,B: $o] :
% 0.20/0.46 ( ( paraco1147068288nge_tv @ F2 @ ( paraco1344940915le_Det @ B ) )
% 0.20/0.46 = ( paraco1344940915le_Det @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % change_tv.simps(1)
% 0.20/0.46 thf(fact_9_yes,axiom,
% 0.20/0.46 ( ( paraco1325918602e_eval @ i @ ( paraco1745535428le_Eql @ p1 @ p2 ) )
% 0.20/0.46 = ( paraco1325918602e_eval @ i @ p1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % yes
% 0.20/0.46 thf(fact_10_valid__def,axiom,
% 0.20/0.46 ( paraco327635598_valid
% 0.20/0.46 = ( ^ [P: paraco1604210848lle_fm] :
% 0.20/0.46 ! [I: list_char > paraco1605129243lle_tv] :
% 0.20/0.46 ( ( paraco1325918602e_eval @ I @ P )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % valid_def
% 0.20/0.46 thf(fact_11_eval_Osimps_I2_J,axiom,
% 0.20/0.46 ! [I2: list_char > paraco1605129243lle_tv] :
% 0.20/0.46 ( ( paraco1325918602e_eval @ I2 @ paraco367965286_Truth )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) ) ).
% 0.20/0.46
% 0.20/0.46 % eval.simps(2)
% 0.20/0.46 thf(fact_12_eval_Osimps_I5_J,axiom,
% 0.20/0.46 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 != ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1344940915le_Det @ $false ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eval.simps(5)
% 0.20/0.46 thf(fact_13_eval__equality__simplify,axiom,
% 0.20/0.46 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1344940915le_Det
% 0.20/0.46 @ ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ Q ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eval_equality_simplify
% 0.20/0.46 thf(fact_14_eval_Osimps_I4_J,axiom,
% 0.20/0.46 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 != ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.20/0.46 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ Q ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 != ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.20/0.46 != ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eval.simps(4)
% 0.20/0.46 thf(fact_15_tv_Osimps_I5_J,axiom,
% 0.20/0.46 ! [F1: $o > paraco1605129243lle_tv,F22: nat > paraco1605129243lle_tv,X1: $o] :
% 0.20/0.46 ( ( paraco2051596139lle_tv @ F1 @ F22 @ ( paraco1344940915le_Det @ X1 ) )
% 0.20/0.46 = ( F1 @ X1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % tv.simps(5)
% 0.20/0.46 thf(fact_16_eval__negation,axiom,
% 0.20/0.46 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 = ( paraco1344940915le_Det @ $false ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 != ( paraco1344940915le_Det @ $false ) )
% 0.20/0.46 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.20/0.46 = ( paraco1344940915le_Det @ $false ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 != ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eval_negation
% 0.20/0.46 thf(fact_17_assms,axiom,
% 0.20/0.46 inj_on_nat_nat @ f @ top_top_set_nat ).
% 0.20/0.46
% 0.20/0.46 % assms
% 0.20/0.46 thf(fact_18_fm_Oinject_I2_J,axiom,
% 0.20/0.46 ! [X3: paraco1604210848lle_fm,Y3: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( ( paraco445776468le_Neg @ X3 )
% 0.20/0.46 = ( paraco445776468le_Neg @ Y3 ) )
% 0.20/0.46 = ( X3 = Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.inject(2)
% 0.20/0.46 thf(fact_19_fm_Oinject_I3_J,axiom,
% 0.20/0.46 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,Y41: paraco1604210848lle_fm,Y42: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.20/0.46 = ( paraco69239110le_Con @ Y41 @ Y42 ) )
% 0.20/0.46 = ( ( X41 = Y41 )
% 0.20/0.46 & ( X42 = Y42 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.inject(3)
% 0.20/0.46 thf(fact_20_fm_Oinject_I5_J,axiom,
% 0.20/0.46 ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm,Y61: paraco1604210848lle_fm,Y62: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( ( paraco1745535428le_Eql @ X61 @ X62 )
% 0.20/0.46 = ( paraco1745535428le_Eql @ Y61 @ Y62 ) )
% 0.20/0.46 = ( ( X61 = Y61 )
% 0.20/0.46 & ( X62 = Y62 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.inject(5)
% 0.20/0.46 thf(fact_21_fm_Oinject_I4_J,axiom,
% 0.20/0.46 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,Y51: paraco1604210848lle_fm,Y52: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.20/0.46 = ( paraco1389086619le_Eql @ Y51 @ Y52 ) )
% 0.20/0.46 = ( ( X51 = Y51 )
% 0.20/0.46 & ( X52 = Y52 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.inject(4)
% 0.20/0.46 thf(fact_22_fm_Odistinct_I29_J,axiom,
% 0.20/0.46 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.20/0.46 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(29)
% 0.20/0.46 thf(fact_23_fm_Odistinct_I27_J,axiom,
% 0.20/0.46 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.20/0.46 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(27)
% 0.20/0.46 thf(fact_24_fm_Odistinct_I25_J,axiom,
% 0.20/0.46 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.20/0.46 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(25)
% 0.20/0.46 thf(fact_25_fm_Odistinct_I23_J,axiom,
% 0.20/0.46 ! [X3: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( paraco445776468le_Neg @ X3 )
% 0.20/0.46 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(23)
% 0.20/0.46 thf(fact_26_fm_Odistinct_I21_J,axiom,
% 0.20/0.46 ! [X3: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( paraco445776468le_Neg @ X3 )
% 0.20/0.46 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(21)
% 0.20/0.46 thf(fact_27_fm_Odistinct_I19_J,axiom,
% 0.20/0.46 ! [X3: paraco1604210848lle_fm,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( paraco445776468le_Neg @ X3 )
% 0.20/0.46 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(19)
% 0.20/0.46 thf(fact_28_fm_Odistinct_I17_J,axiom,
% 0.20/0.46 ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.20/0.46 ( paraco367965286_Truth
% 0.20/0.46 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(17)
% 0.20/0.46 thf(fact_29_fm_Odistinct_I15_J,axiom,
% 0.20/0.46 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.20/0.46 ( paraco367965286_Truth
% 0.20/0.46 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(15)
% 0.20/0.46 thf(fact_30_fm_Odistinct_I13_J,axiom,
% 0.20/0.46 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.20/0.46 ( paraco367965286_Truth
% 0.20/0.46 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(13)
% 0.20/0.46 thf(fact_31_fm_Odistinct_I11_J,axiom,
% 0.20/0.46 ! [X3: paraco1604210848lle_fm] :
% 0.20/0.46 ( paraco367965286_Truth
% 0.20/0.46 != ( paraco445776468le_Neg @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % fm.distinct(11)
% 0.20/0.46 thf(fact_32_conjunction,axiom,
% 0.20/0.46 ! [P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( paraco327635598_valid @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.20/0.46 = ( ( paraco327635598_valid @ P2 )
% 0.20/0.46 & ( paraco327635598_valid @ Q ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % conjunction
% 0.20/0.46 thf(fact_33_eval__equality,axiom,
% 0.20/0.46 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.20/0.46 ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 != ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.20/0.46 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ Q ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 != ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.20/0.46 = ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.20/0.46 != ( paraco1344940915le_Det @ $true ) )
% 0.20/0.46 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 = ( paraco1344940915le_Det @ $false ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ Q ) ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.20/0.46 != ( paraco1344940915le_Det @ $false ) )
% 0.20/0.46 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.20/0.46 = ( paraco1344940915le_Det @ $false ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) ) ) )
% 0.20/0.46 & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.20/0.46 != ( paraco1344940915le_Det @ $false ) )
% 0.20/0.46 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.20/0.46 = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eval_equality
% 0.20/0.46 thf(fact_34_double__negation,axiom,
% 0.20/0.46 ( paraco1325918602e_eval
% 0.20/0.46 = ( ^ [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ P ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % double_negation
% 0.20/0.46 thf(fact_35_UNIV__I,axiom,
% 0.20/0.46 ! [X: produc596913417at_nat] : ( member1234290208at_nat @ X @ top_to730292591at_nat ) ).
% 0.20/0.46
% 0.20/0.46 % UNIV_I
% 0.20/0.46 thf(fact_36_UNIV__I,axiom,
% 0.20/0.46 ! [X: produc1443694919lle_tv] : ( member74361182lle_tv @ X @ top_to378694061lle_tv ) ).
% 0.20/0.46
% 0.20/0.46 % UNIV_I
% 0.20/0.46 thf(fact_37_UNIV__I,axiom,
% 0.20/0.46 ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 0.20/0.46
% 0.20/0.46 % UNIV_I
% 0.20/0.46 thf(fact_38_UNIV__I,axiom,
% 0.20/0.46 ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 0.20/0.46
% 0.20/0.46 % UNIV_I
% 0.20/0.46 thf(fact_39_UNIV__I,axiom,
% 0.20/0.46 ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.20/0.46
% 0.20/0.46 % UNIV_I
% 0.20/0.46 thf(fact_40_UNIV__I,axiom,
% 0.20/0.46 ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.20/0.46
% 0.20/0.46 % UNIV_I
% 0.20/0.46 thf(fact_41_UNIV__I,axiom,
% 0.20/0.46 ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.20/0.46
% 0.20/0.46 % UNIV_I
% 0.20/0.46 thf(fact_42_UNIV__I,axiom,
% 0.20/0.46 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.20/0.46
% 0.20/0.46 % UNIV_I
% 0.20/0.46 thf(fact_43_UNIV__I,axiom,
% 0.20/0.46 ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.20/0.46
% 0.20/0.46 % UNIV_I
% 0.20/0.46 thf(fact_44_iso__tuple__UNIV__I,axiom,
% 0.20/0.46 ! [X: produc596913417at_nat] : ( member1234290208at_nat @ X @ top_to730292591at_nat ) ).
% 0.20/0.46
% 0.20/0.46 % iso_tuple_UNIV_I
% 0.20/0.46 thf(fact_45_iso__tuple__UNIV__I,axiom,
% 0.20/0.46 ! [X: produc1443694919lle_tv] : ( member74361182lle_tv @ X @ top_to378694061lle_tv ) ).
% 0.20/0.46
% 0.20/0.46 % iso_tuple_UNIV_I
% 0.20/0.46 thf(fact_46_iso__tuple__UNIV__I,axiom,
% 0.20/0.46 ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 0.20/0.46
% 0.20/0.46 % iso_tuple_UNIV_I
% 0.20/0.46 thf(fact_47_iso__tuple__UNIV__I,axiom,
% 0.20/0.46 ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 0.20/0.46
% 0.20/0.46 % iso_tuple_UNIV_I
% 0.20/0.46 thf(fact_48_iso__tuple__UNIV__I,axiom,
% 0.20/0.46 ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.20/0.46
% 0.20/0.46 % iso_tuple_UNIV_I
% 0.20/0.46 thf(fact_49_iso__tuple__UNIV__I,axiom,
% 0.20/0.46 ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.20/0.46
% 0.20/0.46 % iso_tuple_UNIV_I
% 0.20/0.46 thf(fact_50_iso__tuple__UNIV__I,axiom,
% 0.20/0.46 ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.20/0.46
% 0.20/0.46 % iso_tuple_UNIV_I
% 0.20/0.46 thf(fact_51_iso__tuple__UNIV__I,axiom,
% 0.20/0.46 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.20/0.46
% 0.20/0.46 % iso_tuple_UNIV_I
% 0.20/0.46 thf(fact_52_iso__tuple__UNIV__I,axiom,
% 0.20/0.46 ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.20/0.46
% 0.20/0.46 % iso_tuple_UNIV_I
% 0.20/0.46 thf(fact_53_top__apply,axiom,
% 0.20/0.46 ( top_to1299250770e_tv_o
% 0.20/0.46 = ( ^ [X2: paraco1605129243lle_tv] : top_top_o ) ) ).
% 0.20/0.46
% 0.20/0.46 % top_apply
% 0.20/0.46 thf(fact_54_top__apply,axiom,
% 0.20/0.46 ( top_top_nat_o
% 0.20/0.46 = ( ^ [X2: nat] : top_top_o ) ) ).
% 0.20/0.46
% 0.20/0.46 % top_apply
% 0.20/0.46 thf(fact_55_injD,axiom,
% 0.20/0.46 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.20/0.46 ( ( inj_on2112487900lle_tv @ F2 @ top_to1871154984lle_tv )
% 0.20/0.46 => ( ( ( F2 @ X )
% 0.20/0.46 = ( F2 @ Y ) )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % injD
% 0.20/0.46 thf(fact_56_injD,axiom,
% 0.20/0.46 ! [F2: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.20/0.46 ( ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.46 => ( ( ( F2 @ X )
% 0.20/0.46 = ( F2 @ Y ) )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % injD
% 0.20/0.46 thf(fact_57_injD,axiom,
% 0.20/0.46 ! [F2: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.20/0.46 ( ( inj_on552895452tv_nat @ F2 @ top_to975729152tv_nat )
% 0.20/0.46 => ( ( ( F2 @ X )
% 0.20/0.46 = ( F2 @ Y ) )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % injD
% 0.20/0.46 thf(fact_58_injD,axiom,
% 0.20/0.46 ! [F2: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.20/0.46 ( ( inj_on1745913142lle_tv @ F2 @ top_to1411004326lle_tv )
% 0.20/0.46 => ( ( ( F2 @ X )
% 0.20/0.46 = ( F2 @ Y ) )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % injD
% 0.20/0.46 thf(fact_59_injD,axiom,
% 0.20/0.46 ! [F2: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.20/0.46 ( ( inj_on26176689at_nat @ F2 @ top_to1555900337at_nat )
% 0.20/0.46 => ( ( ( F2 @ X )
% 0.20/0.46 = ( F2 @ Y ) )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % injD
% 0.20/0.46 thf(fact_60_injD,axiom,
% 0.20/0.46 ! [F2: nat > nat,X: nat,Y: nat] :
% 0.20/0.46 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.46 => ( ( ( F2 @ X )
% 0.20/0.46 = ( F2 @ Y ) )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % injD
% 0.20/0.46 thf(fact_61_injD,axiom,
% 0.20/0.46 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.46 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.46 => ( ( ( F2 @ X )
% 0.20/0.46 = ( F2 @ Y ) )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % injD
% 0.20/0.46 thf(fact_62_injI,axiom,
% 0.20/0.46 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.20/0.46 ( ! [X4: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 0.20/0.46 ( ( ( F2 @ X4 )
% 0.20/0.46 = ( F2 @ Y2 ) )
% 0.20/0.46 => ( X4 = Y2 ) )
% 0.20/0.46 => ( inj_on2112487900lle_tv @ F2 @ top_to1871154984lle_tv ) ) ).
% 0.20/0.46
% 0.20/0.46 % injI
% 0.20/0.46 thf(fact_63_injI,axiom,
% 0.20/0.46 ! [F2: nat > paraco1605129243lle_tv] :
% 0.20/0.46 ( ! [X4: nat,Y2: nat] :
% 0.20/0.46 ( ( ( F2 @ X4 )
% 0.20/0.46 = ( F2 @ Y2 ) )
% 0.20/0.46 => ( X4 = Y2 ) )
% 0.20/0.46 => ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % injI
% 0.20/0.46 thf(fact_64_injI,axiom,
% 0.20/0.46 ! [F2: produc194167194tv_nat > produc194167194tv_nat] :
% 0.20/0.46 ( ! [X4: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 0.20/0.46 ( ( ( F2 @ X4 )
% 0.20/0.46 = ( F2 @ Y2 ) )
% 0.20/0.46 => ( X4 = Y2 ) )
% 0.20/0.46 => ( inj_on552895452tv_nat @ F2 @ top_to975729152tv_nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % injI
% 0.20/0.46 thf(fact_65_injI,axiom,
% 0.20/0.46 ! [F2: produc270694976lle_tv > produc270694976lle_tv] :
% 0.20/0.46 ( ! [X4: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 0.20/0.46 ( ( ( F2 @ X4 )
% 0.20/0.46 = ( F2 @ Y2 ) )
% 0.20/0.46 => ( X4 = Y2 ) )
% 0.20/0.46 => ( inj_on1745913142lle_tv @ F2 @ top_to1411004326lle_tv ) ) ).
% 0.20/0.46
% 0.20/0.46 % injI
% 0.20/0.46 thf(fact_66_injI,axiom,
% 0.20/0.46 ! [F2: product_prod_nat_nat > product_prod_nat_nat] :
% 0.20/0.46 ( ! [X4: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.20/0.46 ( ( ( F2 @ X4 )
% 0.20/0.46 = ( F2 @ Y2 ) )
% 0.20/0.46 => ( X4 = Y2 ) )
% 0.20/0.46 => ( inj_on26176689at_nat @ F2 @ top_to1555900337at_nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % injI
% 0.20/0.46 thf(fact_67_injI,axiom,
% 0.20/0.46 ! [F2: nat > nat] :
% 0.20/0.46 ( ! [X4: nat,Y2: nat] :
% 0.20/0.46 ( ( ( F2 @ X4 )
% 0.20/0.46 = ( F2 @ Y2 ) )
% 0.20/0.46 => ( X4 = Y2 ) )
% 0.20/0.46 => ( inj_on_nat_nat @ F2 @ top_top_set_nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % injI
% 0.20/0.46 thf(fact_68_injI,axiom,
% 0.20/0.46 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.46 ( ! [X4: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 0.20/0.46 ( ( ( F2 @ X4 )
% 0.20/0.46 = ( F2 @ Y2 ) )
% 0.20/0.46 => ( X4 = Y2 ) )
% 0.20/0.46 => ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv ) ) ).
% 0.20/0.46
% 0.20/0.46 % injI
% 0.20/0.46 thf(fact_69_inj__eq,axiom,
% 0.20/0.46 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.20/0.46 ( ( inj_on2112487900lle_tv @ F2 @ top_to1871154984lle_tv )
% 0.20/0.46 => ( ( ( F2 @ X )
% 0.20/0.46 = ( F2 @ Y ) )
% 0.20/0.46 = ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inj_eq
% 0.20/0.46 thf(fact_70_inj__eq,axiom,
% 0.20/0.46 ! [F2: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.20/0.46 ( ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.46 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_eq
% 0.20/0.47 thf(fact_71_inj__eq,axiom,
% 0.20/0.47 ! [F2: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.20/0.47 ( ( inj_on552895452tv_nat @ F2 @ top_to975729152tv_nat )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_eq
% 0.20/0.47 thf(fact_72_inj__eq,axiom,
% 0.20/0.47 ! [F2: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.20/0.47 ( ( inj_on1745913142lle_tv @ F2 @ top_to1411004326lle_tv )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_eq
% 0.20/0.47 thf(fact_73_inj__eq,axiom,
% 0.20/0.47 ! [F2: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.20/0.47 ( ( inj_on26176689at_nat @ F2 @ top_to1555900337at_nat )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_eq
% 0.20/0.47 thf(fact_74_inj__eq,axiom,
% 0.20/0.47 ! [F2: nat > nat,X: nat,Y: nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_eq
% 0.20/0.47 thf(fact_75_inj__eq,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_eq
% 0.20/0.47 thf(fact_76_inj__def,axiom,
% 0.20/0.47 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.20/0.47 ( ( inj_on2112487900lle_tv @ F2 @ top_to1871154984lle_tv )
% 0.20/0.47 = ( ! [X2: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
% 0.20/0.47 ( ( ( F2 @ X2 )
% 0.20/0.47 = ( F2 @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_def
% 0.20/0.47 thf(fact_77_inj__def,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.47 = ( ! [X2: nat,Y4: nat] :
% 0.20/0.47 ( ( ( F2 @ X2 )
% 0.20/0.47 = ( F2 @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_def
% 0.20/0.47 thf(fact_78_inj__def,axiom,
% 0.20/0.47 ! [F2: produc194167194tv_nat > produc194167194tv_nat] :
% 0.20/0.47 ( ( inj_on552895452tv_nat @ F2 @ top_to975729152tv_nat )
% 0.20/0.47 = ( ! [X2: produc194167194tv_nat,Y4: produc194167194tv_nat] :
% 0.20/0.47 ( ( ( F2 @ X2 )
% 0.20/0.47 = ( F2 @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_def
% 0.20/0.47 thf(fact_79_inj__def,axiom,
% 0.20/0.47 ! [F2: produc270694976lle_tv > produc270694976lle_tv] :
% 0.20/0.47 ( ( inj_on1745913142lle_tv @ F2 @ top_to1411004326lle_tv )
% 0.20/0.47 = ( ! [X2: produc270694976lle_tv,Y4: produc270694976lle_tv] :
% 0.20/0.47 ( ( ( F2 @ X2 )
% 0.20/0.47 = ( F2 @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_def
% 0.20/0.47 thf(fact_80_inj__def,axiom,
% 0.20/0.47 ! [F2: product_prod_nat_nat > product_prod_nat_nat] :
% 0.20/0.47 ( ( inj_on26176689at_nat @ F2 @ top_to1555900337at_nat )
% 0.20/0.47 = ( ! [X2: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 0.20/0.47 ( ( ( F2 @ X2 )
% 0.20/0.47 = ( F2 @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_def
% 0.20/0.47 thf(fact_81_inj__def,axiom,
% 0.20/0.47 ! [F2: nat > nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 = ( ! [X2: nat,Y4: nat] :
% 0.20/0.47 ( ( ( F2 @ X2 )
% 0.20/0.47 = ( F2 @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_def
% 0.20/0.47 thf(fact_82_inj__def,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 = ( ! [X2: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( F2 @ X2 )
% 0.20/0.47 = ( F2 @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_def
% 0.20/0.47 thf(fact_83_fm_Oinduct,axiom,
% 0.20/0.47 ! [P3: paraco1604210848lle_fm > $o,Fm: paraco1604210848lle_fm] :
% 0.20/0.47 ( ! [X4: list_char] : ( P3 @ ( paraco1480028776le_Pro @ X4 ) )
% 0.20/0.47 => ( ( P3 @ paraco367965286_Truth )
% 0.20/0.47 => ( ! [X4: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ X4 )
% 0.20/0.47 => ( P3 @ ( paraco445776468le_Neg @ X4 ) ) )
% 0.20/0.47 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ X1a )
% 0.20/0.47 => ( ( P3 @ X22 )
% 0.20/0.47 => ( P3 @ ( paraco69239110le_Con @ X1a @ X22 ) ) ) )
% 0.20/0.47 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ X1a )
% 0.20/0.47 => ( ( P3 @ X22 )
% 0.20/0.47 => ( P3 @ ( paraco1389086619le_Eql @ X1a @ X22 ) ) ) )
% 0.20/0.47 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ X1a )
% 0.20/0.47 => ( ( P3 @ X22 )
% 0.20/0.47 => ( P3 @ ( paraco1745535428le_Eql @ X1a @ X22 ) ) ) )
% 0.20/0.47 => ( P3 @ Fm ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fm.induct
% 0.20/0.47 thf(fact_84_fm_Oexhaust,axiom,
% 0.20/0.47 ! [Y: paraco1604210848lle_fm] :
% 0.20/0.47 ( ! [X12: list_char] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( paraco1480028776le_Pro @ X12 ) )
% 0.20/0.47 => ( ( Y != paraco367965286_Truth )
% 0.20/0.47 => ( ! [X32: paraco1604210848lle_fm] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( paraco445776468le_Neg @ X32 ) )
% 0.20/0.47 => ( ! [X412: paraco1604210848lle_fm,X422: paraco1604210848lle_fm] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( paraco69239110le_Con @ X412 @ X422 ) )
% 0.20/0.47 => ( ! [X512: paraco1604210848lle_fm,X522: paraco1604210848lle_fm] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( paraco1389086619le_Eql @ X512 @ X522 ) )
% 0.20/0.47 => ~ ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fm.exhaust
% 0.20/0.47 thf(fact_85_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: produc596913417at_nat,P3: produc596913417at_nat > $o] :
% 0.20/0.47 ( ( member1234290208at_nat @ A @ ( collec1288997470at_nat @ P3 ) )
% 0.20/0.47 = ( P3 @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_86_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: produc1443694919lle_tv,P3: produc1443694919lle_tv > $o] :
% 0.20/0.47 ( ( member74361182lle_tv @ A @ ( collec1582599068lle_tv @ P3 ) )
% 0.20/0.47 = ( P3 @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_87_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: produc696645085lle_fm,P3: produc696645085lle_fm > $o] :
% 0.20/0.47 ( ( member1474794996lle_fm @ A @ ( collec835549234lle_fm @ P3 ) )
% 0.20/0.47 = ( P3 @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_88_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: produc931990033lle_tv,P3: produc931990033lle_tv > $o] :
% 0.20/0.47 ( ( member1569366824lle_tv @ A @ ( collec1624074086lle_tv @ P3 ) )
% 0.20/0.47 = ( P3 @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_89_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: paraco1605129243lle_tv,P3: paraco1605129243lle_tv > $o] :
% 0.20/0.47 ( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ P3 ) )
% 0.20/0.47 = ( P3 @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_90_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: nat,P3: nat > $o] :
% 0.20/0.47 ( ( member_nat @ A @ ( collect_nat @ P3 ) )
% 0.20/0.47 = ( P3 @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_91_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A2: set_Pr840833727at_nat] :
% 0.20/0.47 ( ( collec1288997470at_nat
% 0.20/0.47 @ ^ [X2: produc596913417at_nat] : ( member1234290208at_nat @ X2 @ A2 ) )
% 0.20/0.47 = A2 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_92_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A2: set_Pr1723822845lle_tv] :
% 0.20/0.47 ( ( collec1582599068lle_tv
% 0.20/0.47 @ ^ [X2: produc1443694919lle_tv] : ( member74361182lle_tv @ X2 @ A2 ) )
% 0.20/0.47 = A2 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_93_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A2: set_Pr2120184979lle_fm] :
% 0.20/0.47 ( ( collec835549234lle_fm
% 0.20/0.47 @ ^ [X2: produc696645085lle_fm] : ( member1474794996lle_fm @ X2 @ A2 ) )
% 0.20/0.47 = A2 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_94_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A2: set_Pr560526279lle_tv] :
% 0.20/0.47 ( ( collec1624074086lle_tv
% 0.20/0.47 @ ^ [X2: produc931990033lle_tv] : ( member1569366824lle_tv @ X2 @ A2 ) )
% 0.20/0.47 = A2 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_95_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A2: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( collec1111687558lle_tv
% 0.20/0.47 @ ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ A2 ) )
% 0.20/0.47 = A2 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_96_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A2: set_nat] :
% 0.20/0.47 ( ( collect_nat
% 0.20/0.47 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 0.20/0.47 = A2 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_97_Collect__cong,axiom,
% 0.20/0.47 ! [P3: paraco1605129243lle_tv > $o,Q2: paraco1605129243lle_tv > $o] :
% 0.20/0.47 ( ! [X4: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( P3 @ X4 )
% 0.20/0.47 = ( Q2 @ X4 ) )
% 0.20/0.47 => ( ( collec1111687558lle_tv @ P3 )
% 0.20/0.47 = ( collec1111687558lle_tv @ Q2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_98_Collect__cong,axiom,
% 0.20/0.47 ! [P3: nat > $o,Q2: nat > $o] :
% 0.20/0.47 ( ! [X4: nat] :
% 0.20/0.47 ( ( P3 @ X4 )
% 0.20/0.47 = ( Q2 @ X4 ) )
% 0.20/0.47 => ( ( collect_nat @ P3 )
% 0.20/0.47 = ( collect_nat @ Q2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_99_props_Ocases,axiom,
% 0.20/0.47 ! [X: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( X != paraco367965286_Truth )
% 0.20/0.47 => ( ! [S2: list_char] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( paraco1480028776le_Pro @ S2 ) )
% 0.20/0.47 => ( ! [P4: paraco1604210848lle_fm] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( paraco445776468le_Neg @ P4 ) )
% 0.20/0.47 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( paraco69239110le_Con @ P4 @ Q3 ) )
% 0.20/0.47 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( paraco1389086619le_Eql @ P4 @ Q3 ) )
% 0.20/0.47 => ~ ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % props.cases
% 0.20/0.47 thf(fact_100_fm_Oinject_I1_J,axiom,
% 0.20/0.47 ! [X1: list_char,Y1: list_char] :
% 0.20/0.47 ( ( ( paraco1480028776le_Pro @ X1 )
% 0.20/0.47 = ( paraco1480028776le_Pro @ Y1 ) )
% 0.20/0.47 = ( X1 = Y1 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fm.inject(1)
% 0.20/0.47 thf(fact_101_top__set__def,axiom,
% 0.20/0.47 ( top_to975729152tv_nat
% 0.20/0.47 = ( collec848462447tv_nat @ top_to900819589_nat_o ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_set_def
% 0.20/0.47 thf(fact_102_top__set__def,axiom,
% 0.20/0.47 ( top_to1411004326lle_tv
% 0.20/0.47 = ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_set_def
% 0.20/0.47 thf(fact_103_top__set__def,axiom,
% 0.20/0.47 ( top_to1555900337at_nat
% 0.20/0.47 = ( collec7649004at_nat @ top_to632227436_nat_o ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_set_def
% 0.20/0.47 thf(fact_104_top__set__def,axiom,
% 0.20/0.47 ( top_top_set_nat
% 0.20/0.47 = ( collect_nat @ top_top_nat_o ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_set_def
% 0.20/0.47 thf(fact_105_top__set__def,axiom,
% 0.20/0.47 ( top_to1057771083lle_tv
% 0.20/0.47 = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_set_def
% 0.20/0.47 thf(fact_106_eval_Osimps_I1_J,axiom,
% 0.20/0.47 ! [I2: list_char > paraco1605129243lle_tv,S3: list_char] :
% 0.20/0.47 ( ( paraco1325918602e_eval @ I2 @ ( paraco1480028776le_Pro @ S3 ) )
% 0.20/0.47 = ( I2 @ S3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % eval.simps(1)
% 0.20/0.47 thf(fact_107_fm_Odistinct_I3_J,axiom,
% 0.20/0.47 ! [X1: list_char,X3: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.20/0.47 != ( paraco445776468le_Neg @ X3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fm.distinct(3)
% 0.20/0.47 thf(fact_108_fm_Odistinct_I5_J,axiom,
% 0.20/0.47 ! [X1: list_char,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.20/0.47 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fm.distinct(5)
% 0.20/0.47 thf(fact_109_fm_Odistinct_I9_J,axiom,
% 0.20/0.47 ! [X1: list_char,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.20/0.47 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fm.distinct(9)
% 0.20/0.47 thf(fact_110_fm_Odistinct_I7_J,axiom,
% 0.20/0.47 ! [X1: list_char,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.20/0.47 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fm.distinct(7)
% 0.20/0.47 thf(fact_111_fm_Odistinct_I1_J,axiom,
% 0.20/0.47 ! [X1: list_char] :
% 0.20/0.47 ( ( paraco1480028776le_Pro @ X1 )
% 0.20/0.47 != paraco367965286_Truth ) ).
% 0.20/0.47
% 0.20/0.47 % fm.distinct(1)
% 0.20/0.47 thf(fact_112_change__tv__injection,axiom,
% 0.20/0.47 ! [F2: nat > nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 => ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ F2 ) @ top_to1057771083lle_tv ) ) ).
