%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP139^1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:51 AM UTC 2026
% Result : Theorem 3.11s 1.94s
% Output : Refutation 3.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 56 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 207 ( 11 ~; 3 |; 0 &; 149 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 277 ( 273 usr; 12 con; 0-3 aty)
% ( 11 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 36 ( 23 ^; 13 !; 0 ?; 36 :)
% 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,
produc194167194tv_nat: $tType ).
thf(type_def_14,type,
set_Pr13445366lle_tv: $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_set_nat: $tType ).
thf(type_def_19,type,
set_se800614875lle_tv: $tType ).
thf(func_def_0,type,
set_Pr2014382200lle_tv: $tType ).
thf(func_def_1,type,
produc1647334210lle_tv: $tType ).
thf(func_def_2,type,
set_Pr1725653840tv_nat: $tType ).
thf(func_def_3,type,
set_Pr13445366lle_tv: $tType ).
thf(func_def_4,type,
produc194167194tv_nat: $tType ).
thf(func_def_5,type,
produc270694976lle_tv: $tType ).
thf(func_def_6,type,
set_se800614875lle_tv: $tType ).
thf(func_def_7,type,
set_Pr1986765409at_nat: $tType ).
thf(func_def_8,type,
set_Pa1764573435lle_tv: $tType ).
thf(func_def_9,type,
product_prod_nat_nat: $tType ).
thf(func_def_10,type,
paraco1605129243lle_tv: $tType ).
thf(func_def_11,type,
set_set_nat: $tType ).
thf(func_def_12,type,
set_nat: $tType ).
thf(func_def_13,type,
nat: $tType ).
thf(func_def_14,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(func_def_15,type,
inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
thf(func_def_16,type,
inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
thf(func_def_17,type,
inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
thf(func_def_18,type,
inj_on642995232at_nat: ( product_prod_nat_nat > nat ) > set_Pr1986765409at_nat > $o ).
thf(func_def_19,type,
inj_on520021963lle_tv: ( product_prod_nat_nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat > $o ).
thf(func_def_20,type,
inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
thf(func_def_21,type,
inj_on1840679568lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > $o ).
thf(func_def_22,type,
inj_on1764151786tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > $o ).
thf(func_def_23,type,
inj_on936843139tv_nat: ( produc270694976lle_tv > nat ) > set_Pr13445366lle_tv > $o ).
thf(func_def_24,type,
inj_on394919723lle_tv: ( produc270694976lle_tv > paraco1605129243lle_tv ) > set_Pr13445366lle_tv > $o ).
thf(func_def_25,type,
inj_on1954136462at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > $o ).
thf(func_def_26,type,
inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
thf(func_def_27,type,
inj_on808253149at_nat: ( produc194167194tv_nat > nat ) > set_Pr1725653840tv_nat > $o ).
thf(func_def_28,type,
inj_on1612474245lle_tv: ( produc194167194tv_nat > paraco1605129243lle_tv ) > set_Pr1725653840tv_nat > $o ).
thf(func_def_29,type,
inj_on1971554740at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > $o ).
thf(func_def_30,type,
inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
thf(func_def_31,type,
inj_on967082628lle_tv: ( produc194167194tv_nat > produc1647334210lle_tv ) > set_Pr1725653840tv_nat > $o ).
thf(func_def_32,type,
inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
thf(func_def_33,type,
strict2146030304at_nat: ( nat > nat ) > set_nat > $o ).
thf(func_def_34,type,
strict1310998166et_nat: ( nat > set_nat ) > set_nat > $o ).
thf(func_def_35,type,
strict1658340843lle_tv: ( nat > set_Pa1764573435lle_tv ) > set_nat > $o ).
thf(func_def_36,type,
strict1802283670at_nat: ( set_nat > nat ) > set_set_nat > $o ).
thf(func_def_37,type,
strict473775692et_nat: ( set_nat > set_nat ) > set_set_nat > $o ).
thf(func_def_38,type,
strict172559285lle_tv: ( set_nat > set_Pa1764573435lle_tv ) > set_set_nat > $o ).
thf(func_def_39,type,
strict1125660301tv_nat: ( set_Pa1764573435lle_tv > nat ) > set_se800614875lle_tv > $o ).
thf(func_def_40,type,
strict1455779395et_nat: ( set_Pa1764573435lle_tv > set_nat ) > set_se800614875lle_tv > $o ).
thf(func_def_41,type,
strict592849515lle_tv: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_se800614875lle_tv > $o ).
thf(func_def_42,type,
the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
thf(func_def_43,type,
the_in138087638lle_tv: set_nat > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > nat ).
thf(func_def_44,type,
the_in1509933432tv_nat: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > nat ) > nat > paraco1605129243lle_tv ).
thf(func_def_45,type,
the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_46,type,
the_in2068894451at_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_47,type,
the_in744013006lle_tv: set_Pr1986765409at_nat > ( product_prod_nat_nat > produc270694976lle_tv ) > produc270694976lle_tv > product_prod_nat_nat ).
thf(func_def_48,type,
the_in667485224tv_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > produc194167194tv_nat ) > produc194167194tv_nat > product_prod_nat_nat ).
thf(func_def_49,type,
the_in857469900at_nat: set_Pr13445366lle_tv > ( produc270694976lle_tv > product_prod_nat_nat ) > product_prod_nat_nat > produc270694976lle_tv ).
thf(func_def_50,type,
the_in1388677748lle_tv: set_Pr13445366lle_tv > ( produc270694976lle_tv > produc270694976lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
thf(func_def_51,type,
the_in874888178at_nat: set_Pr1725653840tv_nat > ( produc194167194tv_nat > product_prod_nat_nat ) > product_prod_nat_nat > produc194167194tv_nat ).
thf(func_def_52,type,
the_in195660058tv_nat: set_Pr1725653840tv_nat > ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat > produc194167194tv_nat ).
thf(func_def_53,type,
the_in427240730lle_tv: set_Pr2014382200lle_tv > ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
thf(func_def_54,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_55,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_56,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(func_def_57,type,
ord_le727057319lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
thf(func_def_58,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_59,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_60,type,
ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
thf(func_def_61,type,
order_769474267at_nat: ( nat > nat ) > $o ).
thf(func_def_62,type,
top_top_nat_o: nat > $o ).
thf(func_def_63,type,
top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
thf(func_def_64,type,
top_to632227436_nat_o: product_prod_nat_nat > $o ).
thf(func_def_65,type,
top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
thf(func_def_66,type,
top_to900819589_nat_o: produc194167194tv_nat > $o ).
thf(func_def_68,type,
top_top_set_nat: set_nat ).
thf(func_def_69,type,
top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
thf(func_def_70,type,
top_to1555900337at_nat: set_Pr1986765409at_nat ).
thf(func_def_71,type,
top_to1411004326lle_tv: set_Pr13445366lle_tv ).
thf(func_def_72,type,
top_to975729152tv_nat: set_Pr1725653840tv_nat ).
thf(func_def_73,type,
top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
thf(func_def_74,type,
paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_75,type,
paraco793048302_Indet: nat > paraco1605129243lle_tv ).
thf(func_def_76,type,
produc1320959600at_nat: ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_77,type,
produc237097339lle_tv: ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
thf(func_def_78,type,
produc1608943133tv_nat: ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
thf(func_def_79,type,
produc1804670661lle_tv: ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc1647334210lle_tv ).
thf(func_def_80,type,
produc2040316391tv_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
thf(func_def_81,type,
produc1408152463lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
thf(func_def_82,type,
produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_83,type,
produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
thf(func_def_84,type,
produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
thf(func_def_85,type,
produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
thf(func_def_86,type,
produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
thf(func_def_87,type,
produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
thf(func_def_88,type,
produc51277375tv_nat: ( paraco1605129243lle_tv > nat ) > ( paraco1605129243lle_tv > nat ) > produc1647334210lle_tv > product_prod_nat_nat ).
thf(func_def_89,type,
produc1095080935lle_tv: ( paraco1605129243lle_tv > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc270694976lle_tv ).
thf(func_def_90,type,
produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
thf(func_def_91,type,
produc1521089895lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc1647334210lle_tv ).
thf(func_def_92,type,
produc1500159719tv_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc1647334210lle_tv > produc194167194tv_nat ).
thf(func_def_93,type,
produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
thf(func_def_94,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_95,type,
collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(func_def_96,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_97,type,
collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
thf(func_def_98,type,
collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
thf(func_def_99,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_100,type,
image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
thf(func_def_101,type,
image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
thf(func_def_102,type,
image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(func_def_103,type,
image_1397137548at_nat: ( product_prod_nat_nat > nat ) > set_Pr1986765409at_nat > set_nat ).
thf(func_def_104,type,
image_1093035615lle_tv: ( product_prod_nat_nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat > set_Pa1764573435lle_tv ).
thf(func_def_105,type,
image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_106,type,
image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
thf(func_def_107,type,
image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
thf(func_def_108,type,
image_1509856791tv_nat: ( produc270694976lle_tv > nat ) > set_Pr13445366lle_tv > set_nat ).
thf(func_def_109,type,
image_802013119lle_tv: ( produc270694976lle_tv > paraco1605129243lle_tv ) > set_Pr13445366lle_tv > set_Pa1764573435lle_tv ).
thf(func_def_110,type,
image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
thf(func_def_111,type,
image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
thf(func_def_112,type,
image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
thf(func_def_113,type,
image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
thf(func_def_114,type,
image_1381266801at_nat: ( produc194167194tv_nat > nat ) > set_Pr1725653840tv_nat > set_nat ).
thf(func_def_115,type,
image_2019567641lle_tv: ( produc194167194tv_nat > paraco1605129243lle_tv ) > set_Pr1725653840tv_nat > set_Pa1764573435lle_tv ).
thf(func_def_116,type,
image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
thf(func_def_117,type,
image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
thf(func_def_118,type,
image_1104296520tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > set_Pr1725653840tv_nat ).
thf(func_def_119,type,
image_228488944lle_tv: ( produc194167194tv_nat > produc1647334210lle_tv ) > set_Pr1725653840tv_nat > set_Pr2014382200lle_tv ).
thf(func_def_120,type,
image_901203832at_nat: ( produc1647334210lle_tv > product_prod_nat_nat ) > set_Pr2014382200lle_tv > set_Pr1986765409at_nat ).
thf(func_def_121,type,
image_1892891680lle_tv: ( produc1647334210lle_tv > produc270694976lle_tv ) > set_Pr2014382200lle_tv > set_Pr13445366lle_tv ).
thf(func_def_122,type,
image_1796815776tv_nat: ( produc1647334210lle_tv > produc194167194tv_nat ) > set_Pr2014382200lle_tv > set_Pr1725653840tv_nat ).
thf(func_def_123,type,
image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).
thf(func_def_124,type,
member_nat: nat > set_nat > $o ).
thf(func_def_125,type,
member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
thf(func_def_126,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_127,type,
member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
thf(func_def_128,type,
member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
thf(func_def_129,type,
member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
thf(func_def_130,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_131,type,
member1875402276lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv > $o ).
thf(func_def_132,type,
f: nat > nat ).
thf(func_def_147,type,
sK0: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_148,type,
sK1: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_149,type,
sK2: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_150,type,
sK3: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_151,type,
sK4: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_152,type,
sK5: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_153,type,
sK6: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_154,type,
sK7: paraco1605129243lle_tv ).
thf(func_def_155,type,
sK8: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_156,type,
sK9: set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_158,type,
sK11: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(func_def_159,type,
sK12: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_160,type,
sK13: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_161,type,
sK14: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_162,type,
sK15: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_163,type,
sK16: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_164,type,
sK17: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_165,type,
sK18: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_166,type,
sK19: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_167,type,
sK20: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_168,type,
sK21: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_169,type,
sK22: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_170,type,
sK23: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_171,type,
sK24: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_172,type,
sK25: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_173,type,
sK26: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_174,type,
sK27: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_175,type,
sK28: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_176,type,
sK29: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_177,type,
sK30: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_178,type,
sK31: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_179,type,
sK32: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_180,type,
sK33: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_181,type,
sK34: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_182,type,
sK35: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_183,type,
sK36: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_184,type,
sK37: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_185,type,
sK38: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_186,type,
sK39: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_187,type,
sK40: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_188,type,
sK41: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_189,type,
sK42: paraco1605129243lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_190,type,
sK43: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_191,type,
sK44: paraco1605129243lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_192,type,
sK45: paraco1605129243lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_193,type,
sK46: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_194,type,
sK47: paraco1605129243lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(func_def_195,type,
sK48: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_196,type,
sK49: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_197,type,
sK50: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_198,type,
sK51: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_199,type,
sK52: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_200,type,
sK53: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_201,type,
sK54: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_202,type,
sK55: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_203,type,
sK56: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_204,type,
sK57: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_205,type,
sK58: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_206,type,
sK59: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_207,type,
sK60: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_208,type,
sK61: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_209,type,
sK62: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_210,type,
sK63: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_211,type,
sK64: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_212,type,
sK65: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_213,type,
sK66: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_214,type,
sK67: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_215,type,
sK68: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_216,type,
sK69: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_217,type,
sK70: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_218,type,
sK71: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_219,type,
sK72: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_220,type,
sK73: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_221,type,
sK74: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_222,type,
sK75: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_223,type,
sK76: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_224,type,
sK77: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_225,type,
sK78: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_226,type,
sK79: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_227,type,
sK80: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_228,type,
sK81: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_229,type,
sK82: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_230,type,
sK83: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_231,type,
sK84: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_232,type,
sK85: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_233,type,
sK86: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_234,type,
sK87: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_235,type,
sK88: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_236,type,
sK89: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_237,type,
sK90: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_238,type,
sK91: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_239,type,
sK92: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_240,type,
sK93: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_241,type,
sK94: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_242,type,
sK95: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_243,type,
sK96: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_244,type,
sK97: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_245,type,
sK98: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_246,type,
sK99: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_247,type,
sK100: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_248,type,
sK101: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_249,type,
sK102: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_250,type,
sK103: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_251,type,
sK104: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_252,type,
sK105: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_253,type,
sK106: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_254,type,
sK107: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_255,type,
sK108: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_256,type,
sK109: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_257,type,
sK110: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_258,type,
sK111: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_259,type,
sK112: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_260,type,
sK113: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_261,type,
sK114: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_262,type,
sK115: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_263,type,
sK116: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_264,type,
sK117: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_265,type,
sK118: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_266,type,
sK119: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_267,type,
sK120: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_268,type,
sK121: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_269,type,
sK122: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_270,type,
sK123: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_271,type,
sK124: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_272,type,
sK125: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_273,type,
sK126: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_274,type,
sK127: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_275,type,
sK128: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_276,type,
sK129: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_277,type,
sK130: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_278,type,
sK131: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_279,type,
sK132: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_280,type,
sK133: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_281,type,
sK134: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_282,type,
sK135: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_283,type,
sK136: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_284,type,
sK137: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_285,type,
sK138: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_286,type,
sK139: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_287,type,
sK140: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_288,type,
sK141: paraco1605129243lle_tv ).
thf(func_def_289,type,
sK142: paraco1605129243lle_tv ).
thf(func_def_290,type,
sK143: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_291,type,
sK144: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_292,type,
sK145: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_293,type,
sK146: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_294,type,
sK147: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_295,type,
sK148: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).
thf(func_def_296,type,
sK149: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_297,type,
sK150: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_298,type,
sK151: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_299,type,
sK152: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_300,type,
sK153: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_301,type,
sK154: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).
thf(func_def_302,type,
ph155:
!>[X0: $tType] : X0 ).
thf(f3167,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f3166,f3011]) ).
thf(f3011,plain,
sK141 != sK142,
inference(equality_proxy_clausification,[status(thm)],[f3008]) ).
thf(f3008,plain,
( ( sK141 = sK142 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f3006]) ).
thf(f3006,plain,
( ( ( ( paraco1147068288nge_tv @ f @ sK142 )
= ( paraco1147068288nge_tv @ f @ sK141 ) )
=> ( sK141 = sK142 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f3005]) ).
thf(f3005,plain,
( $false
= ( ( member266900804lle_tv @ sK142 @ top_to1057771083lle_tv )
=> ( ( ( paraco1147068288nge_tv @ f @ sK142 )
= ( paraco1147068288nge_tv @ f @ sK141 ) )
=> ( sK141 = sK142 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3004]) ).
thf(f3004,plain,
( $false
= ( ^ [Y0: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y0 @ top_to1057771083lle_tv )
=> ( ( ( paraco1147068288nge_tv @ f @ Y0 )
= ( paraco1147068288nge_tv @ f @ sK141 ) )
=> ( sK141 = Y0 ) ) )
@ sK142 ) ),
inference(sigma_clausification,[status(thm)],[f3002]) ).
thf(f3002,plain,
( $false
= ( !! @ paraco1605129243lle_tv
@ ^ [Y0: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y0 @ top_to1057771083lle_tv )
=> ( ( ( paraco1147068288nge_tv @ f @ Y0 )
= ( paraco1147068288nge_tv @ f @ sK141 ) )
=> ( sK141 = Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f3001]) ).
thf(f3001,plain,
( ( ( member266900804lle_tv @ sK141 @ top_to1057771083lle_tv )
=> ( !! @ paraco1605129243lle_tv
@ ^ [Y0: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y0 @ top_to1057771083lle_tv )
=> ( ( ( paraco1147068288nge_tv @ f @ Y0 )
= ( paraco1147068288nge_tv @ f @ sK141 ) )
=> ( sK141 = Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f3000]) ).
thf(f3000,plain,
( ( ^ [Y0: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y0 @ top_to1057771083lle_tv )
=> ( !! @ paraco1605129243lle_tv
@ ^ [Y1: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y1 @ top_to1057771083lle_tv )
=> ( ( ( paraco1147068288nge_tv @ f @ Y1 )
= ( paraco1147068288nge_tv @ f @ Y0 ) )
=> ( Y0 = Y1 ) ) ) ) )
@ sK141 )
= $false ),
inference(sigma_clausification,[status(thm)],[f2999]) ).
thf(f2999,plain,
( ( !! @ paraco1605129243lle_tv
@ ^ [Y0: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y0 @ top_to1057771083lle_tv )
=> ( !! @ paraco1605129243lle_tv
@ ^ [Y1: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y1 @ top_to1057771083lle_tv )
=> ( ( ( paraco1147068288nge_tv @ f @ Y1 )
= ( paraco1147068288nge_tv @ f @ Y0 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f1124]) ).
thf(f1124,plain,
( $true
!= ( ^ [Y0: paraco1605129243lle_tv > paraco1605129243lle_tv,Y1: set_Pa1764573435lle_tv] :
( !! @ paraco1605129243lle_tv
@ ^ [Y2: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y2 @ Y1 )
=> ( !! @ paraco1605129243lle_tv
@ ^ [Y3: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y3 @ Y1 )
=> ( ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
@ ( paraco1147068288nge_tv @ f )
@ top_to1057771083lle_tv ) ),
inference(definition_unfolding,[status(thm)],[f1074,f1105]) ).
thf(f1105,plain,
( inj_on772319074lle_tv
= ( ^ [Y0: paraco1605129243lle_tv > paraco1605129243lle_tv,Y1: set_Pa1764573435lle_tv] :
( !! @ paraco1605129243lle_tv
@ ^ [Y2: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y2 @ Y1 )
=> ( !! @ paraco1605129243lle_tv
@ ^ [Y3: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y3 @ Y1 )
=> ( ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f890]) ).
thf(f890,plain,
( inj_on772319074lle_tv
= ( ^ [Y0: paraco1605129243lle_tv > paraco1605129243lle_tv,Y1: set_Pa1764573435lle_tv] :
( !! @ paraco1605129243lle_tv
@ ^ [Y2: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y2 @ Y1 )
=> ( !! @ paraco1605129243lle_tv
@ ^ [Y3: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y3 @ Y1 )
=> ( ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f889]) ).
thf(f889,plain,
( ( ^ [X0: paraco1605129243lle_tv > paraco1605129243lle_tv,X1: set_Pa1764573435lle_tv] :
! [X2: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ X2 @ X1 )
=> ! [X3: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ X3 @ X1 )
=> ( ( ( X0 @ X3 )
= ( X0 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
= inj_on772319074lle_tv ),
inference(rectify,[status(thm)],[f61]) ).
thf(f61,axiom,
( ( ^ [X10: paraco1605129243lle_tv > paraco1605129243lle_tv,X11: set_Pa1764573435lle_tv] :
! [X3: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ X3 @ X11 )
=> ! [X8: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ X8 @ X11 )
=> ( ( ( X10 @ X3 )
= ( X10 @ X8 ) )
=> ( X3 = X8 ) ) ) ) )
= inj_on772319074lle_tv ),
file('/export/starexec/sandbox2/tmp/tmp.8VRe1TRbh8/DTF2THF_11108.p',fact_60_inj__on__def) ).
thf(f1074,plain,
( ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv )
!= $true ),
inference(cnf_transformation,[status(thm)],[f993]) ).
thf(f993,plain,
( ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv )
!= $true ),
inference(flattening,[status(thm)],[f438]) ).
thf(f438,plain,
( ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv )
!= $true ),
inference(fool_elimination,[status(thm)],[f437]) ).
thf(f437,plain,
~ ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv,
file('/export/starexec/sandbox2/tmp/tmp.8VRe1TRbh8/DTF2THF_11108.p',conj_0) ).
thf(f3166,plain,
sK141 = sK142,
inference(equality_resolution,[status(thm)],[f3137]) ).
thf(f3137,plain,
! [X0: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ f @ X0 )
!= ( paraco1147068288nge_tv @ f @ sK141 ) )
| ( sK142 = X0 ) ),
inference(superposition,[status(thm)],[f1084,f3010]) ).
thf(f3010,plain,
( ( paraco1147068288nge_tv @ f @ sK142 )
= ( paraco1147068288nge_tv @ f @ sK141 ) ),
inference(equality_proxy_clausification,[status(thm)],[f3009]) ).
thf(f3009,plain,
( ( ( paraco1147068288nge_tv @ f @ sK142 )
= ( paraco1147068288nge_tv @ f @ sK141 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f3006]) ).
thf(f1084,plain,
! [X0: paraco1605129243lle_tv,X1: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ f @ X0 )
!= ( paraco1147068288nge_tv @ f @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f1046]) ).
thf(f1046,plain,
! [X0: paraco1605129243lle_tv,X1: paraco1605129243lle_tv] :
( ( X0 = X1 )
| ( ( paraco1147068288nge_tv @ f @ X0 )
!= ( paraco1147068288nge_tv @ f @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f997]) ).
thf(f997,plain,
! [X0: paraco1605129243lle_tv,X1: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ f @ X0 )
= ( paraco1147068288nge_tv @ f @ X1 ) )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: paraco1605129243lle_tv,X0: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ f @ X0 )
= ( paraco1147068288nge_tv @ f @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.8VRe1TRbh8/DTF2THF_11108.p',fact_0__092_060open_062_092_060And_062tv2_Atv1_O_Achange__tv_Af_Atv1_A_061_Achange__tv_Af_Atv2_A_092_060Longrightarrow_062_Atv1_A_061_Atv2_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP139^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:27:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : ITP139^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.47 % Domain : Interactive Theorem Proving
% 0.30/0.47 % Problem : Sledgehammer Paraconsistency problem prob_881__3274616_1
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Des21]
% 0.30/0.47 % Names : Paraconsistency/prob_881__3274616_1 [Des21]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.30/0.47 % Syntax : Number of formulae : 489 ( 97 unt; 133 typ; 0 def)
% 0.30/0.47 % Number of atoms : 1235 ( 485 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 9 ( 3 avg)
% 0.30/0.47 % Number of connectives : 3051 ( 29 ~; 1 |; 47 &;2368 @)
% 0.30/0.47 % ( 0 <=>; 606 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 14 ( 7 avg)
% 0.30/0.47 % Number of types : 15 ( 14 usr)
% 0.30/0.47 % Number of type conns : 679 ( 679 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 120 ( 119 usr; 7 con; 0-3 aty)
% 0.30/0.47 % Number of variables : 1095 ( 49 ^;1006 !; 40 ?;1095 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:39:29.911
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % Could-be-implicit typings (14)
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.30/0.47 set_Pr2014382200lle_tv: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 produc1647334210lle_tv: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 0.30/0.47 set_Pr1725653840tv_nat: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.30/0.47 set_Pr13445366lle_tv: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.30/0.47 produc194167194tv_nat: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 produc270694976lle_tv: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.30/0.47 set_se800614875lle_tv: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.30/0.47 set_Pr1986765409at_nat: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 set_Pa1764573435lle_tv: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.47 product_prod_nat_nat: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 paraco1605129243lle_tv: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.30/0.47 set_set_nat: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.47 set_nat: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.30/0.47 nat: $tType ).
% 0.30/0.47
% 0.30/0.47 % Explicit typings (119)
% 0.30/0.47 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.47 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.47 inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 0.30/0.47 inj_on642995232at_nat: ( product_prod_nat_nat > nat ) > set_Pr1986765409at_nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 inj_on520021963lle_tv: ( product_prod_nat_nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat > $o ).
% 0.30/0.47
% 0.30/0.47 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,
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% 0.30/0.47
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% 0.30/0.47
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% 0.30/0.47 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Nat__Onat,type,
% 0.30/0.47 inj_on936843139tv_nat: ( produc270694976lle_tv > nat ) > set_Pr13445366lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 inj_on394919723lle_tv: ( produc270694976lle_tv > paraco1605129243lle_tv ) > set_Pr13445366lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 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__Nat__Onat_J,type,
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% 0.30/0.47
% 0.30/0.47 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,
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% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Nat__Onat,type,
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% 0.30/0.47 inj_on1612474245lle_tv: ( produc194167194tv_nat > paraco1605129243lle_tv ) > set_Pr1725653840tv_nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Oinj__on_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,
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% 0.30/0.47
% 0.30/0.47 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,
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% 0.30/0.47
% 0.30/0.47 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__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
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% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
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% 0.30/0.47
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% 0.30/0.47
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% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
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% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
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% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Nat__Onat,type,
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% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.47 strict1455779395et_nat: ( set_Pa1764573435lle_tv > set_nat ) > set_se800614875lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 strict592849515lle_tv: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_se800614875lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 the_in138087638lle_tv: set_nat > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.47 the_in1509933432tv_nat: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > nat ) > nat > paraco1605129243lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.47 the_in2068894451at_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_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,
% 0.30/0.47 the_in744013006lle_tv: set_Pr1986765409at_nat > ( product_prod_nat_nat > produc270694976lle_tv ) > produc270694976lle_tv > product_prod_nat_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_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,
% 0.30/0.47 the_in667485224tv_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > produc194167194tv_nat ) > produc194167194tv_nat > product_prod_nat_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_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,
% 0.30/0.47 the_in857469900at_nat: set_Pr13445366lle_tv > ( produc270694976lle_tv > product_prod_nat_nat ) > product_prod_nat_nat > produc270694976lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_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,
% 0.30/0.47 the_in1388677748lle_tv: set_Pr13445366lle_tv > ( produc270694976lle_tv > produc270694976lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_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,
% 0.30/0.47 the_in874888178at_nat: set_Pr1725653840tv_nat > ( produc194167194tv_nat > product_prod_nat_nat ) > product_prod_nat_nat > produc194167194tv_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_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,
% 0.30/0.47 the_in195660058tv_nat: set_Pr1725653840tv_nat > ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Fun_Othe__inv__into_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,
% 0.30/0.47 the_in427240730lle_tv: set_Pr2014382200lle_tv > ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
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% 0.30/0.47
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% 0.30/0.47
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% 0.30/0.47
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% 0.30/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
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% 0.30/0.47
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% 0.30/0.47
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% 0.30/0.47
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% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 produc1408152463lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.47 produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.47 produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.47 produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.47 produc51277375tv_nat: ( paraco1605129243lle_tv > nat ) > ( paraco1605129243lle_tv > nat ) > produc1647334210lle_tv > product_prod_nat_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 produc1095080935lle_tv: ( paraco1605129243lle_tv > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc270694976lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.47 produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 produc1521089895lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc1647334210lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.47 produc1500159719tv_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc1647334210lle_tv > produc194167194tv_nat ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.30/0.47 collect_nat: ( nat > $o ) > set_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OCollect_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.47 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.30/0.47 collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.47 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.47 image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 0.30/0.47 image_1397137548at_nat: ( product_prod_nat_nat > nat ) > set_Pr1986765409at_nat > set_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 image_1093035615lle_tv: ( product_prod_nat_nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat > set_Pa1764573435lle_tv ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Nat__Onat,type,
% 0.30/0.47 image_1509856791tv_nat: ( produc270694976lle_tv > nat ) > set_Pr13445366lle_tv > set_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 image_802013119lle_tv: ( produc270694976lle_tv > paraco1605129243lle_tv ) > set_Pr13445366lle_tv > set_Pa1764573435lle_tv ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 0.30/0.47 image_1381266801at_nat: ( produc194167194tv_nat > nat ) > set_Pr1725653840tv_nat > set_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 image_2019567641lle_tv: ( produc194167194tv_nat > paraco1605129243lle_tv ) > set_Pr1725653840tv_nat > set_Pa1764573435lle_tv ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
% 0.30/0.47
% 0.30/0.47 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,
% 0.30/0.47 image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_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,
% 0.30/0.47 image_1104296520tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > set_Pr1725653840tv_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 image_228488944lle_tv: ( produc194167194tv_nat > produc1647334210lle_tv ) > set_Pr1725653840tv_nat > set_Pr2014382200lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.47 image_901203832at_nat: ( produc1647334210lle_tv > product_prod_nat_nat ) > set_Pr2014382200lle_tv > set_Pr1986765409at_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 image_1892891680lle_tv: ( produc1647334210lle_tv > produc270694976lle_tv ) > set_Pr2014382200lle_tv > set_Pr13445366lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_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__Nat__Onat_J,type,
% 0.30/0.47 image_1796815776tv_nat: ( produc1647334210lle_tv > produc194167194tv_nat ) > set_Pr2014382200lle_tv > set_Pr1725653840tv_nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oimage_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,
% 0.30/0.47 image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Nat__Onat,type,
% 0.30/0.47 member_nat: nat > set_nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.47 member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.47 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.30/0.47 member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.47 member_set_nat: set_nat > set_set_nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.47 member1875402276lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_f,type,
% 0.30/0.47 f: nat > nat ).