% 0.20/0.47
% 0.20/0.47 % change_tv_injection
% 0.20/0.47 thf(fact_113_UNIV__witness,axiom,
% 0.20/0.47 ? [X4: produc596913417at_nat] : ( member1234290208at_nat @ X4 @ top_to730292591at_nat ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_114_UNIV__witness,axiom,
% 0.20/0.47 ? [X4: produc1443694919lle_tv] : ( member74361182lle_tv @ X4 @ top_to378694061lle_tv ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_115_UNIV__witness,axiom,
% 0.20/0.47 ? [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ top_to775056195lle_fm ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_116_UNIV__witness,axiom,
% 0.20/0.47 ? [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ top_to449985143lle_tv ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_117_UNIV__witness,axiom,
% 0.20/0.47 ? [X4: produc194167194tv_nat] : ( member737151281tv_nat @ X4 @ top_to975729152tv_nat ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_118_UNIV__witness,axiom,
% 0.20/0.47 ? [X4: produc270694976lle_tv] : ( member813679063lle_tv @ X4 @ top_to1411004326lle_tv ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_119_UNIV__witness,axiom,
% 0.20/0.47 ? [X4: product_prod_nat_nat] : ( member701585322at_nat @ X4 @ top_to1555900337at_nat ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_120_UNIV__witness,axiom,
% 0.20/0.47 ? [X4: nat] : ( member_nat @ X4 @ top_top_set_nat ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_121_UNIV__witness,axiom,
% 0.20/0.47 ? [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ top_to1057771083lle_tv ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_122_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A2: set_Pr840833727at_nat] :
% 0.20/0.47 ( ! [X4: produc596913417at_nat] : ( member1234290208at_nat @ X4 @ A2 )
% 0.20/0.47 => ( top_to730292591at_nat = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_123_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A2: set_Pr1723822845lle_tv] :
% 0.20/0.47 ( ! [X4: produc1443694919lle_tv] : ( member74361182lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( top_to378694061lle_tv = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_124_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A2: set_Pr2120184979lle_fm] :
% 0.20/0.47 ( ! [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ A2 )
% 0.20/0.47 => ( top_to775056195lle_fm = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_125_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A2: set_Pr560526279lle_tv] :
% 0.20/0.47 ( ! [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( top_to449985143lle_tv = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_126_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A2: set_Pr1725653840tv_nat] :
% 0.20/0.47 ( ! [X4: produc194167194tv_nat] : ( member737151281tv_nat @ X4 @ A2 )
% 0.20/0.47 => ( top_to975729152tv_nat = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_127_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A2: set_Pr13445366lle_tv] :
% 0.20/0.47 ( ! [X4: produc270694976lle_tv] : ( member813679063lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( top_to1411004326lle_tv = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_128_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A2: set_Pr1986765409at_nat] :
% 0.20/0.47 ( ! [X4: product_prod_nat_nat] : ( member701585322at_nat @ X4 @ A2 )
% 0.20/0.47 => ( top_to1555900337at_nat = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_129_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A2: set_nat] :
% 0.20/0.47 ( ! [X4: nat] : ( member_nat @ X4 @ A2 )
% 0.20/0.47 => ( top_top_set_nat = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_130_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A2: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ! [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( top_to1057771083lle_tv = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_131_inj__on__inverseI,axiom,
% 0.20/0.47 ! [A2: set_Pr2014382200lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv,F2: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.20/0.47 ( ! [X4: produc1647334210lle_tv] :
% 0.20/0.47 ( ( member1531318361lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 ) )
% 0.20/0.47 => ( inj_on2112487900lle_tv @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_inverseI
% 0.20/0.47 thf(fact_132_inj__on__inverseI,axiom,
% 0.20/0.47 ! [A2: set_Pr1725653840tv_nat,G: produc194167194tv_nat > produc194167194tv_nat,F2: produc194167194tv_nat > produc194167194tv_nat] :
% 0.20/0.47 ( ! [X4: produc194167194tv_nat] :
% 0.20/0.47 ( ( member737151281tv_nat @ X4 @ A2 )
% 0.20/0.47 => ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 ) )
% 0.20/0.47 => ( inj_on552895452tv_nat @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_inverseI
% 0.20/0.47 thf(fact_133_inj__on__inverseI,axiom,
% 0.20/0.47 ! [A2: set_Pr13445366lle_tv,G: produc270694976lle_tv > produc270694976lle_tv,F2: produc270694976lle_tv > produc270694976lle_tv] :
% 0.20/0.47 ( ! [X4: produc270694976lle_tv] :
% 0.20/0.47 ( ( member813679063lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 ) )
% 0.20/0.47 => ( inj_on1745913142lle_tv @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_inverseI
% 0.20/0.47 thf(fact_134_inj__on__inverseI,axiom,
% 0.20/0.47 ! [A2: set_Pr1986765409at_nat,G: product_prod_nat_nat > product_prod_nat_nat,F2: product_prod_nat_nat > product_prod_nat_nat] :
% 0.20/0.47 ( ! [X4: product_prod_nat_nat] :
% 0.20/0.47 ( ( member701585322at_nat @ X4 @ A2 )
% 0.20/0.47 => ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 ) )
% 0.20/0.47 => ( inj_on26176689at_nat @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_inverseI
% 0.20/0.47 thf(fact_135_inj__on__inverseI,axiom,
% 0.20/0.47 ! [A2: set_nat,G: paraco1605129243lle_tv > nat,F2: nat > paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [X4: nat] :
% 0.20/0.47 ( ( member_nat @ X4 @ A2 )
% 0.20/0.47 => ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 ) )
% 0.20/0.47 => ( inj_on1955349912lle_tv @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_inverseI
% 0.20/0.47 thf(fact_136_inj__on__inverseI,axiom,
% 0.20/0.47 ! [A2: set_nat,G: nat > nat,F2: nat > nat] :
% 0.20/0.47 ( ! [X4: nat] :
% 0.20/0.47 ( ( member_nat @ X4 @ A2 )
% 0.20/0.47 => ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 ) )
% 0.20/0.47 => ( inj_on_nat_nat @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_inverseI
% 0.20/0.47 thf(fact_137_inj__on__inverseI,axiom,
% 0.20/0.47 ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [X4: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member266900804lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 ) )
% 0.20/0.47 => ( inj_on772319074lle_tv @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_inverseI
% 0.20/0.47 thf(fact_138_inj__on__contraD,axiom,
% 0.20/0.47 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.20/0.47 ( ( inj_on2112487900lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( X != Y )
% 0.20/0.47 => ( ( member1531318361lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.20/0.47 => ( ( F2 @ X )
% 0.20/0.47 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_contraD
% 0.20/0.47 thf(fact_139_inj__on__contraD,axiom,
% 0.20/0.47 ! [F2: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.20/0.47 ( ( inj_on552895452tv_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( X != Y )
% 0.20/0.47 => ( ( member737151281tv_nat @ X @ A2 )
% 0.20/0.47 => ( ( member737151281tv_nat @ Y @ A2 )
% 0.20/0.47 => ( ( F2 @ X )
% 0.20/0.47 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_contraD
% 0.20/0.47 thf(fact_140_inj__on__contraD,axiom,
% 0.20/0.47 ! [F2: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.20/0.47 ( ( inj_on1745913142lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( X != Y )
% 0.20/0.47 => ( ( member813679063lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( member813679063lle_tv @ Y @ A2 )
% 0.20/0.47 => ( ( F2 @ X )
% 0.20/0.47 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_contraD
% 0.20/0.47 thf(fact_141_inj__on__contraD,axiom,
% 0.20/0.47 ! [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.20/0.47 ( ( inj_on26176689at_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( X != Y )
% 0.20/0.47 => ( ( member701585322at_nat @ X @ A2 )
% 0.20/0.47 => ( ( member701585322at_nat @ Y @ A2 )
% 0.20/0.47 => ( ( F2 @ X )
% 0.20/0.47 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_contraD
% 0.20/0.47 thf(fact_142_inj__on__contraD,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.20/0.47 ( ( inj_on1955349912lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( X != Y )
% 0.20/0.47 => ( ( member_nat @ X @ A2 )
% 0.20/0.47 => ( ( member_nat @ Y @ A2 )
% 0.20/0.47 => ( ( F2 @ X )
% 0.20/0.47 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_contraD
% 0.20/0.47 thf(fact_143_inj__on__contraD,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( X != Y )
% 0.20/0.47 => ( ( member_nat @ X @ A2 )
% 0.20/0.47 => ( ( member_nat @ Y @ A2 )
% 0.20/0.47 => ( ( F2 @ X )
% 0.20/0.47 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_contraD
% 0.20/0.47 thf(fact_144_inj__on__contraD,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( X != Y )
% 0.20/0.47 => ( ( member266900804lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( member266900804lle_tv @ Y @ A2 )
% 0.20/0.47 => ( ( F2 @ X )
% 0.20/0.47 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_contraD
% 0.20/0.47 thf(fact_145_inj__on__eq__iff,axiom,
% 0.20/0.47 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.20/0.47 ( ( inj_on2112487900lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( member1531318361lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_eq_iff
% 0.20/0.47 thf(fact_146_inj__on__eq__iff,axiom,
% 0.20/0.47 ! [F2: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.20/0.47 ( ( inj_on552895452tv_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( member737151281tv_nat @ X @ A2 )
% 0.20/0.47 => ( ( member737151281tv_nat @ Y @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_eq_iff
% 0.20/0.47 thf(fact_147_inj__on__eq__iff,axiom,
% 0.20/0.47 ! [F2: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.20/0.47 ( ( inj_on1745913142lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( member813679063lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( member813679063lle_tv @ Y @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_eq_iff
% 0.20/0.47 thf(fact_148_inj__on__eq__iff,axiom,
% 0.20/0.47 ! [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.20/0.47 ( ( inj_on26176689at_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( member701585322at_nat @ X @ A2 )
% 0.20/0.47 => ( ( member701585322at_nat @ Y @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_eq_iff
% 0.20/0.47 thf(fact_149_inj__on__eq__iff,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.20/0.47 ( ( inj_on1955349912lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( member_nat @ X @ A2 )
% 0.20/0.47 => ( ( member_nat @ Y @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_eq_iff
% 0.20/0.47 thf(fact_150_inj__on__eq__iff,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( member_nat @ X @ A2 )
% 0.20/0.47 => ( ( member_nat @ Y @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_eq_iff
% 0.20/0.47 thf(fact_151_inj__on__eq__iff,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( member266900804lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( member266900804lle_tv @ Y @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_eq_iff
% 0.20/0.47 thf(fact_152_inj__on__cong,axiom,
% 0.20/0.47 ! [A2: set_Pr2014382200lle_tv,F2: produc1647334210lle_tv > produc1647334210lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.20/0.47 ( ! [A3: produc1647334210lle_tv] :
% 0.20/0.47 ( ( member1531318361lle_tv @ A3 @ A2 )
% 0.20/0.47 => ( ( F2 @ A3 )
% 0.20/0.47 = ( G @ A3 ) ) )
% 0.20/0.47 => ( ( inj_on2112487900lle_tv @ F2 @ A2 )
% 0.20/0.47 = ( inj_on2112487900lle_tv @ G @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_cong
% 0.20/0.47 thf(fact_153_inj__on__cong,axiom,
% 0.20/0.47 ! [A2: set_Pr1725653840tv_nat,F2: produc194167194tv_nat > produc194167194tv_nat,G: produc194167194tv_nat > produc194167194tv_nat] :
% 0.20/0.47 ( ! [A3: produc194167194tv_nat] :
% 0.20/0.47 ( ( member737151281tv_nat @ A3 @ A2 )
% 0.20/0.47 => ( ( F2 @ A3 )
% 0.20/0.47 = ( G @ A3 ) ) )
% 0.20/0.47 => ( ( inj_on552895452tv_nat @ F2 @ A2 )
% 0.20/0.47 = ( inj_on552895452tv_nat @ G @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_cong
% 0.20/0.47 thf(fact_154_inj__on__cong,axiom,
% 0.20/0.47 ! [A2: set_Pr13445366lle_tv,F2: produc270694976lle_tv > produc270694976lle_tv,G: produc270694976lle_tv > produc270694976lle_tv] :
% 0.20/0.47 ( ! [A3: produc270694976lle_tv] :
% 0.20/0.47 ( ( member813679063lle_tv @ A3 @ A2 )
% 0.20/0.47 => ( ( F2 @ A3 )
% 0.20/0.47 = ( G @ A3 ) ) )
% 0.20/0.47 => ( ( inj_on1745913142lle_tv @ F2 @ A2 )
% 0.20/0.47 = ( inj_on1745913142lle_tv @ G @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_cong
% 0.20/0.47 thf(fact_155_inj__on__cong,axiom,
% 0.20/0.47 ! [A2: set_Pr1986765409at_nat,F2: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 0.20/0.47 ( ! [A3: product_prod_nat_nat] :
% 0.20/0.47 ( ( member701585322at_nat @ A3 @ A2 )
% 0.20/0.47 => ( ( F2 @ A3 )
% 0.20/0.47 = ( G @ A3 ) ) )
% 0.20/0.47 => ( ( inj_on26176689at_nat @ F2 @ A2 )
% 0.20/0.47 = ( inj_on26176689at_nat @ G @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_cong
% 0.20/0.47 thf(fact_156_inj__on__cong,axiom,
% 0.20/0.47 ! [A2: set_nat,F2: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [A3: nat] :
% 0.20/0.47 ( ( member_nat @ A3 @ A2 )
% 0.20/0.47 => ( ( F2 @ A3 )
% 0.20/0.47 = ( G @ A3 ) ) )
% 0.20/0.47 => ( ( inj_on1955349912lle_tv @ F2 @ A2 )
% 0.20/0.47 = ( inj_on1955349912lle_tv @ G @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_cong
% 0.20/0.47 thf(fact_157_inj__on__cong,axiom,
% 0.20/0.47 ! [A2: set_nat,F2: nat > nat,G: nat > nat] :
% 0.20/0.47 ( ! [A3: nat] :
% 0.20/0.47 ( ( member_nat @ A3 @ A2 )
% 0.20/0.47 => ( ( F2 @ A3 )
% 0.20/0.47 = ( G @ A3 ) ) )
% 0.20/0.47 => ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 = ( inj_on_nat_nat @ G @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_cong
% 0.20/0.47 thf(fact_158_inj__on__cong,axiom,
% 0.20/0.47 ! [A2: set_Pa1764573435lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [A3: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member266900804lle_tv @ A3 @ A2 )
% 0.20/0.47 => ( ( F2 @ A3 )
% 0.20/0.47 = ( G @ A3 ) ) )
% 0.20/0.47 => ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_cong
% 0.20/0.47 thf(fact_159_inj__on__def,axiom,
% 0.20/0.47 ( inj_on2112487900lle_tv
% 0.20/0.47 = ( ^ [F: produc1647334210lle_tv > produc1647334210lle_tv,A4: set_Pr2014382200lle_tv] :
% 0.20/0.47 ! [X2: produc1647334210lle_tv] :
% 0.20/0.47 ( ( member1531318361lle_tv @ X2 @ A4 )
% 0.20/0.47 => ! [Y4: produc1647334210lle_tv] :
% 0.20/0.47 ( ( member1531318361lle_tv @ Y4 @ A4 )
% 0.20/0.47 => ( ( ( F @ X2 )
% 0.20/0.47 = ( F @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_def
% 0.20/0.47 thf(fact_160_inj__on__def,axiom,
% 0.20/0.47 ( inj_on552895452tv_nat
% 0.20/0.47 = ( ^ [F: produc194167194tv_nat > produc194167194tv_nat,A4: set_Pr1725653840tv_nat] :
% 0.20/0.47 ! [X2: produc194167194tv_nat] :
% 0.20/0.47 ( ( member737151281tv_nat @ X2 @ A4 )
% 0.20/0.47 => ! [Y4: produc194167194tv_nat] :
% 0.20/0.47 ( ( member737151281tv_nat @ Y4 @ A4 )
% 0.20/0.47 => ( ( ( F @ X2 )
% 0.20/0.47 = ( F @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_def
% 0.20/0.47 thf(fact_161_inj__on__def,axiom,
% 0.20/0.47 ( inj_on1745913142lle_tv
% 0.20/0.47 = ( ^ [F: produc270694976lle_tv > produc270694976lle_tv,A4: set_Pr13445366lle_tv] :
% 0.20/0.47 ! [X2: produc270694976lle_tv] :
% 0.20/0.47 ( ( member813679063lle_tv @ X2 @ A4 )
% 0.20/0.47 => ! [Y4: produc270694976lle_tv] :
% 0.20/0.47 ( ( member813679063lle_tv @ Y4 @ A4 )
% 0.20/0.47 => ( ( ( F @ X2 )
% 0.20/0.47 = ( F @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_def
% 0.20/0.47 thf(fact_162_inj__on__def,axiom,
% 0.20/0.47 ( inj_on26176689at_nat
% 0.20/0.47 = ( ^ [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1986765409at_nat] :
% 0.20/0.47 ! [X2: product_prod_nat_nat] :
% 0.20/0.47 ( ( member701585322at_nat @ X2 @ A4 )
% 0.20/0.47 => ! [Y4: product_prod_nat_nat] :
% 0.20/0.47 ( ( member701585322at_nat @ Y4 @ A4 )
% 0.20/0.47 => ( ( ( F @ X2 )
% 0.20/0.47 = ( F @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_def
% 0.20/0.47 thf(fact_163_inj__on__def,axiom,
% 0.20/0.47 ( inj_on1955349912lle_tv
% 0.20/0.47 = ( ^ [F: nat > paraco1605129243lle_tv,A4: set_nat] :
% 0.20/0.47 ! [X2: nat] :
% 0.20/0.47 ( ( member_nat @ X2 @ A4 )
% 0.20/0.47 => ! [Y4: nat] :
% 0.20/0.47 ( ( member_nat @ Y4 @ A4 )
% 0.20/0.47 => ( ( ( F @ X2 )
% 0.20/0.47 = ( F @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_def
% 0.20/0.47 thf(fact_164_inj__on__def,axiom,
% 0.20/0.47 ( inj_on_nat_nat
% 0.20/0.47 = ( ^ [F: nat > nat,A4: set_nat] :
% 0.20/0.47 ! [X2: nat] :
% 0.20/0.47 ( ( member_nat @ X2 @ A4 )
% 0.20/0.47 => ! [Y4: nat] :
% 0.20/0.47 ( ( member_nat @ Y4 @ A4 )
% 0.20/0.47 => ( ( ( F @ X2 )
% 0.20/0.47 = ( F @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_def
% 0.20/0.47 thf(fact_165_inj__on__def,axiom,
% 0.20/0.47 ( inj_on772319074lle_tv
% 0.20/0.47 = ( ^ [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A4: set_Pa1764573435lle_tv] :
% 0.20/0.47 ! [X2: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member266900804lle_tv @ X2 @ A4 )
% 0.20/0.47 => ! [Y4: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member266900804lle_tv @ Y4 @ A4 )
% 0.20/0.47 => ( ( ( F @ X2 )
% 0.20/0.47 = ( F @ Y4 ) )
% 0.20/0.47 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_def
% 0.20/0.47 thf(fact_166_inj__onI,axiom,
% 0.20/0.47 ! [A2: set_Pr2014382200lle_tv,F2: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.20/0.47 ( ! [X4: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 0.20/0.47 ( ( member1531318361lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( ( member1531318361lle_tv @ Y2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X4 )
% 0.20/0.47 = ( F2 @ Y2 ) )
% 0.20/0.47 => ( X4 = Y2 ) ) ) )
% 0.20/0.47 => ( inj_on2112487900lle_tv @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onI
% 0.20/0.47 thf(fact_167_inj__onI,axiom,
% 0.20/0.47 ! [A2: set_Pr1725653840tv_nat,F2: produc194167194tv_nat > produc194167194tv_nat] :
% 0.20/0.47 ( ! [X4: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 0.20/0.47 ( ( member737151281tv_nat @ X4 @ A2 )
% 0.20/0.47 => ( ( member737151281tv_nat @ Y2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X4 )
% 0.20/0.47 = ( F2 @ Y2 ) )
% 0.20/0.47 => ( X4 = Y2 ) ) ) )
% 0.20/0.47 => ( inj_on552895452tv_nat @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onI
% 0.20/0.47 thf(fact_168_inj__onI,axiom,
% 0.20/0.47 ! [A2: set_Pr13445366lle_tv,F2: produc270694976lle_tv > produc270694976lle_tv] :
% 0.20/0.47 ( ! [X4: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 0.20/0.47 ( ( member813679063lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( ( member813679063lle_tv @ Y2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X4 )
% 0.20/0.47 = ( F2 @ Y2 ) )
% 0.20/0.47 => ( X4 = Y2 ) ) ) )
% 0.20/0.47 => ( inj_on1745913142lle_tv @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onI
% 0.20/0.47 thf(fact_169_inj__onI,axiom,
% 0.20/0.47 ! [A2: set_Pr1986765409at_nat,F2: product_prod_nat_nat > product_prod_nat_nat] :
% 0.20/0.47 ( ! [X4: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.20/0.47 ( ( member701585322at_nat @ X4 @ A2 )
% 0.20/0.47 => ( ( member701585322at_nat @ Y2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X4 )
% 0.20/0.47 = ( F2 @ Y2 ) )
% 0.20/0.47 => ( X4 = Y2 ) ) ) )
% 0.20/0.47 => ( inj_on26176689at_nat @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onI
% 0.20/0.47 thf(fact_170_inj__onI,axiom,
% 0.20/0.47 ! [A2: set_nat,F2: nat > paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [X4: nat,Y2: nat] :
% 0.20/0.47 ( ( member_nat @ X4 @ A2 )
% 0.20/0.47 => ( ( member_nat @ Y2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X4 )
% 0.20/0.47 = ( F2 @ Y2 ) )
% 0.20/0.47 => ( X4 = Y2 ) ) ) )
% 0.20/0.47 => ( inj_on1955349912lle_tv @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onI
% 0.20/0.47 thf(fact_171_inj__onI,axiom,
% 0.20/0.47 ! [A2: set_nat,F2: nat > nat] :
% 0.20/0.47 ( ! [X4: nat,Y2: nat] :
% 0.20/0.47 ( ( member_nat @ X4 @ A2 )
% 0.20/0.47 => ( ( member_nat @ Y2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X4 )
% 0.20/0.47 = ( F2 @ Y2 ) )
% 0.20/0.47 => ( X4 = Y2 ) ) ) )
% 0.20/0.47 => ( inj_on_nat_nat @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onI
% 0.20/0.47 thf(fact_172_inj__onI,axiom,
% 0.20/0.47 ! [A2: set_Pa1764573435lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [X4: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member266900804lle_tv @ X4 @ A2 )
% 0.20/0.47 => ( ( member266900804lle_tv @ Y2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X4 )
% 0.20/0.47 = ( F2 @ Y2 ) )
% 0.20/0.47 => ( X4 = Y2 ) ) ) )
% 0.20/0.47 => ( inj_on772319074lle_tv @ F2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onI
% 0.20/0.47 thf(fact_173_inj__onD,axiom,
% 0.20/0.47 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.20/0.47 ( ( inj_on2112487900lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 => ( ( member1531318361lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.20/0.47 => ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onD
% 0.20/0.47 thf(fact_174_inj__onD,axiom,
% 0.20/0.47 ! [F2: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.20/0.47 ( ( inj_on552895452tv_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 => ( ( member737151281tv_nat @ X @ A2 )
% 0.20/0.47 => ( ( member737151281tv_nat @ Y @ A2 )
% 0.20/0.47 => ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onD
% 0.20/0.47 thf(fact_175_inj__onD,axiom,
% 0.20/0.47 ! [F2: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.20/0.47 ( ( inj_on1745913142lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 => ( ( member813679063lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( member813679063lle_tv @ Y @ A2 )
% 0.20/0.47 => ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onD
% 0.20/0.47 thf(fact_176_inj__onD,axiom,
% 0.20/0.47 ! [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.20/0.47 ( ( inj_on26176689at_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 => ( ( member701585322at_nat @ X @ A2 )
% 0.20/0.47 => ( ( member701585322at_nat @ Y @ A2 )
% 0.20/0.47 => ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onD
% 0.20/0.47 thf(fact_177_inj__onD,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.20/0.47 ( ( inj_on1955349912lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 => ( ( member_nat @ X @ A2 )
% 0.20/0.47 => ( ( member_nat @ Y @ A2 )
% 0.20/0.47 => ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onD
% 0.20/0.47 thf(fact_178_inj__onD,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 => ( ( member_nat @ X @ A2 )
% 0.20/0.47 => ( ( member_nat @ Y @ A2 )
% 0.20/0.47 => ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onD
% 0.20/0.47 thf(fact_179_inj__onD,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = ( F2 @ Y ) )
% 0.20/0.47 => ( ( member266900804lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( member266900804lle_tv @ Y @ A2 )
% 0.20/0.47 => ( X = Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_onD
% 0.20/0.47 thf(fact_180_props_Oinduct,axiom,
% 0.20/0.47 ! [P3: paraco1604210848lle_fm > $o,A0: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ paraco367965286_Truth )
% 0.20/0.47 => ( ! [S2: list_char] : ( P3 @ ( paraco1480028776le_Pro @ S2 ) )
% 0.20/0.47 => ( ! [P4: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ P4 )
% 0.20/0.47 => ( P3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 0.20/0.47 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ P4 )
% 0.20/0.47 => ( ( P3 @ Q3 )
% 0.20/0.47 => ( P3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) ) )
% 0.20/0.47 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ P4 )
% 0.20/0.47 => ( ( P3 @ Q3 )
% 0.20/0.47 => ( P3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) ) )
% 0.20/0.47 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ P4 )
% 0.20/0.47 => ( ( P3 @ Q3 )
% 0.20/0.47 => ( P3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) )
% 0.20/0.47 => ( P3 @ A0 ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % props.induct
% 0.20/0.47 thf(fact_181_eval_Ocases,axiom,
% 0.20/0.47 ! [X: produc696645085lle_fm] :
% 0.20/0.47 ( ! [I3: list_char > paraco1605129243lle_tv,S2: list_char] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco1480028776le_Pro @ S2 ) ) )
% 0.20/0.47 => ( ! [I3: list_char > paraco1605129243lle_tv] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( produc1710735575lle_fm @ I3 @ paraco367965286_Truth ) )
% 0.20/0.47 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 0.20/0.47 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) )
% 0.20/0.47 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) )
% 0.20/0.47 => ~ ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( produc1710735575lle_fm @ I3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % eval.cases
% 0.20/0.47 thf(fact_182_top__empty__eq,axiom,
% 0.20/0.47 ( top_to900819589_nat_o
% 0.20/0.47 = ( ^ [X2: produc194167194tv_nat] : ( member737151281tv_nat @ X2 @ top_to975729152tv_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_empty_eq
% 0.20/0.47 thf(fact_183_top__empty__eq,axiom,
% 0.20/0.47 ( top_to1889334367e_tv_o
% 0.20/0.47 = ( ^ [X2: produc270694976lle_tv] : ( member813679063lle_tv @ X2 @ top_to1411004326lle_tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_empty_eq
% 0.20/0.47 thf(fact_184_top__empty__eq,axiom,
% 0.20/0.47 ( top_to632227436_nat_o
% 0.20/0.47 = ( ^ [X2: product_prod_nat_nat] : ( member701585322at_nat @ X2 @ top_to1555900337at_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_empty_eq
% 0.20/0.47 thf(fact_185_top__empty__eq,axiom,
% 0.20/0.47 ( top_top_nat_o
% 0.20/0.47 = ( ^ [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_empty_eq
% 0.20/0.47 thf(fact_186_top__empty__eq,axiom,
% 0.20/0.47 ( top_to1299250770e_tv_o
% 0.20/0.47 = ( ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_empty_eq
% 0.20/0.47 thf(fact_187_change__tv_Oelims,axiom,
% 0.20/0.47 ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 0.20/0.47 = Y )
% 0.20/0.47 => ( ! [B2: $o] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( paraco1344940915le_Det @ B2 ) )
% 0.20/0.47 => ( Y
% 0.20/0.47 != ( paraco1344940915le_Det @ B2 ) ) )
% 0.20/0.47 => ~ ! [N: nat] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( paraco793048302_Indet @ N ) )
% 0.20/0.47 => ( Y
% 0.20/0.47 != ( paraco793048302_Indet @ ( X @ N ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % change_tv.elims
% 0.20/0.47 thf(fact_188_valid__valid__in,axiom,
% 0.20/0.47 ! [P2: paraco1604210848lle_fm,U: set_nat] :
% 0.20/0.47 ( ( paraco327635598_valid @ P2 )
% 0.20/0.47 => ( paraco55203475lid_in @ U @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % valid_valid_in
% 0.20/0.47 thf(fact_189_transfer,axiom,
% 0.20/0.47 ! [U: set_nat,P2: paraco1604210848lle_fm] :
% 0.20/0.47 ( ~ ( paraco55203475lid_in @ U @ P2 )
% 0.20/0.47 => ~ ( paraco327635598_valid @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % transfer
% 0.20/0.47 thf(fact_190_the__inv__f__f,axiom,
% 0.20/0.47 ! [F2: nat > nat,X: nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 => ( ( the_inv_into_nat_nat @ top_top_set_nat @ F2 @ ( F2 @ X ) )
% 0.20/0.47 = X ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_f_f
% 0.20/0.47 thf(fact_191_the__inv__f__f,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ F2 @ ( F2 @ X ) )
% 0.20/0.47 = X ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_f_f
% 0.20/0.47 thf(fact_192_conjunction__in,axiom,
% 0.20/0.47 ! [U: set_nat,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( paraco55203475lid_in @ U @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.20/0.47 = ( ( paraco55203475lid_in @ U @ P2 )
% 0.20/0.47 & ( paraco55203475lid_in @ U @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conjunction_in
% 0.20/0.47 thf(fact_193_tv_Oinject_I2_J,axiom,
% 0.20/0.47 ! [X23: nat,Y22: nat] :
% 0.20/0.47 ( ( ( paraco793048302_Indet @ X23 )
% 0.20/0.47 = ( paraco793048302_Indet @ Y22 ) )
% 0.20/0.47 = ( X23 = Y22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % tv.inject(2)
% 0.20/0.47 thf(fact_194_string__tv_Oinduct,axiom,
% 0.20/0.47 ! [P3: paraco1605129243lle_tv > $o,A0: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( P3 @ ( paraco1344940915le_Det @ $true ) )
% 0.20/0.47 => ( ( P3 @ ( paraco1344940915le_Det @ $false ) )
% 0.20/0.47 => ( ! [N: nat] : ( P3 @ ( paraco793048302_Indet @ N ) )
% 0.20/0.47 => ( P3 @ A0 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % string_tv.induct
% 0.20/0.47 thf(fact_195_change__tv_Oinduct,axiom,
% 0.20/0.47 ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,A0: nat > nat,A1: paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [F3: nat > nat,B2: $o] : ( P3 @ F3 @ ( paraco1344940915le_Det @ B2 ) )
% 0.20/0.47 => ( ! [F3: nat > nat,N: nat] : ( P3 @ F3 @ ( paraco793048302_Indet @ N ) )
% 0.20/0.47 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % change_tv.induct
% 0.20/0.47 thf(fact_196_string__tv_Ocases,axiom,
% 0.20/0.47 ! [X: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( X
% 0.20/0.47 != ( paraco1344940915le_Det @ $true ) )
% 0.20/0.47 => ( ( X
% 0.20/0.47 != ( paraco1344940915le_Det @ $false ) )
% 0.20/0.47 => ~ ! [N: nat] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( paraco793048302_Indet @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % string_tv.cases
% 0.20/0.47 thf(fact_197_tv_Oexhaust,axiom,
% 0.20/0.47 ! [Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [X12: $o] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( paraco1344940915le_Det @ X12 ) )
% 0.20/0.47 => ~ ! [X22: nat] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( paraco793048302_Indet @ X22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % tv.exhaust
% 0.20/0.47 thf(fact_198_tv_Oinduct,axiom,
% 0.20/0.47 ! [P3: paraco1605129243lle_tv > $o,Tv: paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [X4: $o] : ( P3 @ ( paraco1344940915le_Det @ X4 ) )
% 0.20/0.47 => ( ! [X4: nat] : ( P3 @ ( paraco793048302_Indet @ X4 ) )
% 0.20/0.47 => ( P3 @ Tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % tv.induct
% 0.20/0.47 thf(fact_199_tv_Odistinct_I1_J,axiom,
% 0.20/0.47 ! [X1: $o,X23: nat] :
% 0.20/0.47 ( ( paraco1344940915le_Det @ X1 )
% 0.20/0.47 != ( paraco793048302_Indet @ X23 ) ) ).
% 0.20/0.47
% 0.20/0.47 % tv.distinct(1)
% 0.20/0.47 thf(fact_200_the__inv__into__f__f,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,X: nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( member_nat @ X @ A2 )
% 0.20/0.47 => ( ( the_inv_into_nat_nat @ A2 @ F2 @ ( F2 @ X ) )
% 0.20/0.47 = X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_into_f_f
% 0.20/0.47 thf(fact_201_the__inv__into__f__f,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( member266900804lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( the_in452116896lle_tv @ A2 @ F2 @ ( F2 @ X ) )
% 0.20/0.47 = X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_into_f_f
% 0.20/0.47 thf(fact_202_the__inv__into__f__eq,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = Y )
% 0.20/0.47 => ( ( member_nat @ X @ A2 )
% 0.20/0.47 => ( ( the_inv_into_nat_nat @ A2 @ F2 @ Y )
% 0.20/0.47 = X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_into_f_eq
% 0.20/0.47 thf(fact_203_the__inv__into__f__eq,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( ( F2 @ X )
% 0.20/0.47 = Y )
% 0.20/0.47 => ( ( member266900804lle_tv @ X @ A2 )
% 0.20/0.47 => ( ( the_in452116896lle_tv @ A2 @ F2 @ Y )
% 0.20/0.47 = X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_into_f_eq
% 0.20/0.47 thf(fact_204_tv_Osimps_I6_J,axiom,
% 0.20/0.47 ! [F1: $o > paraco1605129243lle_tv,F22: nat > paraco1605129243lle_tv,X23: nat] :
% 0.20/0.47 ( ( paraco2051596139lle_tv @ F1 @ F22 @ ( paraco793048302_Indet @ X23 ) )
% 0.20/0.47 = ( F22 @ X23 ) ) ).
% 0.20/0.47
% 0.20/0.47 % tv.simps(6)
% 0.20/0.47 thf(fact_205_change__tv_Osimps_I2_J,axiom,
% 0.20/0.47 ! [F2: nat > nat,N2: nat] :
% 0.20/0.47 ( ( paraco1147068288nge_tv @ F2 @ ( paraco793048302_Indet @ N2 ) )
% 0.20/0.47 = ( paraco793048302_Indet @ ( F2 @ N2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % change_tv.simps(2)
% 0.20/0.47 thf(fact_206_prod_Oinject,axiom,
% 0.20/0.47 ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm,Y1: list_char > paraco1605129243lle_tv,Y22: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( ( produc1710735575lle_fm @ X1 @ X23 )
% 0.20/0.47 = ( produc1710735575lle_fm @ Y1 @ Y22 ) )
% 0.20/0.47 = ( ( X1 = Y1 )
% 0.20/0.47 & ( X23 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inject
% 0.20/0.47 thf(fact_207_prod_Oinject,axiom,
% 0.20/0.47 ! [X1: nat > nat,X23: paraco1605129243lle_tv,Y1: nat > nat,Y22: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( produc1680557635lle_tv @ X1 @ X23 )
% 0.20/0.47 = ( produc1680557635lle_tv @ Y1 @ Y22 ) )
% 0.20/0.47 = ( ( X1 = Y1 )
% 0.20/0.47 & ( X23 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inject
% 0.20/0.47 thf(fact_208_old_Oprod_Oinject,axiom,
% 0.20/0.47 ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( ( produc1710735575lle_fm @ A @ B )
% 0.20/0.47 = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 0.20/0.47 = ( ( A = A5 )
% 0.20/0.47 & ( B = B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inject
% 0.20/0.47 thf(fact_209_old_Oprod_Oinject,axiom,
% 0.20/0.47 ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( produc1680557635lle_tv @ A @ B )
% 0.20/0.47 = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 0.20/0.47 = ( ( A = A5 )
% 0.20/0.47 & ( B = B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inject
% 0.20/0.47 thf(fact_210_eval_Osimps_I3_J,axiom,
% 0.20/0.47 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.20/0.47 = ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % eval.simps(3)
% 0.20/0.47 thf(fact_211_surj__pair,axiom,
% 0.20/0.47 ! [P2: produc696645085lle_fm] :
% 0.20/0.47 ? [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.20/0.47 ( P2
% 0.20/0.47 = ( produc1710735575lle_fm @ X4 @ Y2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_pair
% 0.20/0.47 thf(fact_212_surj__pair,axiom,
% 0.20/0.47 ! [P2: produc931990033lle_tv] :
% 0.20/0.47 ? [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.20/0.47 ( P2
% 0.20/0.47 = ( produc1680557635lle_tv @ X4 @ Y2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_pair
% 0.20/0.47 thf(fact_213_bool_Osplit__sel__asm,axiom,
% 0.20/0.47 ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 0.20/0.47 ( ( P3 @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 0.20/0.47 = ( ~ ( ( Bool
% 0.20/0.47 & ~ ( P3 @ F1 ) )
% 0.20/0.47 | ( ~ Bool
% 0.20/0.47 & ~ ( P3 @ F22 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % bool.split_sel_asm
% 0.20/0.47 thf(fact_214_bool_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: paraco1605129243lle_tv > paraco1605129243lle_tv,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 0.20/0.47 ( ( H @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 0.20/0.47 = ( produc234482697lle_tv @ ( H @ F1 ) @ ( H @ F22 ) @ Bool ) ) ).
% 0.20/0.47
% 0.20/0.47 % bool.case_distrib
% 0.20/0.47 thf(fact_215_bool_Ocase__eq__if,axiom,
% 0.20/0.47 ( produc234482697lle_tv
% 0.20/0.47 = ( ^ [F12: paraco1605129243lle_tv,F23: paraco1605129243lle_tv,Bool2: $o] : ( if_Par1134130401lle_tv @ Bool2 @ F12 @ F23 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % bool.case_eq_if
% 0.20/0.47 thf(fact_216_bool_Osplit__sel,axiom,
% 0.20/0.47 ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 0.20/0.47 ( ( P3 @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 0.20/0.47 = ( ( Bool
% 0.20/0.47 => ( P3 @ F1 ) )
% 0.20/0.47 & ( ~ Bool
% 0.20/0.47 => ( P3 @ F22 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % bool.split_sel
% 0.20/0.47 thf(fact_217_old_Obool_Osimps_I3_J,axiom,
% 0.20/0.47 ! [F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc234482697lle_tv @ F1 @ F22 @ $true )
% 0.20/0.47 = F1 ) ).
% 0.20/0.47
% 0.20/0.47 % old.bool.simps(3)
% 0.20/0.47 thf(fact_218_old_Obool_Osimps_I4_J,axiom,
% 0.20/0.47 ! [F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc234482697lle_tv @ F1 @ F22 @ $false )
% 0.20/0.47 = F22 ) ).
% 0.20/0.47
% 0.20/0.47 % old.bool.simps(4)
% 0.20/0.47 thf(fact_219_change__tv_Ocases,axiom,
% 0.20/0.47 ! [X: produc931990033lle_tv] :
% 0.20/0.47 ( ! [F3: nat > nat,B2: $o] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( produc1680557635lle_tv @ F3 @ ( paraco1344940915le_Det @ B2 ) ) )
% 0.20/0.47 => ~ ! [F3: nat > nat,N: nat] :
% 0.20/0.47 ( X
% 0.20/0.47 != ( produc1680557635lle_tv @ F3 @ ( paraco793048302_Indet @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % change_tv.cases
% 0.20/0.47 thf(fact_220_old_Oprod_Oinducts,axiom,
% 0.20/0.47 ! [P3: produc696645085lle_fm > $o,Prod: produc696645085lle_fm] :
% 0.20/0.47 ( ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A3 @ B2 ) )
% 0.20/0.47 => ( P3 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inducts
% 0.20/0.47 thf(fact_221_old_Oprod_Oinducts,axiom,
% 0.20/0.47 ! [P3: produc931990033lle_tv > $o,Prod: produc931990033lle_tv] :
% 0.20/0.47 ( ! [A3: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A3 @ B2 ) )
% 0.20/0.47 => ( P3 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inducts
% 0.20/0.47 thf(fact_222_old_Oprod_Oexhaust,axiom,
% 0.20/0.47 ! [Y: produc696645085lle_fm] :
% 0.20/0.47 ~ ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( produc1710735575lle_fm @ A3 @ B2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.exhaust
% 0.20/0.47 thf(fact_223_old_Oprod_Oexhaust,axiom,
% 0.20/0.47 ! [Y: produc931990033lle_tv] :
% 0.20/0.47 ~ ! [A3: nat > nat,B2: paraco1605129243lle_tv] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( produc1680557635lle_tv @ A3 @ B2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.exhaust
% 0.20/0.47 thf(fact_224_Pair__inject,axiom,
% 0.20/0.47 ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( ( produc1710735575lle_fm @ A @ B )
% 0.20/0.47 = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 0.20/0.47 => ~ ( ( A = A5 )
% 0.20/0.47 => ( B != B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_inject
% 0.20/0.47 thf(fact_225_Pair__inject,axiom,
% 0.20/0.47 ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( produc1680557635lle_tv @ A @ B )
% 0.20/0.47 = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 0.20/0.47 => ~ ( ( A = A5 )
% 0.20/0.47 => ( B != B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Pair_inject
% 0.20/0.47 thf(fact_226_prod__cases,axiom,
% 0.20/0.47 ! [P3: produc696645085lle_fm > $o,P2: produc696645085lle_fm] :
% 0.20/0.47 ( ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A3 @ B2 ) )
% 0.20/0.47 => ( P3 @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_cases
% 0.20/0.47 thf(fact_227_prod__cases,axiom,
% 0.20/0.47 ! [P3: produc931990033lle_tv > $o,P2: produc931990033lle_tv] :
% 0.20/0.47 ( ! [A3: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A3 @ B2 ) )
% 0.20/0.47 => ( P3 @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_cases
% 0.20/0.47 thf(fact_228_ssubst__Pair__rhs,axiom,
% 0.20/0.47 ! [R: list_char > paraco1605129243lle_tv,S3: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,S4: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S3 ) @ R2 )
% 0.20/0.47 => ( ( S4 = S3 )
% 0.20/0.47 => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S4 ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ssubst_Pair_rhs
% 0.20/0.47 thf(fact_229_ssubst__Pair__rhs,axiom,
% 0.20/0.47 ! [R: nat > nat,S3: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,S4: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S3 ) @ R2 )
% 0.20/0.47 => ( ( S4 = S3 )
% 0.20/0.47 => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S4 ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ssubst_Pair_rhs
% 0.20/0.47 thf(fact_230_apfst__conv,axiom,
% 0.20/0.47 ! [F2: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( produc1942165868lle_fm @ F2 @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.20/0.47 = ( produc1710735575lle_fm @ ( F2 @ X ) @ Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % apfst_conv
% 0.20/0.47 thf(fact_231_apfst__conv,axiom,
% 0.20/0.47 ! [F2: ( nat > nat ) > nat > nat,X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc939316703lle_tv @ F2 @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.20/0.47 = ( produc1680557635lle_tv @ ( F2 @ X ) @ Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % apfst_conv
% 0.20/0.47 thf(fact_232_apsnd__conv,axiom,
% 0.20/0.47 ! [F2: paraco1604210848lle_fm > paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( produc1807466521lle_tv @ F2 @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.20/0.47 = ( produc1710735575lle_fm @ X @ ( F2 @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % apsnd_conv
% 0.20/0.47 thf(fact_233_apsnd__conv,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc109093078at_nat @ F2 @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.20/0.47 = ( produc1680557635lle_tv @ X @ ( F2 @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % apsnd_conv
% 0.20/0.47 thf(fact_234_change__tv_Opelims,axiom,
% 0.20/0.47 ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 0.20/0.47 = Y )
% 0.20/0.47 => ( ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ Xa ) )
% 0.20/0.47 => ( ! [B2: $o] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( paraco1344940915le_Det @ B2 ) )
% 0.20/0.47 => ( ( Y
% 0.20/0.47 = ( paraco1344940915le_Det @ B2 ) )
% 0.20/0.47 => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco1344940915le_Det @ B2 ) ) ) ) )
% 0.20/0.47 => ~ ! [N: nat] :
% 0.20/0.47 ( ( Xa
% 0.20/0.47 = ( paraco793048302_Indet @ N ) )
% 0.20/0.47 => ( ( Y
% 0.20/0.47 = ( paraco793048302_Indet @ ( X @ N ) ) )
% 0.20/0.47 => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco793048302_Indet @ N ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % change_tv.pelims
% 0.20/0.47 thf(fact_235_prod_Oinj__map,axiom,
% 0.20/0.47 ! [F1: nat > nat,F22: nat > nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.20/0.47 => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 0.20/0.47 => ( inj_on26176689at_nat @ ( produc505105722at_nat @ F1 @ F22 ) @ top_to1555900337at_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inj_map
% 0.20/0.47 thf(fact_236_prod_Oinj__map,axiom,
% 0.20/0.47 ! [F1: nat > nat,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.20/0.47 => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ F1 @ F22 ) @ top_to1411004326lle_tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inj_map
% 0.20/0.47 thf(fact_237_prod_Oinj__map,axiom,
% 0.20/0.47 ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: nat > nat] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 0.20/0.47 => ( inj_on552895452tv_nat @ ( produc42536895at_nat @ F1 @ F22 ) @ top_to975729152tv_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inj_map
% 0.20/0.47 thf(fact_238_prod_Oinj__map,axiom,
% 0.20/0.47 ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ F1 @ F22 ) @ top_to1871154984lle_tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inj_map
% 0.20/0.47 thf(fact_239_curryI,axiom,
% 0.20/0.47 ! [F2: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( F2 @ ( produc1710735575lle_fm @ A @ B ) )
% 0.20/0.47 => ( produc275353523e_fm_o @ F2 @ A @ B ) ) ).
% 0.20/0.47
% 0.20/0.47 % curryI
% 0.20/0.47 thf(fact_240_curryI,axiom,
% 0.20/0.47 ! [F2: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( F2 @ ( produc1680557635lle_tv @ A @ B ) )
% 0.20/0.47 => ( produc752649287e_tv_o @ F2 @ A @ B ) ) ).
% 0.20/0.47
% 0.20/0.47 % curryI
% 0.20/0.47 thf(fact_241_map__prod__simp,axiom,
% 0.20/0.47 ! [F2: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( produc1900967599lle_fm @ F2 @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 0.20/0.47 = ( produc1710735575lle_fm @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_simp
% 0.20/0.47 thf(fact_242_map__prod__simp,axiom,
% 0.20/0.47 ! [F2: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( produc1566550641lle_tv @ F2 @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 0.20/0.47 = ( produc1680557635lle_tv @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_simp
% 0.20/0.47 thf(fact_243_map__prod__simp,axiom,
% 0.20/0.47 ! [F2: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc951033137lle_fm @ F2 @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 0.20/0.47 = ( produc1710735575lle_fm @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_simp
% 0.20/0.47 thf(fact_244_map__prod__simp,axiom,
% 0.20/0.47 ! [F2: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc532909085lle_tv @ F2 @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 0.20/0.47 = ( produc1680557635lle_tv @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_simp
% 0.20/0.47 thf(fact_245_curryD,axiom,
% 0.20/0.47 ! [F2: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( produc275353523e_fm_o @ F2 @ A @ B )
% 0.20/0.47 => ( F2 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % curryD
% 0.20/0.47 thf(fact_246_curryD,axiom,
% 0.20/0.47 ! [F2: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc752649287e_tv_o @ F2 @ A @ B )
% 0.20/0.47 => ( F2 @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % curryD
% 0.20/0.47 thf(fact_247_curryE,axiom,
% 0.20/0.47 ! [F2: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( produc275353523e_fm_o @ F2 @ A @ B )
% 0.20/0.47 => ( F2 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % curryE
% 0.20/0.47 thf(fact_248_curryE,axiom,
% 0.20/0.47 ! [F2: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc752649287e_tv_o @ F2 @ A @ B )
% 0.20/0.47 => ( F2 @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % curryE
% 0.20/0.47 thf(fact_249_the__inv__into__onto,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F2 ) @ ( image_nat_nat @ F2 @ A2 ) )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_into_onto
% 0.20/0.47 thf(fact_250_the__inv__into__onto,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ A2 @ F2 ) @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_into_onto
% 0.20/0.47 thf(fact_251_map__prod__imageI,axiom,
% 0.20/0.47 ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F2: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm] :
% 0.20/0.47 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 0.20/0.47 => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F2 @ G ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_imageI
% 0.20/0.47 thf(fact_252_map__prod__imageI,axiom,
% 0.20/0.47 ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F2: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 0.20/0.47 => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F2 @ G ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_imageI
% 0.20/0.47 thf(fact_253_map__prod__imageI,axiom,
% 0.20/0.47 ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F2: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm] :
% 0.20/0.47 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 0.20/0.47 => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F2 @ G ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_imageI
% 0.20/0.47 thf(fact_254_map__prod__imageI,axiom,
% 0.20/0.47 ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F2: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 0.20/0.47 => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F2 @ G ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_imageI
% 0.20/0.47 thf(fact_255_swap__simp,axiom,
% 0.20/0.47 ! [X: paraco1604210848lle_fm,Y: list_char > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc1232814113lle_tv @ ( produc1943344577lle_tv @ X @ Y ) )
% 0.20/0.47 = ( produc1710735575lle_fm @ Y @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % swap_simp
% 0.20/0.47 thf(fact_256_swap__simp,axiom,
% 0.20/0.47 ! [X: paraco1605129243lle_tv,Y: nat > nat] :
% 0.20/0.47 ( ( produc178635363at_nat @ ( produc1633679363at_nat @ X @ Y ) )
% 0.20/0.47 = ( produc1680557635lle_tv @ Y @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % swap_simp
% 0.20/0.47 thf(fact_257_swap__simp,axiom,
% 0.20/0.47 ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( produc1000205111lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.20/0.47 = ( produc1943344577lle_tv @ Y @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % swap_simp
% 0.20/0.47 thf(fact_258_swap__simp,axiom,
% 0.20/0.47 ! [X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc225513635lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.20/0.47 = ( produc1633679363at_nat @ Y @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % swap_simp
% 0.20/0.47 thf(fact_259_pair__in__swap__image,axiom,
% 0.20/0.47 ! [Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,A2: set_Pr2120184979lle_fm] :
% 0.20/0.47 ( ( member74361182lle_tv @ ( produc1943344577lle_tv @ Y @ X ) @ ( image_924970994lle_tv @ produc1000205111lle_fm @ A2 ) )
% 0.20/0.47 = ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X @ Y ) @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % pair_in_swap_image
% 0.20/0.47 thf(fact_260_pair__in__swap__image,axiom,
% 0.20/0.47 ! [Y: paraco1605129243lle_tv,X: nat > nat,A2: set_Pr560526279lle_tv] :
% 0.20/0.47 ( ( member1234290208at_nat @ ( produc1633679363at_nat @ Y @ X ) @ ( image_1724396928at_nat @ produc225513635lle_tv @ A2 ) )
% 0.20/0.47 = ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X @ Y ) @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % pair_in_swap_image
% 0.20/0.47 thf(fact_261_pair__in__swap__image,axiom,
% 0.20/0.47 ! [Y: list_char > paraco1605129243lle_tv,X: paraco1604210848lle_fm,A2: set_Pr1723822845lle_tv] :
% 0.20/0.47 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ Y @ X ) @ ( image_326034184lle_fm @ produc1232814113lle_tv @ A2 ) )
% 0.20/0.47 = ( member74361182lle_tv @ ( produc1943344577lle_tv @ X @ Y ) @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % pair_in_swap_image
% 0.20/0.47 thf(fact_262_pair__in__swap__image,axiom,
% 0.20/0.47 ! [Y: nat > nat,X: paraco1605129243lle_tv,A2: set_Pr840833727at_nat] :
% 0.20/0.47 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ Y @ X ) @ ( image_769496456lle_tv @ produc178635363at_nat @ A2 ) )
% 0.20/0.47 = ( member1234290208at_nat @ ( produc1633679363at_nat @ X @ Y ) @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % pair_in_swap_image
% 0.20/0.47 thf(fact_263_inj__on__image__iff,axiom,
% 0.20/0.47 ! [A2: set_nat,G: nat > nat,F2: nat > nat] :
% 0.20/0.47 ( ! [X4: nat] :
% 0.20/0.47 ( ( member_nat @ X4 @ A2 )
% 0.20/0.47 => ! [Xa2: nat] :
% 0.20/0.47 ( ( member_nat @ Xa2 @ A2 )
% 0.20/0.47 => ( ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = ( G @ ( F2 @ Xa2 ) ) )
% 0.20/0.47 = ( ( G @ X4 )
% 0.20/0.47 = ( G @ Xa2 ) ) ) ) )
% 0.20/0.47 => ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F2 @ A2 ) )
% 0.20/0.47 = ( inj_on_nat_nat @ G @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_image_iff
% 0.20/0.47 thf(fact_264_inj__on__image__iff,axiom,
% 0.20/0.47 ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [X4: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member266900804lle_tv @ X4 @ A2 )
% 0.20/0.47 => ! [Xa2: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member266900804lle_tv @ Xa2 @ A2 )
% 0.20/0.47 => ( ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = ( G @ ( F2 @ Xa2 ) ) )
% 0.20/0.47 = ( ( G @ X4 )
% 0.20/0.47 = ( G @ Xa2 ) ) ) ) )
% 0.20/0.47 => ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( inj_on772319074lle_tv @ G @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.20/0.47 = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_image_iff
% 0.20/0.47 thf(fact_265_surjD,axiom,
% 0.20/0.47 ! [F2: nat > nat,Y: nat] :
% 0.20/0.47 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ? [X4: nat] :
% 0.20/0.47 ( Y
% 0.20/0.47 = ( F2 @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjD
% 0.20/0.47 thf(fact_266_surjD,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ? [X4: nat] :
% 0.20/0.47 ( Y
% 0.20/0.47 = ( F2 @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjD
% 0.20/0.47 thf(fact_267_surjD,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > nat,Y: nat] :
% 0.20/0.47 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ? [X4: paraco1605129243lle_tv] :
% 0.20/0.47 ( Y
% 0.20/0.47 = ( F2 @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjD
% 0.20/0.47 thf(fact_268_surjD,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_335818702lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ? [X4: paraco1605129243lle_tv] :
% 0.20/0.47 ( Y
% 0.20/0.47 = ( F2 @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjD
% 0.20/0.47 thf(fact_269_surjE,axiom,
% 0.20/0.47 ! [F2: nat > nat,Y: nat] :
% 0.20/0.47 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ~ ! [X4: nat] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( F2 @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjE
% 0.20/0.47 thf(fact_270_surjE,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ~ ! [X4: nat] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( F2 @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjE
% 0.20/0.47 thf(fact_271_surjE,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > nat,Y: nat] :
% 0.20/0.47 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ~ ! [X4: paraco1605129243lle_tv] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( F2 @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjE
% 0.20/0.47 thf(fact_272_surjE,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_335818702lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ~ ! [X4: paraco1605129243lle_tv] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( F2 @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjE
% 0.20/0.47 thf(fact_273_surjI,axiom,
% 0.20/0.47 ! [G: nat > nat,F2: nat > nat] :
% 0.20/0.47 ( ! [X4: nat] :
% 0.20/0.47 ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 )
% 0.20/0.47 => ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjI
% 0.20/0.47 thf(fact_274_surjI,axiom,
% 0.20/0.47 ! [G: nat > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > nat] :
% 0.20/0.47 ( ! [X4: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 )
% 0.20/0.47 => ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjI
% 0.20/0.47 thf(fact_275_surjI,axiom,
% 0.20/0.47 ! [G: paraco1605129243lle_tv > nat,F2: nat > paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [X4: nat] :
% 0.20/0.47 ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 )
% 0.20/0.47 => ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.20/0.47 = top_top_set_nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjI
% 0.20/0.47 thf(fact_276_surjI,axiom,
% 0.20/0.47 ! [G: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ! [X4: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( G @ ( F2 @ X4 ) )
% 0.20/0.47 = X4 )
% 0.20/0.47 => ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.20/0.47 = top_to1057771083lle_tv ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjI
% 0.20/0.47 thf(fact_277_surj__def,axiom,
% 0.20/0.47 ! [F2: nat > nat] :
% 0.20/0.47 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 = ( ! [Y4: nat] :
% 0.20/0.47 ? [X2: nat] :
% 0.20/0.47 ( Y4
% 0.20/0.47 = ( F2 @ X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_def
% 0.20/0.47 thf(fact_278_surj__def,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 = ( ! [Y4: paraco1605129243lle_tv] :
% 0.20/0.47 ? [X2: nat] :
% 0.20/0.47 ( Y4
% 0.20/0.47 = ( F2 @ X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_def
% 0.20/0.47 thf(fact_279_surj__def,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > nat] :
% 0.20/0.47 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 = ( ! [Y4: nat] :
% 0.20/0.47 ? [X2: paraco1605129243lle_tv] :
% 0.20/0.47 ( Y4
% 0.20/0.47 = ( F2 @ X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_def
% 0.20/0.47 thf(fact_280_surj__def,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_335818702lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 = ( ! [Y4: paraco1605129243lle_tv] :
% 0.20/0.47 ? [X2: paraco1605129243lle_tv] :
% 0.20/0.47 ( Y4
% 0.20/0.47 = ( F2 @ X2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_def
% 0.20/0.47 thf(fact_281_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: nat > nat,G: nat > nat] :
% 0.20/0.47 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( image_815163717at_nat @ ( produc505105722at_nat @ F2 @ G ) @ top_to1555900337at_nat )
% 0.20/0.47 = top_to1555900337at_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_282_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: nat > nat,G: nat > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ( ( image_1674248956lle_tv @ ( produc313957681lle_tv @ F2 @ G ) @ top_to1555900337at_nat )
% 0.20/0.47 = top_to1411004326lle_tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_283_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: nat > nat,G: paraco1605129243lle_tv > nat] :
% 0.20/0.47 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( image_1787705850at_nat @ ( produc1685803475tv_nat @ F2 @ G ) @ top_to1411004326lle_tv )
% 0.20/0.47 = top_to1555900337at_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_284_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ( ( image_149830562lle_tv @ ( produc2101297531lle_tv @ F2 @ G ) @ top_to1411004326lle_tv )
% 0.20/0.47 = top_to1411004326lle_tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_285_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,G: nat > nat] :
% 0.20/0.47 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( image_1597721174tv_nat @ ( produc1250721397at_nat @ F2 @ G ) @ top_to1555900337at_nat )
% 0.20/0.47 = top_to975729152tv_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_286_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ( ( image_1507992062lle_tv @ ( produc210389789lle_tv @ F2 @ G ) @ top_to1555900337at_nat )
% 0.20/0.47 = top_to1871154984lle_tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_287_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 0.20/0.47 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ F2 @ G ) @ top_to1411004326lle_tv )
% 0.20/0.47 = top_to975729152tv_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_288_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ F2 @ G ) @ top_to1411004326lle_tv )
% 0.20/0.47 = top_to1871154984lle_tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_289_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > nat,G: nat > nat] :
% 0.20/0.47 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( image_1805124128at_nat @ ( produc386540311at_nat @ F2 @ G ) @ top_to975729152tv_nat )
% 0.20/0.47 = top_to1555900337at_nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_290_map__prod__surj,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > nat,G: nat > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 = top_top_set_nat )
% 0.20/0.47 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.20/0.47 = top_to1057771083lle_tv )
% 0.20/0.47 => ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ F2 @ G ) @ top_to975729152tv_nat )
% 0.20/0.47 = top_to1411004326lle_tv ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_prod_surj
% 0.20/0.47 thf(fact_291_range__ex1__eq,axiom,
% 0.20/0.47 ! [F2: nat > nat,B: nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 => ( ( member_nat @ B @ ( image_nat_nat @ F2 @ top_top_set_nat ) )
% 0.20/0.47 = ( ? [X2: nat] :
% 0.20/0.47 ( ( B
% 0.20/0.47 = ( F2 @ X2 ) )
% 0.20/0.47 & ! [Y4: nat] :
% 0.20/0.47 ( ( B
% 0.20/0.47 = ( F2 @ Y4 ) )
% 0.20/0.47 => ( Y4 = X2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % range_ex1_eq
% 0.20/0.47 thf(fact_292_range__ex1__eq,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( member266900804lle_tv @ B @ ( image_335818702lle_tv @ F2 @ top_to1057771083lle_tv ) )
% 0.20/0.47 = ( ? [X2: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( B
% 0.20/0.47 = ( F2 @ X2 ) )
% 0.20/0.47 & ! [Y4: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( B
% 0.20/0.47 = ( F2 @ Y4 ) )
% 0.20/0.47 => ( Y4 = X2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % range_ex1_eq
% 0.20/0.47 thf(fact_293_inj__image__eq__iff,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,B4: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 => ( ( ( image_nat_nat @ F2 @ A2 )
% 0.20/0.47 = ( image_nat_nat @ F2 @ B4 ) )
% 0.20/0.47 = ( A2 = B4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_image_eq_iff
% 0.20/0.47 thf(fact_294_inj__image__eq__iff,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( ( image_335818702lle_tv @ F2 @ A2 )
% 0.20/0.47 = ( image_335818702lle_tv @ F2 @ B4 ) )
% 0.20/0.47 = ( A2 = B4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_image_eq_iff
% 0.20/0.47 thf(fact_295_inj__image__mem__iff,axiom,
% 0.20/0.47 ! [F2: nat > nat,A: nat,A2: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 => ( ( member_nat @ ( F2 @ A ) @ ( image_nat_nat @ F2 @ A2 ) )
% 0.20/0.47 = ( member_nat @ A @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_image_mem_iff
% 0.20/0.47 thf(fact_296_inj__image__mem__iff,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( member266900804lle_tv @ ( F2 @ A ) @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.20/0.47 = ( member266900804lle_tv @ A @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_image_mem_iff
% 0.20/0.47 thf(fact_297_prod__fun__imageE,axiom,
% 0.20/0.47 ! [C: produc696645085lle_fm,F2: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm] :
% 0.20/0.47 ( ( member1474794996lle_fm @ C @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F2 @ G ) @ R2 ) )
% 0.20/0.47 => ~ ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( C
% 0.20/0.47 = ( produc1710735575lle_fm @ ( F2 @ X4 ) @ ( G @ Y2 ) ) )
% 0.20/0.47 => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_fun_imageE
% 0.20/0.47 thf(fact_298_prod__fun__imageE,axiom,
% 0.20/0.47 ! [C: produc696645085lle_fm,F2: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,R2: set_Pr560526279lle_tv] :
% 0.20/0.47 ( ( member1474794996lle_fm @ C @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F2 @ G ) @ R2 ) )
% 0.20/0.47 => ~ ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( C
% 0.20/0.47 = ( produc1710735575lle_fm @ ( F2 @ X4 ) @ ( G @ Y2 ) ) )
% 0.20/0.47 => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_fun_imageE
% 0.20/0.47 thf(fact_299_prod__fun__imageE,axiom,
% 0.20/0.47 ! [C: produc931990033lle_tv,F2: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,R2: set_Pr2120184979lle_fm] :
% 0.20/0.47 ( ( member1569366824lle_tv @ C @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F2 @ G ) @ R2 ) )
% 0.20/0.47 => ~ ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( C
% 0.20/0.47 = ( produc1680557635lle_tv @ ( F2 @ X4 ) @ ( G @ Y2 ) ) )
% 0.20/0.47 => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_fun_imageE
% 0.20/0.47 thf(fact_300_prod__fun__imageE,axiom,
% 0.20/0.47 ! [C: produc931990033lle_tv,F2: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,R2: set_Pr560526279lle_tv] :
% 0.20/0.47 ( ( member1569366824lle_tv @ C @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F2 @ G ) @ R2 ) )
% 0.20/0.47 => ~ ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( C
% 0.20/0.47 = ( produc1680557635lle_tv @ ( F2 @ X4 ) @ ( G @ Y2 ) ) )
% 0.20/0.47 => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_fun_imageE
% 0.20/0.47 thf(fact_301_f__the__inv__into__f,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,Y: nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( member_nat @ Y @ ( image_nat_nat @ F2 @ A2 ) )
% 0.20/0.47 => ( ( F2 @ ( the_inv_into_nat_nat @ A2 @ F2 @ Y ) )
% 0.20/0.47 = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % f_the_inv_into_f
% 0.20/0.47 thf(fact_302_f__the__inv__into__f,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( member266900804lle_tv @ Y @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.20/0.47 => ( ( F2 @ ( the_in452116896lle_tv @ A2 @ F2 @ Y ) )
% 0.20/0.47 = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % f_the_inv_into_f
% 0.20/0.47 thf(fact_303_inj__on__the__inv__into,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F2 ) @ ( image_nat_nat @ F2 @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_the_inv_into
% 0.20/0.47 thf(fact_304_inj__on__the__inv__into,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ A2 @ F2 ) @ ( image_335818702lle_tv @ F2 @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_the_inv_into
% 0.20/0.47 thf(fact_305_total__inv__image,axiom,
% 0.20/0.47 ! [F2: nat > nat,R: set_Pr1986765409at_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 => ( ( total_on_nat @ top_top_set_nat @ R )
% 0.20/0.47 => ( total_on_nat @ top_top_set_nat @ ( inv_image_nat_nat @ R @ F2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % total_inv_image
% 0.20/0.47 thf(fact_306_total__inv__image,axiom,
% 0.20/0.47 ! [F2: nat > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 0.20/0.47 ( ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat )
% 0.20/0.47 => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.20/0.47 => ( total_on_nat @ top_top_set_nat @ ( inv_im516950809tv_nat @ R @ F2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % total_inv_image
% 0.20/0.47 thf(fact_307_total__inv__image,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > nat,R: set_Pr1986765409at_nat] :
% 0.20/0.47 ( ( inj_on1179712058tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( total_on_nat @ top_top_set_nat @ R )
% 0.20/0.47 => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im1292588663lle_tv @ R @ F2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % total_inv_image
% 0.20/0.47 thf(fact_308_total__inv__image,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.20/0.47 => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im719552961lle_tv @ R @ F2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % total_inv_image
% 0.20/0.47 thf(fact_309_the__inv__into__into,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,X: nat,B4: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( member_nat @ X @ ( image_nat_nat @ F2 @ A2 ) )
% 0.20/0.47 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.20/0.47 => ( member_nat @ ( the_inv_into_nat_nat @ A2 @ F2 @ X ) @ B4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_into_into
% 0.20/0.47 thf(fact_310_the__inv__into__into,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.20/0.47 => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.20/0.47 => ( member266900804lle_tv @ ( the_in452116896lle_tv @ A2 @ F2 @ X ) @ B4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % the_inv_into_into
% 0.20/0.47 thf(fact_311_prod_Ocollapse,axiom,
% 0.20/0.47 ! [Prod: produc696645085lle_fm] :
% 0.20/0.47 ( ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) )
% 0.20/0.47 = Prod ) ).