% 0.30/0.47
% 0.30/0.47 % Relevant facts (355)
% 0.30/0.47 thf(fact_0__092_060open_062_092_060And_062tv2_Atv1_O_Achange__tv_Af_Atv1_A_061_Achange__tv_Af_Atv2_A_092_060Longrightarrow_062_Atv1_A_061_Atv2_092_060close_062,axiom,
% 0.30/0.47 ! [Tv1: paraco1605129243lle_tv,Tv2: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( ( paraco1147068288nge_tv @ f @ Tv1 )
% 0.30/0.47 = ( paraco1147068288nge_tv @ f @ Tv2 ) )
% 0.30/0.47 => ( Tv1 = Tv2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % \<open>\<And>tv2 tv1. change_tv f tv1 = change_tv f tv2 \<Longrightarrow> tv1 = tv2\<close>
% 0.30/0.47 thf(fact_1_UNIV__I,axiom,
% 0.30/0.47 ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_I
% 0.30/0.47 thf(fact_2_UNIV__I,axiom,
% 0.30/0.47 ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_I
% 0.30/0.47 thf(fact_3_UNIV__I,axiom,
% 0.30/0.47 ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_I
% 0.30/0.47 thf(fact_4_UNIV__I,axiom,
% 0.30/0.47 ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_I
% 0.30/0.47 thf(fact_5_UNIV__I,axiom,
% 0.30/0.47 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_I
% 0.30/0.47 thf(fact_6_iso__tuple__UNIV__I,axiom,
% 0.30/0.47 ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.30/0.47
% 0.30/0.47 % iso_tuple_UNIV_I
% 0.30/0.47 thf(fact_7_iso__tuple__UNIV__I,axiom,
% 0.30/0.47 ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.30/0.47
% 0.30/0.47 % iso_tuple_UNIV_I
% 0.30/0.47 thf(fact_8_iso__tuple__UNIV__I,axiom,
% 0.30/0.47 ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.30/0.47
% 0.30/0.47 % iso_tuple_UNIV_I
% 0.30/0.47 thf(fact_9_iso__tuple__UNIV__I,axiom,
% 0.30/0.47 ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.30/0.47
% 0.30/0.47 % iso_tuple_UNIV_I
% 0.30/0.47 thf(fact_10_iso__tuple__UNIV__I,axiom,
% 0.30/0.47 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.30/0.47
% 0.30/0.47 % iso_tuple_UNIV_I
% 0.30/0.47 thf(fact_11_top__apply,axiom,
% 0.30/0.47 ( top_to1299250770e_tv_o
% 0.30/0.47 = ( ^ [X2: paraco1605129243lle_tv] : top_top_o ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_apply
% 0.30/0.47 thf(fact_12_top__apply,axiom,
% 0.30/0.47 ( top_top_nat_o
% 0.30/0.47 = ( ^ [X2: nat] : top_top_o ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_apply
% 0.30/0.47 thf(fact_13_injD,axiom,
% 0.30/0.47 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.47 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % injD
% 0.30/0.47 thf(fact_14_injD,axiom,
% 0.30/0.47 ! [F: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % injD
% 0.30/0.47 thf(fact_15_injD,axiom,
% 0.30/0.47 ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.47 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % injD
% 0.30/0.47 thf(fact_16_injD,axiom,
% 0.30/0.47 ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.47 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % injD
% 0.30/0.47 thf(fact_17_injD,axiom,
% 0.30/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.47 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % injD
% 0.30/0.47 thf(fact_18_injD,axiom,
% 0.30/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % injD
% 0.30/0.47 thf(fact_19_injD,axiom,
% 0.30/0.47 ! [F: nat > nat,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % injD
% 0.30/0.47 thf(fact_20_injI,axiom,
% 0.30/0.47 ! [F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.30/0.47 ( ! [X3: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 0.30/0.47 ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) )
% 0.30/0.47 => ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv ) ) ).
% 0.30/0.47
% 0.30/0.47 % injI
% 0.30/0.47 thf(fact_21_injI,axiom,
% 0.30/0.47 ! [F: nat > paraco1605129243lle_tv] :
% 0.30/0.47 ( ! [X3: nat,Y2: nat] :
% 0.30/0.47 ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) )
% 0.30/0.47 => ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 0.30/0.47
% 0.30/0.47 % injI
% 0.30/0.47 thf(fact_22_injI,axiom,
% 0.30/0.47 ! [F: produc194167194tv_nat > produc194167194tv_nat] :
% 0.30/0.47 ( ! [X3: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 0.30/0.47 ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) )
% 0.30/0.47 => ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat ) ) ).
% 0.30/0.47
% 0.30/0.47 % injI
% 0.30/0.47 thf(fact_23_injI,axiom,
% 0.30/0.47 ! [F: produc270694976lle_tv > produc270694976lle_tv] :
% 0.30/0.47 ( ! [X3: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 0.30/0.47 ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) )
% 0.30/0.47 => ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv ) ) ).
% 0.30/0.47
% 0.30/0.47 % injI
% 0.30/0.47 thf(fact_24_injI,axiom,
% 0.30/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.47 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.30/0.47 ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) )
% 0.30/0.47 => ( inj_on26176689at_nat @ F @ top_to1555900337at_nat ) ) ).
% 0.30/0.47
% 0.30/0.47 % injI
% 0.30/0.47 thf(fact_25_injI,axiom,
% 0.30/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.47 ( ! [X3: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) )
% 0.30/0.47 => ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 0.30/0.47
% 0.30/0.47 % injI
% 0.30/0.47 thf(fact_26_injI,axiom,
% 0.30/0.47 ! [F: nat > nat] :
% 0.30/0.47 ( ! [X3: nat,Y2: nat] :
% 0.30/0.47 ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) )
% 0.30/0.47 => ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 0.30/0.47
% 0.30/0.47 % injI
% 0.30/0.47 thf(fact_27_inj__eq,axiom,
% 0.30/0.47 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.47 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_eq
% 0.30/0.47 thf(fact_28_inj__eq,axiom,
% 0.30/0.47 ! [F: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_eq
% 0.30/0.47 thf(fact_29_inj__eq,axiom,
% 0.30/0.47 ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.47 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_eq
% 0.30/0.47 thf(fact_30_inj__eq,axiom,
% 0.30/0.47 ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.47 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_eq
% 0.30/0.47 thf(fact_31_inj__eq,axiom,
% 0.30/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.47 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_eq
% 0.30/0.47 thf(fact_32_inj__eq,axiom,
% 0.30/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_eq
% 0.30/0.47 thf(fact_33_inj__eq,axiom,
% 0.30/0.47 ! [F: nat > nat,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_eq
% 0.30/0.47 thf(fact_34_inj__def,axiom,
% 0.30/0.47 ! [F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.30/0.47 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 0.30/0.47 = ( ! [X2: produc1647334210lle_tv,Y3: produc1647334210lle_tv] :
% 0.30/0.47 ( ( ( F @ X2 )
% 0.30/0.47 = ( F @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_def
% 0.30/0.47 thf(fact_35_inj__def,axiom,
% 0.30/0.47 ! [F: nat > paraco1605129243lle_tv] :
% 0.30/0.47 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.47 = ( ! [X2: nat,Y3: nat] :
% 0.30/0.47 ( ( ( F @ X2 )
% 0.30/0.47 = ( F @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_def
% 0.30/0.47 thf(fact_36_inj__def,axiom,
% 0.30/0.47 ! [F: produc194167194tv_nat > produc194167194tv_nat] :
% 0.30/0.47 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 0.30/0.47 = ( ! [X2: produc194167194tv_nat,Y3: produc194167194tv_nat] :
% 0.30/0.47 ( ( ( F @ X2 )
% 0.30/0.47 = ( F @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_def
% 0.30/0.47 thf(fact_37_inj__def,axiom,
% 0.30/0.47 ! [F: produc270694976lle_tv > produc270694976lle_tv] :
% 0.30/0.47 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.47 = ( ! [X2: produc270694976lle_tv,Y3: produc270694976lle_tv] :
% 0.30/0.47 ( ( ( F @ X2 )
% 0.30/0.47 = ( F @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_def
% 0.30/0.47 thf(fact_38_inj__def,axiom,
% 0.30/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.47 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.47 = ( ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.30/0.47 ( ( ( F @ X2 )
% 0.30/0.47 = ( F @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_def
% 0.30/0.47 thf(fact_39_inj__def,axiom,
% 0.30/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.47 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47 = ( ! [X2: paraco1605129243lle_tv,Y3: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( ( F @ X2 )
% 0.30/0.47 = ( F @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_def
% 0.30/0.47 thf(fact_40_inj__def,axiom,
% 0.30/0.47 ! [F: nat > nat] :
% 0.30/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47 = ( ! [X2: nat,Y3: nat] :
% 0.30/0.47 ( ( ( F @ X2 )
% 0.30/0.47 = ( F @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_def
% 0.30/0.47 thf(fact_41_inj__onD,axiom,
% 0.30/0.47 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.47 ( ( inj_on2112487900lle_tv @ F @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( ( member1531318361lle_tv @ X @ A )
% 0.30/0.47 => ( ( member1531318361lle_tv @ Y @ A )
% 0.30/0.47 => ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onD
% 0.30/0.47 thf(fact_42_inj__onD,axiom,
% 0.30/0.47 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.47 ( ( inj_on552895452tv_nat @ F @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( ( member737151281tv_nat @ X @ A )
% 0.30/0.47 => ( ( member737151281tv_nat @ Y @ A )
% 0.30/0.47 => ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onD
% 0.30/0.47 thf(fact_43_inj__onD,axiom,
% 0.30/0.47 ! [F: produc270694976lle_tv > produc270694976lle_tv,A: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.47 ( ( inj_on1745913142lle_tv @ F @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( ( member813679063lle_tv @ X @ A )
% 0.30/0.47 => ( ( member813679063lle_tv @ Y @ A )
% 0.30/0.47 => ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onD
% 0.30/0.47 thf(fact_44_inj__onD,axiom,
% 0.30/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.47 ( ( inj_on26176689at_nat @ F @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( ( member701585322at_nat @ X @ A )
% 0.30/0.47 => ( ( member701585322at_nat @ Y @ A )
% 0.30/0.47 => ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onD
% 0.30/0.47 thf(fact_45_inj__onD,axiom,
% 0.30/0.47 ! [F: nat > paraco1605129243lle_tv,A: set_nat,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on1955349912lle_tv @ F @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( ( member_nat @ X @ A )
% 0.30/0.47 => ( ( member_nat @ Y @ A )
% 0.30/0.47 => ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onD
% 0.30/0.47 thf(fact_46_inj__onD,axiom,
% 0.30/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( ( member266900804lle_tv @ X @ A )
% 0.30/0.47 => ( ( member266900804lle_tv @ Y @ A )
% 0.30/0.47 => ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onD
% 0.30/0.47 thf(fact_47_inj__onD,axiom,
% 0.30/0.47 ! [F: nat > nat,A: set_nat,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 => ( ( member_nat @ X @ A )
% 0.30/0.47 => ( ( member_nat @ Y @ A )
% 0.30/0.47 => ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onD
% 0.30/0.47 thf(fact_48_inj__onI,axiom,
% 0.30/0.47 ! [A: set_Pr2014382200lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.30/0.47 ( ! [X3: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 0.30/0.47 ( ( member1531318361lle_tv @ X3 @ A )
% 0.30/0.47 => ( ( member1531318361lle_tv @ Y2 @ A )
% 0.30/0.47 => ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) ) ) )
% 0.30/0.47 => ( inj_on2112487900lle_tv @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onI
% 0.30/0.47 thf(fact_49_inj__onI,axiom,
% 0.30/0.47 ! [A: set_Pr1725653840tv_nat,F: produc194167194tv_nat > produc194167194tv_nat] :
% 0.30/0.47 ( ! [X3: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 0.30/0.47 ( ( member737151281tv_nat @ X3 @ A )
% 0.30/0.47 => ( ( member737151281tv_nat @ Y2 @ A )
% 0.30/0.47 => ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) ) ) )
% 0.30/0.47 => ( inj_on552895452tv_nat @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onI
% 0.30/0.47 thf(fact_50_inj__onI,axiom,
% 0.30/0.47 ! [A: set_Pr13445366lle_tv,F: produc270694976lle_tv > produc270694976lle_tv] :
% 0.30/0.47 ( ! [X3: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 0.30/0.47 ( ( member813679063lle_tv @ X3 @ A )
% 0.30/0.47 => ( ( member813679063lle_tv @ Y2 @ A )
% 0.30/0.47 => ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) ) ) )
% 0.30/0.47 => ( inj_on1745913142lle_tv @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onI
% 0.30/0.47 thf(fact_51_inj__onI,axiom,
% 0.30/0.47 ! [A: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.47 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.30/0.47 ( ( member701585322at_nat @ X3 @ A )
% 0.30/0.47 => ( ( member701585322at_nat @ Y2 @ A )
% 0.30/0.47 => ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) ) ) )
% 0.30/0.47 => ( inj_on26176689at_nat @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onI
% 0.30/0.47 thf(fact_52_inj__onI,axiom,
% 0.30/0.47 ! [A: set_nat,F: nat > paraco1605129243lle_tv] :
% 0.30/0.47 ( ! [X3: nat,Y2: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 => ( ( member_nat @ Y2 @ A )
% 0.30/0.47 => ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) ) ) )
% 0.30/0.47 => ( inj_on1955349912lle_tv @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onI
% 0.30/0.47 thf(fact_53_inj__onI,axiom,
% 0.30/0.47 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.47 ( ! [X3: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( member266900804lle_tv @ X3 @ A )
% 0.30/0.47 => ( ( member266900804lle_tv @ Y2 @ A )
% 0.30/0.47 => ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) ) ) )
% 0.30/0.47 => ( inj_on772319074lle_tv @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onI
% 0.30/0.47 thf(fact_54_inj__onI,axiom,
% 0.30/0.47 ! [A: set_nat,F: nat > nat] :
% 0.30/0.47 ( ! [X3: nat,Y2: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 => ( ( member_nat @ Y2 @ A )
% 0.30/0.47 => ( ( ( F @ X3 )
% 0.30/0.47 = ( F @ Y2 ) )
% 0.30/0.47 => ( X3 = Y2 ) ) ) )
% 0.30/0.47 => ( inj_on_nat_nat @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_onI
% 0.30/0.47 thf(fact_55_inj__on__def,axiom,
% 0.30/0.47 ( inj_on2112487900lle_tv
% 0.30/0.47 = ( ^ [F2: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv] :
% 0.30/0.47 ! [X2: produc1647334210lle_tv] :
% 0.30/0.47 ( ( member1531318361lle_tv @ X2 @ A2 )
% 0.30/0.47 => ! [Y3: produc1647334210lle_tv] :
% 0.30/0.47 ( ( member1531318361lle_tv @ Y3 @ A2 )
% 0.30/0.47 => ( ( ( F2 @ X2 )
% 0.30/0.47 = ( F2 @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_def
% 0.30/0.47 thf(fact_56_inj__on__def,axiom,
% 0.30/0.47 ( inj_on552895452tv_nat
% 0.30/0.47 = ( ^ [F2: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat] :
% 0.30/0.47 ! [X2: produc194167194tv_nat] :
% 0.30/0.47 ( ( member737151281tv_nat @ X2 @ A2 )
% 0.30/0.47 => ! [Y3: produc194167194tv_nat] :
% 0.30/0.47 ( ( member737151281tv_nat @ Y3 @ A2 )
% 0.30/0.47 => ( ( ( F2 @ X2 )
% 0.30/0.47 = ( F2 @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_def
% 0.30/0.47 thf(fact_57_inj__on__def,axiom,
% 0.30/0.47 ( inj_on1745913142lle_tv
% 0.30/0.47 = ( ^ [F2: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv] :
% 0.30/0.47 ! [X2: produc270694976lle_tv] :
% 0.30/0.47 ( ( member813679063lle_tv @ X2 @ A2 )
% 0.30/0.47 => ! [Y3: produc270694976lle_tv] :
% 0.30/0.47 ( ( member813679063lle_tv @ Y3 @ A2 )
% 0.30/0.47 => ( ( ( F2 @ X2 )
% 0.30/0.47 = ( F2 @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_def
% 0.30/0.47 thf(fact_58_inj__on__def,axiom,
% 0.30/0.47 ( inj_on26176689at_nat
% 0.30/0.47 = ( ^ [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.30/0.47 ! [X2: product_prod_nat_nat] :
% 0.30/0.47 ( ( member701585322at_nat @ X2 @ A2 )
% 0.30/0.47 => ! [Y3: product_prod_nat_nat] :
% 0.30/0.47 ( ( member701585322at_nat @ Y3 @ A2 )
% 0.30/0.47 => ( ( ( F2 @ X2 )
% 0.30/0.47 = ( F2 @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_def
% 0.30/0.47 thf(fact_59_inj__on__def,axiom,
% 0.30/0.47 ( inj_on1955349912lle_tv
% 0.30/0.47 = ( ^ [F2: nat > paraco1605129243lle_tv,A2: set_nat] :
% 0.30/0.47 ! [X2: nat] :
% 0.30/0.47 ( ( member_nat @ X2 @ A2 )
% 0.30/0.47 => ! [Y3: nat] :
% 0.30/0.47 ( ( member_nat @ Y3 @ A2 )
% 0.30/0.47 => ( ( ( F2 @ X2 )
% 0.30/0.47 = ( F2 @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_def
% 0.30/0.47 thf(fact_60_inj__on__def,axiom,
% 0.30/0.47 ( inj_on772319074lle_tv
% 0.30/0.47 = ( ^ [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.30/0.47 ! [X2: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( member266900804lle_tv @ X2 @ A2 )
% 0.30/0.47 => ! [Y3: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( member266900804lle_tv @ Y3 @ A2 )
% 0.30/0.47 => ( ( ( F2 @ X2 )
% 0.30/0.47 = ( F2 @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_def
% 0.30/0.47 thf(fact_61_inj__on__def,axiom,
% 0.30/0.47 ( inj_on_nat_nat
% 0.30/0.47 = ( ^ [F2: nat > nat,A2: set_nat] :
% 0.30/0.47 ! [X2: nat] :
% 0.30/0.47 ( ( member_nat @ X2 @ A2 )
% 0.30/0.47 => ! [Y3: nat] :
% 0.30/0.47 ( ( member_nat @ Y3 @ A2 )
% 0.30/0.47 => ( ( ( F2 @ X2 )
% 0.30/0.47 = ( F2 @ Y3 ) )
% 0.30/0.47 => ( X2 = Y3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_def
% 0.30/0.47 thf(fact_62_inj__on__cong,axiom,
% 0.30/0.47 ! [A: set_Pr2014382200lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.30/0.47 ( ! [A3: produc1647334210lle_tv] :
% 0.30/0.47 ( ( member1531318361lle_tv @ A3 @ A )
% 0.30/0.47 => ( ( F @ A3 )
% 0.30/0.47 = ( G @ A3 ) ) )
% 0.30/0.47 => ( ( inj_on2112487900lle_tv @ F @ A )
% 0.30/0.47 = ( inj_on2112487900lle_tv @ G @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_cong
% 0.30/0.47 thf(fact_63_inj__on__cong,axiom,
% 0.30/0.47 ! [A: set_Pr1725653840tv_nat,F: produc194167194tv_nat > produc194167194tv_nat,G: produc194167194tv_nat > produc194167194tv_nat] :
% 0.30/0.47 ( ! [A3: produc194167194tv_nat] :
% 0.30/0.47 ( ( member737151281tv_nat @ A3 @ A )
% 0.30/0.47 => ( ( F @ A3 )
% 0.30/0.47 = ( G @ A3 ) ) )
% 0.30/0.47 => ( ( inj_on552895452tv_nat @ F @ A )
% 0.30/0.47 = ( inj_on552895452tv_nat @ G @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_cong
% 0.30/0.47 thf(fact_64_inj__on__cong,axiom,
% 0.30/0.47 ! [A: set_Pr13445366lle_tv,F: produc270694976lle_tv > produc270694976lle_tv,G: produc270694976lle_tv > produc270694976lle_tv] :
% 0.30/0.47 ( ! [A3: produc270694976lle_tv] :
% 0.30/0.47 ( ( member813679063lle_tv @ A3 @ A )
% 0.30/0.47 => ( ( F @ A3 )
% 0.30/0.47 = ( G @ A3 ) ) )
% 0.30/0.47 => ( ( inj_on1745913142lle_tv @ F @ A )
% 0.30/0.47 = ( inj_on1745913142lle_tv @ G @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_cong
% 0.30/0.47 thf(fact_65_inj__on__cong,axiom,
% 0.30/0.47 ! [A: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.47 ( ! [A3: product_prod_nat_nat] :
% 0.30/0.47 ( ( member701585322at_nat @ A3 @ A )
% 0.30/0.47 => ( ( F @ A3 )
% 0.30/0.47 = ( G @ A3 ) ) )
% 0.30/0.47 => ( ( inj_on26176689at_nat @ F @ A )
% 0.30/0.47 = ( inj_on26176689at_nat @ G @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_cong
% 0.30/0.47 thf(fact_66_inj__on__cong,axiom,
% 0.30/0.47 ! [A: set_nat,F: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.30/0.47 ( ! [A3: nat] :
% 0.30/0.47 ( ( member_nat @ A3 @ A )
% 0.30/0.47 => ( ( F @ A3 )
% 0.30/0.47 = ( G @ A3 ) ) )
% 0.30/0.47 => ( ( inj_on1955349912lle_tv @ F @ A )
% 0.30/0.47 = ( inj_on1955349912lle_tv @ G @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_cong
% 0.30/0.47 thf(fact_67_inj__on__cong,axiom,
% 0.30/0.47 ! [A: set_nat,F: nat > nat,G: nat > nat] :
% 0.30/0.47 ( ! [A3: nat] :
% 0.30/0.47 ( ( member_nat @ A3 @ A )
% 0.30/0.47 => ( ( F @ A3 )
% 0.30/0.47 = ( G @ A3 ) ) )
% 0.30/0.47 => ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.47 = ( inj_on_nat_nat @ G @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_cong
% 0.30/0.47 thf(fact_68_inj__on__cong,axiom,
% 0.30/0.47 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.47 ( ! [A3: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( member266900804lle_tv @ A3 @ A )
% 0.30/0.47 => ( ( F @ A3 )
% 0.30/0.47 = ( G @ A3 ) ) )
% 0.30/0.47 => ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.47 = ( inj_on772319074lle_tv @ G @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_cong
% 0.30/0.47 thf(fact_69_inj__on__eq__iff,axiom,
% 0.30/0.47 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.47 ( ( inj_on2112487900lle_tv @ F @ A )
% 0.30/0.47 => ( ( member1531318361lle_tv @ X @ A )
% 0.30/0.47 => ( ( member1531318361lle_tv @ Y @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_eq_iff
% 0.30/0.47 thf(fact_70_inj__on__eq__iff,axiom,
% 0.30/0.47 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.47 ( ( inj_on552895452tv_nat @ F @ A )
% 0.30/0.47 => ( ( member737151281tv_nat @ X @ A )
% 0.30/0.47 => ( ( member737151281tv_nat @ Y @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_eq_iff
% 0.30/0.47 thf(fact_71_inj__on__eq__iff,axiom,
% 0.30/0.47 ! [F: produc270694976lle_tv > produc270694976lle_tv,A: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.47 ( ( inj_on1745913142lle_tv @ F @ A )
% 0.30/0.47 => ( ( member813679063lle_tv @ X @ A )
% 0.30/0.47 => ( ( member813679063lle_tv @ Y @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_eq_iff
% 0.30/0.47 thf(fact_72_inj__on__eq__iff,axiom,
% 0.30/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.47 ( ( inj_on26176689at_nat @ F @ A )
% 0.30/0.47 => ( ( member701585322at_nat @ X @ A )
% 0.30/0.47 => ( ( member701585322at_nat @ Y @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_eq_iff
% 0.30/0.47 thf(fact_73_inj__on__eq__iff,axiom,
% 0.30/0.47 ! [F: nat > paraco1605129243lle_tv,A: set_nat,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on1955349912lle_tv @ F @ A )
% 0.30/0.47 => ( ( member_nat @ X @ A )
% 0.30/0.47 => ( ( member_nat @ Y @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_eq_iff
% 0.30/0.47 thf(fact_74_inj__on__eq__iff,axiom,
% 0.30/0.47 ! [F: nat > nat,A: set_nat,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.47 => ( ( member_nat @ X @ A )
% 0.30/0.47 => ( ( member_nat @ Y @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_eq_iff
% 0.30/0.47 thf(fact_75_inj__on__eq__iff,axiom,
% 0.30/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.47 => ( ( member266900804lle_tv @ X @ A )
% 0.30/0.47 => ( ( member266900804lle_tv @ Y @ A )
% 0.30/0.47 => ( ( ( F @ X )
% 0.30/0.47 = ( F @ Y ) )
% 0.30/0.47 = ( X = Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_eq_iff
% 0.30/0.47 thf(fact_76_assms,axiom,
% 0.30/0.47 inj_on_nat_nat @ f @ top_top_set_nat ).