% 0.20/0.47
% 0.20/0.47 % prod.collapse
% 0.20/0.47 thf(fact_312_prod_Ocollapse,axiom,
% 0.20/0.47 ! [Prod: produc931990033lle_tv] :
% 0.20/0.47 ( ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) )
% 0.20/0.47 = Prod ) ).
% 0.20/0.47
% 0.20/0.47 % prod.collapse
% 0.20/0.47 thf(fact_313_prod_Oswap__def,axiom,
% 0.20/0.47 ( produc1232814113lle_tv
% 0.20/0.47 = ( ^ [P: produc1443694919lle_tv] : ( produc1710735575lle_fm @ ( produc381314067lle_tv @ P ) @ ( produc262413013lle_tv @ P ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.swap_def
% 0.20/0.47 thf(fact_314_prod_Oswap__def,axiom,
% 0.20/0.47 ( produc178635363at_nat
% 0.20/0.47 = ( ^ [P: produc596913417at_nat] : ( produc1680557635lle_tv @ ( produc500618325at_nat @ P ) @ ( produc1589291287at_nat @ P ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.swap_def
% 0.20/0.47 thf(fact_315_fst__eqD,axiom,
% 0.20/0.47 ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.20/0.47 = A )
% 0.20/0.47 => ( X = A ) ) ).
% 0.20/0.47
% 0.20/0.47 % fst_eqD
% 0.20/0.47 thf(fact_316_fst__eqD,axiom,
% 0.20/0.47 ! [X: nat > nat,Y: paraco1605129243lle_tv,A: nat > nat] :
% 0.20/0.47 ( ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.20/0.47 = A )
% 0.20/0.47 => ( X = A ) ) ).
% 0.20/0.47
% 0.20/0.47 % fst_eqD
% 0.20/0.47 thf(fact_317_snd__eqD,axiom,
% 0.20/0.47 ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.20/0.47 = A )
% 0.20/0.47 => ( Y = A ) ) ).
% 0.20/0.47
% 0.20/0.47 % snd_eqD
% 0.20/0.47 thf(fact_318_snd__eqD,axiom,
% 0.20/0.47 ! [X: nat > nat,Y: paraco1605129243lle_tv,A: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.20/0.47 = A )
% 0.20/0.47 => ( Y = A ) ) ).
% 0.20/0.47
% 0.20/0.47 % snd_eqD
% 0.20/0.47 thf(fact_319_fst__conv,axiom,
% 0.20/0.47 ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X1 @ X23 ) )
% 0.20/0.47 = X1 ) ).
% 0.20/0.47
% 0.20/0.47 % fst_conv
% 0.20/0.47 thf(fact_320_fst__conv,axiom,
% 0.20/0.47 ! [X1: nat > nat,X23: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X1 @ X23 ) )
% 0.20/0.47 = X1 ) ).
% 0.20/0.47
% 0.20/0.47 % fst_conv
% 0.20/0.47 thf(fact_321_snd__conv,axiom,
% 0.20/0.47 ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X1 @ X23 ) )
% 0.20/0.47 = X23 ) ).
% 0.20/0.47
% 0.20/0.47 % snd_conv
% 0.20/0.47 thf(fact_322_snd__conv,axiom,
% 0.20/0.47 ! [X1: nat > nat,X23: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X1 @ X23 ) )
% 0.20/0.47 = X23 ) ).
% 0.20/0.47
% 0.20/0.47 % snd_conv
% 0.20/0.47 thf(fact_323_prod_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Prod: produc696645085lle_fm] :
% 0.20/0.47 ( Prod
% 0.20/0.47 = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.exhaust_sel
% 0.20/0.47 thf(fact_324_prod_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Prod: produc931990033lle_tv] :
% 0.20/0.47 ( Prod
% 0.20/0.47 = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.exhaust_sel
% 0.20/0.47 thf(fact_325_surjective__pairing,axiom,
% 0.20/0.47 ! [T: produc696645085lle_fm] :
% 0.20/0.47 ( T
% 0.20/0.47 = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ T ) @ ( produc148705065lle_fm @ T ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjective_pairing
% 0.20/0.47 thf(fact_326_surjective__pairing,axiom,
% 0.20/0.47 ! [T: produc931990033lle_tv] :
% 0.20/0.47 ( T
% 0.20/0.47 = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ T ) @ ( produc547496597lle_tv @ T ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjective_pairing
% 0.20/0.47 thf(fact_327_subrelI,axiom,
% 0.20/0.47 ! [R: set_Pr2120184979lle_fm,S3: set_Pr2120184979lle_fm] :
% 0.20/0.47 ( ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R )
% 0.20/0.47 => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ S3 ) )
% 0.20/0.47 => ( ord_le1007985907lle_fm @ R @ S3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % subrelI
% 0.20/0.47 thf(fact_328_subrelI,axiom,
% 0.20/0.47 ! [R: set_Pr560526279lle_tv,S3: set_Pr560526279lle_tv] :
% 0.20/0.47 ( ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R )
% 0.20/0.47 => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ S3 ) )
% 0.20/0.47 => ( ord_le1784136743lle_tv @ R @ S3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % subrelI
% 0.20/0.47 thf(fact_329_top__greatest,axiom,
% 0.20/0.47 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 0.20/0.47
% 0.20/0.47 % top_greatest
% 0.20/0.47 thf(fact_330_top__greatest,axiom,
% 0.20/0.47 ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ) ).
% 0.20/0.47
% 0.20/0.47 % top_greatest
% 0.20/0.47 thf(fact_331_top_Oextremum__unique,axiom,
% 0.20/0.47 ! [A: set_nat] :
% 0.20/0.47 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 0.20/0.47 = ( A = top_top_set_nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % top.extremum_unique
% 0.20/0.47 thf(fact_332_top_Oextremum__unique,axiom,
% 0.20/0.47 ! [A: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
% 0.20/0.47 = ( A = top_to1057771083lle_tv ) ) ).
% 0.20/0.47
% 0.20/0.47 % top.extremum_unique
% 0.20/0.47 thf(fact_333_top_Oextremum__uniqueI,axiom,
% 0.20/0.47 ! [A: set_nat] :
% 0.20/0.47 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 0.20/0.47 => ( A = top_top_set_nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % top.extremum_uniqueI
% 0.20/0.47 thf(fact_334_top_Oextremum__uniqueI,axiom,
% 0.20/0.47 ! [A: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
% 0.20/0.47 => ( A = top_to1057771083lle_tv ) ) ).
% 0.20/0.47
% 0.20/0.47 % top.extremum_uniqueI
% 0.20/0.47 thf(fact_335_subset__UNIV,axiom,
% 0.20/0.47 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ top_top_set_nat ) ).
% 0.20/0.47
% 0.20/0.47 % subset_UNIV
% 0.20/0.47 thf(fact_336_subset__UNIV,axiom,
% 0.20/0.47 ! [A2: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A2 @ top_to1057771083lle_tv ) ).
% 0.20/0.47
% 0.20/0.47 % subset_UNIV
% 0.20/0.47 thf(fact_337_inj__on__subset,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,B4: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.20/0.47 => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 0.20/0.47 => ( inj_on_nat_nat @ F2 @ B4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_subset
% 0.20/0.47 thf(fact_338_inj__on__subset,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.20/0.47 => ( ( ord_le241064091lle_tv @ B4 @ A2 )
% 0.20/0.47 => ( inj_on772319074lle_tv @ F2 @ B4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_subset
% 0.20/0.47 thf(fact_339_subset__inj__on,axiom,
% 0.20/0.47 ! [F2: nat > nat,B4: set_nat,A2: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ B4 )
% 0.20/0.47 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.20/0.47 => ( inj_on_nat_nat @ F2 @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_inj_on
% 0.20/0.47 thf(fact_340_subset__inj__on,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ B4 )
% 0.20/0.47 => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.20/0.47 => ( inj_on772319074lle_tv @ F2 @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_inj_on
% 0.20/0.47 thf(fact_341_inj__on__image__mem__iff,axiom,
% 0.20/0.47 ! [F2: nat > nat,B4: set_nat,A: nat,A2: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ B4 )
% 0.20/0.47 => ( ( member_nat @ A @ B4 )
% 0.20/0.47 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.20/0.47 => ( ( member_nat @ ( F2 @ A ) @ ( image_nat_nat @ F2 @ A2 ) )
% 0.20/0.47 = ( member_nat @ A @ A2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_image_mem_iff
% 0.20/0.47 thf(fact_342_inj__on__image__mem__iff,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ B4 )
% 0.20/0.47 => ( ( member266900804lle_tv @ A @ B4 )
% 0.20/0.47 => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.20/0.47 => ( ( member266900804lle_tv @ ( F2 @ A ) @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.20/0.47 = ( member266900804lle_tv @ A @ A2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_image_mem_iff
% 0.20/0.47 thf(fact_343_inj__on__image__eq__iff,axiom,
% 0.20/0.47 ! [F2: nat > nat,C2: set_nat,A2: set_nat,B4: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ C2 )
% 0.20/0.47 => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.20/0.47 => ( ( ord_less_eq_set_nat @ B4 @ C2 )
% 0.20/0.47 => ( ( ( image_nat_nat @ F2 @ A2 )
% 0.20/0.47 = ( image_nat_nat @ F2 @ B4 ) )
% 0.20/0.47 = ( A2 = B4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_image_eq_iff
% 0.20/0.47 thf(fact_344_inj__on__image__eq__iff,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,C2: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ C2 )
% 0.20/0.47 => ( ( ord_le241064091lle_tv @ A2 @ C2 )
% 0.20/0.47 => ( ( ord_le241064091lle_tv @ B4 @ C2 )
% 0.20/0.47 => ( ( ( image_335818702lle_tv @ F2 @ A2 )
% 0.20/0.47 = ( image_335818702lle_tv @ F2 @ B4 ) )
% 0.20/0.47 = ( A2 = B4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_image_eq_iff
% 0.20/0.47 thf(fact_345_inj__image__subset__iff,axiom,
% 0.20/0.47 ! [F2: nat > nat,A2: set_nat,B4: set_nat] :
% 0.20/0.47 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.20/0.47 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F2 @ A2 ) @ ( image_nat_nat @ F2 @ B4 ) )
% 0.20/0.47 = ( ord_less_eq_set_nat @ A2 @ B4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_image_subset_iff
% 0.20/0.47 thf(fact_346_inj__image__subset__iff,axiom,
% 0.20/0.47 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.20/0.47 => ( ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F2 @ A2 ) @ ( image_335818702lle_tv @ F2 @ B4 ) )
% 0.20/0.47 = ( ord_le241064091lle_tv @ A2 @ B4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_image_subset_iff
% 0.20/0.47 thf(fact_347_exI__realizer,axiom,
% 0.20/0.47 ! [P3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > $o,Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv] :
% 0.20/0.47 ( ( P3 @ Y @ X )
% 0.20/0.47 => ( P3 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % exI_realizer
% 0.20/0.47 thf(fact_348_exI__realizer,axiom,
% 0.20/0.47 ! [P3: paraco1605129243lle_tv > ( nat > nat ) > $o,Y: paraco1605129243lle_tv,X: nat > nat] :
% 0.20/0.47 ( ( P3 @ Y @ X )
% 0.20/0.47 => ( P3 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % exI_realizer
% 0.20/0.47 thf(fact_349_conjI__realizer,axiom,
% 0.20/0.47 ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,P2: list_char > paraco1605129243lle_tv,Q2: paraco1604210848lle_fm > $o,Q: paraco1604210848lle_fm] :
% 0.20/0.47 ( ( P3 @ P2 )
% 0.20/0.47 => ( ( Q2 @ Q )
% 0.20/0.47 => ( ( P3 @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) )
% 0.20/0.47 & ( Q2 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conjI_realizer
% 0.20/0.47 thf(fact_350_conjI__realizer,axiom,
% 0.20/0.47 ! [P3: ( nat > nat ) > $o,P2: nat > nat,Q2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( P3 @ P2 )
% 0.20/0.47 => ( ( Q2 @ Q )
% 0.20/0.47 => ( ( P3 @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ P2 @ Q ) ) )
% 0.20/0.47 & ( Q2 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ P2 @ Q ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % conjI_realizer
% 0.20/0.47 thf(fact_351_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.47 ! [P3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: produc696645085lle_fm] :
% 0.20/0.47 ( ( P3 @ X @ Y )
% 0.20/0.47 => ( ( A
% 0.20/0.47 = ( produc1710735575lle_fm @ X @ Y ) )
% 0.20/0.47 => ( P3 @ ( produc29804011lle_fm @ A ) @ ( produc148705065lle_fm @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.47 thf(fact_352_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.47 ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,X: nat > nat,Y: paraco1605129243lle_tv,A: produc931990033lle_tv] :
% 0.20/0.47 ( ( P3 @ X @ Y )
% 0.20/0.47 => ( ( A
% 0.20/0.47 = ( produc1680557635lle_tv @ X @ Y ) )
% 0.20/0.47 => ( P3 @ ( produc1636169559lle_tv @ A ) @ ( produc547496597lle_tv @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.47 thf(fact_353_subset__image__inj,axiom,
% 0.20/0.47 ! [S5: set_nat,F2: nat > nat,T2: set_nat] :
% 0.20/0.47 ( ( ord_less_eq_set_nat @ S5 @ ( image_nat_nat @ F2 @ T2 ) )
% 0.20/0.47 = ( ? [U2: set_nat] :
% 0.20/0.47 ( ( ord_less_eq_set_nat @ U2 @ T2 )
% 0.20/0.47 & ( inj_on_nat_nat @ F2 @ U2 )
% 0.20/0.47 & ( S5
% 0.20/0.47 = ( image_nat_nat @ F2 @ U2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_image_inj
% 0.20/0.47 thf(fact_354_subset__image__inj,axiom,
% 0.20/0.47 ! [S5: set_Pa1764573435lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv,T2: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( ord_le241064091lle_tv @ S5 @ ( image_335818702lle_tv @ F2 @ T2 ) )
% 0.20/0.47 = ( ? [U2: set_Pa1764573435lle_tv] :
% 0.20/0.47 ( ( ord_le241064091lle_tv @ U2 @ T2 )
% 0.20/0.47 & ( inj_on772319074lle_tv @ F2 @ U2 )
% 0.20/0.47 & ( S5
% 0.20/0.47 = ( image_335818702lle_tv @ F2 @ U2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subset_image_inj
% 0.20/0.47
% 0.20/0.47 % Helper facts (3)
% 0.20/0.47 thf(help_If_3_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.20/0.47 ! [P3: $o] :
% 0.20/0.47 ( ( P3 = $true )
% 0.20/0.47 | ( P3 = $false ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(help_If_2_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.20/0.47 ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( if_Par1134130401lle_tv @ $false @ X @ Y )
% 0.20/0.47 = Y ) ).
% 0.20/0.47
% 0.20/0.47 thf(help_If_1_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.20/0.47 ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.20/0.47 ( ( if_Par1134130401lle_tv @ $true @ X @ Y )
% 0.20/0.47 = X ) ).
% 0.20/0.47
% 0.20/0.47 % Conjectures (1)
% 0.20/0.47 thf(conj_0,conjecture,
% 0.20/0.47 ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 0.20/0.47 = ( paraco1344940915le_Det @ $true ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 0.31/1.60 ---- Embedded in THF ---
% 0.31/1.60 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.60 %%% Generated on Tue Feb 24 08:28:34 EST 2026
% 0.31/1.60 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.60 %%% Logic specification used:
% 0.31/1.60 %%% thf(spec, logic, $$dhol).
% 0.31/1.60
% 0.31/1.60 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.cKDKiLlZzx/DTF2DTF30016.p
% See solution above
% 0.31/1.60 ------------------------
% 0.31/1.64 ---- Cleaned THF ---
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 0.31/1.64 set_Pr1723822845lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.31/1.64 set_Pr2120184979lle_fm: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 produc1443694919lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 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,
% 0.31/1.64 produc696645085lle_fm: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 set_Pr2014382200lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.31/1.64 set_Pr840833727at_nat: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 set_Pr560526279lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 produc1647334210lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.31/1.64 produc596913417at_nat: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 produc931990033lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 0.31/1.64 set_Pr1725653840tv_nat: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 set_Pr13445366lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.31/1.64 produc194167194tv_nat: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 produc270694976lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.31/1.64 set_Pr1986765409at_nat: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 set_Pa1764573435lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 product_prod_nat_nat: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 paraco1605129243lle_tv: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.31/1.64 paraco1604210848lle_fm: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 0.31/1.64 list_char: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/1.64 set_nat: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(ty_n_t__Nat__Onat,type,
% 0.31/1.64 nat: $tType ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.31/1.64 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.31/1.64 inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.31/1.64 inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.31/1.64 the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/1.64 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.31/1.64 ord_le1007985907lle_fm: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 ord_le1784136743lle_tv: set_Pr560526279lle_tv > set_Pr560526279lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.31/1.64 top_top_nat_o: nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 0.31/1.64 top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.31/1.64 top_to632227436_nat_o: product_prod_nat_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_Eo_J,type,
% 0.31/1.64 top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.31/1.64 top_to900819589_nat_o: produc194167194tv_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
% 0.31/1.64 top_top_o: $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/1.64 top_top_set_nat: set_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.31/1.64 top_to775056195lle_fm: set_Pr2120184979lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 top_to449985143lle_tv: set_Pr560526279lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.31/1.64 top_to1555900337at_nat: set_Pr1986765409at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 top_to1411004326lle_tv: set_Pr13445366lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 0.31/1.64 top_to378694061lle_tv: set_Pr1723822845lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.31/1.64 top_to730292591at_nat: set_Pr840833727at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 0.31/1.64 top_to975729152tv_nat: set_Pr1725653840tv_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__int,type,
% 0.31/1.64 paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv,type,
% 0.31/1.64 paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv__rel,type,
% 0.31/1.64 paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Oeval,type,
% 0.31/1.64 paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OCon_H,type,
% 0.31/1.64 paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql,type,
% 0.31/1.64 paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql_H,type,
% 0.31/1.64 paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_ONeg_H,type,
% 0.31/1.64 paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OPro,type,
% 0.31/1.64 paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OTruth,type,
% 0.31/1.64 paraco367965286_Truth: paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_ODet,type,
% 0.31/1.64 paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_OIndet,type,
% 0.31/1.64 paraco793048302_Indet: nat > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_Ocase__tv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid,type,
% 0.31/1.64 paraco327635598_valid: paraco1604210848lle_fm > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid__in,type,
% 0.31/1.64 paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
% 0.31/1.64
% 0.31/1.64 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,
% 0.31/1.64 produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 produc1633679363at_nat: paraco1605129243lle_tv > ( nat > nat ) > produc596913417at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oapfst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.31/1.64 produc1942165868lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > produc696645085lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oapfst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 produc1807466521lle_tv: ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 produc109093078at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Obool_Ocase__bool_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Ocurry_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_Eo,type,
% 0.31/1.64 produc275353523e_fm_o: ( produc696645085lle_fm > $o ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Ocurry_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_Eo,type,
% 0.31/1.64 produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.31/1.64 produc1900967599lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc1566550641lle_tv: ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > produc696645085lle_fm > produc931990033lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.31/1.64 produc951033137lle_fm: ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc931990033lle_tv > produc696645085lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.31/1.64 produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc313957681lle_tv: ( nat > nat ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.31/1.64 produc1685803475tv_nat: ( nat > nat ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > product_prod_nat_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.31/1.64 produc1250721397at_nat: ( nat > paraco1605129243lle_tv ) > ( nat > nat ) > product_prod_nat_nat > produc194167194tv_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc210389789lle_tv: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc1647334210lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.31/1.64 produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.31/1.64 produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.31/1.64 produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.31/1.64 produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc1636169559lle_tv: produc931990033lle_tv > nat > nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.31/1.64 produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Osnd_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Osnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 produc500618325at_nat: produc596913417at_nat > nat > nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.31/1.64 produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Oswap_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Product__Type_Oprod_Oswap_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.31/1.64 inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 inv_im1292588663lle_tv: set_Pr1986765409at_nat > ( paraco1605129243lle_tv > nat ) > set_Pr2014382200lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.31/1.64 inv_im516950809tv_nat: set_Pr2014382200lle_tv > ( nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 inv_im719552961lle_tv: set_Pr2014382200lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
% 0.31/1.64 total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Relation_Ototal__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.31/1.64 collect_nat: ( nat > $o ) > set_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_OCollect_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_OCollect_001t__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,
% 0.31/1.64 collec835549234lle_fm: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 collec1624074086lle_tv: ( produc931990033lle_tv > $o ) > set_Pr560526279lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 collec1582599068lle_tv: ( produc1443694919lle_tv > $o ) > set_Pr1723822845lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.31/1.64 collec1288997470at_nat: ( produc596913417at_nat > $o ) > set_Pr840833727at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.31/1.64 collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.31/1.64 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.31/1.64 image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__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,
% 0.31/1.64 image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 image_1154804148lle_tv: ( produc696645085lle_fm > produc931990033lle_tv ) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__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,
% 0.31/1.64 image_1585092542lle_fm: ( produc931990033lle_tv > produc696645085lle_fm ) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 image_1751508608lle_tv: ( produc931990033lle_tv > produc931990033lle_tv ) > set_Pr560526279lle_tv > set_Pr560526279lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.31/1.64 image_1724396928at_nat: ( produc931990033lle_tv > produc596913417at_nat ) > set_Pr560526279lle_tv > set_Pr840833727at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.31/1.64 image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 image_1507992062lle_tv: ( product_prod_nat_nat > produc1647334210lle_tv ) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.31/1.64 image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_001t__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,
% 0.31/1.64 image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 image_769496456lle_tv: ( produc596913417at_nat > produc931990033lle_tv ) > set_Pr840833727at_nat > set_Pr560526279lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__Nat__Onat,type,
% 0.31/1.64 member_nat: nat > set_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.31/1.64 member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__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,
% 0.31/1.64 member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/1.64 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.31/1.64 member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.31/1.64 member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
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% 0.31/1.64
% 0.31/1.64 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.31/1.64 member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
% 0.31/1.64
% 0.31/1.64 thf(sy_v_f,type,
% 0.31/1.64 f: nat > nat ).
% 0.31/1.64
% 0.31/1.64 thf(sy_v_i,type,
% 0.31/1.64 i: list_char > paraco1605129243lle_tv ).
% 0.31/1.64
% 0.31/1.64 thf(sy_v_p1____,type,
% 0.31/1.64 p1: paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(sy_v_p2____,type,
% 0.31/1.64 p2: paraco1604210848lle_fm ).
% 0.31/1.64
% 0.31/1.64 thf(fact_0_a,axiom,
% 0.31/1.64 ( ( paraco1325918602e_eval @ i @ p2 )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062,axiom,
% 0.31/1.64 ( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_2_ih2,axiom,
% 0.31/1.64 ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 0.31/1.64 = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_3_tv_Oinject_I1_J,axiom,
% 0.31/1.64 ! [X1: $o,Y1: $o] :
% 0.31/1.64 ( ( ( paraco1344940915le_Det @ X1 )
% 0.31/1.64 = ( paraco1344940915le_Det @ Y1 ) )
% 0.31/1.64 = ( X1 = Y1 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_4_a_H_H,axiom,
% 0.31/1.64 ( ( paraco1325918602e_eval @ i @ p1 )
% 0.31/1.64 != ( paraco1344940915le_Det @ $true ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_5_a_H,axiom,
% 0.31/1.64 ( ( paraco1325918602e_eval @ i @ p1 )
% 0.31/1.64 != ( paraco1325918602e_eval @ i @ p2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_6_ih1,axiom,
% 0.31/1.64 ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 0.31/1.64 = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p1 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_7_change__int__def,axiom,
% 0.31/1.64 ( paraco761681009ge_int
% 0.31/1.64 = ( ^ [F: nat > nat,I: list_char > paraco1605129243lle_tv,S: list_char] : ( paraco1147068288nge_tv @ F @ ( I @ S ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_8_change__tv_Osimps_I1_J,axiom,
% 0.31/1.64 ! [F2: nat > nat,B: $o] :
% 0.31/1.64 ( ( paraco1147068288nge_tv @ F2 @ ( paraco1344940915le_Det @ B ) )
% 0.31/1.64 = ( paraco1344940915le_Det @ B ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_9_yes,axiom,
% 0.31/1.64 ( ( paraco1325918602e_eval @ i @ ( paraco1745535428le_Eql @ p1 @ p2 ) )
% 0.31/1.64 = ( paraco1325918602e_eval @ i @ p1 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_10_valid__def,axiom,
% 0.31/1.64 ( paraco327635598_valid
% 0.31/1.64 = ( ^ [P: paraco1604210848lle_fm] :
% 0.31/1.64 ! [I: list_char > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( paraco1325918602e_eval @ I @ P )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_11_eval_Osimps_I2_J,axiom,
% 0.31/1.64 ! [I2: list_char > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( paraco1325918602e_eval @ I2 @ paraco367965286_Truth )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_12_eval_Osimps_I5_J,axiom,
% 0.31/1.64 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 != ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1344940915le_Det @ $false ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_13_eval__equality__simplify,axiom,
% 0.31/1.64 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1344940915le_Det
% 0.31/1.64 @ ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ Q ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_14_eval_Osimps_I4_J,axiom,
% 0.31/1.64 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 != ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.31/1.64 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ Q ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 != ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.31/1.64 != ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_15_tv_Osimps_I5_J,axiom,
% 0.31/1.64 ! [F1: $o > paraco1605129243lle_tv,F22: nat > paraco1605129243lle_tv,X1: $o] :
% 0.31/1.64 ( ( paraco2051596139lle_tv @ F1 @ F22 @ ( paraco1344940915le_Det @ X1 ) )
% 0.31/1.64 = ( F1 @ X1 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_16_eval__negation,axiom,
% 0.31/1.64 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 = ( paraco1344940915le_Det @ $false ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 != ( paraco1344940915le_Det @ $false ) )
% 0.31/1.64 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.31/1.64 = ( paraco1344940915le_Det @ $false ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 != ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_17_assms,axiom,
% 0.31/1.64 inj_on_nat_nat @ f @ top_top_set_nat ).