% 0.30/0.47
% 0.30/0.47 % assms
% 0.30/0.47 thf(fact_77_top__set__def,axiom,
% 0.30/0.47 ( top_to975729152tv_nat
% 0.30/0.47 = ( collec848462447tv_nat @ top_to900819589_nat_o ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_set_def
% 0.30/0.47 thf(fact_78_top__set__def,axiom,
% 0.30/0.47 ( top_to1411004326lle_tv
% 0.30/0.47 = ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_set_def
% 0.30/0.47 thf(fact_79_top__set__def,axiom,
% 0.30/0.47 ( top_to1555900337at_nat
% 0.30/0.47 = ( collec7649004at_nat @ top_to632227436_nat_o ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_set_def
% 0.30/0.47 thf(fact_80_top__set__def,axiom,
% 0.30/0.47 ( top_to1057771083lle_tv
% 0.30/0.47 = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_set_def
% 0.30/0.47 thf(fact_81_top__set__def,axiom,
% 0.30/0.47 ( top_top_set_nat
% 0.30/0.47 = ( collect_nat @ top_top_nat_o ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_set_def
% 0.30/0.47 thf(fact_82_UNIV__witness,axiom,
% 0.30/0.47 ? [X3: produc194167194tv_nat] : ( member737151281tv_nat @ X3 @ top_to975729152tv_nat ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_witness
% 0.30/0.47 thf(fact_83_UNIV__witness,axiom,
% 0.30/0.47 ? [X3: produc270694976lle_tv] : ( member813679063lle_tv @ X3 @ top_to1411004326lle_tv ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_witness
% 0.30/0.47 thf(fact_84_UNIV__witness,axiom,
% 0.30/0.47 ? [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ top_to1555900337at_nat ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_witness
% 0.30/0.47 thf(fact_85_UNIV__witness,axiom,
% 0.30/0.47 ? [X3: paraco1605129243lle_tv] : ( member266900804lle_tv @ X3 @ top_to1057771083lle_tv ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_witness
% 0.30/0.47 thf(fact_86_UNIV__witness,axiom,
% 0.30/0.47 ? [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_witness
% 0.30/0.47 thf(fact_87_UNIV__eq__I,axiom,
% 0.30/0.47 ! [A: set_Pr1725653840tv_nat] :
% 0.30/0.47 ( ! [X3: produc194167194tv_nat] : ( member737151281tv_nat @ X3 @ A )
% 0.30/0.47 => ( top_to975729152tv_nat = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_eq_I
% 0.30/0.47 thf(fact_88_UNIV__eq__I,axiom,
% 0.30/0.47 ! [A: set_Pr13445366lle_tv] :
% 0.30/0.47 ( ! [X3: produc270694976lle_tv] : ( member813679063lle_tv @ X3 @ A )
% 0.30/0.47 => ( top_to1411004326lle_tv = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_eq_I
% 0.30/0.47 thf(fact_89_UNIV__eq__I,axiom,
% 0.30/0.47 ! [A: set_Pr1986765409at_nat] :
% 0.30/0.47 ( ! [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ A )
% 0.30/0.47 => ( top_to1555900337at_nat = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_eq_I
% 0.30/0.47 thf(fact_90_UNIV__eq__I,axiom,
% 0.30/0.47 ! [A: set_Pa1764573435lle_tv] :
% 0.30/0.47 ( ! [X3: paraco1605129243lle_tv] : ( member266900804lle_tv @ X3 @ A )
% 0.30/0.47 => ( top_to1057771083lle_tv = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_eq_I
% 0.30/0.47 thf(fact_91_UNIV__eq__I,axiom,
% 0.30/0.47 ! [A: set_nat] :
% 0.30/0.47 ( ! [X3: nat] : ( member_nat @ X3 @ A )
% 0.30/0.47 => ( top_top_set_nat = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % UNIV_eq_I
% 0.30/0.47 thf(fact_92_inj__on__inverseI,axiom,
% 0.30/0.47 ! [A: set_Pr2014382200lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.30/0.47 ( ! [X3: produc1647334210lle_tv] :
% 0.30/0.47 ( ( member1531318361lle_tv @ X3 @ A )
% 0.30/0.47 => ( ( G @ ( F @ X3 ) )
% 0.30/0.47 = X3 ) )
% 0.30/0.47 => ( inj_on2112487900lle_tv @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_inverseI
% 0.30/0.47 thf(fact_93_inj__on__inverseI,axiom,
% 0.30/0.47 ! [A: set_Pr1725653840tv_nat,G: produc194167194tv_nat > produc194167194tv_nat,F: produc194167194tv_nat > produc194167194tv_nat] :
% 0.30/0.47 ( ! [X3: produc194167194tv_nat] :
% 0.30/0.47 ( ( member737151281tv_nat @ X3 @ A )
% 0.30/0.47 => ( ( G @ ( F @ X3 ) )
% 0.30/0.47 = X3 ) )
% 0.30/0.47 => ( inj_on552895452tv_nat @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_inverseI
% 0.30/0.47 thf(fact_94_inj__on__inverseI,axiom,
% 0.30/0.47 ! [A: set_Pr13445366lle_tv,G: produc270694976lle_tv > produc270694976lle_tv,F: produc270694976lle_tv > produc270694976lle_tv] :
% 0.30/0.47 ( ! [X3: produc270694976lle_tv] :
% 0.30/0.47 ( ( member813679063lle_tv @ X3 @ A )
% 0.30/0.47 => ( ( G @ ( F @ X3 ) )
% 0.30/0.47 = X3 ) )
% 0.30/0.47 => ( inj_on1745913142lle_tv @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_inverseI
% 0.30/0.47 thf(fact_95_inj__on__inverseI,axiom,
% 0.30/0.47 ! [A: set_Pr1986765409at_nat,G: product_prod_nat_nat > product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.47 ( ! [X3: product_prod_nat_nat] :
% 0.30/0.47 ( ( member701585322at_nat @ X3 @ A )
% 0.30/0.47 => ( ( G @ ( F @ X3 ) )
% 0.30/0.47 = X3 ) )
% 0.30/0.47 => ( inj_on26176689at_nat @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_inverseI
% 0.30/0.47 thf(fact_96_inj__on__inverseI,axiom,
% 0.30/0.47 ! [A: set_nat,G: paraco1605129243lle_tv > nat,F: nat > paraco1605129243lle_tv] :
% 0.30/0.47 ( ! [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 => ( ( G @ ( F @ X3 ) )
% 0.30/0.47 = X3 ) )
% 0.30/0.47 => ( inj_on1955349912lle_tv @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_inverseI
% 0.30/0.47 thf(fact_97_inj__on__inverseI,axiom,
% 0.30/0.47 ! [A: set_nat,G: nat > nat,F: nat > nat] :
% 0.30/0.47 ( ! [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 => ( ( G @ ( F @ X3 ) )
% 0.30/0.47 = X3 ) )
% 0.30/0.47 => ( inj_on_nat_nat @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_inverseI
% 0.30/0.47 thf(fact_98_inj__on__inverseI,axiom,
% 0.30/0.47 ! [A: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.47 ( ! [X3: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( member266900804lle_tv @ X3 @ A )
% 0.30/0.47 => ( ( G @ ( F @ X3 ) )
% 0.30/0.47 = X3 ) )
% 0.30/0.47 => ( inj_on772319074lle_tv @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_inverseI
% 0.30/0.47 thf(fact_99_inj__on__contraD,axiom,
% 0.30/0.47 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.47 ( ( inj_on2112487900lle_tv @ F @ A )
% 0.30/0.47 => ( ( X != Y )
% 0.30/0.47 => ( ( member1531318361lle_tv @ X @ A )
% 0.30/0.47 => ( ( member1531318361lle_tv @ Y @ A )
% 0.30/0.47 => ( ( F @ X )
% 0.30/0.47 != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_contraD
% 0.30/0.47 thf(fact_100_inj__on__contraD,axiom,
% 0.30/0.47 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.47 ( ( inj_on552895452tv_nat @ F @ A )
% 0.30/0.47 => ( ( X != Y )
% 0.30/0.47 => ( ( member737151281tv_nat @ X @ A )
% 0.30/0.47 => ( ( member737151281tv_nat @ Y @ A )
% 0.30/0.47 => ( ( F @ X )
% 0.30/0.47 != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_contraD
% 0.30/0.47 thf(fact_101_inj__on__contraD,axiom,
% 0.30/0.47 ! [F: produc270694976lle_tv > produc270694976lle_tv,A: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.47 ( ( inj_on1745913142lle_tv @ F @ A )
% 0.30/0.47 => ( ( X != Y )
% 0.30/0.47 => ( ( member813679063lle_tv @ X @ A )
% 0.30/0.47 => ( ( member813679063lle_tv @ Y @ A )
% 0.30/0.47 => ( ( F @ X )
% 0.30/0.47 != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_contraD
% 0.30/0.47 thf(fact_102_inj__on__contraD,axiom,
% 0.30/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.47 ( ( inj_on26176689at_nat @ F @ A )
% 0.30/0.47 => ( ( X != Y )
% 0.30/0.47 => ( ( member701585322at_nat @ X @ A )
% 0.30/0.47 => ( ( member701585322at_nat @ Y @ A )
% 0.30/0.47 => ( ( F @ X )
% 0.30/0.47 != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_contraD
% 0.30/0.47 thf(fact_103_inj__on__contraD,axiom,
% 0.30/0.47 ! [F: nat > paraco1605129243lle_tv,A: set_nat,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on1955349912lle_tv @ F @ A )
% 0.30/0.47 => ( ( X != Y )
% 0.30/0.47 => ( ( member_nat @ X @ A )
% 0.30/0.47 => ( ( member_nat @ Y @ A )
% 0.30/0.47 => ( ( F @ X )
% 0.30/0.47 != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_contraD
% 0.30/0.47 thf(fact_104_inj__on__contraD,axiom,
% 0.30/0.47 ! [F: nat > nat,A: set_nat,X: nat,Y: nat] :
% 0.30/0.47 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.47 => ( ( X != Y )
% 0.30/0.47 => ( ( member_nat @ X @ A )
% 0.30/0.47 => ( ( member_nat @ Y @ A )
% 0.30/0.47 => ( ( F @ X )
% 0.30/0.47 != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_contraD
% 0.30/0.47 thf(fact_105_inj__on__contraD,axiom,
% 0.30/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.47 => ( ( X != Y )
% 0.30/0.47 => ( ( member266900804lle_tv @ X @ A )
% 0.30/0.47 => ( ( member266900804lle_tv @ Y @ A )
% 0.30/0.47 => ( ( F @ X )
% 0.30/0.47 != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inj_on_contraD
% 0.30/0.47 thf(fact_106_top__empty__eq,axiom,
% 0.30/0.47 ( top_to900819589_nat_o
% 0.30/0.47 = ( ^ [X2: produc194167194tv_nat] : ( member737151281tv_nat @ X2 @ top_to975729152tv_nat ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_empty_eq
% 0.30/0.47 thf(fact_107_top__empty__eq,axiom,
% 0.30/0.47 ( top_to1889334367e_tv_o
% 0.30/0.47 = ( ^ [X2: produc270694976lle_tv] : ( member813679063lle_tv @ X2 @ top_to1411004326lle_tv ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_empty_eq
% 0.30/0.47 thf(fact_108_top__empty__eq,axiom,
% 0.30/0.47 ( top_to632227436_nat_o
% 0.30/0.47 = ( ^ [X2: product_prod_nat_nat] : ( member701585322at_nat @ X2 @ top_to1555900337at_nat ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_empty_eq
% 0.30/0.47 thf(fact_109_top__empty__eq,axiom,
% 0.30/0.47 ( top_to1299250770e_tv_o
% 0.30/0.47 = ( ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_empty_eq
% 0.30/0.47 thf(fact_110_top__empty__eq,axiom,
% 0.30/0.47 ( top_top_nat_o
% 0.30/0.47 = ( ^ [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_empty_eq
% 0.30/0.47 thf(fact_111_the__inv__f__f,axiom,
% 0.30/0.47 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv] :
% 0.30/0.47 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 0.30/0.47 => ( ( the_in427240730lle_tv @ top_to1871154984lle_tv @ F @ ( F @ X ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % the_inv_f_f
% 0.30/0.47 thf(fact_112_the__inv__f__f,axiom,
% 0.30/0.47 ! [F: paraco1605129243lle_tv > nat,X: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( inj_on1179712058tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.47 => ( ( the_in1509933432tv_nat @ top_to1057771083lle_tv @ F @ ( F @ X ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % the_inv_f_f
% 0.30/0.47 thf(fact_113_the__inv__f__f,axiom,
% 0.30/0.47 ! [F: nat > paraco1605129243lle_tv,X: nat] :
% 0.30/0.47 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.47 => ( ( the_in138087638lle_tv @ top_top_set_nat @ F @ ( F @ X ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % the_inv_f_f
% 0.30/0.47 thf(fact_114_the__inv__f__f,axiom,
% 0.30/0.47 ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat] :
% 0.30/0.47 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 0.30/0.47 => ( ( the_in195660058tv_nat @ top_to975729152tv_nat @ F @ ( F @ X ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % the_inv_f_f
% 0.30/0.47 thf(fact_115_the__inv__f__f,axiom,
% 0.30/0.47 ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv] :
% 0.30/0.47 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.47 => ( ( the_in1388677748lle_tv @ top_to1411004326lle_tv @ F @ ( F @ X ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % the_inv_f_f
% 0.30/0.47 thf(fact_116_the__inv__f__f,axiom,
% 0.30/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.30/0.47 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.47 => ( ( the_in2068894451at_nat @ top_to1555900337at_nat @ F @ ( F @ X ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % the_inv_f_f
% 0.30/0.47 thf(fact_117_the__inv__f__f,axiom,
% 0.30/0.47 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 0.30/0.47 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47 => ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ F @ ( F @ X ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % the_inv_f_f
% 0.30/0.47 thf(fact_118_the__inv__f__f,axiom,
% 0.30/0.47 ! [F: nat > nat,X: nat] :
% 0.30/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47 => ( ( the_inv_into_nat_nat @ top_top_set_nat @ F @ ( F @ X ) )
% 0.30/0.47 = X ) ) ).
% 0.30/0.47
% 0.30/0.47 % the_inv_f_f
% 0.30/0.47 thf(fact_119_strict__mono__on__imp__inj__on,axiom,
% 0.30/0.47 ! [F: nat > nat,A: set_nat] :
% 0.30/0.47 ( ( strict2146030304at_nat @ F @ A )
% 0.30/0.47 => ( inj_on_nat_nat @ F @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % strict_mono_on_imp_inj_on
% 0.30/0.47 thf(fact_120_linorder__injI,axiom,
% 0.30/0.47 ! [F: nat > paraco1605129243lle_tv] :
% 0.30/0.47 ( ! [X3: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X3 @ Y2 )
% 0.30/0.47 => ( ( F @ X3 )
% 0.30/0.47 != ( F @ Y2 ) ) )
% 0.30/0.47 => ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_injI
% 0.30/0.47 thf(fact_121_linorder__injI,axiom,
% 0.30/0.47 ! [F: nat > nat] :
% 0.30/0.47 ( ! [X3: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X3 @ Y2 )
% 0.30/0.47 => ( ( F @ X3 )
% 0.30/0.47 != ( F @ Y2 ) ) )
% 0.30/0.47 => ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % linorder_injI
% 0.30/0.48 thf(fact_122_inj__add__left,axiom,
% 0.30/0.48 ! [A4: nat] : ( inj_on_nat_nat @ ( plus_plus_nat @ A4 ) @ top_top_set_nat ) ).
% 0.30/0.48
% 0.30/0.48 % inj_add_left
% 0.30/0.48 thf(fact_123_change__tv_Osimps_I2_J,axiom,
% 0.30/0.48 ! [F: nat > nat,N: nat] :
% 0.30/0.48 ( ( paraco1147068288nge_tv @ F @ ( paraco793048302_Indet @ N ) )
% 0.30/0.48 = ( paraco793048302_Indet @ ( F @ N ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % change_tv.simps(2)
% 0.30/0.48 thf(fact_124_inj__apsnd,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on2112487900lle_tv @ ( produc1408152463lle_tv @ F ) @ top_to1871154984lle_tv )
% 0.30/0.48 = ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_apsnd
% 0.30/0.48 thf(fact_125_inj__apsnd,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on967082628lle_tv @ ( produc1804670661lle_tv @ F ) @ top_to975729152tv_nat )
% 0.30/0.48 = ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_apsnd
% 0.30/0.48 thf(fact_126_inj__apsnd,axiom,
% 0.30/0.48 ! [F: nat > nat] :
% 0.30/0.48 ( ( inj_on552895452tv_nat @ ( produc237097339lle_tv @ F ) @ top_to975729152tv_nat )
% 0.30/0.48 = ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_apsnd
% 0.30/0.48 thf(fact_127_inj__apsnd,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on1745913142lle_tv @ ( produc2040316391tv_nat @ F ) @ top_to1411004326lle_tv )
% 0.30/0.48 = ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_apsnd
% 0.30/0.48 thf(fact_128_inj__apsnd,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on1840679568lle_tv @ ( produc1608943133tv_nat @ F ) @ top_to1555900337at_nat )
% 0.30/0.48 = ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_apsnd
% 0.30/0.48 thf(fact_129_inj__apsnd,axiom,
% 0.30/0.48 ! [F: nat > nat] :
% 0.30/0.48 ( ( inj_on26176689at_nat @ ( produc1320959600at_nat @ F ) @ top_to1555900337at_nat )
% 0.30/0.48 = ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_apsnd
% 0.30/0.48 thf(fact_130_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,A4: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on1179712058tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.48 => ( ( member_nat @ ( F @ A4 ) @ ( image_376325286tv_nat @ F @ A ) )
% 0.30/0.48 = ( member266900804lle_tv @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_131_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A4: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_335818702lle_tv @ F @ A ) )
% 0.30/0.48 = ( member266900804lle_tv @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_132_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: nat > nat,A4: nat,A: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.48 => ( ( member_nat @ ( F @ A4 ) @ ( image_nat_nat @ F @ A ) )
% 0.30/0.48 = ( member_nat @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_133_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,A4: nat,A: set_nat] :
% 0.30/0.48 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.48 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_1151963140lle_tv @ F @ A ) )
% 0.30/0.48 = ( member_nat @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_134_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: produc194167194tv_nat > nat,A4: produc194167194tv_nat,A: set_Pr1725653840tv_nat] :
% 0.30/0.48 ( ( inj_on808253149at_nat @ F @ top_to975729152tv_nat )
% 0.30/0.48 => ( ( member_nat @ ( F @ A4 ) @ ( image_1381266801at_nat @ F @ A ) )
% 0.30/0.48 = ( member737151281tv_nat @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_135_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: produc194167194tv_nat > paraco1605129243lle_tv,A4: produc194167194tv_nat,A: set_Pr1725653840tv_nat] :
% 0.30/0.48 ( ( inj_on1612474245lle_tv @ F @ top_to975729152tv_nat )
% 0.30/0.48 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_2019567641lle_tv @ F @ A ) )
% 0.30/0.48 = ( member737151281tv_nat @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_136_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: produc270694976lle_tv > nat,A4: produc270694976lle_tv,A: set_Pr13445366lle_tv] :
% 0.30/0.48 ( ( inj_on936843139tv_nat @ F @ top_to1411004326lle_tv )
% 0.30/0.48 => ( ( member_nat @ ( F @ A4 ) @ ( image_1509856791tv_nat @ F @ A ) )
% 0.30/0.48 = ( member813679063lle_tv @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_137_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: produc270694976lle_tv > paraco1605129243lle_tv,A4: produc270694976lle_tv,A: set_Pr13445366lle_tv] :
% 0.30/0.48 ( ( inj_on394919723lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.48 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_802013119lle_tv @ F @ A ) )
% 0.30/0.48 = ( member813679063lle_tv @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_138_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > nat,A4: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( inj_on642995232at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.48 => ( ( member_nat @ ( F @ A4 ) @ ( image_1397137548at_nat @ F @ A ) )
% 0.30/0.48 = ( member701585322at_nat @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_139_inj__image__mem__iff,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > paraco1605129243lle_tv,A4: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( inj_on520021963lle_tv @ F @ top_to1555900337at_nat )
% 0.30/0.48 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_1093035615lle_tv @ F @ A ) )
% 0.30/0.48 = ( member701585322at_nat @ A4 @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_mem_iff
% 0.30/0.48 thf(fact_140_inj__image__eq__iff,axiom,
% 0.30/0.48 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv,B: set_Pr2014382200lle_tv] :
% 0.30/0.48 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 0.30/0.48 => ( ( ( image_1221801032lle_tv @ F @ A )
% 0.30/0.48 = ( image_1221801032lle_tv @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_eq_iff
% 0.30/0.48 thf(fact_141_inj__image__eq__iff,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,A: set_nat,B: set_nat] :
% 0.30/0.48 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.48 => ( ( ( image_1151963140lle_tv @ F @ A )
% 0.30/0.48 = ( image_1151963140lle_tv @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_eq_iff
% 0.30/0.48 thf(fact_142_inj__image__eq__iff,axiom,
% 0.30/0.48 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat,B: set_Pr1725653840tv_nat] :
% 0.30/0.48 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 0.30/0.48 => ( ( ( image_1104296520tv_nat @ F @ A )
% 0.30/0.48 = ( image_1104296520tv_nat @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_eq_iff
% 0.30/0.48 thf(fact_143_inj__image__eq__iff,axiom,
% 0.30/0.48 ! [F: produc270694976lle_tv > produc270694976lle_tv,A: set_Pr13445366lle_tv,B: set_Pr13445366lle_tv] :
% 0.30/0.48 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.48 => ( ( ( image_149830562lle_tv @ F @ A )
% 0.30/0.48 = ( image_149830562lle_tv @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_eq_iff
% 0.30/0.48 thf(fact_144_inj__image__eq__iff,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( inj_on1764151786tv_nat @ F @ top_to1555900337at_nat )
% 0.30/0.48 => ( ( ( image_1597721174tv_nat @ F @ A )
% 0.30/0.48 = ( image_1597721174tv_nat @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_eq_iff
% 0.30/0.48 thf(fact_145_inj__image__eq__iff,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( inj_on1840679568lle_tv @ F @ top_to1555900337at_nat )
% 0.30/0.48 => ( ( ( image_1674248956lle_tv @ F @ A )
% 0.30/0.48 = ( image_1674248956lle_tv @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_eq_iff
% 0.30/0.48 thf(fact_146_inj__image__eq__iff,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.48 => ( ( ( image_815163717at_nat @ F @ A )
% 0.30/0.48 = ( image_815163717at_nat @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_eq_iff
% 0.30/0.48 thf(fact_147_inj__image__eq__iff,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 => ( ( ( image_335818702lle_tv @ F @ A )
% 0.30/0.48 = ( image_335818702lle_tv @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_eq_iff
% 0.30/0.48 thf(fact_148_inj__image__eq__iff,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,B: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.48 => ( ( ( image_nat_nat @ F @ A )
% 0.30/0.48 = ( image_nat_nat @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_eq_iff
% 0.30/0.48 thf(fact_149_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,B2: nat] :
% 0.30/0.48 ( ( inj_on1179712058tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.48 => ( ( member_nat @ B2 @ ( image_376325286tv_nat @ F @ top_to1057771083lle_tv ) )
% 0.30/0.48 = ( ? [X2: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_150_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 => ( ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ top_to1057771083lle_tv ) )
% 0.30/0.48 = ( ? [X2: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_151_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: nat > nat,B2: nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.48 => ( ( member_nat @ B2 @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 0.30/0.48 = ( ? [X2: nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_152_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.48 => ( ( member266900804lle_tv @ B2 @ ( image_1151963140lle_tv @ F @ top_top_set_nat ) )
% 0.30/0.48 = ( ? [X2: nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_153_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: produc194167194tv_nat > nat,B2: nat] :
% 0.30/0.48 ( ( inj_on808253149at_nat @ F @ top_to975729152tv_nat )
% 0.30/0.48 => ( ( member_nat @ B2 @ ( image_1381266801at_nat @ F @ top_to975729152tv_nat ) )
% 0.30/0.48 = ( ? [X2: produc194167194tv_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: produc194167194tv_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_154_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: produc194167194tv_nat > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on1612474245lle_tv @ F @ top_to975729152tv_nat )
% 0.30/0.48 => ( ( member266900804lle_tv @ B2 @ ( image_2019567641lle_tv @ F @ top_to975729152tv_nat ) )
% 0.30/0.48 = ( ? [X2: produc194167194tv_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: produc194167194tv_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_155_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: produc270694976lle_tv > nat,B2: nat] :
% 0.30/0.48 ( ( inj_on936843139tv_nat @ F @ top_to1411004326lle_tv )
% 0.30/0.48 => ( ( member_nat @ B2 @ ( image_1509856791tv_nat @ F @ top_to1411004326lle_tv ) )
% 0.30/0.48 = ( ? [X2: produc270694976lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: produc270694976lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_156_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: produc270694976lle_tv > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on394919723lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.48 => ( ( member266900804lle_tv @ B2 @ ( image_802013119lle_tv @ F @ top_to1411004326lle_tv ) )
% 0.30/0.48 = ( ? [X2: produc270694976lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: produc270694976lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_157_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > nat,B2: nat] :
% 0.30/0.48 ( ( inj_on642995232at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.48 => ( ( member_nat @ B2 @ ( image_1397137548at_nat @ F @ top_to1555900337at_nat ) )
% 0.30/0.48 = ( ? [X2: product_prod_nat_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: product_prod_nat_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_158_range__ex1__eq,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on520021963lle_tv @ F @ top_to1555900337at_nat )
% 0.30/0.48 => ( ( member266900804lle_tv @ B2 @ ( image_1093035615lle_tv @ F @ top_to1555900337at_nat ) )
% 0.30/0.48 = ( ? [X2: product_prod_nat_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X2 ) )
% 0.30/0.48 & ! [Y3: product_prod_nat_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ Y3 ) )
% 0.30/0.48 => ( Y3 = X2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_ex1_eq
% 0.30/0.48 thf(fact_159_strict__mono__imp__inj__on,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat] :
% 0.30/0.48 ( ( order_769474267at_nat @ F )
% 0.30/0.48 => ( inj_on_nat_nat @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_imp_inj_on
% 0.30/0.48 thf(fact_160_image__eqI,axiom,
% 0.30/0.48 ! [B2: produc194167194tv_nat,F: product_prod_nat_nat > produc194167194tv_nat,X: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( ( member701585322at_nat @ X @ A )
% 0.30/0.48 => ( member737151281tv_nat @ B2 @ ( image_1597721174tv_nat @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_eqI
% 0.30/0.48 thf(fact_161_image__eqI,axiom,
% 0.30/0.48 ! [B2: produc270694976lle_tv,F: product_prod_nat_nat > produc270694976lle_tv,X: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( ( member701585322at_nat @ X @ A )
% 0.30/0.48 => ( member813679063lle_tv @ B2 @ ( image_1674248956lle_tv @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_eqI
% 0.30/0.48 thf(fact_162_image__eqI,axiom,
% 0.30/0.48 ! [B2: product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( ( member701585322at_nat @ X @ A )
% 0.30/0.48 => ( member701585322at_nat @ B2 @ ( image_815163717at_nat @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_eqI
% 0.30/0.48 thf(fact_163_image__eqI,axiom,
% 0.30/0.48 ! [B2: nat,F: nat > nat,X: nat,A: set_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( ( member_nat @ X @ A )
% 0.30/0.48 => ( member_nat @ B2 @ ( image_nat_nat @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_eqI
% 0.30/0.48 thf(fact_164_image__eqI,axiom,
% 0.30/0.48 ! [B2: paraco1605129243lle_tv,F: nat > paraco1605129243lle_tv,X: nat,A: set_nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( ( member_nat @ X @ A )
% 0.30/0.48 => ( member266900804lle_tv @ B2 @ ( image_1151963140lle_tv @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_eqI
% 0.30/0.48 thf(fact_165_image__eqI,axiom,
% 0.30/0.48 ! [B2: nat,F: paraco1605129243lle_tv > nat,X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( ( member266900804lle_tv @ X @ A )
% 0.30/0.48 => ( member_nat @ B2 @ ( image_376325286tv_nat @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_eqI
% 0.30/0.48 thf(fact_166_image__eqI,axiom,
% 0.30/0.48 ! [B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( ( member266900804lle_tv @ X @ A )
% 0.30/0.48 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_eqI
% 0.30/0.48 thf(fact_167_tv_Oinject_I2_J,axiom,
% 0.30/0.48 ! [X22: nat,Y22: nat] :
% 0.30/0.48 ( ( ( paraco793048302_Indet @ X22 )
% 0.30/0.48 = ( paraco793048302_Indet @ Y22 ) )
% 0.30/0.48 = ( X22 = Y22 ) ) ).
% 0.30/0.48
% 0.30/0.48 % tv.inject(2)
% 0.30/0.48 thf(fact_168_top1I,axiom,
% 0.30/0.48 ! [X: paraco1605129243lle_tv] : ( top_to1299250770e_tv_o @ X ) ).
% 0.30/0.48
% 0.30/0.48 % top1I
% 0.30/0.48 thf(fact_169_top1I,axiom,
% 0.30/0.48 ! [X: nat] : ( top_top_nat_o @ X ) ).
% 0.30/0.48
% 0.30/0.48 % top1I
% 0.30/0.48 thf(fact_170_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.48 => ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ A @ F ) @ ( image_335818702lle_tv @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_171_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.48 => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A @ F ) @ ( image_nat_nat @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_172_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,A: set_nat] :
% 0.30/0.48 ( ( inj_on1955349912lle_tv @ F @ A )
% 0.30/0.48 => ( ( image_376325286tv_nat @ ( the_in138087638lle_tv @ A @ F ) @ ( image_1151963140lle_tv @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_173_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on1179712058tv_nat @ F @ A )
% 0.30/0.48 => ( ( image_1151963140lle_tv @ ( the_in1509933432tv_nat @ A @ F ) @ ( image_376325286tv_nat @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_174_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( inj_on1764151786tv_nat @ F @ A )
% 0.30/0.48 => ( ( image_1805124128at_nat @ ( the_in667485224tv_nat @ A @ F ) @ ( image_1597721174tv_nat @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_175_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( inj_on1840679568lle_tv @ F @ A )
% 0.30/0.48 => ( ( image_1787705850at_nat @ ( the_in744013006lle_tv @ A @ F ) @ ( image_1674248956lle_tv @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_176_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: produc194167194tv_nat > product_prod_nat_nat,A: set_Pr1725653840tv_nat] :
% 0.30/0.48 ( ( inj_on1971554740at_nat @ F @ A )
% 0.30/0.48 => ( ( image_1597721174tv_nat @ ( the_in874888178at_nat @ A @ F ) @ ( image_1805124128at_nat @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_177_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: produc270694976lle_tv > product_prod_nat_nat,A: set_Pr13445366lle_tv] :
% 0.30/0.48 ( ( inj_on1954136462at_nat @ F @ A )
% 0.30/0.48 => ( ( image_1674248956lle_tv @ ( the_in857469900at_nat @ A @ F ) @ ( image_1787705850at_nat @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_178_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv] :
% 0.30/0.48 ( ( inj_on2112487900lle_tv @ F @ A )
% 0.30/0.48 => ( ( image_1221801032lle_tv @ ( the_in427240730lle_tv @ A @ F ) @ ( image_1221801032lle_tv @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_179_the__inv__into__onto,axiom,
% 0.30/0.48 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat] :
% 0.30/0.48 ( ( inj_on552895452tv_nat @ F @ A )
% 0.30/0.48 => ( ( image_1104296520tv_nat @ ( the_in195660058tv_nat @ A @ F ) @ ( image_1104296520tv_nat @ F @ A ) )
% 0.30/0.48 = A ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_onto
% 0.30/0.48 thf(fact_180_imageI,axiom,
% 0.30/0.48 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,F: product_prod_nat_nat > produc194167194tv_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X @ A )
% 0.30/0.48 => ( member737151281tv_nat @ ( F @ X ) @ ( image_1597721174tv_nat @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % imageI
% 0.30/0.48 thf(fact_181_imageI,axiom,
% 0.30/0.48 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,F: product_prod_nat_nat > produc270694976lle_tv] :
% 0.30/0.48 ( ( member701585322at_nat @ X @ A )
% 0.30/0.48 => ( member813679063lle_tv @ ( F @ X ) @ ( image_1674248956lle_tv @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % imageI
% 0.30/0.48 thf(fact_182_imageI,axiom,
% 0.30/0.48 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X @ A )
% 0.30/0.48 => ( member701585322at_nat @ ( F @ X ) @ ( image_815163717at_nat @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % imageI
% 0.30/0.48 thf(fact_183_imageI,axiom,
% 0.30/0.48 ! [X: nat,A: set_nat,F: nat > nat] :
% 0.30/0.48 ( ( member_nat @ X @ A )
% 0.30/0.48 => ( member_nat @ ( F @ X ) @ ( image_nat_nat @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % imageI
% 0.30/0.48 thf(fact_184_imageI,axiom,
% 0.30/0.48 ! [X: nat,A: set_nat,F: nat > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member_nat @ X @ A )
% 0.30/0.48 => ( member266900804lle_tv @ ( F @ X ) @ ( image_1151963140lle_tv @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % imageI
% 0.30/0.48 thf(fact_185_imageI,axiom,
% 0.30/0.48 ! [X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > nat] :
% 0.30/0.48 ( ( member266900804lle_tv @ X @ A )
% 0.30/0.48 => ( member_nat @ ( F @ X ) @ ( image_376325286tv_nat @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % imageI
% 0.30/0.48 thf(fact_186_imageI,axiom,
% 0.30/0.48 ! [X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ X @ A )
% 0.30/0.48 => ( member266900804lle_tv @ ( F @ X ) @ ( image_335818702lle_tv @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % imageI
% 0.30/0.48 thf(fact_187_image__iff,axiom,
% 0.30/0.48 ! [Z: produc194167194tv_nat,F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( member737151281tv_nat @ Z @ ( image_1597721174tv_nat @ F @ A ) )
% 0.30/0.48 = ( ? [X2: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X2 @ A )
% 0.30/0.48 & ( Z
% 0.30/0.48 = ( F @ X2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_iff
% 0.30/0.48 thf(fact_188_image__iff,axiom,
% 0.30/0.48 ! [Z: produc270694976lle_tv,F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( member813679063lle_tv @ Z @ ( image_1674248956lle_tv @ F @ A ) )
% 0.30/0.48 = ( ? [X2: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X2 @ A )
% 0.30/0.48 & ( Z
% 0.30/0.48 = ( F @ X2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_iff
% 0.30/0.48 thf(fact_189_image__iff,axiom,
% 0.30/0.48 ! [Z: product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ Z @ ( image_815163717at_nat @ F @ A ) )
% 0.30/0.48 = ( ? [X2: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X2 @ A )
% 0.30/0.48 & ( Z
% 0.30/0.48 = ( F @ X2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_iff
% 0.30/0.48 thf(fact_190_image__iff,axiom,
% 0.30/0.48 ! [Z: nat,F: nat > nat,A: set_nat] :
% 0.30/0.48 ( ( member_nat @ Z @ ( image_nat_nat @ F @ A ) )
% 0.30/0.48 = ( ? [X2: nat] :
% 0.30/0.48 ( ( member_nat @ X2 @ A )
% 0.30/0.48 & ( Z
% 0.30/0.48 = ( F @ X2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_iff
% 0.30/0.48 thf(fact_191_image__iff,axiom,
% 0.30/0.48 ! [Z: paraco1605129243lle_tv,F: nat > paraco1605129243lle_tv,A: set_nat] :
% 0.30/0.48 ( ( member266900804lle_tv @ Z @ ( image_1151963140lle_tv @ F @ A ) )
% 0.30/0.48 = ( ? [X2: nat] :
% 0.30/0.48 ( ( member_nat @ X2 @ A )
% 0.30/0.48 & ( Z
% 0.30/0.48 = ( F @ X2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_iff
% 0.30/0.48 thf(fact_192_bex__imageD,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat,P: produc194167194tv_nat > $o] :
% 0.30/0.48 ( ? [X4: produc194167194tv_nat] :
% 0.30/0.48 ( ( member737151281tv_nat @ X4 @ ( image_1597721174tv_nat @ F @ A ) )
% 0.30/0.48 & ( P @ X4 ) )
% 0.30/0.48 => ? [X3: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X3 @ A )
% 0.30/0.48 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % bex_imageD
% 0.30/0.48 thf(fact_193_bex__imageD,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat,P: produc270694976lle_tv > $o] :
% 0.30/0.48 ( ? [X4: produc270694976lle_tv] :
% 0.30/0.48 ( ( member813679063lle_tv @ X4 @ ( image_1674248956lle_tv @ F @ A ) )
% 0.30/0.48 & ( P @ X4 ) )
% 0.30/0.48 => ? [X3: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X3 @ A )
% 0.30/0.48 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % bex_imageD
% 0.30/0.48 thf(fact_194_bex__imageD,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,P: product_prod_nat_nat > $o] :
% 0.30/0.48 ( ? [X4: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X4 @ ( image_815163717at_nat @ F @ A ) )
% 0.30/0.48 & ( P @ X4 ) )
% 0.30/0.48 => ? [X3: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X3 @ A )
% 0.30/0.48 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % bex_imageD
% 0.30/0.48 thf(fact_195_bex__imageD,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,A: set_nat,P: paraco1605129243lle_tv > $o] :
% 0.30/0.48 ( ? [X4: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ X4 @ ( image_1151963140lle_tv @ F @ A ) )
% 0.30/0.48 & ( P @ X4 ) )
% 0.30/0.48 => ? [X3: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ A )
% 0.30/0.48 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % bex_imageD
% 0.30/0.48 thf(fact_196_bex__imageD,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,P: nat > $o] :
% 0.30/0.48 ( ? [X4: nat] :
% 0.30/0.48 ( ( member_nat @ X4 @ ( image_nat_nat @ F @ A ) )
% 0.30/0.48 & ( P @ X4 ) )
% 0.30/0.48 => ? [X3: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ A )
% 0.30/0.48 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % bex_imageD
% 0.30/0.48 thf(fact_197_image__cong,axiom,
% 0.30/0.48 ! [M: set_Pr1986765409at_nat,N2: set_Pr1986765409at_nat,F: product_prod_nat_nat > produc194167194tv_nat,G: product_prod_nat_nat > produc194167194tv_nat] :
% 0.30/0.48 ( ( M = N2 )
% 0.30/0.48 => ( ! [X3: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X3 @ N2 )
% 0.30/0.48 => ( ( F @ X3 )
% 0.30/0.48 = ( G @ X3 ) ) )
% 0.30/0.48 => ( ( image_1597721174tv_nat @ F @ M )
% 0.30/0.48 = ( image_1597721174tv_nat @ G @ N2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_cong
% 0.30/0.48 thf(fact_198_image__cong,axiom,
% 0.30/0.48 ! [M: set_Pr1986765409at_nat,N2: set_Pr1986765409at_nat,F: product_prod_nat_nat > produc270694976lle_tv,G: product_prod_nat_nat > produc270694976lle_tv] :
% 0.30/0.48 ( ( M = N2 )
% 0.30/0.48 => ( ! [X3: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X3 @ N2 )
% 0.30/0.48 => ( ( F @ X3 )
% 0.30/0.48 = ( G @ X3 ) ) )
% 0.30/0.48 => ( ( image_1674248956lle_tv @ F @ M )
% 0.30/0.48 = ( image_1674248956lle_tv @ G @ N2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_cong
% 0.30/0.48 thf(fact_199_image__cong,axiom,
% 0.30/0.48 ! [M: set_Pr1986765409at_nat,N2: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.48 ( ( M = N2 )
% 0.30/0.48 => ( ! [X3: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X3 @ N2 )
% 0.30/0.48 => ( ( F @ X3 )
% 0.30/0.48 = ( G @ X3 ) ) )
% 0.30/0.48 => ( ( image_815163717at_nat @ F @ M )
% 0.30/0.48 = ( image_815163717at_nat @ G @ N2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_cong
% 0.30/0.48 thf(fact_200_image__cong,axiom,
% 0.30/0.48 ! [M: set_nat,N2: set_nat,F: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( M = N2 )
% 0.30/0.48 => ( ! [X3: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ N2 )
% 0.30/0.48 => ( ( F @ X3 )
% 0.30/0.48 = ( G @ X3 ) ) )
% 0.30/0.48 => ( ( image_1151963140lle_tv @ F @ M )
% 0.30/0.48 = ( image_1151963140lle_tv @ G @ N2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_cong
% 0.30/0.48 thf(fact_201_image__cong,axiom,
% 0.30/0.48 ! [M: set_nat,N2: set_nat,F: nat > nat,G: nat > nat] :
% 0.30/0.48 ( ( M = N2 )
% 0.30/0.48 => ( ! [X3: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ N2 )
% 0.30/0.48 => ( ( F @ X3 )
% 0.30/0.48 = ( G @ X3 ) ) )
% 0.30/0.48 => ( ( image_nat_nat @ F @ M )
% 0.30/0.48 = ( image_nat_nat @ G @ N2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_cong
% 0.30/0.48 thf(fact_202_ball__imageD,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat,P: produc194167194tv_nat > $o] :
% 0.30/0.48 ( ! [X3: produc194167194tv_nat] :
% 0.30/0.48 ( ( member737151281tv_nat @ X3 @ ( image_1597721174tv_nat @ F @ A ) )
% 0.30/0.48 => ( P @ X3 ) )
% 0.30/0.48 => ! [X4: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X4 @ A )
% 0.30/0.48 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ball_imageD
% 0.30/0.48 thf(fact_203_ball__imageD,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat,P: produc270694976lle_tv > $o] :
% 0.30/0.48 ( ! [X3: produc270694976lle_tv] :
% 0.30/0.48 ( ( member813679063lle_tv @ X3 @ ( image_1674248956lle_tv @ F @ A ) )
% 0.30/0.48 => ( P @ X3 ) )
% 0.30/0.48 => ! [X4: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X4 @ A )
% 0.30/0.48 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ball_imageD
% 0.30/0.48 thf(fact_204_ball__imageD,axiom,
% 0.30/0.48 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,P: product_prod_nat_nat > $o] :
% 0.30/0.48 ( ! [X3: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X3 @ ( image_815163717at_nat @ F @ A ) )
% 0.30/0.48 => ( P @ X3 ) )
% 0.30/0.48 => ! [X4: product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X4 @ A )
% 0.30/0.48 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ball_imageD
% 0.30/0.48 thf(fact_205_ball__imageD,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,A: set_nat,P: paraco1605129243lle_tv > $o] :
% 0.30/0.48 ( ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ X3 @ ( image_1151963140lle_tv @ F @ A ) )
% 0.30/0.48 => ( P @ X3 ) )
% 0.30/0.48 => ! [X4: nat] :
% 0.30/0.48 ( ( member_nat @ X4 @ A )
% 0.30/0.48 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ball_imageD
% 0.30/0.48 thf(fact_206_ball__imageD,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,P: nat > $o] :
% 0.30/0.48 ( ! [X3: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ ( image_nat_nat @ F @ A ) )
% 0.30/0.48 => ( P @ X3 ) )
% 0.30/0.48 => ! [X4: nat] :
% 0.30/0.48 ( ( member_nat @ X4 @ A )
% 0.30/0.48 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ball_imageD
% 0.30/0.48 thf(fact_207_rev__image__eqI,axiom,
% 0.30/0.48 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,B2: produc194167194tv_nat,F: product_prod_nat_nat > produc194167194tv_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X @ A )
% 0.30/0.48 => ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member737151281tv_nat @ B2 @ ( image_1597721174tv_nat @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_image_eqI
% 0.30/0.48 thf(fact_208_rev__image__eqI,axiom,
% 0.30/0.48 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,B2: produc270694976lle_tv,F: product_prod_nat_nat > produc270694976lle_tv] :
% 0.30/0.48 ( ( member701585322at_nat @ X @ A )
% 0.30/0.48 => ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member813679063lle_tv @ B2 @ ( image_1674248956lle_tv @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_image_eqI
% 0.30/0.48 thf(fact_209_rev__image__eqI,axiom,
% 0.30/0.48 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,B2: product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.48 ( ( member701585322at_nat @ X @ A )
% 0.30/0.48 => ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member701585322at_nat @ B2 @ ( image_815163717at_nat @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_image_eqI
% 0.30/0.48 thf(fact_210_rev__image__eqI,axiom,
% 0.30/0.48 ! [X: nat,A: set_nat,B2: nat,F: nat > nat] :
% 0.30/0.48 ( ( member_nat @ X @ A )
% 0.30/0.48 => ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member_nat @ B2 @ ( image_nat_nat @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_image_eqI
% 0.30/0.48 thf(fact_211_rev__image__eqI,axiom,
% 0.30/0.48 ! [X: nat,A: set_nat,B2: paraco1605129243lle_tv,F: nat > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member_nat @ X @ A )
% 0.30/0.48 => ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member266900804lle_tv @ B2 @ ( image_1151963140lle_tv @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_image_eqI
% 0.30/0.48 thf(fact_212_rev__image__eqI,axiom,
% 0.30/0.48 ! [X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: nat,F: paraco1605129243lle_tv > nat] :
% 0.30/0.48 ( ( member266900804lle_tv @ X @ A )
% 0.30/0.48 => ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member_nat @ B2 @ ( image_376325286tv_nat @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_image_eqI
% 0.30/0.48 thf(fact_213_rev__image__eqI,axiom,
% 0.30/0.48 ! [X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ X @ A )
% 0.30/0.48 => ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_image_eqI
% 0.30/0.48 thf(fact_214_strict__mono__onD,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,R: nat,S: nat] :
% 0.30/0.48 ( ( strict2146030304at_nat @ F @ A )
% 0.30/0.48 => ( ( member_nat @ R @ A )
% 0.30/0.48 => ( ( member_nat @ S @ A )
% 0.30/0.48 => ( ( ord_less_nat @ R @ S )
% 0.30/0.48 => ( ord_less_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onD
% 0.30/0.48 thf(fact_215_strict__mono__onD,axiom,
% 0.30/0.48 ! [F: nat > set_nat,A: set_nat,R: nat,S: nat] :
% 0.30/0.48 ( ( strict1310998166et_nat @ F @ A )
% 0.30/0.48 => ( ( member_nat @ R @ A )
% 0.30/0.48 => ( ( member_nat @ S @ A )
% 0.30/0.48 => ( ( ord_less_nat @ R @ S )
% 0.30/0.48 => ( ord_less_set_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onD
% 0.30/0.48 thf(fact_216_strict__mono__onD,axiom,
% 0.30/0.48 ! [F: nat > set_Pa1764573435lle_tv,A: set_nat,R: nat,S: nat] :
% 0.30/0.48 ( ( strict1658340843lle_tv @ F @ A )
% 0.30/0.48 => ( ( member_nat @ R @ A )
% 0.30/0.48 => ( ( member_nat @ S @ A )
% 0.30/0.48 => ( ( ord_less_nat @ R @ S )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onD
% 0.30/0.48 thf(fact_217_strict__mono__onD,axiom,
% 0.30/0.48 ! [F: set_nat > nat,A: set_set_nat,R: set_nat,S: set_nat] :
% 0.30/0.48 ( ( strict1802283670at_nat @ F @ A )
% 0.30/0.48 => ( ( member_set_nat @ R @ A )
% 0.30/0.48 => ( ( member_set_nat @ S @ A )
% 0.30/0.48 => ( ( ord_less_set_nat @ R @ S )
% 0.30/0.48 => ( ord_less_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onD
% 0.30/0.48 thf(fact_218_strict__mono__onD,axiom,
% 0.30/0.48 ! [F: set_nat > set_nat,A: set_set_nat,R: set_nat,S: set_nat] :
% 0.30/0.48 ( ( strict473775692et_nat @ F @ A )
% 0.30/0.48 => ( ( member_set_nat @ R @ A )
% 0.30/0.48 => ( ( member_set_nat @ S @ A )
% 0.30/0.48 => ( ( ord_less_set_nat @ R @ S )
% 0.30/0.48 => ( ord_less_set_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onD
% 0.30/0.48 thf(fact_219_strict__mono__onD,axiom,
% 0.30/0.48 ! [F: set_nat > set_Pa1764573435lle_tv,A: set_set_nat,R: set_nat,S: set_nat] :
% 0.30/0.48 ( ( strict172559285lle_tv @ F @ A )
% 0.30/0.48 => ( ( member_set_nat @ R @ A )
% 0.30/0.48 => ( ( member_set_nat @ S @ A )
% 0.30/0.48 => ( ( ord_less_set_nat @ R @ S )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onD
% 0.30/0.48 thf(fact_220_strict__mono__onD,axiom,
% 0.30/0.48 ! [F: set_Pa1764573435lle_tv > nat,A: set_se800614875lle_tv,R: set_Pa1764573435lle_tv,S: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( strict1125660301tv_nat @ F @ A )
% 0.30/0.48 => ( ( member1875402276lle_tv @ R @ A )
% 0.30/0.48 => ( ( member1875402276lle_tv @ S @ A )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ R @ S )
% 0.30/0.48 => ( ord_less_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onD
% 0.30/0.48 thf(fact_221_strict__mono__onD,axiom,
% 0.30/0.48 ! [F: set_Pa1764573435lle_tv > set_nat,A: set_se800614875lle_tv,R: set_Pa1764573435lle_tv,S: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( strict1455779395et_nat @ F @ A )
% 0.30/0.48 => ( ( member1875402276lle_tv @ R @ A )
% 0.30/0.48 => ( ( member1875402276lle_tv @ S @ A )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ R @ S )
% 0.30/0.48 => ( ord_less_set_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onD
% 0.30/0.48 thf(fact_222_strict__mono__onD,axiom,
% 0.30/0.48 ! [F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,A: set_se800614875lle_tv,R: set_Pa1764573435lle_tv,S: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( strict592849515lle_tv @ F @ A )
% 0.30/0.48 => ( ( member1875402276lle_tv @ R @ A )
% 0.30/0.48 => ( ( member1875402276lle_tv @ S @ A )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ R @ S )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onD
% 0.30/0.48 thf(fact_223_strict__mono__onI,axiom,
% 0.30/0.48 ! [A: set_nat,F: nat > nat] :
% 0.30/0.48 ( ! [R2: nat,S2: nat] :
% 0.30/0.48 ( ( member_nat @ R2 @ A )
% 0.30/0.48 => ( ( member_nat @ S2 @ A )
% 0.30/0.48 => ( ( ord_less_nat @ R2 @ S2 )
% 0.30/0.48 => ( ord_less_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 0.30/0.48 => ( strict2146030304at_nat @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onI
% 0.30/0.48 thf(fact_224_strict__mono__onI,axiom,
% 0.30/0.48 ! [A: set_nat,F: nat > set_nat] :
% 0.30/0.48 ( ! [R2: nat,S2: nat] :
% 0.30/0.48 ( ( member_nat @ R2 @ A )
% 0.30/0.48 => ( ( member_nat @ S2 @ A )
% 0.30/0.48 => ( ( ord_less_nat @ R2 @ S2 )
% 0.30/0.48 => ( ord_less_set_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 0.30/0.48 => ( strict1310998166et_nat @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onI
% 0.30/0.48 thf(fact_225_strict__mono__onI,axiom,
% 0.30/0.48 ! [A: set_nat,F: nat > set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ! [R2: nat,S2: nat] :
% 0.30/0.48 ( ( member_nat @ R2 @ A )
% 0.30/0.48 => ( ( member_nat @ S2 @ A )
% 0.30/0.48 => ( ( ord_less_nat @ R2 @ S2 )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 0.30/0.48 => ( strict1658340843lle_tv @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onI
% 0.30/0.48 thf(fact_226_strict__mono__onI,axiom,
% 0.30/0.48 ! [A: set_set_nat,F: set_nat > nat] :
% 0.30/0.48 ( ! [R2: set_nat,S2: set_nat] :
% 0.30/0.48 ( ( member_set_nat @ R2 @ A )
% 0.30/0.48 => ( ( member_set_nat @ S2 @ A )
% 0.30/0.48 => ( ( ord_less_set_nat @ R2 @ S2 )
% 0.30/0.48 => ( ord_less_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 0.30/0.48 => ( strict1802283670at_nat @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onI
% 0.30/0.48 thf(fact_227_strict__mono__onI,axiom,
% 0.30/0.48 ! [A: set_set_nat,F: set_nat > set_nat] :
% 0.30/0.48 ( ! [R2: set_nat,S2: set_nat] :
% 0.30/0.48 ( ( member_set_nat @ R2 @ A )
% 0.30/0.48 => ( ( member_set_nat @ S2 @ A )
% 0.30/0.48 => ( ( ord_less_set_nat @ R2 @ S2 )
% 0.30/0.48 => ( ord_less_set_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 0.30/0.48 => ( strict473775692et_nat @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onI
% 0.30/0.48 thf(fact_228_strict__mono__onI,axiom,
% 0.30/0.48 ! [A: set_set_nat,F: set_nat > set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ! [R2: set_nat,S2: set_nat] :
% 0.30/0.48 ( ( member_set_nat @ R2 @ A )
% 0.30/0.48 => ( ( member_set_nat @ S2 @ A )
% 0.30/0.48 => ( ( ord_less_set_nat @ R2 @ S2 )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 0.30/0.48 => ( strict172559285lle_tv @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onI
% 0.30/0.48 thf(fact_229_strict__mono__onI,axiom,
% 0.30/0.48 ! [A: set_se800614875lle_tv,F: set_Pa1764573435lle_tv > nat] :
% 0.30/0.48 ( ! [R2: set_Pa1764573435lle_tv,S2: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( member1875402276lle_tv @ R2 @ A )
% 0.30/0.48 => ( ( member1875402276lle_tv @ S2 @ A )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ R2 @ S2 )
% 0.30/0.48 => ( ord_less_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 0.30/0.48 => ( strict1125660301tv_nat @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onI
% 0.30/0.48 thf(fact_230_strict__mono__onI,axiom,
% 0.30/0.48 ! [A: set_se800614875lle_tv,F: set_Pa1764573435lle_tv > set_nat] :
% 0.30/0.48 ( ! [R2: set_Pa1764573435lle_tv,S2: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( member1875402276lle_tv @ R2 @ A )
% 0.30/0.48 => ( ( member1875402276lle_tv @ S2 @ A )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ R2 @ S2 )
% 0.30/0.48 => ( ord_less_set_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 0.30/0.48 => ( strict1455779395et_nat @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onI
% 0.30/0.48 thf(fact_231_strict__mono__onI,axiom,
% 0.30/0.48 ! [A: set_se800614875lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ! [R2: set_Pa1764573435lle_tv,S2: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( member1875402276lle_tv @ R2 @ A )
% 0.30/0.48 => ( ( member1875402276lle_tv @ S2 @ A )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ R2 @ S2 )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 0.30/0.48 => ( strict592849515lle_tv @ F @ A ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_onI
% 0.30/0.48 thf(fact_232_strict__mono__on__def,axiom,
% 0.30/0.48 ( strict2146030304at_nat
% 0.30/0.48 = ( ^ [F2: nat > nat,A2: set_nat] :
% 0.30/0.48 ! [R3: nat,S3: nat] :
% 0.30/0.48 ( ( ( member_nat @ R3 @ A2 )
% 0.30/0.48 & ( member_nat @ S3 @ A2 )
% 0.30/0.48 & ( ord_less_nat @ R3 @ S3 ) )
% 0.30/0.48 => ( ord_less_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_on_def
% 0.30/0.48 thf(fact_233_strict__mono__on__def,axiom,
% 0.30/0.48 ( strict1310998166et_nat
% 0.30/0.48 = ( ^ [F2: nat > set_nat,A2: set_nat] :
% 0.30/0.48 ! [R3: nat,S3: nat] :
% 0.30/0.48 ( ( ( member_nat @ R3 @ A2 )
% 0.30/0.48 & ( member_nat @ S3 @ A2 )
% 0.30/0.48 & ( ord_less_nat @ R3 @ S3 ) )
% 0.30/0.48 => ( ord_less_set_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_on_def
% 0.30/0.48 thf(fact_234_strict__mono__on__def,axiom,
% 0.30/0.48 ( strict1658340843lle_tv
% 0.30/0.48 = ( ^ [F2: nat > set_Pa1764573435lle_tv,A2: set_nat] :
% 0.30/0.48 ! [R3: nat,S3: nat] :
% 0.30/0.48 ( ( ( member_nat @ R3 @ A2 )
% 0.30/0.48 & ( member_nat @ S3 @ A2 )
% 0.30/0.48 & ( ord_less_nat @ R3 @ S3 ) )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_on_def
% 0.30/0.48 thf(fact_235_strict__mono__on__def,axiom,
% 0.30/0.48 ( strict1802283670at_nat
% 0.30/0.48 = ( ^ [F2: set_nat > nat,A2: set_set_nat] :
% 0.30/0.48 ! [R3: set_nat,S3: set_nat] :
% 0.30/0.48 ( ( ( member_set_nat @ R3 @ A2 )
% 0.30/0.48 & ( member_set_nat @ S3 @ A2 )
% 0.30/0.48 & ( ord_less_set_nat @ R3 @ S3 ) )
% 0.30/0.48 => ( ord_less_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_on_def
% 0.30/0.48 thf(fact_236_strict__mono__on__def,axiom,
% 0.30/0.48 ( strict473775692et_nat
% 0.30/0.48 = ( ^ [F2: set_nat > set_nat,A2: set_set_nat] :
% 0.30/0.48 ! [R3: set_nat,S3: set_nat] :
% 0.30/0.48 ( ( ( member_set_nat @ R3 @ A2 )
% 0.30/0.48 & ( member_set_nat @ S3 @ A2 )
% 0.30/0.48 & ( ord_less_set_nat @ R3 @ S3 ) )
% 0.30/0.48 => ( ord_less_set_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_on_def
% 0.30/0.48 thf(fact_237_strict__mono__on__def,axiom,
% 0.30/0.48 ( strict172559285lle_tv
% 0.30/0.48 = ( ^ [F2: set_nat > set_Pa1764573435lle_tv,A2: set_set_nat] :
% 0.30/0.48 ! [R3: set_nat,S3: set_nat] :
% 0.30/0.48 ( ( ( member_set_nat @ R3 @ A2 )
% 0.30/0.48 & ( member_set_nat @ S3 @ A2 )
% 0.30/0.48 & ( ord_less_set_nat @ R3 @ S3 ) )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_on_def
% 0.30/0.48 thf(fact_238_strict__mono__on__def,axiom,
% 0.30/0.48 ( strict1125660301tv_nat
% 0.30/0.48 = ( ^ [F2: set_Pa1764573435lle_tv > nat,A2: set_se800614875lle_tv] :
% 0.30/0.48 ! [R3: set_Pa1764573435lle_tv,S3: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ( member1875402276lle_tv @ R3 @ A2 )
% 0.30/0.48 & ( member1875402276lle_tv @ S3 @ A2 )
% 0.30/0.48 & ( ord_le727057319lle_tv @ R3 @ S3 ) )
% 0.30/0.48 => ( ord_less_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_on_def
% 0.30/0.48 thf(fact_239_strict__mono__on__def,axiom,
% 0.30/0.48 ( strict1455779395et_nat
% 0.30/0.48 = ( ^ [F2: set_Pa1764573435lle_tv > set_nat,A2: set_se800614875lle_tv] :
% 0.30/0.48 ! [R3: set_Pa1764573435lle_tv,S3: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ( member1875402276lle_tv @ R3 @ A2 )
% 0.30/0.48 & ( member1875402276lle_tv @ S3 @ A2 )
% 0.30/0.48 & ( ord_le727057319lle_tv @ R3 @ S3 ) )
% 0.30/0.48 => ( ord_less_set_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_on_def
% 0.30/0.48 thf(fact_240_strict__mono__on__def,axiom,
% 0.30/0.48 ( strict592849515lle_tv
% 0.30/0.48 = ( ^ [F2: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,A2: set_se800614875lle_tv] :
% 0.30/0.48 ! [R3: set_Pa1764573435lle_tv,S3: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ( member1875402276lle_tv @ R3 @ A2 )
% 0.30/0.48 & ( member1875402276lle_tv @ S3 @ A2 )
% 0.30/0.48 & ( ord_le727057319lle_tv @ R3 @ S3 ) )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_on_def
% 0.30/0.48 thf(fact_241_ord__eq__less__subst,axiom,
% 0.30/0.48 ! [A4: nat,F: nat > nat,B2: nat,C: nat] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( F @ B2 ) )
% 0.30/0.48 => ( ( ord_less_nat @ B2 @ C )
% 0.30/0.48 => ( ! [X3: nat,Y2: nat] :
% 0.30/0.48 ( ( ord_less_nat @ X3 @ Y2 )
% 0.30/0.48 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.30/0.48 => ( ord_less_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_less_subst
% 0.30/0.48 thf(fact_242_ord__eq__less__subst,axiom,
% 0.30/0.48 ! [A4: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( F @ B2 ) )
% 0.30/0.48 => ( ( ord_less_nat @ B2 @ C )
% 0.30/0.48 => ( ! [X3: nat,Y2: nat] :
% 0.30/0.48 ( ( ord_less_nat @ X3 @ Y2 )
% 0.30/0.48 => ( ord_less_set_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.30/0.48 => ( ord_less_set_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_less_subst
% 0.30/0.48 thf(fact_243_ord__eq__less__subst,axiom,
% 0.30/0.48 ! [A4: set_Pa1764573435lle_tv,F: nat > set_Pa1764573435lle_tv,B2: nat,C: nat] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( F @ B2 ) )
% 0.30/0.48 => ( ( ord_less_nat @ B2 @ C )
% 0.30/0.48 => ( ! [X3: nat,Y2: nat] :
% 0.30/0.48 ( ( ord_less_nat @ X3 @ Y2 )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.30/0.48 => ( ord_le727057319lle_tv @ A4 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_less_subst
% 0.30/0.48 thf(fact_244_ord__eq__less__subst,axiom,
% 0.30/0.48 ! [A4: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( F @ B2 ) )
% 0.30/0.48 => ( ( ord_less_set_nat @ B2 @ C )
% 0.30/0.48 => ( ! [X3: set_nat,Y2: set_nat] :
% 0.30/0.48 ( ( ord_less_set_nat @ X3 @ Y2 )
% 0.30/0.48 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.30/0.48 => ( ord_less_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_less_subst
% 0.30/0.48 thf(fact_245_ord__eq__less__subst,axiom,
% 0.30/0.48 ! [A4: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( F @ B2 ) )
% 0.30/0.48 => ( ( ord_less_set_nat @ B2 @ C )
% 0.30/0.48 => ( ! [X3: set_nat,Y2: set_nat] :
% 0.30/0.48 ( ( ord_less_set_nat @ X3 @ Y2 )
% 0.30/0.48 => ( ord_less_set_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.30/0.48 => ( ord_less_set_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_less_subst
% 0.30/0.48 thf(fact_246_ord__eq__less__subst,axiom,
% 0.30/0.48 ! [A4: set_Pa1764573435lle_tv,F: set_nat > set_Pa1764573435lle_tv,B2: set_nat,C: set_nat] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( F @ B2 ) )
% 0.30/0.48 => ( ( ord_less_set_nat @ B2 @ C )
% 0.30/0.48 => ( ! [X3: set_nat,Y2: set_nat] :
% 0.30/0.48 ( ( ord_less_set_nat @ X3 @ Y2 )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.30/0.48 => ( ord_le727057319lle_tv @ A4 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_less_subst
% 0.30/0.48 thf(fact_247_ord__eq__less__subst,axiom,
% 0.30/0.48 ! [A4: nat,F: set_Pa1764573435lle_tv > nat,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( F @ B2 ) )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ B2 @ C )
% 0.30/0.48 => ( ! [X3: set_Pa1764573435lle_tv,Y2: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ord_le727057319lle_tv @ X3 @ Y2 )
% 0.30/0.48 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.30/0.48 => ( ord_less_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_less_subst
% 0.30/0.48 thf(fact_248_ord__eq__less__subst,axiom,
% 0.30/0.48 ! [A4: set_nat,F: set_Pa1764573435lle_tv > set_nat,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( F @ B2 ) )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ B2 @ C )
% 0.30/0.48 => ( ! [X3: set_Pa1764573435lle_tv,Y2: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ord_le727057319lle_tv @ X3 @ Y2 )
% 0.30/0.48 => ( ord_less_set_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.30/0.48 => ( ord_less_set_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_less_subst
% 0.30/0.48 thf(fact_249_ord__eq__less__subst,axiom,
% 0.30/0.48 ! [A4: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( F @ B2 ) )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ B2 @ C )
% 0.30/0.48 => ( ! [X3: set_Pa1764573435lle_tv,Y2: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ord_le727057319lle_tv @ X3 @ Y2 )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.30/0.48 => ( ord_le727057319lle_tv @ A4 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord_eq_less_subst
% 0.30/0.48 thf(fact_250_mem__Collect__eq,axiom,
% 0.30/0.48 ! [A4: nat,P: nat > $o] :
% 0.30/0.48 ( ( member_nat @ A4 @ ( collect_nat @ P ) )
% 0.30/0.48 = ( P @ A4 ) ) ).