% 0.31/1.64
% 0.31/1.64 thf(fact_18_fm_Oinject_I2_J,axiom,
% 0.31/1.64 ! [X3: paraco1604210848lle_fm,Y3: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( paraco445776468le_Neg @ X3 )
% 0.31/1.64 = ( paraco445776468le_Neg @ Y3 ) )
% 0.31/1.64 = ( X3 = Y3 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_19_fm_Oinject_I3_J,axiom,
% 0.31/1.64 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,Y41: paraco1604210848lle_fm,Y42: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.31/1.64 = ( paraco69239110le_Con @ Y41 @ Y42 ) )
% 0.31/1.64 = ( ( X41 = Y41 )
% 0.31/1.64 & ( X42 = Y42 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_20_fm_Oinject_I5_J,axiom,
% 0.31/1.64 ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm,Y61: paraco1604210848lle_fm,Y62: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( paraco1745535428le_Eql @ X61 @ X62 )
% 0.31/1.64 = ( paraco1745535428le_Eql @ Y61 @ Y62 ) )
% 0.31/1.64 = ( ( X61 = Y61 )
% 0.31/1.64 & ( X62 = Y62 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_21_fm_Oinject_I4_J,axiom,
% 0.31/1.64 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,Y51: paraco1604210848lle_fm,Y52: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.31/1.64 = ( paraco1389086619le_Eql @ Y51 @ Y52 ) )
% 0.31/1.64 = ( ( X51 = Y51 )
% 0.31/1.64 & ( X52 = Y52 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_22_fm_Odistinct_I29_J,axiom,
% 0.31/1.64 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.31/1.64 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_23_fm_Odistinct_I27_J,axiom,
% 0.31/1.64 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.31/1.64 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_24_fm_Odistinct_I25_J,axiom,
% 0.31/1.64 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.31/1.64 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_25_fm_Odistinct_I23_J,axiom,
% 0.31/1.64 ! [X3: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco445776468le_Neg @ X3 )
% 0.31/1.64 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_26_fm_Odistinct_I21_J,axiom,
% 0.31/1.64 ! [X3: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco445776468le_Neg @ X3 )
% 0.31/1.64 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_27_fm_Odistinct_I19_J,axiom,
% 0.31/1.64 ! [X3: paraco1604210848lle_fm,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco445776468le_Neg @ X3 )
% 0.31/1.64 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_28_fm_Odistinct_I17_J,axiom,
% 0.31/1.64 ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.31/1.64 ( paraco367965286_Truth
% 0.31/1.64 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_29_fm_Odistinct_I15_J,axiom,
% 0.31/1.64 ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.31/1.64 ( paraco367965286_Truth
% 0.31/1.64 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_30_fm_Odistinct_I13_J,axiom,
% 0.31/1.64 ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.31/1.64 ( paraco367965286_Truth
% 0.31/1.64 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_31_fm_Odistinct_I11_J,axiom,
% 0.31/1.64 ! [X3: paraco1604210848lle_fm] :
% 0.31/1.64 ( paraco367965286_Truth
% 0.31/1.64 != ( paraco445776468le_Neg @ X3 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_32_conjunction,axiom,
% 0.31/1.64 ! [P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco327635598_valid @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.31/1.64 = ( ( paraco327635598_valid @ P2 )
% 0.31/1.64 & ( paraco327635598_valid @ Q ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_33_eval__equality,axiom,
% 0.31/1.64 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 != ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.31/1.64 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ Q ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 != ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.31/1.64 != ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 = ( paraco1344940915le_Det @ $false ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ Q ) ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.31/1.64 != ( paraco1344940915le_Det @ $false ) )
% 0.31/1.64 => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.31/1.64 = ( paraco1344940915le_Det @ $false ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) ) ) )
% 0.31/1.64 & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.31/1.64 != ( paraco1344940915le_Det @ $false ) )
% 0.31/1.64 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.31/1.64 = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_34_double__negation,axiom,
% 0.31/1.64 ( paraco1325918602e_eval
% 0.31/1.64 = ( ^ [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ P ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_35_UNIV__I,axiom,
% 0.31/1.64 ! [X: produc596913417at_nat] : ( member1234290208at_nat @ X @ top_to730292591at_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_36_UNIV__I,axiom,
% 0.31/1.64 ! [X: produc1443694919lle_tv] : ( member74361182lle_tv @ X @ top_to378694061lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_37_UNIV__I,axiom,
% 0.31/1.64 ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_38_UNIV__I,axiom,
% 0.31/1.64 ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_39_UNIV__I,axiom,
% 0.31/1.64 ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_40_UNIV__I,axiom,
% 0.31/1.64 ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_41_UNIV__I,axiom,
% 0.31/1.64 ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_42_UNIV__I,axiom,
% 0.31/1.64 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_43_UNIV__I,axiom,
% 0.31/1.64 ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_44_iso__tuple__UNIV__I,axiom,
% 0.31/1.64 ! [X: produc596913417at_nat] : ( member1234290208at_nat @ X @ top_to730292591at_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_45_iso__tuple__UNIV__I,axiom,
% 0.31/1.64 ! [X: produc1443694919lle_tv] : ( member74361182lle_tv @ X @ top_to378694061lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_46_iso__tuple__UNIV__I,axiom,
% 0.31/1.64 ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_47_iso__tuple__UNIV__I,axiom,
% 0.31/1.64 ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_48_iso__tuple__UNIV__I,axiom,
% 0.31/1.64 ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_49_iso__tuple__UNIV__I,axiom,
% 0.31/1.64 ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_50_iso__tuple__UNIV__I,axiom,
% 0.31/1.64 ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_51_iso__tuple__UNIV__I,axiom,
% 0.31/1.64 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_52_iso__tuple__UNIV__I,axiom,
% 0.31/1.64 ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_53_top__apply,axiom,
% 0.31/1.64 ( top_to1299250770e_tv_o
% 0.31/1.64 = ( ^ [X2: paraco1605129243lle_tv] : top_top_o ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_54_top__apply,axiom,
% 0.31/1.64 ( top_top_nat_o
% 0.31/1.64 = ( ^ [X2: nat] : top_top_o ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_55_injD,axiom,
% 0.31/1.64 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.31/1.64 ( ( inj_on2112487900lle_tv @ F2 @ top_to1871154984lle_tv )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_56_injD,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_57_injD,axiom,
% 0.31/1.64 ! [F2: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.31/1.64 ( ( inj_on552895452tv_nat @ F2 @ top_to975729152tv_nat )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_58_injD,axiom,
% 0.31/1.64 ! [F2: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.31/1.64 ( ( inj_on1745913142lle_tv @ F2 @ top_to1411004326lle_tv )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_59_injD,axiom,
% 0.31/1.64 ! [F2: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.31/1.64 ( ( inj_on26176689at_nat @ F2 @ top_to1555900337at_nat )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_60_injD,axiom,
% 0.31/1.64 ! [F2: nat > nat,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_61_injD,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_62_injI,axiom,
% 0.31/1.64 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.31/1.64 ( ! [X4: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 0.31/1.64 ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) )
% 0.31/1.64 => ( inj_on2112487900lle_tv @ F2 @ top_to1871154984lle_tv ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_63_injI,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: nat,Y2: nat] :
% 0.31/1.64 ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) )
% 0.31/1.64 => ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_64_injI,axiom,
% 0.31/1.64 ! [F2: produc194167194tv_nat > produc194167194tv_nat] :
% 0.31/1.64 ( ! [X4: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 0.31/1.64 ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) )
% 0.31/1.64 => ( inj_on552895452tv_nat @ F2 @ top_to975729152tv_nat ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_65_injI,axiom,
% 0.31/1.64 ! [F2: produc270694976lle_tv > produc270694976lle_tv] :
% 0.31/1.64 ( ! [X4: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 0.31/1.64 ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) )
% 0.31/1.64 => ( inj_on1745913142lle_tv @ F2 @ top_to1411004326lle_tv ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_66_injI,axiom,
% 0.31/1.64 ! [F2: product_prod_nat_nat > product_prod_nat_nat] :
% 0.31/1.64 ( ! [X4: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.31/1.64 ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) )
% 0.31/1.64 => ( inj_on26176689at_nat @ F2 @ top_to1555900337at_nat ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_67_injI,axiom,
% 0.31/1.64 ! [F2: nat > nat] :
% 0.31/1.64 ( ! [X4: nat,Y2: nat] :
% 0.31/1.64 ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) )
% 0.31/1.64 => ( inj_on_nat_nat @ F2 @ top_top_set_nat ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_68_injI,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) )
% 0.31/1.64 => ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_69_inj__eq,axiom,
% 0.31/1.64 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.31/1.64 ( ( inj_on2112487900lle_tv @ F2 @ top_to1871154984lle_tv )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_70_inj__eq,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_71_inj__eq,axiom,
% 0.31/1.64 ! [F2: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.31/1.64 ( ( inj_on552895452tv_nat @ F2 @ top_to975729152tv_nat )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_72_inj__eq,axiom,
% 0.31/1.64 ! [F2: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.31/1.64 ( ( inj_on1745913142lle_tv @ F2 @ top_to1411004326lle_tv )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_73_inj__eq,axiom,
% 0.31/1.64 ! [F2: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.31/1.64 ( ( inj_on26176689at_nat @ F2 @ top_to1555900337at_nat )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_74_inj__eq,axiom,
% 0.31/1.64 ! [F2: nat > nat,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_75_inj__eq,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_76_inj__def,axiom,
% 0.31/1.64 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.31/1.64 ( ( inj_on2112487900lle_tv @ F2 @ top_to1871154984lle_tv )
% 0.31/1.64 = ( ! [X2: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
% 0.31/1.64 ( ( ( F2 @ X2 )
% 0.31/1.64 = ( F2 @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_77_inj__def,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 = ( ! [X2: nat,Y4: nat] :
% 0.31/1.64 ( ( ( F2 @ X2 )
% 0.31/1.64 = ( F2 @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_78_inj__def,axiom,
% 0.31/1.64 ! [F2: produc194167194tv_nat > produc194167194tv_nat] :
% 0.31/1.64 ( ( inj_on552895452tv_nat @ F2 @ top_to975729152tv_nat )
% 0.31/1.64 = ( ! [X2: produc194167194tv_nat,Y4: produc194167194tv_nat] :
% 0.31/1.64 ( ( ( F2 @ X2 )
% 0.31/1.64 = ( F2 @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_79_inj__def,axiom,
% 0.31/1.64 ! [F2: produc270694976lle_tv > produc270694976lle_tv] :
% 0.31/1.64 ( ( inj_on1745913142lle_tv @ F2 @ top_to1411004326lle_tv )
% 0.31/1.64 = ( ! [X2: produc270694976lle_tv,Y4: produc270694976lle_tv] :
% 0.31/1.64 ( ( ( F2 @ X2 )
% 0.31/1.64 = ( F2 @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_80_inj__def,axiom,
% 0.31/1.64 ! [F2: product_prod_nat_nat > product_prod_nat_nat] :
% 0.31/1.64 ( ( inj_on26176689at_nat @ F2 @ top_to1555900337at_nat )
% 0.31/1.64 = ( ! [X2: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 0.31/1.64 ( ( ( F2 @ X2 )
% 0.31/1.64 = ( F2 @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_81_inj__def,axiom,
% 0.31/1.64 ! [F2: nat > nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 = ( ! [X2: nat,Y4: nat] :
% 0.31/1.64 ( ( ( F2 @ X2 )
% 0.31/1.64 = ( F2 @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_82_inj__def,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 = ( ! [X2: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( F2 @ X2 )
% 0.31/1.64 = ( F2 @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_83_fm_Oinduct,axiom,
% 0.31/1.64 ! [P3: paraco1604210848lle_fm > $o,Fm: paraco1604210848lle_fm] :
% 0.31/1.64 ( ! [X4: list_char] : ( P3 @ ( paraco1480028776le_Pro @ X4 ) )
% 0.31/1.64 => ( ( P3 @ paraco367965286_Truth )
% 0.31/1.64 => ( ! [X4: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ X4 )
% 0.31/1.64 => ( P3 @ ( paraco445776468le_Neg @ X4 ) ) )
% 0.31/1.64 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ X1a )
% 0.31/1.64 => ( ( P3 @ X22 )
% 0.31/1.64 => ( P3 @ ( paraco69239110le_Con @ X1a @ X22 ) ) ) )
% 0.31/1.64 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ X1a )
% 0.31/1.64 => ( ( P3 @ X22 )
% 0.31/1.64 => ( P3 @ ( paraco1389086619le_Eql @ X1a @ X22 ) ) ) )
% 0.31/1.64 => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ X1a )
% 0.31/1.64 => ( ( P3 @ X22 )
% 0.31/1.64 => ( P3 @ ( paraco1745535428le_Eql @ X1a @ X22 ) ) ) )
% 0.31/1.64 => ( P3 @ Fm ) ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_84_fm_Oexhaust,axiom,
% 0.31/1.64 ! [Y: paraco1604210848lle_fm] :
% 0.31/1.64 ( ! [X12: list_char] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( paraco1480028776le_Pro @ X12 ) )
% 0.31/1.64 => ( ( Y != paraco367965286_Truth )
% 0.31/1.64 => ( ! [X32: paraco1604210848lle_fm] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( paraco445776468le_Neg @ X32 ) )
% 0.31/1.64 => ( ! [X412: paraco1604210848lle_fm,X422: paraco1604210848lle_fm] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( paraco69239110le_Con @ X412 @ X422 ) )
% 0.31/1.64 => ( ! [X512: paraco1604210848lle_fm,X522: paraco1604210848lle_fm] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( paraco1389086619le_Eql @ X512 @ X522 ) )
% 0.31/1.64 => ~ ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_85_mem__Collect__eq,axiom,
% 0.31/1.64 ! [A: produc596913417at_nat,P3: produc596913417at_nat > $o] :
% 0.31/1.64 ( ( member1234290208at_nat @ A @ ( collec1288997470at_nat @ P3 ) )
% 0.31/1.64 = ( P3 @ A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_86_mem__Collect__eq,axiom,
% 0.31/1.64 ! [A: produc1443694919lle_tv,P3: produc1443694919lle_tv > $o] :
% 0.31/1.64 ( ( member74361182lle_tv @ A @ ( collec1582599068lle_tv @ P3 ) )
% 0.31/1.64 = ( P3 @ A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_87_mem__Collect__eq,axiom,
% 0.31/1.64 ! [A: produc696645085lle_fm,P3: produc696645085lle_fm > $o] :
% 0.31/1.64 ( ( member1474794996lle_fm @ A @ ( collec835549234lle_fm @ P3 ) )
% 0.31/1.64 = ( P3 @ A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_88_mem__Collect__eq,axiom,
% 0.31/1.64 ! [A: produc931990033lle_tv,P3: produc931990033lle_tv > $o] :
% 0.31/1.64 ( ( member1569366824lle_tv @ A @ ( collec1624074086lle_tv @ P3 ) )
% 0.31/1.64 = ( P3 @ A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_89_mem__Collect__eq,axiom,
% 0.31/1.64 ! [A: paraco1605129243lle_tv,P3: paraco1605129243lle_tv > $o] :
% 0.31/1.64 ( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ P3 ) )
% 0.31/1.64 = ( P3 @ A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_90_mem__Collect__eq,axiom,
% 0.31/1.64 ! [A: nat,P3: nat > $o] :
% 0.31/1.64 ( ( member_nat @ A @ ( collect_nat @ P3 ) )
% 0.31/1.64 = ( P3 @ A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_91_Collect__mem__eq,axiom,
% 0.31/1.64 ! [A2: set_Pr840833727at_nat] :
% 0.31/1.64 ( ( collec1288997470at_nat
% 0.31/1.64 @ ^ [X2: produc596913417at_nat] : ( member1234290208at_nat @ X2 @ A2 ) )
% 0.31/1.64 = A2 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_92_Collect__mem__eq,axiom,
% 0.31/1.64 ! [A2: set_Pr1723822845lle_tv] :
% 0.31/1.64 ( ( collec1582599068lle_tv
% 0.31/1.64 @ ^ [X2: produc1443694919lle_tv] : ( member74361182lle_tv @ X2 @ A2 ) )
% 0.31/1.64 = A2 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_93_Collect__mem__eq,axiom,
% 0.31/1.64 ! [A2: set_Pr2120184979lle_fm] :
% 0.31/1.64 ( ( collec835549234lle_fm
% 0.31/1.64 @ ^ [X2: produc696645085lle_fm] : ( member1474794996lle_fm @ X2 @ A2 ) )
% 0.31/1.64 = A2 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_94_Collect__mem__eq,axiom,
% 0.31/1.64 ! [A2: set_Pr560526279lle_tv] :
% 0.31/1.64 ( ( collec1624074086lle_tv
% 0.31/1.64 @ ^ [X2: produc931990033lle_tv] : ( member1569366824lle_tv @ X2 @ A2 ) )
% 0.31/1.64 = A2 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_95_Collect__mem__eq,axiom,
% 0.31/1.64 ! [A2: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( collec1111687558lle_tv
% 0.31/1.64 @ ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ A2 ) )
% 0.31/1.64 = A2 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_96_Collect__mem__eq,axiom,
% 0.31/1.64 ! [A2: set_nat] :
% 0.31/1.64 ( ( collect_nat
% 0.31/1.64 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 0.31/1.64 = A2 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_97_Collect__cong,axiom,
% 0.31/1.64 ! [P3: paraco1605129243lle_tv > $o,Q2: paraco1605129243lle_tv > $o] :
% 0.31/1.64 ( ! [X4: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( P3 @ X4 )
% 0.31/1.64 = ( Q2 @ X4 ) )
% 0.31/1.64 => ( ( collec1111687558lle_tv @ P3 )
% 0.31/1.64 = ( collec1111687558lle_tv @ Q2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_98_Collect__cong,axiom,
% 0.31/1.64 ! [P3: nat > $o,Q2: nat > $o] :
% 0.31/1.64 ( ! [X4: nat] :
% 0.31/1.64 ( ( P3 @ X4 )
% 0.31/1.64 = ( Q2 @ X4 ) )
% 0.31/1.64 => ( ( collect_nat @ P3 )
% 0.31/1.64 = ( collect_nat @ Q2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_99_props_Ocases,axiom,
% 0.31/1.64 ! [X: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( X != paraco367965286_Truth )
% 0.31/1.64 => ( ! [S2: list_char] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( paraco1480028776le_Pro @ S2 ) )
% 0.31/1.64 => ( ! [P4: paraco1604210848lle_fm] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( paraco445776468le_Neg @ P4 ) )
% 0.31/1.64 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( paraco69239110le_Con @ P4 @ Q3 ) )
% 0.31/1.64 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( paraco1389086619le_Eql @ P4 @ Q3 ) )
% 0.31/1.64 => ~ ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_100_fm_Oinject_I1_J,axiom,
% 0.31/1.64 ! [X1: list_char,Y1: list_char] :
% 0.31/1.64 ( ( ( paraco1480028776le_Pro @ X1 )
% 0.31/1.64 = ( paraco1480028776le_Pro @ Y1 ) )
% 0.31/1.64 = ( X1 = Y1 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_101_top__set__def,axiom,
% 0.31/1.64 ( top_to975729152tv_nat
% 0.31/1.64 = ( collec848462447tv_nat @ top_to900819589_nat_o ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_102_top__set__def,axiom,
% 0.31/1.64 ( top_to1411004326lle_tv
% 0.31/1.64 = ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_103_top__set__def,axiom,
% 0.31/1.64 ( top_to1555900337at_nat
% 0.31/1.64 = ( collec7649004at_nat @ top_to632227436_nat_o ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_104_top__set__def,axiom,
% 0.31/1.64 ( top_top_set_nat
% 0.31/1.64 = ( collect_nat @ top_top_nat_o ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_105_top__set__def,axiom,
% 0.31/1.64 ( top_to1057771083lle_tv
% 0.31/1.64 = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_106_eval_Osimps_I1_J,axiom,
% 0.31/1.64 ! [I2: list_char > paraco1605129243lle_tv,S3: list_char] :
% 0.31/1.64 ( ( paraco1325918602e_eval @ I2 @ ( paraco1480028776le_Pro @ S3 ) )
% 0.31/1.64 = ( I2 @ S3 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_107_fm_Odistinct_I3_J,axiom,
% 0.31/1.64 ! [X1: list_char,X3: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco1480028776le_Pro @ X1 )
% 0.31/1.64 != ( paraco445776468le_Neg @ X3 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_108_fm_Odistinct_I5_J,axiom,
% 0.31/1.64 ! [X1: list_char,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco1480028776le_Pro @ X1 )
% 0.31/1.64 != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_109_fm_Odistinct_I9_J,axiom,
% 0.31/1.64 ! [X1: list_char,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco1480028776le_Pro @ X1 )
% 0.31/1.64 != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_110_fm_Odistinct_I7_J,axiom,
% 0.31/1.64 ! [X1: list_char,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco1480028776le_Pro @ X1 )
% 0.31/1.64 != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_111_fm_Odistinct_I1_J,axiom,
% 0.31/1.64 ! [X1: list_char] :
% 0.31/1.64 ( ( paraco1480028776le_Pro @ X1 )
% 0.31/1.64 != paraco367965286_Truth ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_112_change__tv__injection,axiom,
% 0.31/1.64 ! [F2: nat > nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ F2 ) @ top_to1057771083lle_tv ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_113_UNIV__witness,axiom,
% 0.31/1.64 ? [X4: produc596913417at_nat] : ( member1234290208at_nat @ X4 @ top_to730292591at_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_114_UNIV__witness,axiom,
% 0.31/1.64 ? [X4: produc1443694919lle_tv] : ( member74361182lle_tv @ X4 @ top_to378694061lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_115_UNIV__witness,axiom,
% 0.31/1.64 ? [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ top_to775056195lle_fm ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_116_UNIV__witness,axiom,
% 0.31/1.64 ? [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ top_to449985143lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_117_UNIV__witness,axiom,
% 0.31/1.64 ? [X4: produc194167194tv_nat] : ( member737151281tv_nat @ X4 @ top_to975729152tv_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_118_UNIV__witness,axiom,
% 0.31/1.64 ? [X4: produc270694976lle_tv] : ( member813679063lle_tv @ X4 @ top_to1411004326lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_119_UNIV__witness,axiom,
% 0.31/1.64 ? [X4: product_prod_nat_nat] : ( member701585322at_nat @ X4 @ top_to1555900337at_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_120_UNIV__witness,axiom,
% 0.31/1.64 ? [X4: nat] : ( member_nat @ X4 @ top_top_set_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_121_UNIV__witness,axiom,
% 0.31/1.64 ? [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ top_to1057771083lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_122_UNIV__eq__I,axiom,
% 0.31/1.64 ! [A2: set_Pr840833727at_nat] :
% 0.31/1.64 ( ! [X4: produc596913417at_nat] : ( member1234290208at_nat @ X4 @ A2 )
% 0.31/1.64 => ( top_to730292591at_nat = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_123_UNIV__eq__I,axiom,
% 0.31/1.64 ! [A2: set_Pr1723822845lle_tv] :
% 0.31/1.64 ( ! [X4: produc1443694919lle_tv] : ( member74361182lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( top_to378694061lle_tv = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_124_UNIV__eq__I,axiom,
% 0.31/1.64 ! [A2: set_Pr2120184979lle_fm] :
% 0.31/1.64 ( ! [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ A2 )
% 0.31/1.64 => ( top_to775056195lle_fm = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_125_UNIV__eq__I,axiom,
% 0.31/1.64 ! [A2: set_Pr560526279lle_tv] :
% 0.31/1.64 ( ! [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( top_to449985143lle_tv = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_126_UNIV__eq__I,axiom,
% 0.31/1.64 ! [A2: set_Pr1725653840tv_nat] :
% 0.31/1.64 ( ! [X4: produc194167194tv_nat] : ( member737151281tv_nat @ X4 @ A2 )
% 0.31/1.64 => ( top_to975729152tv_nat = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_127_UNIV__eq__I,axiom,
% 0.31/1.64 ! [A2: set_Pr13445366lle_tv] :
% 0.31/1.64 ( ! [X4: produc270694976lle_tv] : ( member813679063lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( top_to1411004326lle_tv = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_128_UNIV__eq__I,axiom,
% 0.31/1.64 ! [A2: set_Pr1986765409at_nat] :
% 0.31/1.64 ( ! [X4: product_prod_nat_nat] : ( member701585322at_nat @ X4 @ A2 )
% 0.31/1.64 => ( top_to1555900337at_nat = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_129_UNIV__eq__I,axiom,
% 0.31/1.64 ! [A2: set_nat] :
% 0.31/1.64 ( ! [X4: nat] : ( member_nat @ X4 @ A2 )
% 0.31/1.64 => ( top_top_set_nat = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_130_UNIV__eq__I,axiom,
% 0.31/1.64 ! [A2: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ! [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( top_to1057771083lle_tv = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_131_inj__on__inverseI,axiom,
% 0.31/1.64 ! [A2: set_Pr2014382200lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv,F2: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.31/1.64 ( ! [X4: produc1647334210lle_tv] :
% 0.31/1.64 ( ( member1531318361lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 ) )
% 0.31/1.64 => ( inj_on2112487900lle_tv @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_132_inj__on__inverseI,axiom,
% 0.31/1.64 ! [A2: set_Pr1725653840tv_nat,G: produc194167194tv_nat > produc194167194tv_nat,F2: produc194167194tv_nat > produc194167194tv_nat] :
% 0.31/1.64 ( ! [X4: produc194167194tv_nat] :
% 0.31/1.64 ( ( member737151281tv_nat @ X4 @ A2 )
% 0.31/1.64 => ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 ) )
% 0.31/1.64 => ( inj_on552895452tv_nat @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_133_inj__on__inverseI,axiom,
% 0.31/1.64 ! [A2: set_Pr13445366lle_tv,G: produc270694976lle_tv > produc270694976lle_tv,F2: produc270694976lle_tv > produc270694976lle_tv] :
% 0.31/1.64 ( ! [X4: produc270694976lle_tv] :
% 0.31/1.64 ( ( member813679063lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 ) )
% 0.31/1.64 => ( inj_on1745913142lle_tv @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_134_inj__on__inverseI,axiom,
% 0.31/1.64 ! [A2: set_Pr1986765409at_nat,G: product_prod_nat_nat > product_prod_nat_nat,F2: product_prod_nat_nat > product_prod_nat_nat] :
% 0.31/1.64 ( ! [X4: product_prod_nat_nat] :
% 0.31/1.64 ( ( member701585322at_nat @ X4 @ A2 )
% 0.31/1.64 => ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 ) )
% 0.31/1.64 => ( inj_on26176689at_nat @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_135_inj__on__inverseI,axiom,
% 0.31/1.64 ! [A2: set_nat,G: paraco1605129243lle_tv > nat,F2: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: nat] :
% 0.31/1.64 ( ( member_nat @ X4 @ A2 )
% 0.31/1.64 => ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 ) )
% 0.31/1.64 => ( inj_on1955349912lle_tv @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_136_inj__on__inverseI,axiom,
% 0.31/1.64 ! [A2: set_nat,G: nat > nat,F2: nat > nat] :
% 0.31/1.64 ( ! [X4: nat] :
% 0.31/1.64 ( ( member_nat @ X4 @ A2 )
% 0.31/1.64 => ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 ) )
% 0.31/1.64 => ( inj_on_nat_nat @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_137_inj__on__inverseI,axiom,
% 0.31/1.64 ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member266900804lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 ) )
% 0.31/1.64 => ( inj_on772319074lle_tv @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_138_inj__on__contraD,axiom,
% 0.31/1.64 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.31/1.64 ( ( inj_on2112487900lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( X != Y )
% 0.31/1.64 => ( ( member1531318361lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.31/1.64 => ( ( F2 @ X )
% 0.31/1.64 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_139_inj__on__contraD,axiom,
% 0.31/1.64 ! [F2: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.31/1.64 ( ( inj_on552895452tv_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( X != Y )
% 0.31/1.64 => ( ( member737151281tv_nat @ X @ A2 )
% 0.31/1.64 => ( ( member737151281tv_nat @ Y @ A2 )
% 0.31/1.64 => ( ( F2 @ X )
% 0.31/1.64 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_140_inj__on__contraD,axiom,
% 0.31/1.64 ! [F2: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.31/1.64 ( ( inj_on1745913142lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( X != Y )
% 0.31/1.64 => ( ( member813679063lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( member813679063lle_tv @ Y @ A2 )
% 0.31/1.64 => ( ( F2 @ X )
% 0.31/1.64 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_141_inj__on__contraD,axiom,
% 0.31/1.64 ! [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.31/1.64 ( ( inj_on26176689at_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( X != Y )
% 0.31/1.64 => ( ( member701585322at_nat @ X @ A2 )
% 0.31/1.64 => ( ( member701585322at_nat @ Y @ A2 )
% 0.31/1.64 => ( ( F2 @ X )
% 0.31/1.64 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_142_inj__on__contraD,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on1955349912lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( X != Y )
% 0.31/1.64 => ( ( member_nat @ X @ A2 )
% 0.31/1.64 => ( ( member_nat @ Y @ A2 )
% 0.31/1.64 => ( ( F2 @ X )
% 0.31/1.64 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_143_inj__on__contraD,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( X != Y )
% 0.31/1.64 => ( ( member_nat @ X @ A2 )
% 0.31/1.64 => ( ( member_nat @ Y @ A2 )
% 0.31/1.64 => ( ( F2 @ X )
% 0.31/1.64 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_144_inj__on__contraD,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( X != Y )
% 0.31/1.64 => ( ( member266900804lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( member266900804lle_tv @ Y @ A2 )
% 0.31/1.64 => ( ( F2 @ X )
% 0.31/1.64 != ( F2 @ Y ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_145_inj__on__eq__iff,axiom,
% 0.31/1.64 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.31/1.64 ( ( inj_on2112487900lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( member1531318361lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_146_inj__on__eq__iff,axiom,
% 0.31/1.64 ! [F2: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.31/1.64 ( ( inj_on552895452tv_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( member737151281tv_nat @ X @ A2 )
% 0.31/1.64 => ( ( member737151281tv_nat @ Y @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_147_inj__on__eq__iff,axiom,
% 0.31/1.64 ! [F2: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.31/1.64 ( ( inj_on1745913142lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( member813679063lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( member813679063lle_tv @ Y @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_148_inj__on__eq__iff,axiom,
% 0.31/1.64 ! [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.31/1.64 ( ( inj_on26176689at_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( member701585322at_nat @ X @ A2 )
% 0.31/1.64 => ( ( member701585322at_nat @ Y @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_149_inj__on__eq__iff,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on1955349912lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( member_nat @ X @ A2 )
% 0.31/1.64 => ( ( member_nat @ Y @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_150_inj__on__eq__iff,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( member_nat @ X @ A2 )
% 0.31/1.64 => ( ( member_nat @ Y @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_151_inj__on__eq__iff,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( member266900804lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( member266900804lle_tv @ Y @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 = ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_152_inj__on__cong,axiom,