% 0.30/0.48
% 0.30/0.48 % mem_Collect_eq
% 0.30/0.48 thf(fact_251_mem__Collect__eq,axiom,
% 0.30/0.48 ! [A4: paraco1605129243lle_tv,P: paraco1605129243lle_tv > $o] :
% 0.30/0.48 ( ( member266900804lle_tv @ A4 @ ( collec1111687558lle_tv @ P ) )
% 0.30/0.48 = ( P @ A4 ) ) ).
% 0.30/0.48
% 0.30/0.48 % mem_Collect_eq
% 0.30/0.48 thf(fact_252_Collect__mem__eq,axiom,
% 0.30/0.48 ! [A: set_nat] :
% 0.30/0.48 ( ( collect_nat
% 0.30/0.48 @ ^ [X2: nat] : ( member_nat @ X2 @ A ) )
% 0.30/0.48 = A ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_mem_eq
% 0.30/0.48 thf(fact_253_Collect__mem__eq,axiom,
% 0.30/0.48 ! [A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( collec1111687558lle_tv
% 0.30/0.48 @ ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ A ) )
% 0.30/0.48 = A ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_mem_eq
% 0.30/0.48 thf(fact_254_Collect__cong,axiom,
% 0.30/0.48 ! [P: nat > $o,Q: nat > $o] :
% 0.30/0.48 ( ! [X3: nat] :
% 0.30/0.48 ( ( P @ X3 )
% 0.30/0.48 = ( Q @ X3 ) )
% 0.30/0.48 => ( ( collect_nat @ P )
% 0.30/0.48 = ( collect_nat @ Q ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_cong
% 0.30/0.48 thf(fact_255_Collect__cong,axiom,
% 0.30/0.48 ! [P: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 0.30/0.48 ( ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( P @ X3 )
% 0.30/0.48 = ( Q @ X3 ) )
% 0.30/0.48 => ( ( collec1111687558lle_tv @ P )
% 0.30/0.48 = ( collec1111687558lle_tv @ Q ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_cong
% 0.30/0.48 thf(fact_256_inj__on__strict__subset,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ B )
% 0.30/0.48 => ( ( ord_le727057319lle_tv @ A @ B )
% 0.30/0.48 => ( ord_le727057319lle_tv @ ( image_335818702lle_tv @ F @ A ) @ ( image_335818702lle_tv @ F @ B ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_strict_subset
% 0.30/0.48 thf(fact_257_inj__on__strict__subset,axiom,
% 0.30/0.48 ! [F: nat > nat,B: set_nat,A: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ B )
% 0.30/0.48 => ( ( ord_less_set_nat @ A @ B )
% 0.30/0.48 => ( ord_less_set_nat @ ( image_nat_nat @ F @ A ) @ ( image_nat_nat @ F @ B ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_strict_subset
% 0.30/0.48 thf(fact_258_inj__on__the__inv__into,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.48 => ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ A @ F ) @ ( image_335818702lle_tv @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_the_inv_into
% 0.30/0.48 thf(fact_259_inj__on__the__inv__into,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.48 => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A @ F ) @ ( image_nat_nat @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_the_inv_into
% 0.30/0.48 thf(fact_260_f__the__inv__into__f,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,Y: nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.48 => ( ( member_nat @ Y @ ( image_nat_nat @ F @ A ) )
% 0.30/0.48 => ( ( F @ ( the_inv_into_nat_nat @ A @ F @ Y ) )
% 0.30/0.48 = Y ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % f_the_inv_into_f
% 0.30/0.48 thf(fact_261_f__the__inv__into__f,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.48 => ( ( member266900804lle_tv @ Y @ ( image_335818702lle_tv @ F @ A ) )
% 0.30/0.48 => ( ( F @ ( the_in452116896lle_tv @ A @ F @ Y ) )
% 0.30/0.48 = Y ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % f_the_inv_into_f
% 0.30/0.48 thf(fact_262_strict__mono__inv,axiom,
% 0.30/0.48 ! [F: nat > nat,G: nat > nat] :
% 0.30/0.48 ( ( order_769474267at_nat @ F )
% 0.30/0.48 => ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ! [X3: nat] :
% 0.30/0.48 ( ( G @ ( F @ X3 ) )
% 0.30/0.48 = X3 )
% 0.30/0.48 => ( order_769474267at_nat @ G ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_mono_inv
% 0.30/0.48 thf(fact_263_surjD,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ? [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( Y
% 0.30/0.48 = ( F @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjD
% 0.30/0.48 thf(fact_264_surjD,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,Y: nat] :
% 0.30/0.48 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ? [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( Y
% 0.30/0.48 = ( F @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjD
% 0.30/0.48 thf(fact_265_surjD,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ? [X3: nat] :
% 0.30/0.48 ( Y
% 0.30/0.48 = ( F @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjD
% 0.30/0.48 thf(fact_266_surjD,axiom,
% 0.30/0.48 ! [F: nat > nat,Y: nat] :
% 0.30/0.48 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ? [X3: nat] :
% 0.30/0.48 ( Y
% 0.30/0.48 = ( F @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjD
% 0.30/0.48 thf(fact_267_surjE,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ~ ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( Y
% 0.30/0.48 != ( F @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjE
% 0.30/0.48 thf(fact_268_surjE,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,Y: nat] :
% 0.30/0.48 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ~ ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( Y
% 0.30/0.48 != ( F @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjE
% 0.30/0.48 thf(fact_269_surjE,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ~ ! [X3: nat] :
% 0.30/0.48 ( Y
% 0.30/0.48 != ( F @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjE
% 0.30/0.48 thf(fact_270_surjE,axiom,
% 0.30/0.48 ! [F: nat > nat,Y: nat] :
% 0.30/0.48 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ~ ! [X3: nat] :
% 0.30/0.48 ( Y
% 0.30/0.48 != ( F @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjE
% 0.30/0.48 thf(fact_271_surjI,axiom,
% 0.30/0.48 ! [G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( G @ ( F @ X3 ) )
% 0.30/0.48 = X3 )
% 0.30/0.48 => ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjI
% 0.30/0.48 thf(fact_272_surjI,axiom,
% 0.30/0.48 ! [G: paraco1605129243lle_tv > nat,F: nat > paraco1605129243lle_tv] :
% 0.30/0.48 ( ! [X3: nat] :
% 0.30/0.48 ( ( G @ ( F @ X3 ) )
% 0.30/0.48 = X3 )
% 0.30/0.48 => ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjI
% 0.30/0.48 thf(fact_273_surjI,axiom,
% 0.30/0.48 ! [G: nat > paraco1605129243lle_tv,F: paraco1605129243lle_tv > nat] :
% 0.30/0.48 ( ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( G @ ( F @ X3 ) )
% 0.30/0.48 = X3 )
% 0.30/0.48 => ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.30/0.48 = top_to1057771083lle_tv ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjI
% 0.30/0.48 thf(fact_274_surjI,axiom,
% 0.30/0.48 ! [G: nat > nat,F: nat > nat] :
% 0.30/0.48 ( ! [X3: nat] :
% 0.30/0.48 ( ( G @ ( F @ X3 ) )
% 0.30/0.48 = X3 )
% 0.30/0.48 => ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.30/0.48 = top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % surjI
% 0.30/0.48 thf(fact_275_rangeI,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,X: paraco1605129243lle_tv] : ( member_nat @ ( F @ X ) @ ( image_376325286tv_nat @ F @ top_to1057771083lle_tv ) ) ).
% 0.30/0.48
% 0.30/0.48 % rangeI
% 0.30/0.48 thf(fact_276_rangeI,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] : ( member266900804lle_tv @ ( F @ X ) @ ( image_335818702lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 0.30/0.48
% 0.30/0.48 % rangeI
% 0.30/0.48 thf(fact_277_rangeI,axiom,
% 0.30/0.48 ! [F: nat > nat,X: nat] : ( member_nat @ ( F @ X ) @ ( image_nat_nat @ F @ top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % rangeI
% 0.30/0.48 thf(fact_278_rangeI,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,X: nat] : ( member266900804lle_tv @ ( F @ X ) @ ( image_1151963140lle_tv @ F @ top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % rangeI
% 0.30/0.48 thf(fact_279_surj__def,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 = ( ! [Y3: paraco1605129243lle_tv] :
% 0.30/0.48 ? [X2: paraco1605129243lle_tv] :
% 0.30/0.48 ( Y3
% 0.30/0.48 = ( F @ X2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surj_def
% 0.30/0.48 thf(fact_280_surj__def,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat] :
% 0.30/0.48 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 = ( ! [Y3: nat] :
% 0.30/0.48 ? [X2: paraco1605129243lle_tv] :
% 0.30/0.48 ( Y3
% 0.30/0.48 = ( F @ X2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surj_def
% 0.30/0.48 thf(fact_281_surj__def,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 = ( ! [Y3: paraco1605129243lle_tv] :
% 0.30/0.48 ? [X2: nat] :
% 0.30/0.48 ( Y3
% 0.30/0.48 = ( F @ X2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surj_def
% 0.30/0.48 thf(fact_282_surj__def,axiom,
% 0.30/0.48 ! [F: nat > nat] :
% 0.30/0.48 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 = ( ! [Y3: nat] :
% 0.30/0.48 ? [X2: nat] :
% 0.30/0.48 ( Y3
% 0.30/0.48 = ( F @ X2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % surj_def
% 0.30/0.48 thf(fact_283_range__eqI,axiom,
% 0.30/0.48 ! [B2: nat,F: paraco1605129243lle_tv > nat,X: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member_nat @ B2 @ ( image_376325286tv_nat @ F @ top_to1057771083lle_tv ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_eqI
% 0.30/0.48 thf(fact_284_range__eqI,axiom,
% 0.30/0.48 ! [B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ top_to1057771083lle_tv ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_eqI
% 0.30/0.48 thf(fact_285_range__eqI,axiom,
% 0.30/0.48 ! [B2: nat,F: nat > nat,X: nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member_nat @ B2 @ ( image_nat_nat @ F @ top_top_set_nat ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_eqI
% 0.30/0.48 thf(fact_286_range__eqI,axiom,
% 0.30/0.48 ! [B2: paraco1605129243lle_tv,F: nat > paraco1605129243lle_tv,X: nat] :
% 0.30/0.48 ( ( B2
% 0.30/0.48 = ( F @ X ) )
% 0.30/0.48 => ( member266900804lle_tv @ B2 @ ( image_1151963140lle_tv @ F @ top_top_set_nat ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % range_eqI
% 0.30/0.48 thf(fact_287_inj__on__image__iff,axiom,
% 0.30/0.48 ! [A: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ X3 @ A )
% 0.30/0.48 => ! [Xa: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ Xa @ A )
% 0.30/0.48 => ( ( ( G @ ( F @ X3 ) )
% 0.30/0.48 = ( G @ ( F @ Xa ) ) )
% 0.30/0.48 = ( ( G @ X3 )
% 0.30/0.48 = ( G @ Xa ) ) ) ) )
% 0.30/0.48 => ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.48 => ( ( inj_on772319074lle_tv @ G @ ( image_335818702lle_tv @ F @ A ) )
% 0.30/0.48 = ( inj_on772319074lle_tv @ G @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_image_iff
% 0.30/0.48 thf(fact_288_inj__on__image__iff,axiom,
% 0.30/0.48 ! [A: set_nat,G: nat > nat,F: nat > nat] :
% 0.30/0.48 ( ! [X3: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ A )
% 0.30/0.48 => ! [Xa: nat] :
% 0.30/0.48 ( ( member_nat @ Xa @ A )
% 0.30/0.48 => ( ( ( G @ ( F @ X3 ) )
% 0.30/0.48 = ( G @ ( F @ Xa ) ) )
% 0.30/0.48 = ( ( G @ X3 )
% 0.30/0.48 = ( G @ Xa ) ) ) ) )
% 0.30/0.48 => ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.48 => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A ) )
% 0.30/0.48 = ( inj_on_nat_nat @ G @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_image_iff
% 0.30/0.48 thf(fact_289_top_Oextremum__strict,axiom,
% 0.30/0.48 ! [A4: set_Pa1764573435lle_tv] :
% 0.30/0.48 ~ ( ord_le727057319lle_tv @ top_to1057771083lle_tv @ A4 ) ).
% 0.30/0.48
% 0.30/0.48 % top.extremum_strict
% 0.30/0.48 thf(fact_290_top_Oextremum__strict,axiom,
% 0.30/0.48 ! [A4: set_nat] :
% 0.30/0.48 ~ ( ord_less_set_nat @ top_top_set_nat @ A4 ) ).
% 0.30/0.48
% 0.30/0.48 % top.extremum_strict
% 0.30/0.48 thf(fact_291_top_Onot__eq__extremum,axiom,
% 0.30/0.48 ! [A4: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( A4 != top_to1057771083lle_tv )
% 0.30/0.48 = ( ord_le727057319lle_tv @ A4 @ top_to1057771083lle_tv ) ) ).
% 0.30/0.48
% 0.30/0.48 % top.not_eq_extremum
% 0.30/0.48 thf(fact_292_top_Onot__eq__extremum,axiom,
% 0.30/0.48 ! [A4: set_nat] :
% 0.30/0.48 ( ( A4 != top_top_set_nat )
% 0.30/0.48 = ( ord_less_set_nat @ A4 @ top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % top.not_eq_extremum
% 0.30/0.48 thf(fact_293_inj__on__add,axiom,
% 0.30/0.48 ! [A4: nat,A: set_nat] : ( inj_on_nat_nat @ ( plus_plus_nat @ A4 ) @ A ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_add
% 0.30/0.48 thf(fact_294_the__inv__into__f__f,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,X: nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.48 => ( ( member_nat @ X @ A )
% 0.30/0.48 => ( ( the_inv_into_nat_nat @ A @ F @ ( F @ X ) )
% 0.30/0.48 = X ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_f_f
% 0.30/0.48 thf(fact_295_the__inv__into__f__f,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.48 => ( ( member266900804lle_tv @ X @ A )
% 0.30/0.48 => ( ( the_in452116896lle_tv @ A @ F @ ( F @ X ) )
% 0.30/0.48 = X ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_f_f
% 0.30/0.48 thf(fact_296_the__inv__into__f__eq,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,X: nat,Y: nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.48 => ( ( ( F @ X )
% 0.30/0.48 = Y )
% 0.30/0.48 => ( ( member_nat @ X @ A )
% 0.30/0.48 => ( ( the_inv_into_nat_nat @ A @ F @ Y )
% 0.30/0.48 = X ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_f_eq
% 0.30/0.48 thf(fact_297_the__inv__into__f__eq,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.48 => ( ( ( F @ X )
% 0.30/0.48 = Y )
% 0.30/0.48 => ( ( member266900804lle_tv @ X @ A )
% 0.30/0.48 => ( ( the_in452116896lle_tv @ A @ F @ Y )
% 0.30/0.48 = X ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_f_eq
% 0.30/0.48 thf(fact_298_psubsetD,axiom,
% 0.30/0.48 ! [A: set_nat,B: set_nat,C: nat] :
% 0.30/0.48 ( ( ord_less_set_nat @ A @ B )
% 0.30/0.48 => ( ( member_nat @ C @ A )
% 0.30/0.48 => ( member_nat @ C @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % psubsetD
% 0.30/0.48 thf(fact_299_psubsetD,axiom,
% 0.30/0.48 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ord_le727057319lle_tv @ A @ B )
% 0.30/0.48 => ( ( member266900804lle_tv @ C @ A )
% 0.30/0.48 => ( member266900804lle_tv @ C @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % psubsetD
% 0.30/0.48 thf(fact_300_the__inv__into__into,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,X: nat,B: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.48 => ( ( member_nat @ X @ ( image_nat_nat @ F @ A ) )
% 0.30/0.48 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.48 => ( member_nat @ ( the_inv_into_nat_nat @ A @ F @ X ) @ B ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_into
% 0.30/0.48 thf(fact_301_the__inv__into__into,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,A: set_Pa1764573435lle_tv,X: nat,B: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on1179712058tv_nat @ F @ A )
% 0.30/0.48 => ( ( member_nat @ X @ ( image_376325286tv_nat @ F @ A ) )
% 0.30/0.48 => ( ( ord_le241064091lle_tv @ A @ B )
% 0.30/0.48 => ( member266900804lle_tv @ ( the_in1509933432tv_nat @ A @ F @ X ) @ B ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_into
% 0.30/0.48 thf(fact_302_the__inv__into__into,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,A: set_nat,X: paraco1605129243lle_tv,B: set_nat] :
% 0.30/0.48 ( ( inj_on1955349912lle_tv @ F @ A )
% 0.30/0.48 => ( ( member266900804lle_tv @ X @ ( image_1151963140lle_tv @ F @ A ) )
% 0.30/0.48 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.48 => ( member_nat @ ( the_in138087638lle_tv @ A @ F @ X ) @ B ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_into
% 0.30/0.48 thf(fact_303_the__inv__into__into,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.48 => ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F @ A ) )
% 0.30/0.48 => ( ( ord_le241064091lle_tv @ A @ B )
% 0.30/0.48 => ( member266900804lle_tv @ ( the_in452116896lle_tv @ A @ F @ X ) @ B ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_inv_into_into
% 0.30/0.48 thf(fact_304_prod_Oinj__map,axiom,
% 0.30/0.48 ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.30/0.48 => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 0.30/0.48 => ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ F1 @ F22 ) @ top_to1871154984lle_tv ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % prod.inj_map
% 0.30/0.48 thf(fact_305_prod_Oinj__map,axiom,
% 0.30/0.48 ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: nat > nat] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.30/0.48 => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 0.30/0.48 => ( inj_on552895452tv_nat @ ( produc42536895at_nat @ F1 @ F22 ) @ top_to975729152tv_nat ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % prod.inj_map
% 0.30/0.48 thf(fact_306_prod_Oinj__map,axiom,
% 0.30/0.48 ! [F1: nat > nat,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.30/0.48 => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 0.30/0.48 => ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ F1 @ F22 ) @ top_to1411004326lle_tv ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % prod.inj_map
% 0.30/0.48 thf(fact_307_prod_Oinj__map,axiom,
% 0.30/0.48 ! [F1: nat > nat,F22: nat > nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.30/0.48 => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 0.30/0.48 => ( inj_on26176689at_nat @ ( produc505105722at_nat @ F1 @ F22 ) @ top_to1555900337at_nat ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % prod.inj_map
% 0.30/0.48 thf(fact_308_subsetI,axiom,
% 0.30/0.48 ! [A: set_nat,B: set_nat] :
% 0.30/0.48 ( ! [X3: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ A )
% 0.30/0.48 => ( member_nat @ X3 @ B ) )
% 0.30/0.48 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.30/0.48
% 0.30/0.48 % subsetI
% 0.30/0.48 thf(fact_309_subsetI,axiom,
% 0.30/0.48 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ X3 @ A )
% 0.30/0.48 => ( member266900804lle_tv @ X3 @ B ) )
% 0.30/0.48 => ( ord_le241064091lle_tv @ A @ B ) ) ).
% 0.30/0.48
% 0.30/0.48 % subsetI
% 0.30/0.48 thf(fact_310_image__subsetI,axiom,
% 0.30/0.48 ! [A: set_nat,F: nat > nat,B: set_nat] :
% 0.30/0.48 ( ! [X3: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ A )
% 0.30/0.48 => ( member_nat @ ( F @ X3 ) @ B ) )
% 0.30/0.48 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A ) @ B ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_subsetI
% 0.30/0.48 thf(fact_311_image__subsetI,axiom,
% 0.30/0.48 ! [A: set_nat,F: nat > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ! [X3: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ A )
% 0.30/0.48 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 0.30/0.48 => ( ord_le241064091lle_tv @ ( image_1151963140lle_tv @ F @ A ) @ B ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_subsetI
% 0.30/0.48 thf(fact_312_image__subsetI,axiom,
% 0.30/0.48 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > nat,B: set_nat] :
% 0.30/0.48 ( ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ X3 @ A )
% 0.30/0.48 => ( member_nat @ ( F @ X3 ) @ B ) )
% 0.30/0.48 => ( ord_less_eq_set_nat @ ( image_376325286tv_nat @ F @ A ) @ B ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_subsetI
% 0.30/0.48 thf(fact_313_image__subsetI,axiom,
% 0.30/0.48 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ! [X3: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ X3 @ A )
% 0.30/0.48 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 0.30/0.48 => ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ A ) @ B ) ) ).
% 0.30/0.48
% 0.30/0.48 % image_subsetI
% 0.30/0.48 thf(fact_314_top_Oextremum__uniqueI,axiom,
% 0.30/0.48 ! [A4: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A4 )
% 0.30/0.48 => ( A4 = top_to1057771083lle_tv ) ) ).
% 0.30/0.48
% 0.30/0.48 % top.extremum_uniqueI
% 0.30/0.48 thf(fact_315_top_Oextremum__uniqueI,axiom,
% 0.30/0.48 ! [A4: set_nat] :
% 0.30/0.48 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A4 )
% 0.30/0.48 => ( A4 = top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % top.extremum_uniqueI
% 0.30/0.48 thf(fact_316_top_Oextremum__unique,axiom,
% 0.30/0.48 ! [A4: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A4 )
% 0.30/0.48 = ( A4 = top_to1057771083lle_tv ) ) ).
% 0.30/0.48
% 0.30/0.48 % top.extremum_unique
% 0.30/0.48 thf(fact_317_top_Oextremum__unique,axiom,
% 0.30/0.48 ! [A4: set_nat] :
% 0.30/0.48 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A4 )
% 0.30/0.48 = ( A4 = top_top_set_nat ) ) ).
% 0.30/0.48
% 0.30/0.48 % top.extremum_unique
% 0.30/0.48 thf(fact_318_top__greatest,axiom,
% 0.30/0.48 ! [A4: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A4 @ top_to1057771083lle_tv ) ).
% 0.30/0.48
% 0.30/0.48 % top_greatest
% 0.30/0.48 thf(fact_319_top__greatest,axiom,
% 0.30/0.48 ! [A4: set_nat] : ( ord_less_eq_set_nat @ A4 @ top_top_set_nat ) ).
% 0.30/0.48
% 0.30/0.48 % top_greatest
% 0.30/0.48 thf(fact_320_subset__UNIV,axiom,
% 0.30/0.48 ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ) ).
% 0.30/0.48
% 0.30/0.48 % subset_UNIV
% 0.30/0.48 thf(fact_321_subset__UNIV,axiom,
% 0.30/0.48 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 0.30/0.48
% 0.30/0.48 % subset_UNIV
% 0.30/0.48 thf(fact_322_subset__inj__on,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ B )
% 0.30/0.48 => ( ( ord_le241064091lle_tv @ A @ B )
% 0.30/0.48 => ( inj_on772319074lle_tv @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_inj_on
% 0.30/0.48 thf(fact_323_subset__inj__on,axiom,
% 0.30/0.48 ! [F: nat > nat,B: set_nat,A: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ B )
% 0.30/0.48 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.48 => ( inj_on_nat_nat @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_inj_on
% 0.30/0.48 thf(fact_324_inj__on__subset,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ A )
% 0.30/0.48 => ( ( ord_le241064091lle_tv @ B @ A )
% 0.30/0.48 => ( inj_on772319074lle_tv @ F @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_subset
% 0.30/0.48 thf(fact_325_inj__on__subset,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,B: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ A )
% 0.30/0.48 => ( ( ord_less_eq_set_nat @ B @ A )
% 0.30/0.48 => ( inj_on_nat_nat @ F @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_subset
% 0.30/0.48 thf(fact_326_in__mono,axiom,
% 0.30/0.48 ! [A: set_nat,B: set_nat,X: nat] :
% 0.30/0.48 ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.48 => ( ( member_nat @ X @ A )
% 0.30/0.48 => ( member_nat @ X @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % in_mono
% 0.30/0.48 thf(fact_327_in__mono,axiom,
% 0.30/0.48 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ord_le241064091lle_tv @ A @ B )
% 0.30/0.48 => ( ( member266900804lle_tv @ X @ A )
% 0.30/0.48 => ( member266900804lle_tv @ X @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % in_mono
% 0.30/0.48 thf(fact_328_subsetD,axiom,
% 0.30/0.48 ! [A: set_nat,B: set_nat,C: nat] :
% 0.30/0.48 ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.48 => ( ( member_nat @ C @ A )
% 0.30/0.48 => ( member_nat @ C @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subsetD
% 0.30/0.48 thf(fact_329_subsetD,axiom,
% 0.30/0.48 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ord_le241064091lle_tv @ A @ B )
% 0.30/0.48 => ( ( member266900804lle_tv @ C @ A )
% 0.30/0.48 => ( member266900804lle_tv @ C @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subsetD
% 0.30/0.48 thf(fact_330_subset__eq,axiom,
% 0.30/0.48 ( ord_less_eq_set_nat
% 0.30/0.48 = ( ^ [A2: set_nat,B3: set_nat] :
% 0.30/0.48 ! [X2: nat] :
% 0.30/0.48 ( ( member_nat @ X2 @ A2 )
% 0.30/0.48 => ( member_nat @ X2 @ B3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_eq
% 0.30/0.48 thf(fact_331_subset__eq,axiom,
% 0.30/0.48 ( ord_le241064091lle_tv
% 0.30/0.48 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 0.30/0.48 ! [X2: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ X2 @ A2 )
% 0.30/0.48 => ( member266900804lle_tv @ X2 @ B3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_eq
% 0.30/0.48 thf(fact_332_subset__iff,axiom,
% 0.30/0.48 ( ord_less_eq_set_nat
% 0.30/0.48 = ( ^ [A2: set_nat,B3: set_nat] :
% 0.30/0.48 ! [T: nat] :
% 0.30/0.48 ( ( member_nat @ T @ A2 )
% 0.30/0.48 => ( member_nat @ T @ B3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_iff
% 0.30/0.48 thf(fact_333_subset__iff,axiom,
% 0.30/0.48 ( ord_le241064091lle_tv
% 0.30/0.48 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 0.30/0.48 ! [T: paraco1605129243lle_tv] :
% 0.30/0.48 ( ( member266900804lle_tv @ T @ A2 )
% 0.30/0.48 => ( member266900804lle_tv @ T @ B3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_iff
% 0.30/0.48 thf(fact_334_linorder__inj__onI,axiom,
% 0.30/0.48 ! [A: set_nat,F: nat > nat] :
% 0.30/0.48 ( ! [X3: nat,Y2: nat] :
% 0.30/0.48 ( ( ord_less_nat @ X3 @ Y2 )
% 0.30/0.48 => ( ( member_nat @ X3 @ A )
% 0.30/0.48 => ( ( member_nat @ Y2 @ A )
% 0.30/0.48 => ( ( F @ X3 )
% 0.30/0.48 != ( F @ Y2 ) ) ) ) )
% 0.30/0.48 => ( ! [X3: nat,Y2: nat] :
% 0.30/0.48 ( ( member_nat @ X3 @ A )
% 0.30/0.48 => ( ( member_nat @ Y2 @ A )
% 0.30/0.48 => ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.30/0.48 | ( ord_less_eq_nat @ Y2 @ X3 ) ) ) )
% 0.30/0.48 => ( inj_on_nat_nat @ F @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % linorder_inj_onI
% 0.30/0.48 thf(fact_335_inj__on__image__mem__iff,axiom,
% 0.30/0.48 ! [F: nat > nat,B: set_nat,A4: nat,A: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ B )
% 0.30/0.48 => ( ( member_nat @ A4 @ B )
% 0.30/0.48 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.48 => ( ( member_nat @ ( F @ A4 ) @ ( image_nat_nat @ F @ A ) )
% 0.30/0.48 = ( member_nat @ A4 @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_image_mem_iff
% 0.30/0.48 thf(fact_336_inj__on__image__mem__iff,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,B: set_nat,A4: nat,A: set_nat] :
% 0.30/0.48 ( ( inj_on1955349912lle_tv @ F @ B )
% 0.30/0.48 => ( ( member_nat @ A4 @ B )
% 0.30/0.48 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.48 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_1151963140lle_tv @ F @ A ) )
% 0.30/0.48 = ( member_nat @ A4 @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_image_mem_iff
% 0.30/0.48 thf(fact_337_inj__on__image__mem__iff,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv,A4: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on1179712058tv_nat @ F @ B )
% 0.30/0.48 => ( ( member266900804lle_tv @ A4 @ B )
% 0.30/0.48 => ( ( ord_le241064091lle_tv @ A @ B )
% 0.30/0.48 => ( ( member_nat @ ( F @ A4 ) @ ( image_376325286tv_nat @ F @ A ) )
% 0.30/0.48 = ( member266900804lle_tv @ A4 @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_image_mem_iff
% 0.30/0.48 thf(fact_338_inj__on__image__mem__iff,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,A4: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ B )
% 0.30/0.48 => ( ( member266900804lle_tv @ A4 @ B )
% 0.30/0.48 => ( ( ord_le241064091lle_tv @ A @ B )
% 0.30/0.48 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_335818702lle_tv @ F @ A ) )
% 0.30/0.48 = ( member266900804lle_tv @ A4 @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_image_mem_iff
% 0.30/0.48 thf(fact_339_inj__on__image__eq__iff,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,C2: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ C2 )
% 0.30/0.48 => ( ( ord_le241064091lle_tv @ A @ C2 )
% 0.30/0.48 => ( ( ord_le241064091lle_tv @ B @ C2 )
% 0.30/0.48 => ( ( ( image_335818702lle_tv @ F @ A )
% 0.30/0.48 = ( image_335818702lle_tv @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_image_eq_iff
% 0.30/0.48 thf(fact_340_inj__on__image__eq__iff,axiom,
% 0.30/0.48 ! [F: nat > nat,C2: set_nat,A: set_nat,B: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ C2 )
% 0.30/0.48 => ( ( ord_less_eq_set_nat @ A @ C2 )
% 0.30/0.48 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 0.30/0.48 => ( ( ( image_nat_nat @ F @ A )
% 0.30/0.48 = ( image_nat_nat @ F @ B ) )
% 0.30/0.48 = ( A = B ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_on_image_eq_iff
% 0.30/0.48 thf(fact_341_inj__image__subset__iff,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 => ( ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ A ) @ ( image_335818702lle_tv @ F @ B ) )
% 0.30/0.48 = ( ord_le241064091lle_tv @ A @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_subset_iff
% 0.30/0.48 thf(fact_342_inj__image__subset__iff,axiom,
% 0.30/0.48 ! [F: nat > nat,A: set_nat,B: set_nat] :
% 0.30/0.48 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.48 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A ) @ ( image_nat_nat @ F @ B ) )
% 0.30/0.48 = ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % inj_image_subset_iff
% 0.30/0.48 thf(fact_343_map__prod__surj,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ F @ G ) @ top_to1871154984lle_tv )
% 0.30/0.48 = top_to1871154984lle_tv ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_344_map__prod__surj,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 0.30/0.48 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ( image_1796815776tv_nat @ ( produc1500159719tv_nat @ F @ G ) @ top_to1871154984lle_tv )
% 0.30/0.48 = top_to975729152tv_nat ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_345_map__prod__surj,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( image_228488944lle_tv @ ( produc1521089895lle_tv @ F @ G ) @ top_to975729152tv_nat )
% 0.30/0.48 = top_to1871154984lle_tv ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_346_map__prod__surj,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: nat > nat] :
% 0.30/0.48 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ( image_1104296520tv_nat @ ( produc42536895at_nat @ F @ G ) @ top_to975729152tv_nat )
% 0.30/0.48 = top_to975729152tv_nat ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_347_map__prod__surj,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( image_1892891680lle_tv @ ( produc1095080935lle_tv @ F @ G ) @ top_to1871154984lle_tv )
% 0.30/0.48 = top_to1411004326lle_tv ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_348_map__prod__surj,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,G: paraco1605129243lle_tv > nat] :
% 0.30/0.48 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ( image_901203832at_nat @ ( produc51277375tv_nat @ F @ G ) @ top_to1871154984lle_tv )
% 0.30/0.48 = top_to1555900337at_nat ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_349_map__prod__surj,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,G: nat > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ F @ G ) @ top_to975729152tv_nat )
% 0.30/0.48 = top_to1411004326lle_tv ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_350_map__prod__surj,axiom,
% 0.30/0.48 ! [F: paraco1605129243lle_tv > nat,G: nat > nat] :
% 0.30/0.48 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ( image_1805124128at_nat @ ( produc386540311at_nat @ F @ G ) @ top_to975729152tv_nat )
% 0.30/0.48 = top_to1555900337at_nat ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_351_map__prod__surj,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.48 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ F @ G ) @ top_to1411004326lle_tv )
% 0.30/0.48 = top_to1871154984lle_tv ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_352_map__prod__surj,axiom,
% 0.30/0.48 ! [F: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 0.30/0.48 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.48 = top_to1057771083lle_tv )
% 0.30/0.48 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.30/0.48 = top_top_set_nat )
% 0.30/0.48 => ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ F @ G ) @ top_to1411004326lle_tv )
% 0.30/0.48 = top_to975729152tv_nat ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_prod_surj
% 0.30/0.48 thf(fact_353_subset__image__inj,axiom,
% 0.30/0.48 ! [S4: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,T2: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ord_le241064091lle_tv @ S4 @ ( image_335818702lle_tv @ F @ T2 ) )
% 0.30/0.48 = ( ? [U: set_Pa1764573435lle_tv] :
% 0.30/0.48 ( ( ord_le241064091lle_tv @ U @ T2 )
% 0.30/0.48 & ( inj_on772319074lle_tv @ F @ U )
% 0.30/0.48 & ( S4
% 0.30/0.48 = ( image_335818702lle_tv @ F @ U ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_image_inj
% 0.30/0.48 thf(fact_354_subset__image__inj,axiom,
% 0.30/0.48 ! [S4: set_nat,F: nat > nat,T2: set_nat] :
% 0.30/0.48 ( ( ord_less_eq_set_nat @ S4 @ ( image_nat_nat @ F @ T2 ) )
% 0.30/0.48 = ( ? [U: set_nat] :
% 0.30/0.48 ( ( ord_less_eq_set_nat @ U @ T2 )
% 0.30/0.48 & ( inj_on_nat_nat @ F @ U )
% 0.30/0.48 & ( S4
% 0.30/0.48 = ( image_nat_nat @ F @ U ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_image_inj
% 0.30/0.48
% 0.30/0.48 % Conjectures (1)
% 0.30/0.48 thf(conj_0,conjecture,
% 0.30/0.48 inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 2.94/1.53 ---- Embedded in THF ---
% 2.94/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.94/1.53 %%% Generated on Tue Feb 24 08:27:43 EST 2026
% 2.94/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.94/1.53 %%% Logic specification used:
% 2.94/1.53 %%% thf(spec, logic, $$dhol).
% 2.94/1.53
% 2.94/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.8VRe1TRbh8/DTF2DTF11108.p
% See solution above
% 2.94/1.54 ------------------------
% 3.05/1.60 ---- Cleaned THF ---
% 3.05/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.05/1.60 set_Pr2014382200lle_tv: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 produc1647334210lle_tv: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 3.05/1.60 set_Pr1725653840tv_nat: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.05/1.60 set_Pr13445366lle_tv: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.05/1.60 produc194167194tv_nat: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 produc270694976lle_tv: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.05/1.60 set_se800614875lle_tv: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.05/1.60 set_Pr1986765409at_nat: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 set_Pa1764573435lle_tv: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.05/1.60 product_prod_nat_nat: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 paraco1605129243lle_tv: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 3.05/1.60 set_set_nat: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 3.05/1.60 set_nat: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(ty_n_t__Nat__Onat,type,
% 3.05/1.60 nat: $tType ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.05/1.60 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.05/1.60 inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 3.05/1.60 inj_on642995232at_nat: ( product_prod_nat_nat > nat ) > set_Pr1986765409at_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 inj_on520021963lle_tv: ( product_prod_nat_nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat > $o ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
% 3.05/1.60
% 3.05/1.60 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__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 inj_on1840679568lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_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,
% 3.05/1.60 inj_on1764151786tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Nat__Onat,type,
% 3.05/1.60 inj_on936843139tv_nat: ( produc270694976lle_tv > nat ) > set_Pr13445366lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 inj_on394919723lle_tv: ( produc270694976lle_tv > paraco1605129243lle_tv ) > set_Pr13445366lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 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__Nat__Onat_J,type,
% 3.05/1.60 inj_on1954136462at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 3.05/1.60 inj_on808253149at_nat: ( produc194167194tv_nat > nat ) > set_Pr1725653840tv_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 inj_on1612474245lle_tv: ( produc194167194tv_nat > paraco1605129243lle_tv ) > set_Pr1725653840tv_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Oinj__on_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,
% 3.05/1.60 inj_on1971554740at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > $o ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
% 3.05/1.60
% 3.05/1.60 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__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 inj_on967082628lle_tv: ( produc194167194tv_nat > produc1647334210lle_tv ) > set_Pr1725653840tv_nat > $o ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.05/1.60 strict2146030304at_nat: ( nat > nat ) > set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.05/1.60 strict1310998166et_nat: ( nat > set_nat ) > set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 strict1658340843lle_tv: ( nat > set_Pa1764573435lle_tv ) > set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 3.05/1.60 strict1802283670at_nat: ( set_nat > nat ) > set_set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.05/1.60 strict473775692et_nat: ( set_nat > set_nat ) > set_set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 strict172559285lle_tv: ( set_nat > set_Pa1764573435lle_tv ) > set_set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Nat__Onat,type,
% 3.05/1.60 strict1125660301tv_nat: ( set_Pa1764573435lle_tv > nat ) > set_se800614875lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.05/1.60 strict1455779395et_nat: ( set_Pa1764573435lle_tv > set_nat ) > set_se800614875lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Ostrict__mono__on_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 strict592849515lle_tv: ( set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ) > set_se800614875lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.05/1.60 the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 the_in138087638lle_tv: set_nat > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.05/1.60 the_in1509933432tv_nat: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > nat ) > nat > paraco1605129243lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.05/1.60 the_in2068894451at_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_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,
% 3.05/1.60 the_in744013006lle_tv: set_Pr1986765409at_nat > ( product_prod_nat_nat > produc270694976lle_tv ) > produc270694976lle_tv > product_prod_nat_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_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,
% 3.05/1.60 the_in667485224tv_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > produc194167194tv_nat ) > produc194167194tv_nat > product_prod_nat_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_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,
% 3.05/1.60 the_in857469900at_nat: set_Pr13445366lle_tv > ( produc270694976lle_tv > product_prod_nat_nat ) > product_prod_nat_nat > produc270694976lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_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,
% 3.05/1.60 the_in1388677748lle_tv: set_Pr13445366lle_tv > ( produc270694976lle_tv > produc270694976lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_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,
% 3.05/1.60 the_in874888178at_nat: set_Pr1725653840tv_nat > ( produc194167194tv_nat > product_prod_nat_nat ) > product_prod_nat_nat > produc194167194tv_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_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,
% 3.05/1.60 the_in195660058tv_nat: set_Pr1725653840tv_nat > ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Fun_Othe__inv__into_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,
% 3.05/1.60 the_in427240730lle_tv: set_Pr2014382200lle_tv > ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 3.05/1.60 plus_plus_nat: nat > nat > nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 3.05/1.60 ord_less_nat: nat > nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.05/1.60 ord_less_set_nat: set_nat > set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 ord_le727057319lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 3.05/1.60 ord_less_eq_nat: nat > nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.05/1.60 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.05/1.60 order_769474267at_nat: ( nat > nat ) > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
% 3.05/1.60 top_top_nat_o: nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 3.05/1.60 top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 3.05/1.60 top_to632227436_nat_o: product_prod_nat_nat > $o ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 top_to900819589_nat_o: produc194167194tv_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
% 3.05/1.60 top_top_o: $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.05/1.60 top_top_set_nat: set_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.05/1.60 top_to1555900337at_nat: set_Pr1986765409at_nat ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 top_to1411004326lle_tv: set_Pr13445366lle_tv ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 top_to975729152tv_nat: set_Pr1725653840tv_nat ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv,type,
% 3.05/1.60 paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_OIndet,type,
% 3.05/1.60 paraco793048302_Indet: nat > paraco1605129243lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.05/1.60 produc1320959600at_nat: ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 produc237097339lle_tv: ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.05/1.60 produc1608943133tv_nat: ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 produc1804670661lle_tv: ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc1647334210lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.05/1.60 produc2040316391tv_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 produc1408152463lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.05/1.60 produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.05/1.60 produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.05/1.60 produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.05/1.60 produc51277375tv_nat: ( paraco1605129243lle_tv > nat ) > ( paraco1605129243lle_tv > nat ) > produc1647334210lle_tv > product_prod_nat_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 produc1095080935lle_tv: ( paraco1605129243lle_tv > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc270694976lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.05/1.60 produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 produc1521089895lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc1647334210lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.05/1.60 produc1500159719tv_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc1647334210lle_tv > produc194167194tv_nat ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 3.05/1.60 collect_nat: ( nat > $o ) > set_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_OCollect_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.05/1.60 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.05/1.60 collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.05/1.60 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.05/1.60 image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 3.05/1.60 image_1397137548at_nat: ( product_prod_nat_nat > nat ) > set_Pr1986765409at_nat > set_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 image_1093035615lle_tv: ( product_prod_nat_nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat > set_Pa1764573435lle_tv ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Nat__Onat,type,
% 3.05/1.60 image_1509856791tv_nat: ( produc270694976lle_tv > nat ) > set_Pr13445366lle_tv > set_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 image_802013119lle_tv: ( produc270694976lle_tv > paraco1605129243lle_tv ) > set_Pr13445366lle_tv > set_Pa1764573435lle_tv ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 3.05/1.60 image_1381266801at_nat: ( produc194167194tv_nat > nat ) > set_Pr1725653840tv_nat > set_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 image_2019567641lle_tv: ( produc194167194tv_nat > paraco1605129243lle_tv ) > set_Pr1725653840tv_nat > set_Pa1764573435lle_tv ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
% 3.05/1.60
% 3.05/1.60 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,
% 3.05/1.60 image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_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,
% 3.05/1.60 image_1104296520tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > set_Pr1725653840tv_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 image_228488944lle_tv: ( produc194167194tv_nat > produc1647334210lle_tv ) > set_Pr1725653840tv_nat > set_Pr2014382200lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.05/1.60 image_901203832at_nat: ( produc1647334210lle_tv > product_prod_nat_nat ) > set_Pr2014382200lle_tv > set_Pr1986765409at_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 image_1892891680lle_tv: ( produc1647334210lle_tv > produc270694976lle_tv ) > set_Pr2014382200lle_tv > set_Pr13445366lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_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__Nat__Onat_J,type,
% 3.05/1.60 image_1796815776tv_nat: ( produc1647334210lle_tv > produc194167194tv_nat ) > set_Pr2014382200lle_tv > set_Pr1725653840tv_nat ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_Set_Oimage_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,
% 3.05/1.60 image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_member_001t__Nat__Onat,type,
% 3.05/1.60 member_nat: nat > set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.05/1.60 member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.05/1.60 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.05/1.60 member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.05/1.60 member_set_nat: set_nat > set_set_nat > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_c_member_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.05/1.60 member1875402276lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv > $o ).
% 3.05/1.60
% 3.05/1.60 thf(sy_v_f,type,
% 3.05/1.60 f: nat > nat ).
% 3.05/1.60
% 3.05/1.60 thf(fact_0__092_060open_062_092_060And_062tv2_Atv1_O_Achange__tv_Af_Atv1_A_061_Achange__tv_Af_Atv2_A_092_060Longrightarrow_062_Atv1_A_061_Atv2_092_060close_062,axiom,
% 3.05/1.60 ! [Tv1: paraco1605129243lle_tv,Tv2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( ( paraco1147068288nge_tv @ f @ Tv1 )
% 3.05/1.60 = ( paraco1147068288nge_tv @ f @ Tv2 ) )
% 3.05/1.60 => ( Tv1 = Tv2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_1_UNIV__I,axiom,
% 3.05/1.60 ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_2_UNIV__I,axiom,
% 3.05/1.60 ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_3_UNIV__I,axiom,
% 3.05/1.60 ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_4_UNIV__I,axiom,
% 3.05/1.60 ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_5_UNIV__I,axiom,
% 3.05/1.60 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_6_iso__tuple__UNIV__I,axiom,
% 3.05/1.60 ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_7_iso__tuple__UNIV__I,axiom,
% 3.05/1.60 ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_8_iso__tuple__UNIV__I,axiom,
% 3.05/1.60 ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_9_iso__tuple__UNIV__I,axiom,
% 3.05/1.60 ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_10_iso__tuple__UNIV__I,axiom,
% 3.05/1.60 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_11_top__apply,axiom,
% 3.05/1.60 ( top_to1299250770e_tv_o
% 3.05/1.60 = ( ^ [X2: paraco1605129243lle_tv] : top_top_o ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_12_top__apply,axiom,
% 3.05/1.60 ( top_top_nat_o
% 3.05/1.60 = ( ^ [X2: nat] : top_top_o ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_13_injD,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_14_injD,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_15_injD,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_16_injD,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 3.05/1.60 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_17_injD,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.05/1.60 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_18_injD,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_19_injD,axiom,
% 3.05/1.60 ! [F: nat > nat,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_20_injI,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 3.05/1.60 ( ! [X3: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 3.05/1.60 ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) )
% 3.05/1.60 => ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_21_injI,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ! [X3: nat,Y2: nat] :
% 3.05/1.60 ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) )
% 3.05/1.60 => ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_22_injI,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat] :
% 3.05/1.60 ( ! [X3: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 3.05/1.60 ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) )
% 3.05/1.60 => ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_23_injI,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > produc270694976lle_tv] :
% 3.05/1.60 ( ! [X3: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 3.05/1.60 ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) )
% 3.05/1.60 => ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_24_injI,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 3.05/1.60 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 3.05/1.60 ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) )
% 3.05/1.60 => ( inj_on26176689at_nat @ F @ top_to1555900337at_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_25_injI,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.60 ( ! [X3: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) )
% 3.05/1.60 => ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_26_injI,axiom,
% 3.05/1.60 ! [F: nat > nat] :
% 3.05/1.60 ( ! [X3: nat,Y2: nat] :
% 3.05/1.60 ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) )
% 3.05/1.60 => ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_27_inj__eq,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_28_inj__eq,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_29_inj__eq,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_30_inj__eq,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 3.05/1.60 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_31_inj__eq,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.05/1.60 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_32_inj__eq,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_33_inj__eq,axiom,
% 3.05/1.60 ! [F: nat > nat,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_34_inj__def,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 3.05/1.60 = ( ! [X2: produc1647334210lle_tv,Y3: produc1647334210lle_tv] :
% 3.05/1.60 ( ( ( F @ X2 )
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_35_inj__def,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 3.05/1.60 = ( ! [X2: nat,Y3: nat] :
% 3.05/1.60 ( ( ( F @ X2 )
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_36_inj__def,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 3.05/1.60 = ( ! [X2: produc194167194tv_nat,Y3: produc194167194tv_nat] :
% 3.05/1.60 ( ( ( F @ X2 )
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_37_inj__def,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > produc270694976lle_tv] :
% 3.05/1.60 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 3.05/1.60 = ( ! [X2: produc270694976lle_tv,Y3: produc270694976lle_tv] :
% 3.05/1.60 ( ( ( F @ X2 )
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_38_inj__def,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 3.05/1.60 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 3.05/1.60 = ( ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 3.05/1.60 ( ( ( F @ X2 )
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_39_inj__def,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.60 = ( ! [X2: paraco1605129243lle_tv,Y3: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( ( F @ X2 )
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_40_inj__def,axiom,
% 3.05/1.60 ! [F: nat > nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.05/1.60 = ( ! [X2: nat,Y3: nat] :
% 3.05/1.60 ( ( ( F @ X2 )
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_41_inj__onD,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ F @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( ( member1531318361lle_tv @ X @ A )
% 3.05/1.60 => ( ( member1531318361lle_tv @ Y @ A )
% 3.05/1.60 => ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_42_inj__onD,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ F @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( ( member737151281tv_nat @ X @ A )
% 3.05/1.60 => ( ( member737151281tv_nat @ Y @ A )
% 3.05/1.60 => ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_43_inj__onD,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > produc270694976lle_tv,A: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 3.05/1.60 ( ( inj_on1745913142lle_tv @ F @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( ( member813679063lle_tv @ X @ A )
% 3.05/1.60 => ( ( member813679063lle_tv @ Y @ A )
% 3.05/1.60 => ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_44_inj__onD,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.05/1.60 ( ( inj_on26176689at_nat @ F @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( ( member701585322at_nat @ Y @ A )
% 3.05/1.60 => ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_45_inj__onD,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,A: set_nat,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( ( member_nat @ X @ A )
% 3.05/1.60 => ( ( member_nat @ Y @ A )
% 3.05/1.60 => ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_46_inj__onD,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( ( member266900804lle_tv @ X @ A )
% 3.05/1.60 => ( ( member266900804lle_tv @ Y @ A )
% 3.05/1.60 => ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_47_inj__onD,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 => ( ( member_nat @ X @ A )
% 3.05/1.60 => ( ( member_nat @ Y @ A )
% 3.05/1.60 => ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_48_inj__onI,axiom,
% 3.05/1.60 ! [A: set_Pr2014382200lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 3.05/1.60 ( ! [X3: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 3.05/1.60 ( ( member1531318361lle_tv @ X3 @ A )
% 3.05/1.60 => ( ( member1531318361lle_tv @ Y2 @ A )
% 3.05/1.60 => ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) ) ) )
% 3.05/1.60 => ( inj_on2112487900lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_49_inj__onI,axiom,
% 3.05/1.60 ! [A: set_Pr1725653840tv_nat,F: produc194167194tv_nat > produc194167194tv_nat] :
% 3.05/1.60 ( ! [X3: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 3.05/1.60 ( ( member737151281tv_nat @ X3 @ A )
% 3.05/1.60 => ( ( member737151281tv_nat @ Y2 @ A )
% 3.05/1.60 => ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) ) ) )
% 3.05/1.60 => ( inj_on552895452tv_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_50_inj__onI,axiom,
% 3.05/1.60 ! [A: set_Pr13445366lle_tv,F: produc270694976lle_tv > produc270694976lle_tv] :
% 3.05/1.60 ( ! [X3: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 3.05/1.60 ( ( member813679063lle_tv @ X3 @ A )
% 3.05/1.60 => ( ( member813679063lle_tv @ Y2 @ A )
% 3.05/1.60 => ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) ) ) )
% 3.05/1.60 => ( inj_on1745913142lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_51_inj__onI,axiom,
% 3.05/1.60 ! [A: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 3.05/1.60 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X3 @ A )
% 3.05/1.60 => ( ( member701585322at_nat @ Y2 @ A )
% 3.05/1.60 => ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) ) ) )
% 3.05/1.60 => ( inj_on26176689at_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_52_inj__onI,axiom,
% 3.05/1.60 ! [A: set_nat,F: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ! [X3: nat,Y2: nat] :
% 3.05/1.60 ( ( member_nat @ X3 @ A )
% 3.05/1.60 => ( ( member_nat @ Y2 @ A )
% 3.05/1.60 => ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) ) ) )
% 3.05/1.60 => ( inj_on1955349912lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_53_inj__onI,axiom,
% 3.05/1.60 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.60 ( ! [X3: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member266900804lle_tv @ X3 @ A )
% 3.05/1.60 => ( ( member266900804lle_tv @ Y2 @ A )
% 3.05/1.60 => ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) ) ) )
% 3.05/1.60 => ( inj_on772319074lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_54_inj__onI,axiom,
% 3.05/1.60 ! [A: set_nat,F: nat > nat] :
% 3.05/1.60 ( ! [X3: nat,Y2: nat] :
% 3.05/1.60 ( ( member_nat @ X3 @ A )
% 3.05/1.60 => ( ( member_nat @ Y2 @ A )
% 3.05/1.60 => ( ( ( F @ X3 )
% 3.05/1.60 = ( F @ Y2 ) )
% 3.05/1.60 => ( X3 = Y2 ) ) ) )
% 3.05/1.60 => ( inj_on_nat_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_55_inj__on__def,axiom,
% 3.05/1.60 ( inj_on2112487900lle_tv
% 3.05/1.60 = ( ^ [F2: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv] :
% 3.05/1.60 ! [X2: produc1647334210lle_tv] :
% 3.05/1.60 ( ( member1531318361lle_tv @ X2 @ A2 )
% 3.05/1.60 => ! [Y3: produc1647334210lle_tv] :
% 3.05/1.60 ( ( member1531318361lle_tv @ Y3 @ A2 )
% 3.05/1.60 => ( ( ( F2 @ X2 )
% 3.05/1.60 = ( F2 @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_56_inj__on__def,axiom,
% 3.05/1.60 ( inj_on552895452tv_nat
% 3.05/1.60 = ( ^ [F2: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat] :
% 3.05/1.60 ! [X2: produc194167194tv_nat] :
% 3.05/1.60 ( ( member737151281tv_nat @ X2 @ A2 )
% 3.05/1.60 => ! [Y3: produc194167194tv_nat] :
% 3.05/1.60 ( ( member737151281tv_nat @ Y3 @ A2 )
% 3.05/1.60 => ( ( ( F2 @ X2 )
% 3.05/1.60 = ( F2 @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_57_inj__on__def,axiom,
% 3.05/1.60 ( inj_on1745913142lle_tv
% 3.05/1.60 = ( ^ [F2: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv] :
% 3.05/1.60 ! [X2: produc270694976lle_tv] :
% 3.05/1.60 ( ( member813679063lle_tv @ X2 @ A2 )
% 3.05/1.60 => ! [Y3: produc270694976lle_tv] :
% 3.05/1.60 ( ( member813679063lle_tv @ Y3 @ A2 )
% 3.05/1.60 => ( ( ( F2 @ X2 )
% 3.05/1.60 = ( F2 @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_58_inj__on__def,axiom,
% 3.05/1.60 ( inj_on26176689at_nat
% 3.05/1.60 = ( ^ [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 3.05/1.60 ! [X2: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X2 @ A2 )
% 3.05/1.60 => ! [Y3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ Y3 @ A2 )
% 3.05/1.60 => ( ( ( F2 @ X2 )
% 3.05/1.60 = ( F2 @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_59_inj__on__def,axiom,
% 3.05/1.60 ( inj_on1955349912lle_tv
% 3.05/1.60 = ( ^ [F2: nat > paraco1605129243lle_tv,A2: set_nat] :
% 3.05/1.60 ! [X2: nat] :
% 3.05/1.60 ( ( member_nat @ X2 @ A2 )
% 3.05/1.60 => ! [Y3: nat] :
% 3.05/1.60 ( ( member_nat @ Y3 @ A2 )
% 3.05/1.60 => ( ( ( F2 @ X2 )
% 3.05/1.60 = ( F2 @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_60_inj__on__def,axiom,
% 3.05/1.60 ( inj_on772319074lle_tv
% 3.05/1.60 = ( ^ [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.05/1.60 ! [X2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member266900804lle_tv @ X2 @ A2 )
% 3.05/1.60 => ! [Y3: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member266900804lle_tv @ Y3 @ A2 )
% 3.05/1.60 => ( ( ( F2 @ X2 )
% 3.05/1.60 = ( F2 @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_61_inj__on__def,axiom,
% 3.05/1.60 ( inj_on_nat_nat
% 3.05/1.60 = ( ^ [F2: nat > nat,A2: set_nat] :
% 3.05/1.60 ! [X2: nat] :
% 3.05/1.60 ( ( member_nat @ X2 @ A2 )
% 3.05/1.60 => ! [Y3: nat] :
% 3.05/1.60 ( ( member_nat @ Y3 @ A2 )
% 3.05/1.60 => ( ( ( F2 @ X2 )
% 3.05/1.60 = ( F2 @ Y3 ) )
% 3.05/1.60 => ( X2 = Y3 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_62_inj__on__cong,axiom,
% 3.05/1.60 ! [A: set_Pr2014382200lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv] :
% 3.05/1.60 ( ! [A3: produc1647334210lle_tv] :
% 3.05/1.60 ( ( member1531318361lle_tv @ A3 @ A )
% 3.05/1.60 => ( ( F @ A3 )
% 3.05/1.60 = ( G @ A3 ) ) )
% 3.05/1.60 => ( ( inj_on2112487900lle_tv @ F @ A )
% 3.05/1.60 = ( inj_on2112487900lle_tv @ G @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_63_inj__on__cong,axiom,
% 3.05/1.60 ! [A: set_Pr1725653840tv_nat,F: produc194167194tv_nat > produc194167194tv_nat,G: produc194167194tv_nat > produc194167194tv_nat] :
% 3.05/1.60 ( ! [A3: produc194167194tv_nat] :
% 3.05/1.60 ( ( member737151281tv_nat @ A3 @ A )
% 3.05/1.60 => ( ( F @ A3 )
% 3.05/1.60 = ( G @ A3 ) ) )
% 3.05/1.60 => ( ( inj_on552895452tv_nat @ F @ A )
% 3.05/1.60 = ( inj_on552895452tv_nat @ G @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_64_inj__on__cong,axiom,
% 3.05/1.60 ! [A: set_Pr13445366lle_tv,F: produc270694976lle_tv > produc270694976lle_tv,G: produc270694976lle_tv > produc270694976lle_tv] :
% 3.05/1.60 ( ! [A3: produc270694976lle_tv] :
% 3.05/1.60 ( ( member813679063lle_tv @ A3 @ A )
% 3.05/1.60 => ( ( F @ A3 )
% 3.05/1.60 = ( G @ A3 ) ) )
% 3.05/1.60 => ( ( inj_on1745913142lle_tv @ F @ A )
% 3.05/1.60 = ( inj_on1745913142lle_tv @ G @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_65_inj__on__cong,axiom,
% 3.05/1.60 ! [A: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 3.05/1.60 ( ! [A3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ A3 @ A )
% 3.05/1.60 => ( ( F @ A3 )
% 3.05/1.60 = ( G @ A3 ) ) )
% 3.05/1.60 => ( ( inj_on26176689at_nat @ F @ A )
% 3.05/1.60 = ( inj_on26176689at_nat @ G @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_66_inj__on__cong,axiom,
% 3.05/1.60 ! [A: set_nat,F: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ! [A3: nat] :
% 3.05/1.60 ( ( member_nat @ A3 @ A )
% 3.05/1.60 => ( ( F @ A3 )
% 3.05/1.60 = ( G @ A3 ) ) )
% 3.05/1.60 => ( ( inj_on1955349912lle_tv @ F @ A )
% 3.05/1.60 = ( inj_on1955349912lle_tv @ G @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_67_inj__on__cong,axiom,
% 3.05/1.60 ! [A: set_nat,F: nat > nat,G: nat > nat] :
% 3.05/1.60 ( ! [A3: nat] :
% 3.05/1.60 ( ( member_nat @ A3 @ A )
% 3.05/1.60 => ( ( F @ A3 )
% 3.05/1.60 = ( G @ A3 ) ) )
% 3.05/1.60 => ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.60 = ( inj_on_nat_nat @ G @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_68_inj__on__cong,axiom,
% 3.05/1.60 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.60 ( ! [A3: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member266900804lle_tv @ A3 @ A )
% 3.05/1.60 => ( ( F @ A3 )
% 3.05/1.60 = ( G @ A3 ) ) )
% 3.05/1.60 => ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.60 = ( inj_on772319074lle_tv @ G @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_69_inj__on__eq__iff,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ F @ A )
% 3.05/1.60 => ( ( member1531318361lle_tv @ X @ A )
% 3.05/1.60 => ( ( member1531318361lle_tv @ Y @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_70_inj__on__eq__iff,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ F @ A )
% 3.05/1.60 => ( ( member737151281tv_nat @ X @ A )
% 3.05/1.60 => ( ( member737151281tv_nat @ Y @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_71_inj__on__eq__iff,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > produc270694976lle_tv,A: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 3.05/1.60 ( ( inj_on1745913142lle_tv @ F @ A )
% 3.05/1.60 => ( ( member813679063lle_tv @ X @ A )
% 3.05/1.60 => ( ( member813679063lle_tv @ Y @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_72_inj__on__eq__iff,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.05/1.60 ( ( inj_on26176689at_nat @ F @ A )
% 3.05/1.60 => ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( ( member701585322at_nat @ Y @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_73_inj__on__eq__iff,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,A: set_nat,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ A )
% 3.05/1.60 => ( ( member_nat @ X @ A )
% 3.05/1.60 => ( ( member_nat @ Y @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_74_inj__on__eq__iff,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.60 => ( ( member_nat @ X @ A )
% 3.05/1.60 => ( ( member_nat @ Y @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_75_inj__on__eq__iff,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.60 => ( ( member266900804lle_tv @ X @ A )
% 3.05/1.60 => ( ( member266900804lle_tv @ Y @ A )
% 3.05/1.60 => ( ( ( F @ X )
% 3.05/1.60 = ( F @ Y ) )
% 3.05/1.60 = ( X = Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_76_assms,axiom,
% 3.05/1.60 inj_on_nat_nat @ f @ top_top_set_nat ).