% 0.31/1.64 ! [A2: set_Pr2014382200lle_tv,F2: produc1647334210lle_tv > produc1647334210lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.31/1.64 ( ! [A3: produc1647334210lle_tv] :
% 0.31/1.64 ( ( member1531318361lle_tv @ A3 @ A2 )
% 0.31/1.64 => ( ( F2 @ A3 )
% 0.31/1.64 = ( G @ A3 ) ) )
% 0.31/1.64 => ( ( inj_on2112487900lle_tv @ F2 @ A2 )
% 0.31/1.64 = ( inj_on2112487900lle_tv @ G @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_153_inj__on__cong,axiom,
% 0.31/1.64 ! [A2: set_Pr1725653840tv_nat,F2: produc194167194tv_nat > produc194167194tv_nat,G: produc194167194tv_nat > produc194167194tv_nat] :
% 0.31/1.64 ( ! [A3: produc194167194tv_nat] :
% 0.31/1.64 ( ( member737151281tv_nat @ A3 @ A2 )
% 0.31/1.64 => ( ( F2 @ A3 )
% 0.31/1.64 = ( G @ A3 ) ) )
% 0.31/1.64 => ( ( inj_on552895452tv_nat @ F2 @ A2 )
% 0.31/1.64 = ( inj_on552895452tv_nat @ G @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_154_inj__on__cong,axiom,
% 0.31/1.64 ! [A2: set_Pr13445366lle_tv,F2: produc270694976lle_tv > produc270694976lle_tv,G: produc270694976lle_tv > produc270694976lle_tv] :
% 0.31/1.64 ( ! [A3: produc270694976lle_tv] :
% 0.31/1.64 ( ( member813679063lle_tv @ A3 @ A2 )
% 0.31/1.64 => ( ( F2 @ A3 )
% 0.31/1.64 = ( G @ A3 ) ) )
% 0.31/1.64 => ( ( inj_on1745913142lle_tv @ F2 @ A2 )
% 0.31/1.64 = ( inj_on1745913142lle_tv @ G @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_155_inj__on__cong,axiom,
% 0.31/1.64 ! [A2: set_Pr1986765409at_nat,F2: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 0.31/1.64 ( ! [A3: product_prod_nat_nat] :
% 0.31/1.64 ( ( member701585322at_nat @ A3 @ A2 )
% 0.31/1.64 => ( ( F2 @ A3 )
% 0.31/1.64 = ( G @ A3 ) ) )
% 0.31/1.64 => ( ( inj_on26176689at_nat @ F2 @ A2 )
% 0.31/1.64 = ( inj_on26176689at_nat @ G @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_156_inj__on__cong,axiom,
% 0.31/1.64 ! [A2: set_nat,F2: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [A3: nat] :
% 0.31/1.64 ( ( member_nat @ A3 @ A2 )
% 0.31/1.64 => ( ( F2 @ A3 )
% 0.31/1.64 = ( G @ A3 ) ) )
% 0.31/1.64 => ( ( inj_on1955349912lle_tv @ F2 @ A2 )
% 0.31/1.64 = ( inj_on1955349912lle_tv @ G @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_157_inj__on__cong,axiom,
% 0.31/1.64 ! [A2: set_nat,F2: nat > nat,G: nat > nat] :
% 0.31/1.64 ( ! [A3: nat] :
% 0.31/1.64 ( ( member_nat @ A3 @ A2 )
% 0.31/1.64 => ( ( F2 @ A3 )
% 0.31/1.64 = ( G @ A3 ) ) )
% 0.31/1.64 => ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 = ( inj_on_nat_nat @ G @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_158_inj__on__cong,axiom,
% 0.31/1.64 ! [A2: set_Pa1764573435lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [A3: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member266900804lle_tv @ A3 @ A2 )
% 0.31/1.64 => ( ( F2 @ A3 )
% 0.31/1.64 = ( G @ A3 ) ) )
% 0.31/1.64 => ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_159_inj__on__def,axiom,
% 0.31/1.64 ( inj_on2112487900lle_tv
% 0.31/1.64 = ( ^ [F: produc1647334210lle_tv > produc1647334210lle_tv,A4: set_Pr2014382200lle_tv] :
% 0.31/1.64 ! [X2: produc1647334210lle_tv] :
% 0.31/1.64 ( ( member1531318361lle_tv @ X2 @ A4 )
% 0.31/1.64 => ! [Y4: produc1647334210lle_tv] :
% 0.31/1.64 ( ( member1531318361lle_tv @ Y4 @ A4 )
% 0.31/1.64 => ( ( ( F @ X2 )
% 0.31/1.64 = ( F @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_160_inj__on__def,axiom,
% 0.31/1.64 ( inj_on552895452tv_nat
% 0.31/1.64 = ( ^ [F: produc194167194tv_nat > produc194167194tv_nat,A4: set_Pr1725653840tv_nat] :
% 0.31/1.64 ! [X2: produc194167194tv_nat] :
% 0.31/1.64 ( ( member737151281tv_nat @ X2 @ A4 )
% 0.31/1.64 => ! [Y4: produc194167194tv_nat] :
% 0.31/1.64 ( ( member737151281tv_nat @ Y4 @ A4 )
% 0.31/1.64 => ( ( ( F @ X2 )
% 0.31/1.64 = ( F @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_161_inj__on__def,axiom,
% 0.31/1.64 ( inj_on1745913142lle_tv
% 0.31/1.64 = ( ^ [F: produc270694976lle_tv > produc270694976lle_tv,A4: set_Pr13445366lle_tv] :
% 0.31/1.64 ! [X2: produc270694976lle_tv] :
% 0.31/1.64 ( ( member813679063lle_tv @ X2 @ A4 )
% 0.31/1.64 => ! [Y4: produc270694976lle_tv] :
% 0.31/1.64 ( ( member813679063lle_tv @ Y4 @ A4 )
% 0.31/1.64 => ( ( ( F @ X2 )
% 0.31/1.64 = ( F @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_162_inj__on__def,axiom,
% 0.31/1.64 ( inj_on26176689at_nat
% 0.31/1.64 = ( ^ [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1986765409at_nat] :
% 0.31/1.64 ! [X2: product_prod_nat_nat] :
% 0.31/1.64 ( ( member701585322at_nat @ X2 @ A4 )
% 0.31/1.64 => ! [Y4: product_prod_nat_nat] :
% 0.31/1.64 ( ( member701585322at_nat @ Y4 @ A4 )
% 0.31/1.64 => ( ( ( F @ X2 )
% 0.31/1.64 = ( F @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_163_inj__on__def,axiom,
% 0.31/1.64 ( inj_on1955349912lle_tv
% 0.31/1.64 = ( ^ [F: nat > paraco1605129243lle_tv,A4: set_nat] :
% 0.31/1.64 ! [X2: nat] :
% 0.31/1.64 ( ( member_nat @ X2 @ A4 )
% 0.31/1.64 => ! [Y4: nat] :
% 0.31/1.64 ( ( member_nat @ Y4 @ A4 )
% 0.31/1.64 => ( ( ( F @ X2 )
% 0.31/1.64 = ( F @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_164_inj__on__def,axiom,
% 0.31/1.64 ( inj_on_nat_nat
% 0.31/1.64 = ( ^ [F: nat > nat,A4: set_nat] :
% 0.31/1.64 ! [X2: nat] :
% 0.31/1.64 ( ( member_nat @ X2 @ A4 )
% 0.31/1.64 => ! [Y4: nat] :
% 0.31/1.64 ( ( member_nat @ Y4 @ A4 )
% 0.31/1.64 => ( ( ( F @ X2 )
% 0.31/1.64 = ( F @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_165_inj__on__def,axiom,
% 0.31/1.64 ( inj_on772319074lle_tv
% 0.31/1.64 = ( ^ [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A4: set_Pa1764573435lle_tv] :
% 0.31/1.64 ! [X2: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member266900804lle_tv @ X2 @ A4 )
% 0.31/1.64 => ! [Y4: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member266900804lle_tv @ Y4 @ A4 )
% 0.31/1.64 => ( ( ( F @ X2 )
% 0.31/1.64 = ( F @ Y4 ) )
% 0.31/1.64 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_166_inj__onI,axiom,
% 0.31/1.64 ! [A2: set_Pr2014382200lle_tv,F2: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.31/1.64 ( ! [X4: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 0.31/1.64 ( ( member1531318361lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( ( member1531318361lle_tv @ Y2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) ) ) )
% 0.31/1.64 => ( inj_on2112487900lle_tv @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_167_inj__onI,axiom,
% 0.31/1.64 ! [A2: set_Pr1725653840tv_nat,F2: produc194167194tv_nat > produc194167194tv_nat] :
% 0.31/1.64 ( ! [X4: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 0.31/1.64 ( ( member737151281tv_nat @ X4 @ A2 )
% 0.31/1.64 => ( ( member737151281tv_nat @ Y2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) ) ) )
% 0.31/1.64 => ( inj_on552895452tv_nat @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_168_inj__onI,axiom,
% 0.31/1.64 ! [A2: set_Pr13445366lle_tv,F2: produc270694976lle_tv > produc270694976lle_tv] :
% 0.31/1.64 ( ! [X4: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 0.31/1.64 ( ( member813679063lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( ( member813679063lle_tv @ Y2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) ) ) )
% 0.31/1.64 => ( inj_on1745913142lle_tv @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_169_inj__onI,axiom,
% 0.31/1.64 ! [A2: set_Pr1986765409at_nat,F2: product_prod_nat_nat > product_prod_nat_nat] :
% 0.31/1.64 ( ! [X4: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.31/1.64 ( ( member701585322at_nat @ X4 @ A2 )
% 0.31/1.64 => ( ( member701585322at_nat @ Y2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) ) ) )
% 0.31/1.64 => ( inj_on26176689at_nat @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_170_inj__onI,axiom,
% 0.31/1.64 ! [A2: set_nat,F2: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: nat,Y2: nat] :
% 0.31/1.64 ( ( member_nat @ X4 @ A2 )
% 0.31/1.64 => ( ( member_nat @ Y2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) ) ) )
% 0.31/1.64 => ( inj_on1955349912lle_tv @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_171_inj__onI,axiom,
% 0.31/1.64 ! [A2: set_nat,F2: nat > nat] :
% 0.31/1.64 ( ! [X4: nat,Y2: nat] :
% 0.31/1.64 ( ( member_nat @ X4 @ A2 )
% 0.31/1.64 => ( ( member_nat @ Y2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) ) ) )
% 0.31/1.64 => ( inj_on_nat_nat @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_172_inj__onI,axiom,
% 0.31/1.64 ! [A2: set_Pa1764573435lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member266900804lle_tv @ X4 @ A2 )
% 0.31/1.64 => ( ( member266900804lle_tv @ Y2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X4 )
% 0.31/1.64 = ( F2 @ Y2 ) )
% 0.31/1.64 => ( X4 = Y2 ) ) ) )
% 0.31/1.64 => ( inj_on772319074lle_tv @ F2 @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_173_inj__onD,axiom,
% 0.31/1.64 ! [F2: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.31/1.64 ( ( inj_on2112487900lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( ( member1531318361lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.31/1.64 => ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_174_inj__onD,axiom,
% 0.31/1.64 ! [F2: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.31/1.64 ( ( inj_on552895452tv_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( ( member737151281tv_nat @ X @ A2 )
% 0.31/1.64 => ( ( member737151281tv_nat @ Y @ A2 )
% 0.31/1.64 => ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_175_inj__onD,axiom,
% 0.31/1.64 ! [F2: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.31/1.64 ( ( inj_on1745913142lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( ( member813679063lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( member813679063lle_tv @ Y @ A2 )
% 0.31/1.64 => ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_176_inj__onD,axiom,
% 0.31/1.64 ! [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.31/1.64 ( ( inj_on26176689at_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( ( member701585322at_nat @ X @ A2 )
% 0.31/1.64 => ( ( member701585322at_nat @ Y @ A2 )
% 0.31/1.64 => ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_177_inj__onD,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on1955349912lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( ( member_nat @ X @ A2 )
% 0.31/1.64 => ( ( member_nat @ Y @ A2 )
% 0.31/1.64 => ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_178_inj__onD,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( ( member_nat @ X @ A2 )
% 0.31/1.64 => ( ( member_nat @ Y @ A2 )
% 0.31/1.64 => ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_179_inj__onD,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = ( F2 @ Y ) )
% 0.31/1.64 => ( ( member266900804lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( member266900804lle_tv @ Y @ A2 )
% 0.31/1.64 => ( X = Y ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_180_props_Oinduct,axiom,
% 0.31/1.64 ! [P3: paraco1604210848lle_fm > $o,A0: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ paraco367965286_Truth )
% 0.31/1.64 => ( ! [S2: list_char] : ( P3 @ ( paraco1480028776le_Pro @ S2 ) )
% 0.31/1.64 => ( ! [P4: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ P4 )
% 0.31/1.64 => ( P3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 0.31/1.64 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ P4 )
% 0.31/1.64 => ( ( P3 @ Q3 )
% 0.31/1.64 => ( P3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) ) )
% 0.31/1.64 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ P4 )
% 0.31/1.64 => ( ( P3 @ Q3 )
% 0.31/1.64 => ( P3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) ) )
% 0.31/1.64 => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ P4 )
% 0.31/1.64 => ( ( P3 @ Q3 )
% 0.31/1.64 => ( P3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) )
% 0.31/1.64 => ( P3 @ A0 ) ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_181_eval_Ocases,axiom,
% 0.31/1.64 ! [X: produc696645085lle_fm] :
% 0.31/1.64 ( ! [I3: list_char > paraco1605129243lle_tv,S2: list_char] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( produc1710735575lle_fm @ I3 @ ( paraco1480028776le_Pro @ S2 ) ) )
% 0.31/1.64 => ( ! [I3: list_char > paraco1605129243lle_tv] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( produc1710735575lle_fm @ I3 @ paraco367965286_Truth ) )
% 0.31/1.64 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( produc1710735575lle_fm @ I3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 0.31/1.64 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( produc1710735575lle_fm @ I3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) )
% 0.31/1.64 => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( produc1710735575lle_fm @ I3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) )
% 0.31/1.64 => ~ ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( produc1710735575lle_fm @ I3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_182_top__empty__eq,axiom,
% 0.31/1.64 ( top_to900819589_nat_o
% 0.31/1.64 = ( ^ [X2: produc194167194tv_nat] : ( member737151281tv_nat @ X2 @ top_to975729152tv_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_183_top__empty__eq,axiom,
% 0.31/1.64 ( top_to1889334367e_tv_o
% 0.31/1.64 = ( ^ [X2: produc270694976lle_tv] : ( member813679063lle_tv @ X2 @ top_to1411004326lle_tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_184_top__empty__eq,axiom,
% 0.31/1.64 ( top_to632227436_nat_o
% 0.31/1.64 = ( ^ [X2: product_prod_nat_nat] : ( member701585322at_nat @ X2 @ top_to1555900337at_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_185_top__empty__eq,axiom,
% 0.31/1.64 ( top_top_nat_o
% 0.31/1.64 = ( ^ [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_186_top__empty__eq,axiom,
% 0.31/1.64 ( top_to1299250770e_tv_o
% 0.31/1.64 = ( ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_187_change__tv_Oelims,axiom,
% 0.31/1.64 ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 0.31/1.64 = Y )
% 0.31/1.64 => ( ! [B2: $o] :
% 0.31/1.64 ( ( Xa
% 0.31/1.64 = ( paraco1344940915le_Det @ B2 ) )
% 0.31/1.64 => ( Y
% 0.31/1.64 != ( paraco1344940915le_Det @ B2 ) ) )
% 0.31/1.64 => ~ ! [N: nat] :
% 0.31/1.64 ( ( Xa
% 0.31/1.64 = ( paraco793048302_Indet @ N ) )
% 0.31/1.64 => ( Y
% 0.31/1.64 != ( paraco793048302_Indet @ ( X @ N ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_188_valid__valid__in,axiom,
% 0.31/1.64 ! [P2: paraco1604210848lle_fm,U: set_nat] :
% 0.31/1.64 ( ( paraco327635598_valid @ P2 )
% 0.31/1.64 => ( paraco55203475lid_in @ U @ P2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_189_transfer,axiom,
% 0.31/1.64 ! [U: set_nat,P2: paraco1604210848lle_fm] :
% 0.31/1.64 ( ~ ( paraco55203475lid_in @ U @ P2 )
% 0.31/1.64 => ~ ( paraco327635598_valid @ P2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_190_the__inv__f__f,axiom,
% 0.31/1.64 ! [F2: nat > nat,X: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( the_inv_into_nat_nat @ top_top_set_nat @ F2 @ ( F2 @ X ) )
% 0.31/1.64 = X ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_191_the__inv__f__f,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ F2 @ ( F2 @ X ) )
% 0.31/1.64 = X ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_192_conjunction__in,axiom,
% 0.31/1.64 ! [U: set_nat,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco55203475lid_in @ U @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.31/1.64 = ( ( paraco55203475lid_in @ U @ P2 )
% 0.31/1.64 & ( paraco55203475lid_in @ U @ Q ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_193_tv_Oinject_I2_J,axiom,
% 0.31/1.64 ! [X23: nat,Y22: nat] :
% 0.31/1.64 ( ( ( paraco793048302_Indet @ X23 )
% 0.31/1.64 = ( paraco793048302_Indet @ Y22 ) )
% 0.31/1.64 = ( X23 = Y22 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_194_string__tv_Oinduct,axiom,
% 0.31/1.64 ! [P3: paraco1605129243lle_tv > $o,A0: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( P3 @ ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( P3 @ ( paraco1344940915le_Det @ $false ) )
% 0.31/1.64 => ( ! [N: nat] : ( P3 @ ( paraco793048302_Indet @ N ) )
% 0.31/1.64 => ( P3 @ A0 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_195_change__tv_Oinduct,axiom,
% 0.31/1.64 ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,A0: nat > nat,A1: paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [F3: nat > nat,B2: $o] : ( P3 @ F3 @ ( paraco1344940915le_Det @ B2 ) )
% 0.31/1.64 => ( ! [F3: nat > nat,N: nat] : ( P3 @ F3 @ ( paraco793048302_Indet @ N ) )
% 0.31/1.64 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_196_string__tv_Ocases,axiom,
% 0.31/1.64 ! [X: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( X
% 0.31/1.64 != ( paraco1344940915le_Det @ $true ) )
% 0.31/1.64 => ( ( X
% 0.31/1.64 != ( paraco1344940915le_Det @ $false ) )
% 0.31/1.64 => ~ ! [N: nat] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( paraco793048302_Indet @ N ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_197_tv_Oexhaust,axiom,
% 0.31/1.64 ! [Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X12: $o] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( paraco1344940915le_Det @ X12 ) )
% 0.31/1.64 => ~ ! [X22: nat] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( paraco793048302_Indet @ X22 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_198_tv_Oinduct,axiom,
% 0.31/1.64 ! [P3: paraco1605129243lle_tv > $o,Tv: paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: $o] : ( P3 @ ( paraco1344940915le_Det @ X4 ) )
% 0.31/1.64 => ( ! [X4: nat] : ( P3 @ ( paraco793048302_Indet @ X4 ) )
% 0.31/1.64 => ( P3 @ Tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_199_tv_Odistinct_I1_J,axiom,
% 0.31/1.64 ! [X1: $o,X23: nat] :
% 0.31/1.64 ( ( paraco1344940915le_Det @ X1 )
% 0.31/1.64 != ( paraco793048302_Indet @ X23 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_200_the__inv__into__f__f,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,X: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( member_nat @ X @ A2 )
% 0.31/1.64 => ( ( the_inv_into_nat_nat @ A2 @ F2 @ ( F2 @ X ) )
% 0.31/1.64 = X ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_201_the__inv__into__f__f,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( member266900804lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( the_in452116896lle_tv @ A2 @ F2 @ ( F2 @ X ) )
% 0.31/1.64 = X ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_202_the__inv__into__f__eq,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = Y )
% 0.31/1.64 => ( ( member_nat @ X @ A2 )
% 0.31/1.64 => ( ( the_inv_into_nat_nat @ A2 @ F2 @ Y )
% 0.31/1.64 = X ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_203_the__inv__into__f__eq,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( ( F2 @ X )
% 0.31/1.64 = Y )
% 0.31/1.64 => ( ( member266900804lle_tv @ X @ A2 )
% 0.31/1.64 => ( ( the_in452116896lle_tv @ A2 @ F2 @ Y )
% 0.31/1.64 = X ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_204_tv_Osimps_I6_J,axiom,
% 0.31/1.64 ! [F1: $o > paraco1605129243lle_tv,F22: nat > paraco1605129243lle_tv,X23: nat] :
% 0.31/1.64 ( ( paraco2051596139lle_tv @ F1 @ F22 @ ( paraco793048302_Indet @ X23 ) )
% 0.31/1.64 = ( F22 @ X23 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_205_change__tv_Osimps_I2_J,axiom,
% 0.31/1.64 ! [F2: nat > nat,N2: nat] :
% 0.31/1.64 ( ( paraco1147068288nge_tv @ F2 @ ( paraco793048302_Indet @ N2 ) )
% 0.31/1.64 = ( paraco793048302_Indet @ ( F2 @ N2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_206_prod_Oinject,axiom,
% 0.31/1.64 ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm,Y1: list_char > paraco1605129243lle_tv,Y22: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( produc1710735575lle_fm @ X1 @ X23 )
% 0.31/1.64 = ( produc1710735575lle_fm @ Y1 @ Y22 ) )
% 0.31/1.64 = ( ( X1 = Y1 )
% 0.31/1.64 & ( X23 = Y22 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_207_prod_Oinject,axiom,
% 0.31/1.64 ! [X1: nat > nat,X23: paraco1605129243lle_tv,Y1: nat > nat,Y22: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( produc1680557635lle_tv @ X1 @ X23 )
% 0.31/1.64 = ( produc1680557635lle_tv @ Y1 @ Y22 ) )
% 0.31/1.64 = ( ( X1 = Y1 )
% 0.31/1.64 & ( X23 = Y22 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_208_old_Oprod_Oinject,axiom,
% 0.31/1.64 ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( produc1710735575lle_fm @ A @ B )
% 0.31/1.64 = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 0.31/1.64 = ( ( A = A5 )
% 0.31/1.64 & ( B = B3 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_209_old_Oprod_Oinject,axiom,
% 0.31/1.64 ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( produc1680557635lle_tv @ A @ B )
% 0.31/1.64 = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 0.31/1.64 = ( ( A = A5 )
% 0.31/1.64 & ( B = B3 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_210_eval_Osimps_I3_J,axiom,
% 0.31/1.64 ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.31/1.64 = ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_211_surj__pair,axiom,
% 0.31/1.64 ! [P2: produc696645085lle_fm] :
% 0.31/1.64 ? [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.31/1.64 ( P2
% 0.31/1.64 = ( produc1710735575lle_fm @ X4 @ Y2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_212_surj__pair,axiom,
% 0.31/1.64 ! [P2: produc931990033lle_tv] :
% 0.31/1.64 ? [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.31/1.64 ( P2
% 0.31/1.64 = ( produc1680557635lle_tv @ X4 @ Y2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_213_bool_Osplit__sel__asm,axiom,
% 0.31/1.64 ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 0.31/1.64 ( ( P3 @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 0.31/1.64 = ( ~ ( ( Bool
% 0.31/1.64 & ~ ( P3 @ F1 ) )
% 0.31/1.64 | ( ~ Bool
% 0.31/1.64 & ~ ( P3 @ F22 ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_214_bool_Ocase__distrib,axiom,
% 0.31/1.64 ! [H: paraco1605129243lle_tv > paraco1605129243lle_tv,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 0.31/1.64 ( ( H @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 0.31/1.64 = ( produc234482697lle_tv @ ( H @ F1 ) @ ( H @ F22 ) @ Bool ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_215_bool_Ocase__eq__if,axiom,
% 0.31/1.64 ( produc234482697lle_tv
% 0.31/1.64 = ( ^ [F12: paraco1605129243lle_tv,F23: paraco1605129243lle_tv,Bool2: $o] : ( if_Par1134130401lle_tv @ Bool2 @ F12 @ F23 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_216_bool_Osplit__sel,axiom,
% 0.31/1.64 ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 0.31/1.64 ( ( P3 @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 0.31/1.64 = ( ( Bool
% 0.31/1.64 => ( P3 @ F1 ) )
% 0.31/1.64 & ( ~ Bool
% 0.31/1.64 => ( P3 @ F22 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_217_old_Obool_Osimps_I3_J,axiom,
% 0.31/1.64 ! [F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc234482697lle_tv @ F1 @ F22 @ $true )
% 0.31/1.64 = F1 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_218_old_Obool_Osimps_I4_J,axiom,
% 0.31/1.64 ! [F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc234482697lle_tv @ F1 @ F22 @ $false )
% 0.31/1.64 = F22 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_219_change__tv_Ocases,axiom,
% 0.31/1.64 ! [X: produc931990033lle_tv] :
% 0.31/1.64 ( ! [F3: nat > nat,B2: $o] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( produc1680557635lle_tv @ F3 @ ( paraco1344940915le_Det @ B2 ) ) )
% 0.31/1.64 => ~ ! [F3: nat > nat,N: nat] :
% 0.31/1.64 ( X
% 0.31/1.64 != ( produc1680557635lle_tv @ F3 @ ( paraco793048302_Indet @ N ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_220_old_Oprod_Oinducts,axiom,
% 0.31/1.64 ! [P3: produc696645085lle_fm > $o,Prod: produc696645085lle_fm] :
% 0.31/1.64 ( ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A3 @ B2 ) )
% 0.31/1.64 => ( P3 @ Prod ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_221_old_Oprod_Oinducts,axiom,
% 0.31/1.64 ! [P3: produc931990033lle_tv > $o,Prod: produc931990033lle_tv] :
% 0.31/1.64 ( ! [A3: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A3 @ B2 ) )
% 0.31/1.64 => ( P3 @ Prod ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_222_old_Oprod_Oexhaust,axiom,
% 0.31/1.64 ! [Y: produc696645085lle_fm] :
% 0.31/1.64 ~ ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( produc1710735575lle_fm @ A3 @ B2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_223_old_Oprod_Oexhaust,axiom,
% 0.31/1.64 ! [Y: produc931990033lle_tv] :
% 0.31/1.64 ~ ! [A3: nat > nat,B2: paraco1605129243lle_tv] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( produc1680557635lle_tv @ A3 @ B2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_224_Pair__inject,axiom,
% 0.31/1.64 ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( produc1710735575lle_fm @ A @ B )
% 0.31/1.64 = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 0.31/1.64 => ~ ( ( A = A5 )
% 0.31/1.64 => ( B != B3 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_225_Pair__inject,axiom,
% 0.31/1.64 ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( produc1680557635lle_tv @ A @ B )
% 0.31/1.64 = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 0.31/1.64 => ~ ( ( A = A5 )
% 0.31/1.64 => ( B != B3 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_226_prod__cases,axiom,
% 0.31/1.64 ! [P3: produc696645085lle_fm > $o,P2: produc696645085lle_fm] :
% 0.31/1.64 ( ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A3 @ B2 ) )
% 0.31/1.64 => ( P3 @ P2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_227_prod__cases,axiom,
% 0.31/1.64 ! [P3: produc931990033lle_tv > $o,P2: produc931990033lle_tv] :
% 0.31/1.64 ( ! [A3: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A3 @ B2 ) )
% 0.31/1.64 => ( P3 @ P2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_228_ssubst__Pair__rhs,axiom,
% 0.31/1.64 ! [R: list_char > paraco1605129243lle_tv,S3: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,S4: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S3 ) @ R2 )
% 0.31/1.64 => ( ( S4 = S3 )
% 0.31/1.64 => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S4 ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_229_ssubst__Pair__rhs,axiom,
% 0.31/1.64 ! [R: nat > nat,S3: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,S4: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S3 ) @ R2 )
% 0.31/1.64 => ( ( S4 = S3 )
% 0.31/1.64 => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S4 ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_230_apfst__conv,axiom,
% 0.31/1.64 ! [F2: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( produc1942165868lle_fm @ F2 @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.31/1.64 = ( produc1710735575lle_fm @ ( F2 @ X ) @ Y ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_231_apfst__conv,axiom,
% 0.31/1.64 ! [F2: ( nat > nat ) > nat > nat,X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc939316703lle_tv @ F2 @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.31/1.64 = ( produc1680557635lle_tv @ ( F2 @ X ) @ Y ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_232_apsnd__conv,axiom,
% 0.31/1.64 ! [F2: paraco1604210848lle_fm > paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( produc1807466521lle_tv @ F2 @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.31/1.64 = ( produc1710735575lle_fm @ X @ ( F2 @ Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_233_apsnd__conv,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc109093078at_nat @ F2 @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.31/1.64 = ( produc1680557635lle_tv @ X @ ( F2 @ Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_234_change__tv_Opelims,axiom,
% 0.31/1.64 ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 0.31/1.64 = Y )
% 0.31/1.64 => ( ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ Xa ) )
% 0.31/1.64 => ( ! [B2: $o] :
% 0.31/1.64 ( ( Xa
% 0.31/1.64 = ( paraco1344940915le_Det @ B2 ) )
% 0.31/1.64 => ( ( Y
% 0.31/1.64 = ( paraco1344940915le_Det @ B2 ) )
% 0.31/1.64 => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco1344940915le_Det @ B2 ) ) ) ) )
% 0.31/1.64 => ~ ! [N: nat] :
% 0.31/1.64 ( ( Xa
% 0.31/1.64 = ( paraco793048302_Indet @ N ) )
% 0.31/1.64 => ( ( Y
% 0.31/1.64 = ( paraco793048302_Indet @ ( X @ N ) ) )
% 0.31/1.64 => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco793048302_Indet @ N ) ) ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_235_prod_Oinj__map,axiom,
% 0.31/1.64 ! [F1: nat > nat,F22: nat > nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.31/1.64 => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 0.31/1.64 => ( inj_on26176689at_nat @ ( produc505105722at_nat @ F1 @ F22 ) @ top_to1555900337at_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_236_prod_Oinj__map,axiom,
% 0.31/1.64 ! [F1: nat > nat,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.31/1.64 => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ F1 @ F22 ) @ top_to1411004326lle_tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_237_prod_Oinj__map,axiom,
% 0.31/1.64 ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: nat > nat] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 0.31/1.64 => ( inj_on552895452tv_nat @ ( produc42536895at_nat @ F1 @ F22 ) @ top_to975729152tv_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_238_prod_Oinj__map,axiom,
% 0.31/1.64 ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ F1 @ F22 ) @ top_to1871154984lle_tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_239_curryI,axiom,
% 0.31/1.64 ! [F2: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( F2 @ ( produc1710735575lle_fm @ A @ B ) )
% 0.31/1.64 => ( produc275353523e_fm_o @ F2 @ A @ B ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_240_curryI,axiom,
% 0.31/1.64 ! [F2: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( F2 @ ( produc1680557635lle_tv @ A @ B ) )
% 0.31/1.64 => ( produc752649287e_tv_o @ F2 @ A @ B ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_241_map__prod__simp,axiom,
% 0.31/1.64 ! [F2: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( produc1900967599lle_fm @ F2 @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 0.31/1.64 = ( produc1710735575lle_fm @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_242_map__prod__simp,axiom,
% 0.31/1.64 ! [F2: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( produc1566550641lle_tv @ F2 @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 0.31/1.64 = ( produc1680557635lle_tv @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_243_map__prod__simp,axiom,
% 0.31/1.64 ! [F2: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc951033137lle_fm @ F2 @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 0.31/1.64 = ( produc1710735575lle_fm @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_244_map__prod__simp,axiom,
% 0.31/1.64 ! [F2: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc532909085lle_tv @ F2 @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 0.31/1.64 = ( produc1680557635lle_tv @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_245_curryD,axiom,
% 0.31/1.64 ! [F2: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( produc275353523e_fm_o @ F2 @ A @ B )
% 0.31/1.64 => ( F2 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_246_curryD,axiom,
% 0.31/1.64 ! [F2: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc752649287e_tv_o @ F2 @ A @ B )
% 0.31/1.64 => ( F2 @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_247_curryE,axiom,
% 0.31/1.64 ! [F2: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( produc275353523e_fm_o @ F2 @ A @ B )
% 0.31/1.64 => ( F2 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_248_curryE,axiom,
% 0.31/1.64 ! [F2: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc752649287e_tv_o @ F2 @ A @ B )
% 0.31/1.64 => ( F2 @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_249_the__inv__into__onto,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F2 ) @ ( image_nat_nat @ F2 @ A2 ) )
% 0.31/1.64 = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_250_the__inv__into__onto,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ A2 @ F2 ) @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.31/1.64 = A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_251_map__prod__imageI,axiom,
% 0.31/1.64 ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F2: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm] :
% 0.31/1.64 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 0.31/1.64 => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F2 @ G ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_252_map__prod__imageI,axiom,