% 3.05/1.60
% 3.05/1.60 thf(fact_77_top__set__def,axiom,
% 3.05/1.60 ( top_to975729152tv_nat
% 3.05/1.60 = ( collec848462447tv_nat @ top_to900819589_nat_o ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_78_top__set__def,axiom,
% 3.05/1.60 ( top_to1411004326lle_tv
% 3.05/1.60 = ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_79_top__set__def,axiom,
% 3.05/1.60 ( top_to1555900337at_nat
% 3.05/1.60 = ( collec7649004at_nat @ top_to632227436_nat_o ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_80_top__set__def,axiom,
% 3.05/1.60 ( top_to1057771083lle_tv
% 3.05/1.60 = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_81_top__set__def,axiom,
% 3.05/1.60 ( top_top_set_nat
% 3.05/1.60 = ( collect_nat @ top_top_nat_o ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_82_UNIV__witness,axiom,
% 3.05/1.60 ? [X3: produc194167194tv_nat] : ( member737151281tv_nat @ X3 @ top_to975729152tv_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_83_UNIV__witness,axiom,
% 3.05/1.60 ? [X3: produc270694976lle_tv] : ( member813679063lle_tv @ X3 @ top_to1411004326lle_tv ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_84_UNIV__witness,axiom,
% 3.05/1.60 ? [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ top_to1555900337at_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_85_UNIV__witness,axiom,
% 3.05/1.60 ? [X3: paraco1605129243lle_tv] : ( member266900804lle_tv @ X3 @ top_to1057771083lle_tv ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_86_UNIV__witness,axiom,
% 3.05/1.60 ? [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_87_UNIV__eq__I,axiom,
% 3.05/1.60 ! [A: set_Pr1725653840tv_nat] :
% 3.05/1.60 ( ! [X3: produc194167194tv_nat] : ( member737151281tv_nat @ X3 @ A )
% 3.05/1.60 => ( top_to975729152tv_nat = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_88_UNIV__eq__I,axiom,
% 3.05/1.60 ! [A: set_Pr13445366lle_tv] :
% 3.05/1.60 ( ! [X3: produc270694976lle_tv] : ( member813679063lle_tv @ X3 @ A )
% 3.05/1.60 => ( top_to1411004326lle_tv = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_89_UNIV__eq__I,axiom,
% 3.05/1.60 ! [A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ! [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ A )
% 3.05/1.60 => ( top_to1555900337at_nat = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_90_UNIV__eq__I,axiom,
% 3.05/1.60 ! [A: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ! [X3: paraco1605129243lle_tv] : ( member266900804lle_tv @ X3 @ A )
% 3.05/1.60 => ( top_to1057771083lle_tv = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_91_UNIV__eq__I,axiom,
% 3.05/1.60 ! [A: set_nat] :
% 3.05/1.60 ( ! [X3: nat] : ( member_nat @ X3 @ A )
% 3.05/1.60 => ( top_top_set_nat = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_92_inj__on__inverseI,axiom,
% 3.05/1.60 ! [A: set_Pr2014382200lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 3.05/1.60 ( ! [X3: produc1647334210lle_tv] :
% 3.05/1.60 ( ( member1531318361lle_tv @ X3 @ A )
% 3.05/1.60 => ( ( G @ ( F @ X3 ) )
% 3.05/1.60 = X3 ) )
% 3.05/1.60 => ( inj_on2112487900lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_93_inj__on__inverseI,axiom,
% 3.05/1.60 ! [A: set_Pr1725653840tv_nat,G: produc194167194tv_nat > produc194167194tv_nat,F: produc194167194tv_nat > produc194167194tv_nat] :
% 3.05/1.60 ( ! [X3: produc194167194tv_nat] :
% 3.05/1.60 ( ( member737151281tv_nat @ X3 @ A )
% 3.05/1.60 => ( ( G @ ( F @ X3 ) )
% 3.05/1.60 = X3 ) )
% 3.05/1.60 => ( inj_on552895452tv_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_94_inj__on__inverseI,axiom,
% 3.05/1.60 ! [A: set_Pr13445366lle_tv,G: produc270694976lle_tv > produc270694976lle_tv,F: produc270694976lle_tv > produc270694976lle_tv] :
% 3.05/1.60 ( ! [X3: produc270694976lle_tv] :
% 3.05/1.60 ( ( member813679063lle_tv @ X3 @ A )
% 3.05/1.60 => ( ( G @ ( F @ X3 ) )
% 3.05/1.60 = X3 ) )
% 3.05/1.60 => ( inj_on1745913142lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_95_inj__on__inverseI,axiom,
% 3.05/1.60 ! [A: set_Pr1986765409at_nat,G: product_prod_nat_nat > product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 3.05/1.60 ( ! [X3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X3 @ A )
% 3.05/1.60 => ( ( G @ ( F @ X3 ) )
% 3.05/1.60 = X3 ) )
% 3.05/1.60 => ( inj_on26176689at_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_96_inj__on__inverseI,axiom,
% 3.05/1.60 ! [A: set_nat,G: paraco1605129243lle_tv > nat,F: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ! [X3: nat] :
% 3.05/1.60 ( ( member_nat @ X3 @ A )
% 3.05/1.60 => ( ( G @ ( F @ X3 ) )
% 3.05/1.60 = X3 ) )
% 3.05/1.60 => ( inj_on1955349912lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_97_inj__on__inverseI,axiom,
% 3.05/1.60 ! [A: set_nat,G: nat > nat,F: nat > nat] :
% 3.05/1.60 ( ! [X3: nat] :
% 3.05/1.60 ( ( member_nat @ X3 @ A )
% 3.05/1.60 => ( ( G @ ( F @ X3 ) )
% 3.05/1.60 = X3 ) )
% 3.05/1.60 => ( inj_on_nat_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_98_inj__on__inverseI,axiom,
% 3.05/1.60 ! [A: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.60 ( ! [X3: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member266900804lle_tv @ X3 @ A )
% 3.05/1.60 => ( ( G @ ( F @ X3 ) )
% 3.05/1.60 = X3 ) )
% 3.05/1.60 => ( inj_on772319074lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_99_inj__on__contraD,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ F @ A )
% 3.05/1.60 => ( ( X != Y )
% 3.05/1.60 => ( ( member1531318361lle_tv @ X @ A )
% 3.05/1.60 => ( ( member1531318361lle_tv @ Y @ A )
% 3.05/1.60 => ( ( F @ X )
% 3.05/1.60 != ( F @ Y ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_100_inj__on__contraD,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ F @ A )
% 3.05/1.60 => ( ( X != Y )
% 3.05/1.60 => ( ( member737151281tv_nat @ X @ A )
% 3.05/1.60 => ( ( member737151281tv_nat @ Y @ A )
% 3.05/1.60 => ( ( F @ X )
% 3.05/1.60 != ( F @ Y ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_101_inj__on__contraD,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > produc270694976lle_tv,A: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 3.05/1.60 ( ( inj_on1745913142lle_tv @ F @ A )
% 3.05/1.60 => ( ( X != Y )
% 3.05/1.60 => ( ( member813679063lle_tv @ X @ A )
% 3.05/1.60 => ( ( member813679063lle_tv @ Y @ A )
% 3.05/1.60 => ( ( F @ X )
% 3.05/1.60 != ( F @ Y ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_102_inj__on__contraD,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.05/1.60 ( ( inj_on26176689at_nat @ F @ A )
% 3.05/1.60 => ( ( X != Y )
% 3.05/1.60 => ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( ( member701585322at_nat @ Y @ A )
% 3.05/1.60 => ( ( F @ X )
% 3.05/1.60 != ( F @ Y ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_103_inj__on__contraD,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,A: set_nat,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ A )
% 3.05/1.60 => ( ( X != Y )
% 3.05/1.60 => ( ( member_nat @ X @ A )
% 3.05/1.60 => ( ( member_nat @ Y @ A )
% 3.05/1.60 => ( ( F @ X )
% 3.05/1.60 != ( F @ Y ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_104_inj__on__contraD,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat,X: nat,Y: nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.60 => ( ( X != Y )
% 3.05/1.60 => ( ( member_nat @ X @ A )
% 3.05/1.60 => ( ( member_nat @ Y @ A )
% 3.05/1.60 => ( ( F @ X )
% 3.05/1.60 != ( F @ Y ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_105_inj__on__contraD,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.60 => ( ( X != Y )
% 3.05/1.60 => ( ( member266900804lle_tv @ X @ A )
% 3.05/1.60 => ( ( member266900804lle_tv @ Y @ A )
% 3.05/1.60 => ( ( F @ X )
% 3.05/1.60 != ( F @ Y ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_106_top__empty__eq,axiom,
% 3.05/1.60 ( top_to900819589_nat_o
% 3.05/1.60 = ( ^ [X2: produc194167194tv_nat] : ( member737151281tv_nat @ X2 @ top_to975729152tv_nat ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_107_top__empty__eq,axiom,
% 3.05/1.60 ( top_to1889334367e_tv_o
% 3.05/1.60 = ( ^ [X2: produc270694976lle_tv] : ( member813679063lle_tv @ X2 @ top_to1411004326lle_tv ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_108_top__empty__eq,axiom,
% 3.05/1.60 ( top_to632227436_nat_o
% 3.05/1.60 = ( ^ [X2: product_prod_nat_nat] : ( member701585322at_nat @ X2 @ top_to1555900337at_nat ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_109_top__empty__eq,axiom,
% 3.05/1.60 ( top_to1299250770e_tv_o
% 3.05/1.60 = ( ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_110_top__empty__eq,axiom,
% 3.05/1.60 ( top_top_nat_o
% 3.05/1.60 = ( ^ [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_111_the__inv__f__f,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 3.05/1.60 => ( ( the_in427240730lle_tv @ top_to1871154984lle_tv @ F @ ( F @ X ) )
% 3.05/1.60 = X ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_112_the__inv__f__f,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > nat,X: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on1179712058tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.60 => ( ( the_in1509933432tv_nat @ top_to1057771083lle_tv @ F @ ( F @ X ) )
% 3.05/1.60 = X ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_113_the__inv__f__f,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,X: nat] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( the_in138087638lle_tv @ top_top_set_nat @ F @ ( F @ X ) )
% 3.05/1.60 = X ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_114_the__inv__f__f,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 3.05/1.60 => ( ( the_in195660058tv_nat @ top_to975729152tv_nat @ F @ ( F @ X ) )
% 3.05/1.60 = X ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_115_the__inv__f__f,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv] :
% 3.05/1.60 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 3.05/1.60 => ( ( the_in1388677748lle_tv @ top_to1411004326lle_tv @ F @ ( F @ X ) )
% 3.05/1.60 = X ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_116_the__inv__f__f,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat] :
% 3.05/1.60 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( the_in2068894451at_nat @ top_to1555900337at_nat @ F @ ( F @ X ) )
% 3.05/1.60 = X ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_117_the__inv__f__f,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.60 => ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ F @ ( F @ X ) )
% 3.05/1.60 = X ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_118_the__inv__f__f,axiom,
% 3.05/1.60 ! [F: nat > nat,X: nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( the_inv_into_nat_nat @ top_top_set_nat @ F @ ( F @ X ) )
% 3.05/1.60 = X ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_119_strict__mono__on__imp__inj__on,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat] :
% 3.05/1.60 ( ( strict2146030304at_nat @ F @ A )
% 3.05/1.60 => ( inj_on_nat_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_120_linorder__injI,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ! [X3: nat,Y2: nat] :
% 3.05/1.60 ( ( ord_less_nat @ X3 @ Y2 )
% 3.05/1.60 => ( ( F @ X3 )
% 3.05/1.60 != ( F @ Y2 ) ) )
% 3.05/1.60 => ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_121_linorder__injI,axiom,
% 3.05/1.60 ! [F: nat > nat] :
% 3.05/1.60 ( ! [X3: nat,Y2: nat] :
% 3.05/1.60 ( ( ord_less_nat @ X3 @ Y2 )
% 3.05/1.60 => ( ( F @ X3 )
% 3.05/1.60 != ( F @ Y2 ) ) )
% 3.05/1.60 => ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_122_inj__add__left,axiom,
% 3.05/1.60 ! [A4: nat] : ( inj_on_nat_nat @ ( plus_plus_nat @ A4 ) @ top_top_set_nat ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_123_change__tv_Osimps_I2_J,axiom,
% 3.05/1.60 ! [F: nat > nat,N: nat] :
% 3.05/1.60 ( ( paraco1147068288nge_tv @ F @ ( paraco793048302_Indet @ N ) )
% 3.05/1.60 = ( paraco793048302_Indet @ ( F @ N ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_124_inj__apsnd,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ ( produc1408152463lle_tv @ F ) @ top_to1871154984lle_tv )
% 3.05/1.60 = ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_125_inj__apsnd,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on967082628lle_tv @ ( produc1804670661lle_tv @ F ) @ top_to975729152tv_nat )
% 3.05/1.60 = ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_126_inj__apsnd,axiom,
% 3.05/1.60 ! [F: nat > nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ ( produc237097339lle_tv @ F ) @ top_to975729152tv_nat )
% 3.05/1.60 = ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_127_inj__apsnd,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on1745913142lle_tv @ ( produc2040316391tv_nat @ F ) @ top_to1411004326lle_tv )
% 3.05/1.60 = ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_128_inj__apsnd,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on1840679568lle_tv @ ( produc1608943133tv_nat @ F ) @ top_to1555900337at_nat )
% 3.05/1.60 = ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_129_inj__apsnd,axiom,
% 3.05/1.60 ! [F: nat > nat] :
% 3.05/1.60 ( ( inj_on26176689at_nat @ ( produc1320959600at_nat @ F ) @ top_to1555900337at_nat )
% 3.05/1.60 = ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_130_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > nat,A4: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( inj_on1179712058tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.60 => ( ( member_nat @ ( F @ A4 ) @ ( image_376325286tv_nat @ F @ A ) )
% 3.05/1.60 = ( member266900804lle_tv @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_131_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A4: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.60 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_335818702lle_tv @ F @ A ) )
% 3.05/1.60 = ( member266900804lle_tv @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_132_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: nat > nat,A4: nat,A: set_nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( member_nat @ ( F @ A4 ) @ ( image_nat_nat @ F @ A ) )
% 3.05/1.60 = ( member_nat @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_133_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,A4: nat,A: set_nat] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_1151963140lle_tv @ F @ A ) )
% 3.05/1.60 = ( member_nat @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_134_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > nat,A4: produc194167194tv_nat,A: set_Pr1725653840tv_nat] :
% 3.05/1.60 ( ( inj_on808253149at_nat @ F @ top_to975729152tv_nat )
% 3.05/1.60 => ( ( member_nat @ ( F @ A4 ) @ ( image_1381266801at_nat @ F @ A ) )
% 3.05/1.60 = ( member737151281tv_nat @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_135_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > paraco1605129243lle_tv,A4: produc194167194tv_nat,A: set_Pr1725653840tv_nat] :
% 3.05/1.60 ( ( inj_on1612474245lle_tv @ F @ top_to975729152tv_nat )
% 3.05/1.60 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_2019567641lle_tv @ F @ A ) )
% 3.05/1.60 = ( member737151281tv_nat @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_136_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > nat,A4: produc270694976lle_tv,A: set_Pr13445366lle_tv] :
% 3.05/1.60 ( ( inj_on936843139tv_nat @ F @ top_to1411004326lle_tv )
% 3.05/1.60 => ( ( member_nat @ ( F @ A4 ) @ ( image_1509856791tv_nat @ F @ A ) )
% 3.05/1.60 = ( member813679063lle_tv @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_137_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > paraco1605129243lle_tv,A4: produc270694976lle_tv,A: set_Pr13445366lle_tv] :
% 3.05/1.60 ( ( inj_on394919723lle_tv @ F @ top_to1411004326lle_tv )
% 3.05/1.60 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_802013119lle_tv @ F @ A ) )
% 3.05/1.60 = ( member813679063lle_tv @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_138_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > nat,A4: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( inj_on642995232at_nat @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( member_nat @ ( F @ A4 ) @ ( image_1397137548at_nat @ F @ A ) )
% 3.05/1.60 = ( member701585322at_nat @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_139_inj__image__mem__iff,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > paraco1605129243lle_tv,A4: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( inj_on520021963lle_tv @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_1093035615lle_tv @ F @ A ) )
% 3.05/1.60 = ( member701585322at_nat @ A4 @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_140_inj__image__eq__iff,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv,B: set_Pr2014382200lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 3.05/1.60 => ( ( ( image_1221801032lle_tv @ F @ A )
% 3.05/1.60 = ( image_1221801032lle_tv @ F @ B ) )
% 3.05/1.60 = ( A = B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_141_inj__image__eq__iff,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,A: set_nat,B: set_nat] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( ( image_1151963140lle_tv @ F @ A )
% 3.05/1.60 = ( image_1151963140lle_tv @ F @ B ) )
% 3.05/1.60 = ( A = B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_142_inj__image__eq__iff,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat,B: set_Pr1725653840tv_nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 3.05/1.60 => ( ( ( image_1104296520tv_nat @ F @ A )
% 3.05/1.60 = ( image_1104296520tv_nat @ F @ B ) )
% 3.05/1.60 = ( A = B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_143_inj__image__eq__iff,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > produc270694976lle_tv,A: set_Pr13445366lle_tv,B: set_Pr13445366lle_tv] :
% 3.05/1.60 ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 3.05/1.60 => ( ( ( image_149830562lle_tv @ F @ A )
% 3.05/1.60 = ( image_149830562lle_tv @ F @ B ) )
% 3.05/1.60 = ( A = B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_144_inj__image__eq__iff,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( inj_on1764151786tv_nat @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( ( image_1597721174tv_nat @ F @ A )
% 3.05/1.60 = ( image_1597721174tv_nat @ F @ B ) )
% 3.05/1.60 = ( A = B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_145_inj__image__eq__iff,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( inj_on1840679568lle_tv @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( ( image_1674248956lle_tv @ F @ A )
% 3.05/1.60 = ( image_1674248956lle_tv @ F @ B ) )
% 3.05/1.60 = ( A = B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_146_inj__image__eq__iff,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( ( image_815163717at_nat @ F @ A )
% 3.05/1.60 = ( image_815163717at_nat @ F @ B ) )
% 3.05/1.60 = ( A = B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_147_inj__image__eq__iff,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.60 => ( ( ( image_335818702lle_tv @ F @ A )
% 3.05/1.60 = ( image_335818702lle_tv @ F @ B ) )
% 3.05/1.60 = ( A = B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_148_inj__image__eq__iff,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat,B: set_nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( ( image_nat_nat @ F @ A )
% 3.05/1.60 = ( image_nat_nat @ F @ B ) )
% 3.05/1.60 = ( A = B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_149_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > nat,B2: nat] :
% 3.05/1.60 ( ( inj_on1179712058tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.60 => ( ( member_nat @ B2 @ ( image_376325286tv_nat @ F @ top_to1057771083lle_tv ) )
% 3.05/1.60 = ( ? [X2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_150_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.60 => ( ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ top_to1057771083lle_tv ) )
% 3.05/1.60 = ( ? [X2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_151_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: nat > nat,B2: nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( member_nat @ B2 @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 3.05/1.60 = ( ? [X2: nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_152_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 3.05/1.60 => ( ( member266900804lle_tv @ B2 @ ( image_1151963140lle_tv @ F @ top_top_set_nat ) )
% 3.05/1.60 = ( ? [X2: nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_153_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > nat,B2: nat] :
% 3.05/1.60 ( ( inj_on808253149at_nat @ F @ top_to975729152tv_nat )
% 3.05/1.60 => ( ( member_nat @ B2 @ ( image_1381266801at_nat @ F @ top_to975729152tv_nat ) )
% 3.05/1.60 = ( ? [X2: produc194167194tv_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: produc194167194tv_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_154_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on1612474245lle_tv @ F @ top_to975729152tv_nat )
% 3.05/1.60 => ( ( member266900804lle_tv @ B2 @ ( image_2019567641lle_tv @ F @ top_to975729152tv_nat ) )
% 3.05/1.60 = ( ? [X2: produc194167194tv_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: produc194167194tv_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_155_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > nat,B2: nat] :
% 3.05/1.60 ( ( inj_on936843139tv_nat @ F @ top_to1411004326lle_tv )
% 3.05/1.60 => ( ( member_nat @ B2 @ ( image_1509856791tv_nat @ F @ top_to1411004326lle_tv ) )
% 3.05/1.60 = ( ? [X2: produc270694976lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: produc270694976lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_156_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on394919723lle_tv @ F @ top_to1411004326lle_tv )
% 3.05/1.60 => ( ( member266900804lle_tv @ B2 @ ( image_802013119lle_tv @ F @ top_to1411004326lle_tv ) )
% 3.05/1.60 = ( ? [X2: produc270694976lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: produc270694976lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_157_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > nat,B2: nat] :
% 3.05/1.60 ( ( inj_on642995232at_nat @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( member_nat @ B2 @ ( image_1397137548at_nat @ F @ top_to1555900337at_nat ) )
% 3.05/1.60 = ( ? [X2: product_prod_nat_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: product_prod_nat_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_158_range__ex1__eq,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( inj_on520021963lle_tv @ F @ top_to1555900337at_nat )
% 3.05/1.60 => ( ( member266900804lle_tv @ B2 @ ( image_1093035615lle_tv @ F @ top_to1555900337at_nat ) )
% 3.05/1.60 = ( ? [X2: product_prod_nat_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X2 ) )
% 3.05/1.60 & ! [Y3: product_prod_nat_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ Y3 ) )
% 3.05/1.60 => ( Y3 = X2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_159_strict__mono__imp__inj__on,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat] :
% 3.05/1.60 ( ( order_769474267at_nat @ F )
% 3.05/1.60 => ( inj_on_nat_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_160_image__eqI,axiom,
% 3.05/1.60 ! [B2: produc194167194tv_nat,F: product_prod_nat_nat > produc194167194tv_nat,X: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( member737151281tv_nat @ B2 @ ( image_1597721174tv_nat @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_161_image__eqI,axiom,
% 3.05/1.60 ! [B2: produc270694976lle_tv,F: product_prod_nat_nat > produc270694976lle_tv,X: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( member813679063lle_tv @ B2 @ ( image_1674248956lle_tv @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_162_image__eqI,axiom,
% 3.05/1.60 ! [B2: product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( member701585322at_nat @ B2 @ ( image_815163717at_nat @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_163_image__eqI,axiom,
% 3.05/1.60 ! [B2: nat,F: nat > nat,X: nat,A: set_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( ( member_nat @ X @ A )
% 3.05/1.60 => ( member_nat @ B2 @ ( image_nat_nat @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_164_image__eqI,axiom,
% 3.05/1.60 ! [B2: paraco1605129243lle_tv,F: nat > paraco1605129243lle_tv,X: nat,A: set_nat] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( ( member_nat @ X @ A )
% 3.05/1.60 => ( member266900804lle_tv @ B2 @ ( image_1151963140lle_tv @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_165_image__eqI,axiom,
% 3.05/1.60 ! [B2: nat,F: paraco1605129243lle_tv > nat,X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( ( member266900804lle_tv @ X @ A )
% 3.05/1.60 => ( member_nat @ B2 @ ( image_376325286tv_nat @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_166_image__eqI,axiom,
% 3.05/1.60 ! [B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( ( member266900804lle_tv @ X @ A )
% 3.05/1.60 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_167_tv_Oinject_I2_J,axiom,
% 3.05/1.60 ! [X22: nat,Y22: nat] :
% 3.05/1.60 ( ( ( paraco793048302_Indet @ X22 )
% 3.05/1.60 = ( paraco793048302_Indet @ Y22 ) )
% 3.05/1.60 = ( X22 = Y22 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_168_top1I,axiom,
% 3.05/1.60 ! [X: paraco1605129243lle_tv] : ( top_to1299250770e_tv_o @ X ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_169_top1I,axiom,
% 3.05/1.60 ! [X: nat] : ( top_top_nat_o @ X ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_170_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.60 => ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ A @ F ) @ ( image_335818702lle_tv @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_171_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.60 => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A @ F ) @ ( image_nat_nat @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_172_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,A: set_nat] :