% 0.31/1.64 ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F2: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 0.31/1.64 => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F2 @ G ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_253_map__prod__imageI,axiom,
% 0.31/1.64 ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F2: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm] :
% 0.31/1.64 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 0.31/1.64 => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F2 @ G ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_254_map__prod__imageI,axiom,
% 0.31/1.64 ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F2: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 0.31/1.64 => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F2 @ G ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_255_swap__simp,axiom,
% 0.31/1.64 ! [X: paraco1604210848lle_fm,Y: list_char > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc1232814113lle_tv @ ( produc1943344577lle_tv @ X @ Y ) )
% 0.31/1.64 = ( produc1710735575lle_fm @ Y @ X ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_256_swap__simp,axiom,
% 0.31/1.64 ! [X: paraco1605129243lle_tv,Y: nat > nat] :
% 0.31/1.64 ( ( produc178635363at_nat @ ( produc1633679363at_nat @ X @ Y ) )
% 0.31/1.64 = ( produc1680557635lle_tv @ Y @ X ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_257_swap__simp,axiom,
% 0.31/1.64 ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( produc1000205111lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.31/1.64 = ( produc1943344577lle_tv @ Y @ X ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_258_swap__simp,axiom,
% 0.31/1.64 ! [X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc225513635lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.31/1.64 = ( produc1633679363at_nat @ Y @ X ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_259_pair__in__swap__image,axiom,
% 0.31/1.64 ! [Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,A2: set_Pr2120184979lle_fm] :
% 0.31/1.64 ( ( member74361182lle_tv @ ( produc1943344577lle_tv @ Y @ X ) @ ( image_924970994lle_tv @ produc1000205111lle_fm @ A2 ) )
% 0.31/1.64 = ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X @ Y ) @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_260_pair__in__swap__image,axiom,
% 0.31/1.64 ! [Y: paraco1605129243lle_tv,X: nat > nat,A2: set_Pr560526279lle_tv] :
% 0.31/1.64 ( ( member1234290208at_nat @ ( produc1633679363at_nat @ Y @ X ) @ ( image_1724396928at_nat @ produc225513635lle_tv @ A2 ) )
% 0.31/1.64 = ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X @ Y ) @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_261_pair__in__swap__image,axiom,
% 0.31/1.64 ! [Y: list_char > paraco1605129243lle_tv,X: paraco1604210848lle_fm,A2: set_Pr1723822845lle_tv] :
% 0.31/1.64 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ Y @ X ) @ ( image_326034184lle_fm @ produc1232814113lle_tv @ A2 ) )
% 0.31/1.64 = ( member74361182lle_tv @ ( produc1943344577lle_tv @ X @ Y ) @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_262_pair__in__swap__image,axiom,
% 0.31/1.64 ! [Y: nat > nat,X: paraco1605129243lle_tv,A2: set_Pr840833727at_nat] :
% 0.31/1.64 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ Y @ X ) @ ( image_769496456lle_tv @ produc178635363at_nat @ A2 ) )
% 0.31/1.64 = ( member1234290208at_nat @ ( produc1633679363at_nat @ X @ Y ) @ A2 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_263_inj__on__image__iff,axiom,
% 0.31/1.64 ! [A2: set_nat,G: nat > nat,F2: nat > nat] :
% 0.31/1.64 ( ! [X4: nat] :
% 0.31/1.64 ( ( member_nat @ X4 @ A2 )
% 0.31/1.64 => ! [Xa2: nat] :
% 0.31/1.64 ( ( member_nat @ Xa2 @ A2 )
% 0.31/1.64 => ( ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = ( G @ ( F2 @ Xa2 ) ) )
% 0.31/1.64 = ( ( G @ X4 )
% 0.31/1.64 = ( G @ Xa2 ) ) ) ) )
% 0.31/1.64 => ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F2 @ A2 ) )
% 0.31/1.64 = ( inj_on_nat_nat @ G @ A2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_264_inj__on__image__iff,axiom,
% 0.31/1.64 ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member266900804lle_tv @ X4 @ A2 )
% 0.31/1.64 => ! [Xa2: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member266900804lle_tv @ Xa2 @ A2 )
% 0.31/1.64 => ( ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = ( G @ ( F2 @ Xa2 ) ) )
% 0.31/1.64 = ( ( G @ X4 )
% 0.31/1.64 = ( G @ Xa2 ) ) ) ) )
% 0.31/1.64 => ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( inj_on772319074lle_tv @ G @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.31/1.64 = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_265_surjD,axiom,
% 0.31/1.64 ! [F2: nat > nat,Y: nat] :
% 0.31/1.64 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ? [X4: nat] :
% 0.31/1.64 ( Y
% 0.31/1.64 = ( F2 @ X4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_266_surjD,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ? [X4: nat] :
% 0.31/1.64 ( Y
% 0.31/1.64 = ( F2 @ X4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_267_surjD,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > nat,Y: nat] :
% 0.31/1.64 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ? [X4: paraco1605129243lle_tv] :
% 0.31/1.64 ( Y
% 0.31/1.64 = ( F2 @ X4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_268_surjD,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_335818702lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ? [X4: paraco1605129243lle_tv] :
% 0.31/1.64 ( Y
% 0.31/1.64 = ( F2 @ X4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_269_surjE,axiom,
% 0.31/1.64 ! [F2: nat > nat,Y: nat] :
% 0.31/1.64 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ~ ! [X4: nat] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( F2 @ X4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_270_surjE,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ~ ! [X4: nat] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( F2 @ X4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_271_surjE,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > nat,Y: nat] :
% 0.31/1.64 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ~ ! [X4: paraco1605129243lle_tv] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( F2 @ X4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_272_surjE,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_335818702lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ~ ! [X4: paraco1605129243lle_tv] :
% 0.31/1.64 ( Y
% 0.31/1.64 != ( F2 @ X4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_273_surjI,axiom,
% 0.31/1.64 ! [G: nat > nat,F2: nat > nat] :
% 0.31/1.64 ( ! [X4: nat] :
% 0.31/1.64 ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 )
% 0.31/1.64 => ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_274_surjI,axiom,
% 0.31/1.64 ! [G: nat > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > nat] :
% 0.31/1.64 ( ! [X4: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 )
% 0.31/1.64 => ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_275_surjI,axiom,
% 0.31/1.64 ! [G: paraco1605129243lle_tv > nat,F2: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: nat] :
% 0.31/1.64 ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 )
% 0.31/1.64 => ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.31/1.64 = top_top_set_nat ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_276_surjI,axiom,
% 0.31/1.64 ! [G: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ! [X4: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( G @ ( F2 @ X4 ) )
% 0.31/1.64 = X4 )
% 0.31/1.64 => ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.31/1.64 = top_to1057771083lle_tv ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_277_surj__def,axiom,
% 0.31/1.64 ! [F2: nat > nat] :
% 0.31/1.64 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 = ( ! [Y4: nat] :
% 0.31/1.64 ? [X2: nat] :
% 0.31/1.64 ( Y4
% 0.31/1.64 = ( F2 @ X2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_278_surj__def,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 = ( ! [Y4: paraco1605129243lle_tv] :
% 0.31/1.64 ? [X2: nat] :
% 0.31/1.64 ( Y4
% 0.31/1.64 = ( F2 @ X2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_279_surj__def,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > nat] :
% 0.31/1.64 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 = ( ! [Y4: nat] :
% 0.31/1.64 ? [X2: paraco1605129243lle_tv] :
% 0.31/1.64 ( Y4
% 0.31/1.64 = ( F2 @ X2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_280_surj__def,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_335818702lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 = ( ! [Y4: paraco1605129243lle_tv] :
% 0.31/1.64 ? [X2: paraco1605129243lle_tv] :
% 0.31/1.64 ( Y4
% 0.31/1.64 = ( F2 @ X2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_281_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: nat > nat,G: nat > nat] :
% 0.31/1.64 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( image_815163717at_nat @ ( produc505105722at_nat @ F2 @ G ) @ top_to1555900337at_nat )
% 0.31/1.64 = top_to1555900337at_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_282_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: nat > nat,G: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ( ( image_1674248956lle_tv @ ( produc313957681lle_tv @ F2 @ G ) @ top_to1555900337at_nat )
% 0.31/1.64 = top_to1411004326lle_tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_283_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: nat > nat,G: paraco1605129243lle_tv > nat] :
% 0.31/1.64 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( image_1787705850at_nat @ ( produc1685803475tv_nat @ F2 @ G ) @ top_to1411004326lle_tv )
% 0.31/1.64 = top_to1555900337at_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_284_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ( ( image_149830562lle_tv @ ( produc2101297531lle_tv @ F2 @ G ) @ top_to1411004326lle_tv )
% 0.31/1.64 = top_to1411004326lle_tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_285_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,G: nat > nat] :
% 0.31/1.64 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( image_1597721174tv_nat @ ( produc1250721397at_nat @ F2 @ G ) @ top_to1555900337at_nat )
% 0.31/1.64 = top_to975729152tv_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_286_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ( ( image_1507992062lle_tv @ ( produc210389789lle_tv @ F2 @ G ) @ top_to1555900337at_nat )
% 0.31/1.64 = top_to1871154984lle_tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_287_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 0.31/1.64 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ F2 @ G ) @ top_to1411004326lle_tv )
% 0.31/1.64 = top_to975729152tv_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_288_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_1151963140lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ F2 @ G ) @ top_to1411004326lle_tv )
% 0.31/1.64 = top_to1871154984lle_tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_289_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > nat,G: nat > nat] :
% 0.31/1.64 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( image_1805124128at_nat @ ( produc386540311at_nat @ F2 @ G ) @ top_to975729152tv_nat )
% 0.31/1.64 = top_to1555900337at_nat ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_290_map__prod__surj,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > nat,G: nat > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( image_376325286tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 = top_top_set_nat )
% 0.31/1.64 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.31/1.64 = top_to1057771083lle_tv )
% 0.31/1.64 => ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ F2 @ G ) @ top_to975729152tv_nat )
% 0.31/1.64 = top_to1411004326lle_tv ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_291_range__ex1__eq,axiom,
% 0.31/1.64 ! [F2: nat > nat,B: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( member_nat @ B @ ( image_nat_nat @ F2 @ top_top_set_nat ) )
% 0.31/1.64 = ( ? [X2: nat] :
% 0.31/1.64 ( ( B
% 0.31/1.64 = ( F2 @ X2 ) )
% 0.31/1.64 & ! [Y4: nat] :
% 0.31/1.64 ( ( B
% 0.31/1.64 = ( F2 @ Y4 ) )
% 0.31/1.64 => ( Y4 = X2 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_292_range__ex1__eq,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( member266900804lle_tv @ B @ ( image_335818702lle_tv @ F2 @ top_to1057771083lle_tv ) )
% 0.31/1.64 = ( ? [X2: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( B
% 0.31/1.64 = ( F2 @ X2 ) )
% 0.31/1.64 & ! [Y4: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( B
% 0.31/1.64 = ( F2 @ Y4 ) )
% 0.31/1.64 => ( Y4 = X2 ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_293_inj__image__eq__iff,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,B4: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( ( image_nat_nat @ F2 @ A2 )
% 0.31/1.64 = ( image_nat_nat @ F2 @ B4 ) )
% 0.31/1.64 = ( A2 = B4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_294_inj__image__eq__iff,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( ( image_335818702lle_tv @ F2 @ A2 )
% 0.31/1.64 = ( image_335818702lle_tv @ F2 @ B4 ) )
% 0.31/1.64 = ( A2 = B4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_295_inj__image__mem__iff,axiom,
% 0.31/1.64 ! [F2: nat > nat,A: nat,A2: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( member_nat @ ( F2 @ A ) @ ( image_nat_nat @ F2 @ A2 ) )
% 0.31/1.64 = ( member_nat @ A @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_296_inj__image__mem__iff,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( member266900804lle_tv @ ( F2 @ A ) @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.31/1.64 = ( member266900804lle_tv @ A @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_297_prod__fun__imageE,axiom,
% 0.31/1.64 ! [C: produc696645085lle_fm,F2: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm] :
% 0.31/1.64 ( ( member1474794996lle_fm @ C @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F2 @ G ) @ R2 ) )
% 0.31/1.64 => ~ ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( C
% 0.31/1.64 = ( produc1710735575lle_fm @ ( F2 @ X4 ) @ ( G @ Y2 ) ) )
% 0.31/1.64 => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_298_prod__fun__imageE,axiom,
% 0.31/1.64 ! [C: produc696645085lle_fm,F2: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,R2: set_Pr560526279lle_tv] :
% 0.31/1.64 ( ( member1474794996lle_fm @ C @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F2 @ G ) @ R2 ) )
% 0.31/1.64 => ~ ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( C
% 0.31/1.64 = ( produc1710735575lle_fm @ ( F2 @ X4 ) @ ( G @ Y2 ) ) )
% 0.31/1.64 => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_299_prod__fun__imageE,axiom,
% 0.31/1.64 ! [C: produc931990033lle_tv,F2: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,R2: set_Pr2120184979lle_fm] :
% 0.31/1.64 ( ( member1569366824lle_tv @ C @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F2 @ G ) @ R2 ) )
% 0.31/1.64 => ~ ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( C
% 0.31/1.64 = ( produc1680557635lle_tv @ ( F2 @ X4 ) @ ( G @ Y2 ) ) )
% 0.31/1.64 => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_300_prod__fun__imageE,axiom,
% 0.31/1.64 ! [C: produc931990033lle_tv,F2: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,R2: set_Pr560526279lle_tv] :
% 0.31/1.64 ( ( member1569366824lle_tv @ C @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F2 @ G ) @ R2 ) )
% 0.31/1.64 => ~ ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( C
% 0.31/1.64 = ( produc1680557635lle_tv @ ( F2 @ X4 ) @ ( G @ Y2 ) ) )
% 0.31/1.64 => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_301_f__the__inv__into__f,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,Y: nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( member_nat @ Y @ ( image_nat_nat @ F2 @ A2 ) )
% 0.31/1.64 => ( ( F2 @ ( the_inv_into_nat_nat @ A2 @ F2 @ Y ) )
% 0.31/1.64 = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_302_f__the__inv__into__f,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( member266900804lle_tv @ Y @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.31/1.64 => ( ( F2 @ ( the_in452116896lle_tv @ A2 @ F2 @ Y ) )
% 0.31/1.64 = Y ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_303_inj__on__the__inv__into,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F2 ) @ ( image_nat_nat @ F2 @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_304_inj__on__the__inv__into,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ A2 @ F2 ) @ ( image_335818702lle_tv @ F2 @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_305_total__inv__image,axiom,
% 0.31/1.64 ! [F2: nat > nat,R: set_Pr1986765409at_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( total_on_nat @ top_top_set_nat @ R )
% 0.31/1.64 => ( total_on_nat @ top_top_set_nat @ ( inv_image_nat_nat @ R @ F2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_306_total__inv__image,axiom,
% 0.31/1.64 ! [F2: nat > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 0.31/1.64 ( ( inj_on1955349912lle_tv @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.31/1.64 => ( total_on_nat @ top_top_set_nat @ ( inv_im516950809tv_nat @ R @ F2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_307_total__inv__image,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > nat,R: set_Pr1986765409at_nat] :
% 0.31/1.64 ( ( inj_on1179712058tv_nat @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( total_on_nat @ top_top_set_nat @ R )
% 0.31/1.64 => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im1292588663lle_tv @ R @ F2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_308_total__inv__image,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.31/1.64 => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im719552961lle_tv @ R @ F2 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_309_the__inv__into__into,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,X: nat,B4: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( member_nat @ X @ ( image_nat_nat @ F2 @ A2 ) )
% 0.31/1.64 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.31/1.64 => ( member_nat @ ( the_inv_into_nat_nat @ A2 @ F2 @ X ) @ B4 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_310_the__inv__into__into,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.31/1.64 => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.31/1.64 => ( member266900804lle_tv @ ( the_in452116896lle_tv @ A2 @ F2 @ X ) @ B4 ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_311_prod_Ocollapse,axiom,
% 0.31/1.64 ! [Prod: produc696645085lle_fm] :
% 0.31/1.64 ( ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) )
% 0.31/1.64 = Prod ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_312_prod_Ocollapse,axiom,
% 0.31/1.64 ! [Prod: produc931990033lle_tv] :
% 0.31/1.64 ( ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) )
% 0.31/1.64 = Prod ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_313_prod_Oswap__def,axiom,
% 0.31/1.64 ( produc1232814113lle_tv
% 0.31/1.64 = ( ^ [P: produc1443694919lle_tv] : ( produc1710735575lle_fm @ ( produc381314067lle_tv @ P ) @ ( produc262413013lle_tv @ P ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_314_prod_Oswap__def,axiom,
% 0.31/1.64 ( produc178635363at_nat
% 0.31/1.64 = ( ^ [P: produc596913417at_nat] : ( produc1680557635lle_tv @ ( produc500618325at_nat @ P ) @ ( produc1589291287at_nat @ P ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_315_fst__eqD,axiom,
% 0.31/1.64 ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.31/1.64 = A )
% 0.31/1.64 => ( X = A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_316_fst__eqD,axiom,
% 0.31/1.64 ! [X: nat > nat,Y: paraco1605129243lle_tv,A: nat > nat] :
% 0.31/1.64 ( ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.31/1.64 = A )
% 0.31/1.64 => ( X = A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_317_snd__eqD,axiom,
% 0.31/1.64 ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.31/1.64 = A )
% 0.31/1.64 => ( Y = A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_318_snd__eqD,axiom,
% 0.31/1.64 ! [X: nat > nat,Y: paraco1605129243lle_tv,A: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.31/1.64 = A )
% 0.31/1.64 => ( Y = A ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_319_fst__conv,axiom,
% 0.31/1.64 ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X1 @ X23 ) )
% 0.31/1.64 = X1 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_320_fst__conv,axiom,
% 0.31/1.64 ! [X1: nat > nat,X23: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X1 @ X23 ) )
% 0.31/1.64 = X1 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_321_snd__conv,axiom,
% 0.31/1.64 ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X1 @ X23 ) )
% 0.31/1.64 = X23 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_322_snd__conv,axiom,
% 0.31/1.64 ! [X1: nat > nat,X23: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X1 @ X23 ) )
% 0.31/1.64 = X23 ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_323_prod_Oexhaust__sel,axiom,
% 0.31/1.64 ! [Prod: produc696645085lle_fm] :
% 0.31/1.64 ( Prod
% 0.31/1.64 = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_324_prod_Oexhaust__sel,axiom,
% 0.31/1.64 ! [Prod: produc931990033lle_tv] :
% 0.31/1.64 ( Prod
% 0.31/1.64 = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_325_surjective__pairing,axiom,
% 0.31/1.64 ! [T: produc696645085lle_fm] :
% 0.31/1.64 ( T
% 0.31/1.64 = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ T ) @ ( produc148705065lle_fm @ T ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_326_surjective__pairing,axiom,
% 0.31/1.64 ! [T: produc931990033lle_tv] :
% 0.31/1.64 ( T
% 0.31/1.64 = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ T ) @ ( produc547496597lle_tv @ T ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_327_subrelI,axiom,
% 0.31/1.64 ! [R: set_Pr2120184979lle_fm,S3: set_Pr2120184979lle_fm] :
% 0.31/1.64 ( ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R )
% 0.31/1.64 => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ S3 ) )
% 0.31/1.64 => ( ord_le1007985907lle_fm @ R @ S3 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_328_subrelI,axiom,
% 0.31/1.64 ! [R: set_Pr560526279lle_tv,S3: set_Pr560526279lle_tv] :
% 0.31/1.64 ( ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R )
% 0.31/1.64 => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ S3 ) )
% 0.31/1.64 => ( ord_le1784136743lle_tv @ R @ S3 ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_329_top__greatest,axiom,
% 0.31/1.64 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_330_top__greatest,axiom,
% 0.31/1.64 ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_331_top_Oextremum__unique,axiom,
% 0.31/1.64 ! [A: set_nat] :
% 0.31/1.64 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 0.31/1.64 = ( A = top_top_set_nat ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_332_top_Oextremum__unique,axiom,
% 0.31/1.64 ! [A: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
% 0.31/1.64 = ( A = top_to1057771083lle_tv ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_333_top_Oextremum__uniqueI,axiom,
% 0.31/1.64 ! [A: set_nat] :
% 0.31/1.64 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 0.31/1.64 => ( A = top_top_set_nat ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_334_top_Oextremum__uniqueI,axiom,
% 0.31/1.64 ! [A: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
% 0.31/1.64 => ( A = top_to1057771083lle_tv ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_335_subset__UNIV,axiom,
% 0.31/1.64 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ top_top_set_nat ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_336_subset__UNIV,axiom,
% 0.31/1.64 ! [A2: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A2 @ top_to1057771083lle_tv ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_337_inj__on__subset,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,B4: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ A2 )
% 0.31/1.64 => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 0.31/1.64 => ( inj_on_nat_nat @ F2 @ B4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_338_inj__on__subset,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ A2 )
% 0.31/1.64 => ( ( ord_le241064091lle_tv @ B4 @ A2 )
% 0.31/1.64 => ( inj_on772319074lle_tv @ F2 @ B4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_339_subset__inj__on,axiom,
% 0.31/1.64 ! [F2: nat > nat,B4: set_nat,A2: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ B4 )
% 0.31/1.64 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.31/1.64 => ( inj_on_nat_nat @ F2 @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_340_subset__inj__on,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ B4 )
% 0.31/1.64 => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.31/1.64 => ( inj_on772319074lle_tv @ F2 @ A2 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_341_inj__on__image__mem__iff,axiom,
% 0.31/1.64 ! [F2: nat > nat,B4: set_nat,A: nat,A2: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ B4 )
% 0.31/1.64 => ( ( member_nat @ A @ B4 )
% 0.31/1.64 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.31/1.64 => ( ( member_nat @ ( F2 @ A ) @ ( image_nat_nat @ F2 @ A2 ) )
% 0.31/1.64 = ( member_nat @ A @ A2 ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_342_inj__on__image__mem__iff,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ B4 )
% 0.31/1.64 => ( ( member266900804lle_tv @ A @ B4 )
% 0.31/1.64 => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.31/1.64 => ( ( member266900804lle_tv @ ( F2 @ A ) @ ( image_335818702lle_tv @ F2 @ A2 ) )
% 0.31/1.64 = ( member266900804lle_tv @ A @ A2 ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_343_inj__on__image__eq__iff,axiom,
% 0.31/1.64 ! [F2: nat > nat,C2: set_nat,A2: set_nat,B4: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ C2 )
% 0.31/1.64 => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.31/1.64 => ( ( ord_less_eq_set_nat @ B4 @ C2 )
% 0.31/1.64 => ( ( ( image_nat_nat @ F2 @ A2 )
% 0.31/1.64 = ( image_nat_nat @ F2 @ B4 ) )
% 0.31/1.64 = ( A2 = B4 ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_344_inj__on__image__eq__iff,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,C2: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ C2 )
% 0.31/1.64 => ( ( ord_le241064091lle_tv @ A2 @ C2 )
% 0.31/1.64 => ( ( ord_le241064091lle_tv @ B4 @ C2 )
% 0.31/1.64 => ( ( ( image_335818702lle_tv @ F2 @ A2 )
% 0.31/1.64 = ( image_335818702lle_tv @ F2 @ B4 ) )
% 0.31/1.64 = ( A2 = B4 ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_345_inj__image__subset__iff,axiom,
% 0.31/1.64 ! [F2: nat > nat,A2: set_nat,B4: set_nat] :
% 0.31/1.64 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.31/1.64 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F2 @ A2 ) @ ( image_nat_nat @ F2 @ B4 ) )
% 0.31/1.64 = ( ord_less_eq_set_nat @ A2 @ B4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_346_inj__image__subset__iff,axiom,
% 0.31/1.64 ! [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.31/1.64 => ( ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F2 @ A2 ) @ ( image_335818702lle_tv @ F2 @ B4 ) )
% 0.31/1.64 = ( ord_le241064091lle_tv @ A2 @ B4 ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_347_exI__realizer,axiom,
% 0.31/1.64 ! [P3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > $o,Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv] :
% 0.31/1.64 ( ( P3 @ Y @ X )
% 0.31/1.64 => ( P3 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_348_exI__realizer,axiom,
% 0.31/1.64 ! [P3: paraco1605129243lle_tv > ( nat > nat ) > $o,Y: paraco1605129243lle_tv,X: nat > nat] :
% 0.31/1.64 ( ( P3 @ Y @ X )
% 0.31/1.64 => ( P3 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_349_conjI__realizer,axiom,
% 0.31/1.64 ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,P2: list_char > paraco1605129243lle_tv,Q2: paraco1604210848lle_fm > $o,Q: paraco1604210848lle_fm] :
% 0.31/1.64 ( ( P3 @ P2 )
% 0.31/1.64 => ( ( Q2 @ Q )
% 0.31/1.64 => ( ( P3 @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) )
% 0.31/1.64 & ( Q2 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_350_conjI__realizer,axiom,
% 0.31/1.64 ! [P3: ( nat > nat ) > $o,P2: nat > nat,Q2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( P3 @ P2 )
% 0.31/1.64 => ( ( Q2 @ Q )
% 0.31/1.64 => ( ( P3 @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ P2 @ Q ) ) )
% 0.31/1.64 & ( Q2 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ P2 @ Q ) ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_351_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.31/1.64 ! [P3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: produc696645085lle_fm] :
% 0.31/1.64 ( ( P3 @ X @ Y )
% 0.31/1.64 => ( ( A
% 0.31/1.64 = ( produc1710735575lle_fm @ X @ Y ) )
% 0.31/1.64 => ( P3 @ ( produc29804011lle_fm @ A ) @ ( produc148705065lle_fm @ A ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_352_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.31/1.64 ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,X: nat > nat,Y: paraco1605129243lle_tv,A: produc931990033lle_tv] :
% 0.31/1.64 ( ( P3 @ X @ Y )
% 0.31/1.64 => ( ( A
% 0.31/1.64 = ( produc1680557635lle_tv @ X @ Y ) )
% 0.31/1.64 => ( P3 @ ( produc1636169559lle_tv @ A ) @ ( produc547496597lle_tv @ A ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_353_subset__image__inj,axiom,
% 0.31/1.64 ! [S5: set_nat,F2: nat > nat,T2: set_nat] :
% 0.31/1.64 ( ( ord_less_eq_set_nat @ S5 @ ( image_nat_nat @ F2 @ T2 ) )
% 0.31/1.64 = ( ? [U2: set_nat] :
% 0.31/1.64 ( ( ord_less_eq_set_nat @ U2 @ T2 )
% 0.31/1.64 & ( inj_on_nat_nat @ F2 @ U2 )
% 0.31/1.64 & ( S5
% 0.31/1.64 = ( image_nat_nat @ F2 @ U2 ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(fact_354_subset__image__inj,axiom,
% 0.31/1.64 ! [S5: set_Pa1764573435lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv,T2: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( ord_le241064091lle_tv @ S5 @ ( image_335818702lle_tv @ F2 @ T2 ) )
% 0.31/1.64 = ( ? [U2: set_Pa1764573435lle_tv] :
% 0.31/1.64 ( ( ord_le241064091lle_tv @ U2 @ T2 )
% 0.31/1.64 & ( inj_on772319074lle_tv @ F2 @ U2 )
% 0.31/1.64 & ( S5
% 0.31/1.64 = ( image_335818702lle_tv @ F2 @ U2 ) ) ) ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(help_If_3_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.31/1.64 ! [P3: $o] :
% 0.31/1.64 ( ( P3 = $true )
% 0.31/1.64 | ( P3 = $false ) ) ).
% 0.31/1.64
% 0.31/1.64 thf(help_If_2_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.31/1.64 ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( if_Par1134130401lle_tv @ $false @ X @ Y )
% 0.31/1.64 = Y ) ).
% 0.31/1.64
% 0.31/1.64 thf(help_If_1_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.31/1.64 ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.31/1.64 ( ( if_Par1134130401lle_tv @ $true @ X @ Y )
% 0.31/1.64 = X ) ).
% 0.31/1.64
% 0.31/1.64 thf(conj_0,conjecture,
% 0.31/1.64 ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 0.31/1.64 = ( paraco1344940915le_Det @ $true ) ) ).
% 0.31/1.64 ------------------------
% 0.31/1.67 % (30191)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_30016 for (2999ds/4Mi)
% 0.31/1.67 % (30190)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30016 for (2999ds/183Mi)
% 0.31/1.67 % (30193)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30016 for (2999ds/2Mi)
% 0.31/1.67 % (30195)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_30016 for (2999ds/275Mi)
% 0.31/1.67 % (30196)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30016 for (2999ds/18Mi)
% 0.31/1.67 % (30193)Instruction limit reached!
% 0.31/1.67 % (30193)------------------------------
% 0.31/1.67 % (30193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.67 % (30193)Termination reason: Unknown
% 0.31/1.67 % (30193)Termination phase: shuffling
% 0.31/1.67
% 0.31/1.67 % (30193)Memory used [KB]: 1535
% 0.31/1.67 % (30193)Time elapsed: 0.002 s
% 0.31/1.67 % (30193)Instructions burned: 2 (million)
% 0.31/1.67 % (30193)------------------------------
% 0.31/1.67 % (30193)------------------------------
% 0.31/1.67 % (30192)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_30016 for (2999ds/27Mi)
% 0.31/1.67 % (30191)Instruction limit reached!
% 0.31/1.67 % (30191)------------------------------
% 0.31/1.67 % (30191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.67 % (30191)Termination reason: Unknown
% 0.31/1.67 % (30191)Termination phase: shuffling
% 0.31/1.67
% 0.31/1.67 % (30191)Memory used [KB]: 1663
% 0.31/1.67 % (30191)Time elapsed: 0.003 s
% 0.31/1.67 % (30191)Instructions burned: 5 (million)
% 0.31/1.67 % (30191)------------------------------
% 0.31/1.67 % (30191)------------------------------
% 0.31/1.67 % (30196)Instruction limit reached!
% 0.31/1.67 % (30196)------------------------------
% 0.31/1.67 % (30196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.67 % (30196)Termination reason: Unknown
% 0.31/1.67 % (30196)Termination phase: shuffling
% 0.31/1.67
% 0.31/1.67 % (30196)Memory used [KB]: 1918
% 0.31/1.67 % (30196)Time elapsed: 0.007 s
% 0.31/1.67 % (30196)Instructions burned: 18 (million)
% 0.31/1.67 % (30196)------------------------------
% 0.31/1.67 % (30196)------------------------------
% 0.31/1.67 % (30194)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_30016 for (2999ds/2Mi)
% 0.31/1.68 % (30194)Instruction limit reached!
% 0.31/1.68 % (30194)------------------------------
% 0.31/1.68 % (30194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.68 % (30194)Termination reason: Unknown
% 0.31/1.68 % (30194)Termination phase: shuffling
% 0.31/1.68
% 0.31/1.68 % (30194)Memory used [KB]: 1535
% 0.31/1.68 % (30194)Time elapsed: 0.004 s
% 0.31/1.68 % (30194)Instructions burned: 3 (million)
% 0.31/1.68 % (30194)------------------------------
% 0.31/1.68 % (30194)------------------------------
% 0.31/1.68 % (30197)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30016 for (2999ds/3Mi)
% 0.31/1.68 % (30192)Instruction limit reached!
% 0.31/1.68 % (30192)------------------------------
% 0.31/1.68 % (30192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.68 % (30192)Termination reason: Unknown
% 0.31/1.68 % (30192)Termination phase: Property scanning
% 0.31/1.68
% 0.31/1.68 % (30192)Memory used [KB]: 2046
% 0.31/1.68 % (30192)Time elapsed: 0.011 s
% 0.31/1.68 % (30192)Instructions burned: 29 (million)
% 0.31/1.68 % (30192)------------------------------
% 0.31/1.68 % (30192)------------------------------
% 0.31/1.68 % (30198)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_30016 for (2999ds/37Mi)
% 0.31/1.68 % (30197)Instruction limit reached!
% 0.31/1.68 % (30197)------------------------------
% 0.31/1.68 % (30197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.68 % (30197)Termination reason: Unknown
% 0.31/1.68 % (30197)Termination phase: shuffling
% 0.31/1.68
% 0.31/1.68 % (30197)Memory used [KB]: 1535
% 0.31/1.68 % (30197)Time elapsed: 0.003 s
% 0.31/1.68 % (30197)Instructions burned: 5 (million)
% 0.31/1.68 % (30197)------------------------------
% 0.31/1.68 % (30197)------------------------------
% 0.31/1.68 % (30195)First to succeed.
% 0.31/1.68 % (30199)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_30016 for (2999ds/15Mi)
% 0.31/1.68 % (30195)Refutation found. Thanks to Tanya!
% 0.31/1.68 % SZS status Theorem for DTF2THF_30016
% 0.31/1.68 % SZS output start Proof for DTF2THF_30016
% 0.31/1.68 thf(type_def_5, type, nat: $tType).
% 0.31/1.68 thf(type_def_7, type, set_nat: $tType).
% 0.31/1.68 thf(type_def_8, type, paraco1605129243lle_tv: $tType).
% 0.31/1.68 thf(type_def_9, type, set_Pa1764573435lle_tv: $tType).
% 0.31/1.68 thf(type_def_10, type, product_prod_nat_nat: $tType).
% 0.31/1.68 thf(type_def_11, type, set_Pr1986765409at_nat: $tType).
% 0.31/1.68 thf(type_def_12, type, produc270694976lle_tv: $tType).
% 0.31/1.68 thf(type_def_13, type, set_Pr13445366lle_tv: $tType).
% 0.31/1.68 thf(type_def_14, type, produc194167194tv_nat: $tType).
% 0.31/1.68 thf(type_def_15, type, set_Pr1725653840tv_nat: $tType).
% 0.31/1.68 thf(type_def_16, type, produc1647334210lle_tv: $tType).
% 0.31/1.68 thf(type_def_17, type, set_Pr2014382200lle_tv: $tType).
% 0.31/1.68 thf(type_def_18, type, set_Pr2120184979lle_fm: $tType).
% 0.31/1.68 thf(type_def_19, type, set_Pr560526279lle_tv: $tType).
% 0.31/1.68 thf(type_def_20, type, set_Pr1723822845lle_tv: $tType).
% 0.31/1.68 thf(type_def_21, type, set_Pr840833727at_nat: $tType).
% 0.31/1.68 thf(type_def_22, type, list_char: $tType).
% 0.31/1.68 thf(type_def_23, type, produc931990033lle_tv: $tType).
% 0.31/1.68 thf(type_def_24, type, paraco1604210848lle_fm: $tType).
% 0.31/1.68 thf(type_def_25, type, produc696645085lle_fm: $tType).
% 0.31/1.68 thf(type_def_26, type, produc1443694919lle_tv: $tType).
% 0.31/1.68 thf(type_def_27, type, produc596913417at_nat: $tType).
% 0.31/1.68 thf(func_def_0, type, set_Pr1723822845lle_tv: $tType).
% 0.31/1.68 thf(func_def_1, type, set_Pr2120184979lle_fm: $tType).
% 0.31/1.68 thf(func_def_2, type, produc1443694919lle_tv: $tType).
% 0.31/1.68 thf(func_def_3, type, produc696645085lle_fm: $tType).
% 0.31/1.68 thf(func_def_4, type, set_Pr2014382200lle_tv: $tType).
% 0.31/1.68 thf(func_def_5, type, set_Pr840833727at_nat: $tType).
% 0.31/1.68 thf(func_def_6, type, set_Pr560526279lle_tv: $tType).
% 0.31/1.68 thf(func_def_7, type, produc1647334210lle_tv: $tType).
% 0.31/1.68 thf(func_def_8, type, produc596913417at_nat: $tType).
% 0.31/1.68 thf(func_def_9, type, produc931990033lle_tv: $tType).
% 0.31/1.68 thf(func_def_10, type, set_Pr1725653840tv_nat: $tType).
% 0.31/1.68 thf(func_def_11, type, set_Pr13445366lle_tv: $tType).
% 0.31/1.68 thf(func_def_12, type, produc194167194tv_nat: $tType).
% 0.31/1.68 thf(func_def_13, type, produc270694976lle_tv: $tType).
% 0.31/1.68 thf(func_def_14, type, set_Pr1986765409at_nat: $tType).
% 0.31/1.68 thf(func_def_15, type, set_Pa1764573435lle_tv: $tType).
% 0.31/1.68 thf(func_def_16, type, product_prod_nat_nat: $tType).
% 0.31/1.68 thf(func_def_17, type, paraco1605129243lle_tv: $tType).
% 0.31/1.68 thf(func_def_18, type, paraco1604210848lle_fm: $tType).
% 0.31/1.68 thf(func_def_19, type, list_char: $tType).
% 0.31/1.68 thf(func_def_20, type, set_nat: $tType).
% 0.31/1.68 thf(func_def_21, type, nat: $tType).
% 0.31/1.68 thf(func_def_22, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 0.31/1.68 thf(func_def_23, type, inj_on1955349912lle_tv: (nat > paraco1605129243lle_tv) > set_nat > $o).
% 0.31/1.68 thf(func_def_24, type, inj_on1179712058tv_nat: (paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > $o).
% 0.31/1.68 thf(func_def_25, type, inj_on772319074lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > $o).
% 0.31/1.68 thf(func_def_26, type, inj_on26176689at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > $o).
% 0.31/1.68 thf(func_def_27, type, inj_on1745913142lle_tv: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > $o).
% 0.31/1.68 thf(func_def_28, type, inj_on552895452tv_nat: (produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > $o).
% 0.31/1.68 thf(func_def_29, type, inj_on2112487900lle_tv: (produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > $o).
% 0.31/1.68 thf(func_def_30, type, the_inv_into_nat_nat: set_nat > (nat > nat) > nat > nat).
% 0.31/1.68 thf(func_def_31, type, the_in452116896lle_tv: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_32, type, if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_33, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 0.31/1.68 thf(func_def_34, type, ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o).
% 0.31/1.68 thf(func_def_35, type, ord_le1007985907lle_fm: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > $o).
% 0.31/1.68 thf(func_def_36, type, ord_le1784136743lle_tv: set_Pr560526279lle_tv > set_Pr560526279lle_tv > $o).
% 0.31/1.68 thf(func_def_37, type, top_top_nat_o: nat > $o).
% 0.31/1.68 thf(func_def_38, type, top_to1299250770e_tv_o: paraco1605129243lle_tv > $o).
% 0.31/1.68 thf(func_def_39, type, top_to632227436_nat_o: product_prod_nat_nat > $o).
% 0.31/1.68 thf(func_def_40, type, top_to1889334367e_tv_o: produc270694976lle_tv > $o).
% 0.31/1.68 thf(func_def_41, type, top_to900819589_nat_o: produc194167194tv_nat > $o).
% 0.31/1.68 thf(func_def_43, type, top_top_set_nat: set_nat).
% 0.31/1.68 thf(func_def_44, type, top_to1057771083lle_tv: set_Pa1764573435lle_tv).
% 0.31/1.68 thf(func_def_45, type, top_to775056195lle_fm: set_Pr2120184979lle_fm).
% 0.31/1.68 thf(func_def_46, type, top_to449985143lle_tv: set_Pr560526279lle_tv).
% 0.31/1.68 thf(func_def_47, type, top_to1555900337at_nat: set_Pr1986765409at_nat).
% 0.31/1.68 thf(func_def_48, type, top_to1411004326lle_tv: set_Pr13445366lle_tv).
% 0.31/1.68 thf(func_def_49, type, top_to378694061lle_tv: set_Pr1723822845lle_tv).
% 0.31/1.68 thf(func_def_50, type, top_to730292591at_nat: set_Pr840833727at_nat).
% 0.31/1.68 thf(func_def_51, type, top_to975729152tv_nat: set_Pr1725653840tv_nat).
% 0.31/1.68 thf(func_def_52, type, top_to1871154984lle_tv: set_Pr2014382200lle_tv).
% 0.31/1.68 thf(func_def_53, type, paraco761681009ge_int: (nat > nat) > (list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_54, type, paraco1147068288nge_tv: (nat > nat) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_55, type, paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o).
% 0.31/1.68 thf(func_def_56, type, paraco1325918602e_eval: (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_57, type, paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_58, type, paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_59, type, paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_60, type, paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_61, type, paraco1480028776le_Pro: list_char > paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_62, type, paraco367965286_Truth: paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_63, type, paraco1344940915le_Det: $o > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_64, type, paraco793048302_Indet: nat > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_65, type, paraco2051596139lle_tv: ($o > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_66, type, paraco327635598_valid: paraco1604210848lle_fm > $o).
% 0.31/1.68 thf(func_def_67, type, paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o).
% 0.31/1.68 thf(func_def_68, type, produc1710735575lle_fm: (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > produc696645085lle_fm).
% 0.31/1.68 thf(func_def_69, type, produc1680557635lle_tv: (nat > nat) > paraco1605129243lle_tv > produc931990033lle_tv).
% 0.31/1.68 thf(func_def_70, type, produc1943344577lle_tv: paraco1604210848lle_fm > (list_char > paraco1605129243lle_tv) > produc1443694919lle_tv).
% 0.31/1.68 thf(func_def_71, type, produc1633679363at_nat: paraco1605129243lle_tv > (nat > nat) > produc596913417at_nat).
% 0.31/1.68 thf(func_def_72, type, produc1942165868lle_fm: ((list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv) > produc696645085lle_fm > produc696645085lle_fm).
% 0.31/1.68 thf(func_def_73, type, produc939316703lle_tv: ((nat > nat) > nat > nat) > produc931990033lle_tv > produc931990033lle_tv).
% 0.31/1.68 thf(func_def_74, type, produc1807466521lle_tv: (paraco1604210848lle_fm > paraco1604210848lle_fm) > produc696645085lle_fm > produc696645085lle_fm).
% 0.31/1.68 thf(func_def_75, type, produc109093078at_nat: (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc931990033lle_tv > produc931990033lle_tv).
% 0.31/1.68 thf(func_def_76, type, produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_77, type, produc275353523e_fm_o: (produc696645085lle_fm > $o) > (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > $o).
% 0.31/1.68 thf(func_def_78, type, produc752649287e_tv_o: (produc931990033lle_tv > $o) > (nat > nat) > paraco1605129243lle_tv > $o).
% 0.31/1.68 thf(func_def_79, type, produc1900967599lle_fm: ((list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv) > (paraco1604210848lle_fm > paraco1604210848lle_fm) > produc696645085lle_fm > produc696645085lle_fm).
% 0.31/1.68 thf(func_def_80, type, produc1566550641lle_tv: ((list_char > paraco1605129243lle_tv) > nat > nat) > (paraco1604210848lle_fm > paraco1605129243lle_tv) > produc696645085lle_fm > produc931990033lle_tv).
% 0.31/1.68 thf(func_def_81, type, produc951033137lle_fm: ((nat > nat) > list_char > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1604210848lle_fm) > produc931990033lle_tv > produc696645085lle_fm).
% 0.31/1.68 thf(func_def_82, type, produc532909085lle_tv: ((nat > nat) > nat > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc931990033lle_tv > produc931990033lle_tv).
% 0.31/1.68 thf(func_def_83, type, produc505105722at_nat: (nat > nat) > (nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 0.31/1.68 thf(func_def_84, type, produc313957681lle_tv: (nat > nat) > (nat > paraco1605129243lle_tv) > product_prod_nat_nat > produc270694976lle_tv).
% 0.31/1.68 thf(func_def_85, type, produc1685803475tv_nat: (nat > nat) > (paraco1605129243lle_tv > nat) > produc270694976lle_tv > product_prod_nat_nat).
% 0.31/1.68 thf(func_def_86, type, produc2101297531lle_tv: (nat > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc270694976lle_tv).
% 0.31/1.68 thf(func_def_87, type, produc1250721397at_nat: (nat > paraco1605129243lle_tv) > (nat > nat) > product_prod_nat_nat > produc194167194tv_nat).
% 0.31/1.68 thf(func_def_88, type, produc210389789lle_tv: (nat > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > product_prod_nat_nat > produc1647334210lle_tv).
% 0.31/1.68 thf(func_def_89, type, produc189459613tv_nat: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > produc270694976lle_tv > produc194167194tv_nat).
% 0.31/1.68 thf(func_def_90, type, produc1975500101lle_tv: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc1647334210lle_tv).
% 0.31/1.68 thf(func_def_91, type, produc386540311at_nat: (paraco1605129243lle_tv > nat) > (nat > nat) > produc194167194tv_nat > product_prod_nat_nat).
% 0.31/1.68 thf(func_def_92, type, produc72207551lle_tv: (paraco1605129243lle_tv > nat) > (nat > paraco1605129243lle_tv) > produc194167194tv_nat > produc270694976lle_tv).
% 0.31/1.68 thf(func_def_93, type, produc42536895at_nat: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (nat > nat) > produc194167194tv_nat > produc194167194tv_nat).
% 0.31/1.68 thf(func_def_94, type, produc1345917071lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc1647334210lle_tv > produc1647334210lle_tv).
% 0.31/1.68 thf(func_def_95, type, produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_96, type, produc1636169559lle_tv: produc931990033lle_tv > nat > nat).
% 0.31/1.68 thf(func_def_97, type, produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_98, type, produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_99, type, produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_100, type, produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_101, type, produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_102, type, produc500618325at_nat: produc596913417at_nat > nat > nat).
% 0.31/1.68 thf(func_def_103, type, produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv).
% 0.31/1.68 thf(func_def_104, type, produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat).
% 0.31/1.68 thf(func_def_105, type, produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm).
% 0.31/1.68 thf(func_def_106, type, produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv).
% 0.31/1.68 thf(func_def_107, type, inv_image_nat_nat: set_Pr1986765409at_nat > (nat > nat) > set_Pr1986765409at_nat).
% 0.31/1.68 thf(func_def_108, type, inv_im1292588663lle_tv: set_Pr1986765409at_nat > (paraco1605129243lle_tv > nat) > set_Pr2014382200lle_tv).
% 0.31/1.68 thf(func_def_109, type, inv_im516950809tv_nat: set_Pr2014382200lle_tv > (nat > paraco1605129243lle_tv) > set_Pr1986765409at_nat).
% 0.31/1.68 thf(func_def_110, type, inv_im719552961lle_tv: set_Pr2014382200lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pr2014382200lle_tv).
% 0.31/1.68 thf(func_def_111, type, total_on_nat: set_nat > set_Pr1986765409at_nat > $o).
% 0.31/1.68 thf(func_def_112, type, total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o).
% 0.31/1.68 thf(func_def_113, type, collect_nat: (nat > $o) > set_nat).
% 0.31/1.68 thf(func_def_114, type, collec1111687558lle_tv: (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv).
% 0.31/1.68 thf(func_def_115, type, collec835549234lle_fm: (produc696645085lle_fm > $o) > set_Pr2120184979lle_fm).
% 0.31/1.68 thf(func_def_116, type, collec1624074086lle_tv: (produc931990033lle_tv > $o) > set_Pr560526279lle_tv).
% 0.31/1.68 thf(func_def_117, type, collec7649004at_nat: (product_prod_nat_nat > $o) > set_Pr1986765409at_nat).
% 0.31/1.68 thf(func_def_118, type, collec924990229lle_tv: (produc270694976lle_tv > $o) > set_Pr13445366lle_tv).
% 0.31/1.68 thf(func_def_119, type, collec1582599068lle_tv: (produc1443694919lle_tv > $o) > set_Pr1723822845lle_tv).
% 0.31/1.68 thf(func_def_120, type, collec1288997470at_nat: (produc596913417at_nat > $o) > set_Pr840833727at_nat).
% 0.31/1.68 thf(func_def_121, type, collec848462447tv_nat: (produc194167194tv_nat > $o) > set_Pr1725653840tv_nat).
% 0.31/1.68 thf(func_def_122, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 0.31/1.68 thf(func_def_123, type, image_1151963140lle_tv: (nat > paraco1605129243lle_tv) > set_nat > set_Pa1764573435lle_tv).
% 0.31/1.68 thf(func_def_124, type, image_376325286tv_nat: (paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > set_nat).
% 0.31/1.68 thf(func_def_125, type, image_335818702lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv).
% 0.31/1.68 thf(func_def_126, type, image_807538418lle_fm: (produc696645085lle_fm > produc696645085lle_fm) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm).
% 0.31/1.68 thf(func_def_127, type, image_1154804148lle_tv: (produc696645085lle_fm > produc931990033lle_tv) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv).
% 0.31/1.68 thf(func_def_128, type, image_924970994lle_tv: (produc696645085lle_fm > produc1443694919lle_tv) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv).
% 0.31/1.68 thf(func_def_129, type, image_1585092542lle_fm: (produc931990033lle_tv > produc696645085lle_fm) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm).
% 0.31/1.68 thf(func_def_130, type, image_1751508608lle_tv: (produc931990033lle_tv > produc931990033lle_tv) > set_Pr560526279lle_tv > set_Pr560526279lle_tv).
% 0.31/1.68 thf(func_def_131, type, image_1724396928at_nat: (produc931990033lle_tv > produc596913417at_nat) > set_Pr560526279lle_tv > set_Pr840833727at_nat).
% 0.31/1.68 thf(func_def_132, type, image_815163717at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 0.31/1.68 thf(func_def_133, type, image_1674248956lle_tv: (product_prod_nat_nat > produc270694976lle_tv) > set_Pr1986765409at_nat > set_Pr13445366lle_tv).
% 0.31/1.68 thf(func_def_134, type, image_1597721174tv_nat: (product_prod_nat_nat > produc194167194tv_nat) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat).
% 0.31/1.68 thf(func_def_135, type, image_1507992062lle_tv: (product_prod_nat_nat > produc1647334210lle_tv) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv).
% 0.31/1.68 thf(func_def_136, type, image_1787705850at_nat: (produc270694976lle_tv > product_prod_nat_nat) > set_Pr13445366lle_tv > set_Pr1986765409at_nat).
% 0.31/1.68 thf(func_def_137, type, image_149830562lle_tv: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > set_Pr13445366lle_tv).
% 0.31/1.68 thf(func_def_138, type, image_53754658tv_nat: (produc270694976lle_tv > produc194167194tv_nat) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat).
% 0.31/1.68 thf(func_def_139, type, image_988201162lle_tv: (produc270694976lle_tv > produc1647334210lle_tv) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv).
% 0.31/1.68 thf(func_def_140, type, image_326034184lle_fm: (produc1443694919lle_tv > produc696645085lle_fm) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm).
% 0.31/1.68 thf(func_def_141, type, image_769496456lle_tv: (produc596913417at_nat > produc931990033lle_tv) > set_Pr840833727at_nat > set_Pr560526279lle_tv).
% 0.31/1.68 thf(func_def_142, type, image_1805124128at_nat: (produc194167194tv_nat > product_prod_nat_nat) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat).
% 0.31/1.68 thf(func_def_143, type, image_1200372424lle_tv: (produc194167194tv_nat > produc270694976lle_tv) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv).
% 0.31/1.68 thf(func_def_144, type, accp_P2085826120lle_tv: (produc931990033lle_tv > produc931990033lle_tv > $o) > produc931990033lle_tv > $o).
% 0.31/1.68 thf(func_def_145, type, member_nat: nat > set_nat > $o).
% 0.31/1.68 thf(func_def_146, type, member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o).
% 0.31/1.68 thf(func_def_147, type, member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o).
% 0.31/1.68 thf(func_def_148, type, member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o).
% 0.31/1.68 thf(func_def_149, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 0.31/1.68 thf(func_def_150, type, member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o).
% 0.31/1.68 thf(func_def_151, type, member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o).
% 0.31/1.68 thf(func_def_152, type, member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o).
% 0.31/1.68 thf(func_def_153, type, member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o).
% 0.31/1.68 thf(func_def_154, type, member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o).
% 0.31/1.68 thf(func_def_155, type, f: nat > nat).
% 0.31/1.68 thf(func_def_156, type, i: list_char > paraco1605129243lle_tv).
% 0.31/1.68 thf(func_def_157, type, p1: paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_158, type, p2: paraco1604210848lle_fm).
% 0.31/1.68 thf(func_def_170, type, sK0: (nat > nat) > paraco1605129243lle_tv > paraco1605129243lle_tv > nat).
% 0.31/1.68 thf(func_def_171, type, sK1: paraco1605129243lle_tv > paraco1605129243lle_tv > $o).
% 0.31/1.68 thf(func_def_172, type, sK2: (nat > nat) > nat).
% 0.31/1.68 thf(func_def_173, type, sK3: (nat > nat) > nat).
% 0.31/1.68 thf(func_def_174, type, sK4: (nat > nat) > nat).
% 0.31/1.68 thf(func_def_175, type, sK5: (nat > nat) > nat).
% 0.31/1.68 thf(func_def_177, type, ph7: !>[X0: $tType]:(X0)).
% 0.31/1.68 thf(f938,plain,(
% 0.31/1.68 $false),
% 0.31/1.68 inference(subsumption_resolution,[status(thm)],[f937,f915])).
% 0.31/1.68 thf(f915,plain,(
% 0.31/1.68 ((paraco1147068288nge_tv @ f @ (paraco1325918602e_eval @ i @ p2)) = (paraco1344940915le_Det @ $true))),
% 0.31/1.68 inference(cnf_transformation,[status(thm)],[f378])).
% 0.31/1.68 thf(f378,plain,(
% 0.31/1.68 ((paraco1147068288nge_tv @ f @ (paraco1325918602e_eval @ i @ p2)) = (paraco1344940915le_Det @ $true))),
% 0.31/1.68 inference(fool_elimination,[status(thm)],[f2])).
% 0.31/1.68 thf(f2,axiom,(
% 0.31/1.68 ((paraco1344940915le_Det @ $true) = (paraco1147068288nge_tv @ f @ (paraco1325918602e_eval @ i @ p2)))),
% 0.31/1.68 file('/export/starexec/sandbox2/tmp/tmp.cKDKiLlZzx/DTF2THF_30016.p',fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062)).
% 0.31/1.68 thf(f937,plain,(
% 0.31/1.68 ((paraco1147068288nge_tv @ f @ (paraco1325918602e_eval @ i @ p2)) != (paraco1344940915le_Det @ $true))),
% 0.31/1.68 inference(superposition,[status(thm)],[f936,f935])).
% 0.31/1.68 thf(f935,plain,(
% 0.31/1.68 ((paraco1147068288nge_tv @ f @ (paraco1325918602e_eval @ i @ p2)) = (paraco1325918602e_eval @ (^[Y0 : list_char]: (paraco1147068288nge_tv @ f @ (i @ Y0))) @ p2))),
% 0.31/1.68 inference(beta_eta_normalization,[status(thm)],[f925])).
% 0.31/1.68 thf(f925,plain,(
% 0.31/1.68 ((paraco1147068288nge_tv @ f @ (paraco1325918602e_eval @ i @ p2)) = (paraco1325918602e_eval @ ((^[Y0 : nat > nat]: ((^[Y1 : list_char > paraco1605129243lle_tv]: ((^[Y2 : list_char]: (paraco1147068288nge_tv @ Y0 @ (Y1 @ Y2))))))) @ f @ i) @ p2))),
% 0.31/1.68 inference(definition_unfolding,[status(thm)],[f904,f901])).
% 0.31/1.68 thf(f901,plain,(
% 0.31/1.68 (paraco761681009ge_int = (^[Y0 : nat > nat]: ((^[Y1 : list_char > paraco1605129243lle_tv]: ((^[Y2 : list_char]: (paraco1147068288nge_tv @ Y0 @ (Y1 @ Y2))))))))),
% 0.31/1.68 inference(cnf_transformation,[status(thm)],[f675])).
% 0.31/1.68 thf(f675,plain,(
% 0.31/1.68 (paraco761681009ge_int = (^[Y0 : nat > nat]: ((^[Y1 : list_char > paraco1605129243lle_tv]: ((^[Y2 : list_char]: (paraco1147068288nge_tv @ Y0 @ (Y1 @ Y2))))))))),
% 0.31/1.68 inference(fool_elimination,[status(thm)],[f674])).
% 0.31/1.68 thf(f674,plain,(
% 0.31/1.68 (paraco761681009ge_int = (^[X0 : nat > nat, X1 : list_char > paraco1605129243lle_tv, X2 : list_char] : (paraco1147068288nge_tv @ X0 @ (X1 @ X2))))),
% 0.31/1.68 inference(rectify,[status(thm)],[f8])).
% 0.31/1.68 thf(f8,axiom,(
% 0.31/1.68 (paraco761681009ge_int = (^[X2 : nat > nat, X3 : list_char > paraco1605129243lle_tv, X4 : list_char] : (paraco1147068288nge_tv @ X2 @ (X3 @ X4))))),
% 0.31/1.68 file('/export/starexec/sandbox2/tmp/tmp.cKDKiLlZzx/DTF2THF_30016.p',fact_7_change__int__def)).
% 0.31/1.68 thf(f904,plain,(
% 0.31/1.68 ((paraco1147068288nge_tv @ f @ (paraco1325918602e_eval @ i @ p2)) = (paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2))),
% 0.31/1.68 inference(cnf_transformation,[status(thm)],[f3])).
% 0.31/1.68 thf(f3,axiom,(
% 0.31/1.68 ((paraco1147068288nge_tv @ f @ (paraco1325918602e_eval @ i @ p2)) = (paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2))),
% 0.31/1.68 file('/export/starexec/sandbox2/tmp/tmp.cKDKiLlZzx/DTF2THF_30016.p',fact_2_ih2)).
% 0.31/1.68 thf(f936,plain,(
% 0.31/1.68 ((paraco1325918602e_eval @ (^[Y0 : list_char]: (paraco1147068288nge_tv @ f @ (i @ Y0))) @ p2) != (paraco1344940915le_Det @ $true))),
% 0.31/1.68 inference(beta_eta_normalization,[status(thm)],[f926])).
% 0.31/1.68 thf(f926,plain,(
% 0.31/1.68 ((paraco1344940915le_Det @ $true) != (paraco1325918602e_eval @ ((^[Y0 : nat > nat]: ((^[Y1 : list_char > paraco1605129243lle_tv]: ((^[Y2 : list_char]: (paraco1147068288nge_tv @ Y0 @ (Y1 @ Y2))))))) @ f @ i) @ p2))),
% 0.31/1.68 inference(definition_unfolding,[status(thm)],[f909,f901])).
% 0.31/1.68 thf(f909,plain,(
% 0.31/1.68 ((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) != (paraco1344940915le_Det @ $true))),
% 0.31/1.68 inference(cnf_transformation,[status(thm)],[f869])).
% 0.31/1.68 thf(f869,plain,(
% 0.31/1.68 ((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) != (paraco1344940915le_Det @ $true))),
% 0.31/1.68 inference(flattening,[status(thm)],[f657])).
% 0.31/1.68 thf(f657,plain,(
% 0.31/1.68 ~((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) = (paraco1344940915le_Det @ $true))),
% 0.31/1.68 inference(fool_elimination,[status(thm)],[f360])).
% 0.31/1.68 thf(f360,negated_conjecture,(
% 0.31/1.68 ~((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) = (paraco1344940915le_Det @ $true))),
% 0.31/1.68 inference(negated_conjecture,[status(cth)],[f359])).
% 0.31/1.68 thf(f359,conjecture,(
% 0.31/1.68 ((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) = (paraco1344940915le_Det @ $true))),
% 0.31/1.68 file('/export/starexec/sandbox2/tmp/tmp.cKDKiLlZzx/DTF2THF_30016.p',conj_0)).
% 0.31/1.68 % SZS output end Proof for DTF2THF_30016
% 0.31/1.68 % (30195)------------------------------
% 0.31/1.68 % (30195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.68 % (30195)Termination reason: Refutation
% 0.31/1.68
% 0.31/1.68 % (30195)Memory used [KB]: 6524
% 0.31/1.68 % (30195)Time elapsed: 0.017 s
% 0.31/1.68 % (30195)Instructions burned: 44 (million)
% 0.31/1.68 % (30195)------------------------------
% 0.31/1.68 % (30195)------------------------------
% 0.31/1.68 % (30189)Success in time 0.039 s
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