% 3.05/1.60 ( ( inj_on1955349912lle_tv @ F @ A )
% 3.05/1.60 => ( ( image_376325286tv_nat @ ( the_in138087638lle_tv @ A @ F ) @ ( image_1151963140lle_tv @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_173_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > nat,A: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( inj_on1179712058tv_nat @ F @ A )
% 3.05/1.60 => ( ( image_1151963140lle_tv @ ( the_in1509933432tv_nat @ A @ F ) @ ( image_376325286tv_nat @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_174_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( inj_on1764151786tv_nat @ F @ A )
% 3.05/1.60 => ( ( image_1805124128at_nat @ ( the_in667485224tv_nat @ A @ F ) @ ( image_1597721174tv_nat @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_175_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( inj_on1840679568lle_tv @ F @ A )
% 3.05/1.60 => ( ( image_1787705850at_nat @ ( the_in744013006lle_tv @ A @ F ) @ ( image_1674248956lle_tv @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_176_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > product_prod_nat_nat,A: set_Pr1725653840tv_nat] :
% 3.05/1.60 ( ( inj_on1971554740at_nat @ F @ A )
% 3.05/1.60 => ( ( image_1597721174tv_nat @ ( the_in874888178at_nat @ A @ F ) @ ( image_1805124128at_nat @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_177_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: produc270694976lle_tv > product_prod_nat_nat,A: set_Pr13445366lle_tv] :
% 3.05/1.60 ( ( inj_on1954136462at_nat @ F @ A )
% 3.05/1.60 => ( ( image_1674248956lle_tv @ ( the_in857469900at_nat @ A @ F ) @ ( image_1787705850at_nat @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_178_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A: set_Pr2014382200lle_tv] :
% 3.05/1.60 ( ( inj_on2112487900lle_tv @ F @ A )
% 3.05/1.60 => ( ( image_1221801032lle_tv @ ( the_in427240730lle_tv @ A @ F ) @ ( image_1221801032lle_tv @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_179_the__inv__into__onto,axiom,
% 3.05/1.60 ! [F: produc194167194tv_nat > produc194167194tv_nat,A: set_Pr1725653840tv_nat] :
% 3.05/1.60 ( ( inj_on552895452tv_nat @ F @ A )
% 3.05/1.60 => ( ( image_1104296520tv_nat @ ( the_in195660058tv_nat @ A @ F ) @ ( image_1104296520tv_nat @ F @ A ) )
% 3.05/1.60 = A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_180_imageI,axiom,
% 3.05/1.60 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,F: product_prod_nat_nat > produc194167194tv_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( member737151281tv_nat @ ( F @ X ) @ ( image_1597721174tv_nat @ F @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_181_imageI,axiom,
% 3.05/1.60 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,F: product_prod_nat_nat > produc270694976lle_tv] :
% 3.05/1.60 ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( member813679063lle_tv @ ( F @ X ) @ ( image_1674248956lle_tv @ F @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_182_imageI,axiom,
% 3.05/1.60 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( member701585322at_nat @ ( F @ X ) @ ( image_815163717at_nat @ F @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_183_imageI,axiom,
% 3.05/1.60 ! [X: nat,A: set_nat,F: nat > nat] :
% 3.05/1.60 ( ( member_nat @ X @ A )
% 3.05/1.60 => ( member_nat @ ( F @ X ) @ ( image_nat_nat @ F @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_184_imageI,axiom,
% 3.05/1.60 ! [X: nat,A: set_nat,F: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member_nat @ X @ A )
% 3.05/1.60 => ( member266900804lle_tv @ ( F @ X ) @ ( image_1151963140lle_tv @ F @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_185_imageI,axiom,
% 3.05/1.60 ! [X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > nat] :
% 3.05/1.60 ( ( member266900804lle_tv @ X @ A )
% 3.05/1.60 => ( member_nat @ ( F @ X ) @ ( image_376325286tv_nat @ F @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_186_imageI,axiom,
% 3.05/1.60 ! [X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member266900804lle_tv @ X @ A )
% 3.05/1.60 => ( member266900804lle_tv @ ( F @ X ) @ ( image_335818702lle_tv @ F @ A ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_187_image__iff,axiom,
% 3.05/1.60 ! [Z: produc194167194tv_nat,F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( member737151281tv_nat @ Z @ ( image_1597721174tv_nat @ F @ A ) )
% 3.05/1.60 = ( ? [X2: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X2 @ A )
% 3.05/1.60 & ( Z
% 3.05/1.60 = ( F @ X2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_188_image__iff,axiom,
% 3.05/1.60 ! [Z: produc270694976lle_tv,F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( member813679063lle_tv @ Z @ ( image_1674248956lle_tv @ F @ A ) )
% 3.05/1.60 = ( ? [X2: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X2 @ A )
% 3.05/1.60 & ( Z
% 3.05/1.60 = ( F @ X2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_189_image__iff,axiom,
% 3.05/1.60 ! [Z: product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ Z @ ( image_815163717at_nat @ F @ A ) )
% 3.05/1.60 = ( ? [X2: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X2 @ A )
% 3.05/1.60 & ( Z
% 3.05/1.60 = ( F @ X2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_190_image__iff,axiom,
% 3.05/1.60 ! [Z: nat,F: nat > nat,A: set_nat] :
% 3.05/1.60 ( ( member_nat @ Z @ ( image_nat_nat @ F @ A ) )
% 3.05/1.60 = ( ? [X2: nat] :
% 3.05/1.60 ( ( member_nat @ X2 @ A )
% 3.05/1.60 & ( Z
% 3.05/1.60 = ( F @ X2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_191_image__iff,axiom,
% 3.05/1.60 ! [Z: paraco1605129243lle_tv,F: nat > paraco1605129243lle_tv,A: set_nat] :
% 3.05/1.60 ( ( member266900804lle_tv @ Z @ ( image_1151963140lle_tv @ F @ A ) )
% 3.05/1.60 = ( ? [X2: nat] :
% 3.05/1.60 ( ( member_nat @ X2 @ A )
% 3.05/1.60 & ( Z
% 3.05/1.60 = ( F @ X2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_192_bex__imageD,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat,P: produc194167194tv_nat > $o] :
% 3.05/1.60 ( ? [X4: produc194167194tv_nat] :
% 3.05/1.60 ( ( member737151281tv_nat @ X4 @ ( image_1597721174tv_nat @ F @ A ) )
% 3.05/1.60 & ( P @ X4 ) )
% 3.05/1.60 => ? [X3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X3 @ A )
% 3.05/1.60 & ( P @ ( F @ X3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_193_bex__imageD,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat,P: produc270694976lle_tv > $o] :
% 3.05/1.60 ( ? [X4: produc270694976lle_tv] :
% 3.05/1.60 ( ( member813679063lle_tv @ X4 @ ( image_1674248956lle_tv @ F @ A ) )
% 3.05/1.60 & ( P @ X4 ) )
% 3.05/1.60 => ? [X3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X3 @ A )
% 3.05/1.60 & ( P @ ( F @ X3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_194_bex__imageD,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,P: product_prod_nat_nat > $o] :
% 3.05/1.60 ( ? [X4: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X4 @ ( image_815163717at_nat @ F @ A ) )
% 3.05/1.60 & ( P @ X4 ) )
% 3.05/1.60 => ? [X3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X3 @ A )
% 3.05/1.60 & ( P @ ( F @ X3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_195_bex__imageD,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,A: set_nat,P: paraco1605129243lle_tv > $o] :
% 3.05/1.60 ( ? [X4: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member266900804lle_tv @ X4 @ ( image_1151963140lle_tv @ F @ A ) )
% 3.05/1.60 & ( P @ X4 ) )
% 3.05/1.60 => ? [X3: nat] :
% 3.05/1.60 ( ( member_nat @ X3 @ A )
% 3.05/1.60 & ( P @ ( F @ X3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_196_bex__imageD,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat,P: nat > $o] :
% 3.05/1.60 ( ? [X4: nat] :
% 3.05/1.60 ( ( member_nat @ X4 @ ( image_nat_nat @ F @ A ) )
% 3.05/1.60 & ( P @ X4 ) )
% 3.05/1.60 => ? [X3: nat] :
% 3.05/1.60 ( ( member_nat @ X3 @ A )
% 3.05/1.60 & ( P @ ( F @ X3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_197_image__cong,axiom,
% 3.05/1.60 ! [M: set_Pr1986765409at_nat,N2: set_Pr1986765409at_nat,F: product_prod_nat_nat > produc194167194tv_nat,G: product_prod_nat_nat > produc194167194tv_nat] :
% 3.05/1.60 ( ( M = N2 )
% 3.05/1.60 => ( ! [X3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X3 @ N2 )
% 3.05/1.60 => ( ( F @ X3 )
% 3.05/1.60 = ( G @ X3 ) ) )
% 3.05/1.60 => ( ( image_1597721174tv_nat @ F @ M )
% 3.05/1.60 = ( image_1597721174tv_nat @ G @ N2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_198_image__cong,axiom,
% 3.05/1.60 ! [M: set_Pr1986765409at_nat,N2: set_Pr1986765409at_nat,F: product_prod_nat_nat > produc270694976lle_tv,G: product_prod_nat_nat > produc270694976lle_tv] :
% 3.05/1.60 ( ( M = N2 )
% 3.05/1.60 => ( ! [X3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X3 @ N2 )
% 3.05/1.60 => ( ( F @ X3 )
% 3.05/1.60 = ( G @ X3 ) ) )
% 3.05/1.60 => ( ( image_1674248956lle_tv @ F @ M )
% 3.05/1.60 = ( image_1674248956lle_tv @ G @ N2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_199_image__cong,axiom,
% 3.05/1.60 ! [M: set_Pr1986765409at_nat,N2: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 3.05/1.60 ( ( M = N2 )
% 3.05/1.60 => ( ! [X3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X3 @ N2 )
% 3.05/1.60 => ( ( F @ X3 )
% 3.05/1.60 = ( G @ X3 ) ) )
% 3.05/1.60 => ( ( image_815163717at_nat @ F @ M )
% 3.05/1.60 = ( image_815163717at_nat @ G @ N2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_200_image__cong,axiom,
% 3.05/1.60 ! [M: set_nat,N2: set_nat,F: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( M = N2 )
% 3.05/1.60 => ( ! [X3: nat] :
% 3.05/1.60 ( ( member_nat @ X3 @ N2 )
% 3.05/1.60 => ( ( F @ X3 )
% 3.05/1.60 = ( G @ X3 ) ) )
% 3.05/1.60 => ( ( image_1151963140lle_tv @ F @ M )
% 3.05/1.60 = ( image_1151963140lle_tv @ G @ N2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_201_image__cong,axiom,
% 3.05/1.60 ! [M: set_nat,N2: set_nat,F: nat > nat,G: nat > nat] :
% 3.05/1.60 ( ( M = N2 )
% 3.05/1.60 => ( ! [X3: nat] :
% 3.05/1.60 ( ( member_nat @ X3 @ N2 )
% 3.05/1.60 => ( ( F @ X3 )
% 3.05/1.60 = ( G @ X3 ) ) )
% 3.05/1.60 => ( ( image_nat_nat @ F @ M )
% 3.05/1.60 = ( image_nat_nat @ G @ N2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_202_ball__imageD,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > produc194167194tv_nat,A: set_Pr1986765409at_nat,P: produc194167194tv_nat > $o] :
% 3.05/1.60 ( ! [X3: produc194167194tv_nat] :
% 3.05/1.60 ( ( member737151281tv_nat @ X3 @ ( image_1597721174tv_nat @ F @ A ) )
% 3.05/1.60 => ( P @ X3 ) )
% 3.05/1.60 => ! [X4: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X4 @ A )
% 3.05/1.60 => ( P @ ( F @ X4 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_203_ball__imageD,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > produc270694976lle_tv,A: set_Pr1986765409at_nat,P: produc270694976lle_tv > $o] :
% 3.05/1.60 ( ! [X3: produc270694976lle_tv] :
% 3.05/1.60 ( ( member813679063lle_tv @ X3 @ ( image_1674248956lle_tv @ F @ A ) )
% 3.05/1.60 => ( P @ X3 ) )
% 3.05/1.60 => ! [X4: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X4 @ A )
% 3.05/1.60 => ( P @ ( F @ X4 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_204_ball__imageD,axiom,
% 3.05/1.60 ! [F: product_prod_nat_nat > product_prod_nat_nat,A: set_Pr1986765409at_nat,P: product_prod_nat_nat > $o] :
% 3.05/1.60 ( ! [X3: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X3 @ ( image_815163717at_nat @ F @ A ) )
% 3.05/1.60 => ( P @ X3 ) )
% 3.05/1.60 => ! [X4: product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X4 @ A )
% 3.05/1.60 => ( P @ ( F @ X4 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_205_ball__imageD,axiom,
% 3.05/1.60 ! [F: nat > paraco1605129243lle_tv,A: set_nat,P: paraco1605129243lle_tv > $o] :
% 3.05/1.60 ( ! [X3: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member266900804lle_tv @ X3 @ ( image_1151963140lle_tv @ F @ A ) )
% 3.05/1.60 => ( P @ X3 ) )
% 3.05/1.60 => ! [X4: nat] :
% 3.05/1.60 ( ( member_nat @ X4 @ A )
% 3.05/1.60 => ( P @ ( F @ X4 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_206_ball__imageD,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat,P: nat > $o] :
% 3.05/1.60 ( ! [X3: nat] :
% 3.05/1.60 ( ( member_nat @ X3 @ ( image_nat_nat @ F @ A ) )
% 3.05/1.60 => ( P @ X3 ) )
% 3.05/1.60 => ! [X4: nat] :
% 3.05/1.60 ( ( member_nat @ X4 @ A )
% 3.05/1.60 => ( P @ ( F @ X4 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_207_rev__image__eqI,axiom,
% 3.05/1.60 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,B2: produc194167194tv_nat,F: product_prod_nat_nat > produc194167194tv_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( member737151281tv_nat @ B2 @ ( image_1597721174tv_nat @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_208_rev__image__eqI,axiom,
% 3.05/1.60 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,B2: produc270694976lle_tv,F: product_prod_nat_nat > produc270694976lle_tv] :
% 3.05/1.60 ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( member813679063lle_tv @ B2 @ ( image_1674248956lle_tv @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_209_rev__image__eqI,axiom,
% 3.05/1.60 ! [X: product_prod_nat_nat,A: set_Pr1986765409at_nat,B2: product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 3.05/1.60 ( ( member701585322at_nat @ X @ A )
% 3.05/1.60 => ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( member701585322at_nat @ B2 @ ( image_815163717at_nat @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_210_rev__image__eqI,axiom,
% 3.05/1.60 ! [X: nat,A: set_nat,B2: nat,F: nat > nat] :
% 3.05/1.60 ( ( member_nat @ X @ A )
% 3.05/1.60 => ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( member_nat @ B2 @ ( image_nat_nat @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_211_rev__image__eqI,axiom,
% 3.05/1.60 ! [X: nat,A: set_nat,B2: paraco1605129243lle_tv,F: nat > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member_nat @ X @ A )
% 3.05/1.60 => ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( member266900804lle_tv @ B2 @ ( image_1151963140lle_tv @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_212_rev__image__eqI,axiom,
% 3.05/1.60 ! [X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: nat,F: paraco1605129243lle_tv > nat] :
% 3.05/1.60 ( ( member266900804lle_tv @ X @ A )
% 3.05/1.60 => ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( member_nat @ B2 @ ( image_376325286tv_nat @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_213_rev__image__eqI,axiom,
% 3.05/1.60 ! [X: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.60 ( ( member266900804lle_tv @ X @ A )
% 3.05/1.60 => ( ( B2
% 3.05/1.60 = ( F @ X ) )
% 3.05/1.60 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ A ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_214_strict__mono__onD,axiom,
% 3.05/1.60 ! [F: nat > nat,A: set_nat,R: nat,S: nat] :
% 3.05/1.60 ( ( strict2146030304at_nat @ F @ A )
% 3.05/1.60 => ( ( member_nat @ R @ A )
% 3.05/1.60 => ( ( member_nat @ S @ A )
% 3.05/1.60 => ( ( ord_less_nat @ R @ S )
% 3.05/1.60 => ( ord_less_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_215_strict__mono__onD,axiom,
% 3.05/1.60 ! [F: nat > set_nat,A: set_nat,R: nat,S: nat] :
% 3.05/1.60 ( ( strict1310998166et_nat @ F @ A )
% 3.05/1.60 => ( ( member_nat @ R @ A )
% 3.05/1.60 => ( ( member_nat @ S @ A )
% 3.05/1.60 => ( ( ord_less_nat @ R @ S )
% 3.05/1.60 => ( ord_less_set_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_216_strict__mono__onD,axiom,
% 3.05/1.60 ! [F: nat > set_Pa1764573435lle_tv,A: set_nat,R: nat,S: nat] :
% 3.05/1.60 ( ( strict1658340843lle_tv @ F @ A )
% 3.05/1.60 => ( ( member_nat @ R @ A )
% 3.05/1.60 => ( ( member_nat @ S @ A )
% 3.05/1.60 => ( ( ord_less_nat @ R @ S )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_217_strict__mono__onD,axiom,
% 3.05/1.60 ! [F: set_nat > nat,A: set_set_nat,R: set_nat,S: set_nat] :
% 3.05/1.60 ( ( strict1802283670at_nat @ F @ A )
% 3.05/1.60 => ( ( member_set_nat @ R @ A )
% 3.05/1.60 => ( ( member_set_nat @ S @ A )
% 3.05/1.60 => ( ( ord_less_set_nat @ R @ S )
% 3.05/1.60 => ( ord_less_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_218_strict__mono__onD,axiom,
% 3.05/1.60 ! [F: set_nat > set_nat,A: set_set_nat,R: set_nat,S: set_nat] :
% 3.05/1.60 ( ( strict473775692et_nat @ F @ A )
% 3.05/1.60 => ( ( member_set_nat @ R @ A )
% 3.05/1.60 => ( ( member_set_nat @ S @ A )
% 3.05/1.60 => ( ( ord_less_set_nat @ R @ S )
% 3.05/1.60 => ( ord_less_set_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_219_strict__mono__onD,axiom,
% 3.05/1.60 ! [F: set_nat > set_Pa1764573435lle_tv,A: set_set_nat,R: set_nat,S: set_nat] :
% 3.05/1.60 ( ( strict172559285lle_tv @ F @ A )
% 3.05/1.60 => ( ( member_set_nat @ R @ A )
% 3.05/1.60 => ( ( member_set_nat @ S @ A )
% 3.05/1.60 => ( ( ord_less_set_nat @ R @ S )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_220_strict__mono__onD,axiom,
% 3.05/1.60 ! [F: set_Pa1764573435lle_tv > nat,A: set_se800614875lle_tv,R: set_Pa1764573435lle_tv,S: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( strict1125660301tv_nat @ F @ A )
% 3.05/1.60 => ( ( member1875402276lle_tv @ R @ A )
% 3.05/1.60 => ( ( member1875402276lle_tv @ S @ A )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ R @ S )
% 3.05/1.60 => ( ord_less_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_221_strict__mono__onD,axiom,
% 3.05/1.60 ! [F: set_Pa1764573435lle_tv > set_nat,A: set_se800614875lle_tv,R: set_Pa1764573435lle_tv,S: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( strict1455779395et_nat @ F @ A )
% 3.05/1.60 => ( ( member1875402276lle_tv @ R @ A )
% 3.05/1.60 => ( ( member1875402276lle_tv @ S @ A )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ R @ S )
% 3.05/1.60 => ( ord_less_set_nat @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_222_strict__mono__onD,axiom,
% 3.05/1.60 ! [F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,A: set_se800614875lle_tv,R: set_Pa1764573435lle_tv,S: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( strict592849515lle_tv @ F @ A )
% 3.05/1.60 => ( ( member1875402276lle_tv @ R @ A )
% 3.05/1.60 => ( ( member1875402276lle_tv @ S @ A )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ R @ S )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F @ R ) @ ( F @ S ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_223_strict__mono__onI,axiom,
% 3.05/1.60 ! [A: set_nat,F: nat > nat] :
% 3.05/1.60 ( ! [R2: nat,S2: nat] :
% 3.05/1.60 ( ( member_nat @ R2 @ A )
% 3.05/1.60 => ( ( member_nat @ S2 @ A )
% 3.05/1.60 => ( ( ord_less_nat @ R2 @ S2 )
% 3.05/1.60 => ( ord_less_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 3.05/1.60 => ( strict2146030304at_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_224_strict__mono__onI,axiom,
% 3.05/1.60 ! [A: set_nat,F: nat > set_nat] :
% 3.05/1.60 ( ! [R2: nat,S2: nat] :
% 3.05/1.60 ( ( member_nat @ R2 @ A )
% 3.05/1.60 => ( ( member_nat @ S2 @ A )
% 3.05/1.60 => ( ( ord_less_nat @ R2 @ S2 )
% 3.05/1.60 => ( ord_less_set_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 3.05/1.60 => ( strict1310998166et_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_225_strict__mono__onI,axiom,
% 3.05/1.60 ! [A: set_nat,F: nat > set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ! [R2: nat,S2: nat] :
% 3.05/1.60 ( ( member_nat @ R2 @ A )
% 3.05/1.60 => ( ( member_nat @ S2 @ A )
% 3.05/1.60 => ( ( ord_less_nat @ R2 @ S2 )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 3.05/1.60 => ( strict1658340843lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_226_strict__mono__onI,axiom,
% 3.05/1.60 ! [A: set_set_nat,F: set_nat > nat] :
% 3.05/1.60 ( ! [R2: set_nat,S2: set_nat] :
% 3.05/1.60 ( ( member_set_nat @ R2 @ A )
% 3.05/1.60 => ( ( member_set_nat @ S2 @ A )
% 3.05/1.60 => ( ( ord_less_set_nat @ R2 @ S2 )
% 3.05/1.60 => ( ord_less_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 3.05/1.60 => ( strict1802283670at_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_227_strict__mono__onI,axiom,
% 3.05/1.60 ! [A: set_set_nat,F: set_nat > set_nat] :
% 3.05/1.60 ( ! [R2: set_nat,S2: set_nat] :
% 3.05/1.60 ( ( member_set_nat @ R2 @ A )
% 3.05/1.60 => ( ( member_set_nat @ S2 @ A )
% 3.05/1.60 => ( ( ord_less_set_nat @ R2 @ S2 )
% 3.05/1.60 => ( ord_less_set_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 3.05/1.60 => ( strict473775692et_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_228_strict__mono__onI,axiom,
% 3.05/1.60 ! [A: set_set_nat,F: set_nat > set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ! [R2: set_nat,S2: set_nat] :
% 3.05/1.60 ( ( member_set_nat @ R2 @ A )
% 3.05/1.60 => ( ( member_set_nat @ S2 @ A )
% 3.05/1.60 => ( ( ord_less_set_nat @ R2 @ S2 )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 3.05/1.60 => ( strict172559285lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_229_strict__mono__onI,axiom,
% 3.05/1.60 ! [A: set_se800614875lle_tv,F: set_Pa1764573435lle_tv > nat] :
% 3.05/1.60 ( ! [R2: set_Pa1764573435lle_tv,S2: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( member1875402276lle_tv @ R2 @ A )
% 3.05/1.60 => ( ( member1875402276lle_tv @ S2 @ A )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ R2 @ S2 )
% 3.05/1.60 => ( ord_less_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 3.05/1.60 => ( strict1125660301tv_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_230_strict__mono__onI,axiom,
% 3.05/1.60 ! [A: set_se800614875lle_tv,F: set_Pa1764573435lle_tv > set_nat] :
% 3.05/1.60 ( ! [R2: set_Pa1764573435lle_tv,S2: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( member1875402276lle_tv @ R2 @ A )
% 3.05/1.60 => ( ( member1875402276lle_tv @ S2 @ A )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ R2 @ S2 )
% 3.05/1.60 => ( ord_less_set_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 3.05/1.60 => ( strict1455779395et_nat @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_231_strict__mono__onI,axiom,
% 3.05/1.60 ! [A: set_se800614875lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ! [R2: set_Pa1764573435lle_tv,S2: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( member1875402276lle_tv @ R2 @ A )
% 3.05/1.60 => ( ( member1875402276lle_tv @ S2 @ A )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ R2 @ S2 )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) )
% 3.05/1.60 => ( strict592849515lle_tv @ F @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_232_strict__mono__on__def,axiom,
% 3.05/1.60 ( strict2146030304at_nat
% 3.05/1.60 = ( ^ [F2: nat > nat,A2: set_nat] :
% 3.05/1.60 ! [R3: nat,S3: nat] :
% 3.05/1.60 ( ( ( member_nat @ R3 @ A2 )
% 3.05/1.60 & ( member_nat @ S3 @ A2 )
% 3.05/1.60 & ( ord_less_nat @ R3 @ S3 ) )
% 3.05/1.60 => ( ord_less_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_233_strict__mono__on__def,axiom,
% 3.05/1.60 ( strict1310998166et_nat
% 3.05/1.60 = ( ^ [F2: nat > set_nat,A2: set_nat] :
% 3.05/1.60 ! [R3: nat,S3: nat] :
% 3.05/1.60 ( ( ( member_nat @ R3 @ A2 )
% 3.05/1.60 & ( member_nat @ S3 @ A2 )
% 3.05/1.60 & ( ord_less_nat @ R3 @ S3 ) )
% 3.05/1.60 => ( ord_less_set_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_234_strict__mono__on__def,axiom,
% 3.05/1.60 ( strict1658340843lle_tv
% 3.05/1.60 = ( ^ [F2: nat > set_Pa1764573435lle_tv,A2: set_nat] :
% 3.05/1.60 ! [R3: nat,S3: nat] :
% 3.05/1.60 ( ( ( member_nat @ R3 @ A2 )
% 3.05/1.60 & ( member_nat @ S3 @ A2 )
% 3.05/1.60 & ( ord_less_nat @ R3 @ S3 ) )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_235_strict__mono__on__def,axiom,
% 3.05/1.60 ( strict1802283670at_nat
% 3.05/1.60 = ( ^ [F2: set_nat > nat,A2: set_set_nat] :
% 3.05/1.60 ! [R3: set_nat,S3: set_nat] :
% 3.05/1.60 ( ( ( member_set_nat @ R3 @ A2 )
% 3.05/1.60 & ( member_set_nat @ S3 @ A2 )
% 3.05/1.60 & ( ord_less_set_nat @ R3 @ S3 ) )
% 3.05/1.60 => ( ord_less_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_236_strict__mono__on__def,axiom,
% 3.05/1.60 ( strict473775692et_nat
% 3.05/1.60 = ( ^ [F2: set_nat > set_nat,A2: set_set_nat] :
% 3.05/1.60 ! [R3: set_nat,S3: set_nat] :
% 3.05/1.60 ( ( ( member_set_nat @ R3 @ A2 )
% 3.05/1.60 & ( member_set_nat @ S3 @ A2 )
% 3.05/1.60 & ( ord_less_set_nat @ R3 @ S3 ) )
% 3.05/1.60 => ( ord_less_set_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_237_strict__mono__on__def,axiom,
% 3.05/1.60 ( strict172559285lle_tv
% 3.05/1.60 = ( ^ [F2: set_nat > set_Pa1764573435lle_tv,A2: set_set_nat] :
% 3.05/1.60 ! [R3: set_nat,S3: set_nat] :
% 3.05/1.60 ( ( ( member_set_nat @ R3 @ A2 )
% 3.05/1.60 & ( member_set_nat @ S3 @ A2 )
% 3.05/1.60 & ( ord_less_set_nat @ R3 @ S3 ) )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_238_strict__mono__on__def,axiom,
% 3.05/1.60 ( strict1125660301tv_nat
% 3.05/1.60 = ( ^ [F2: set_Pa1764573435lle_tv > nat,A2: set_se800614875lle_tv] :
% 3.05/1.60 ! [R3: set_Pa1764573435lle_tv,S3: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( ( member1875402276lle_tv @ R3 @ A2 )
% 3.05/1.60 & ( member1875402276lle_tv @ S3 @ A2 )
% 3.05/1.60 & ( ord_le727057319lle_tv @ R3 @ S3 ) )
% 3.05/1.60 => ( ord_less_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_239_strict__mono__on__def,axiom,
% 3.05/1.60 ( strict1455779395et_nat
% 3.05/1.60 = ( ^ [F2: set_Pa1764573435lle_tv > set_nat,A2: set_se800614875lle_tv] :
% 3.05/1.60 ! [R3: set_Pa1764573435lle_tv,S3: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( ( member1875402276lle_tv @ R3 @ A2 )
% 3.05/1.60 & ( member1875402276lle_tv @ S3 @ A2 )
% 3.05/1.60 & ( ord_le727057319lle_tv @ R3 @ S3 ) )
% 3.05/1.60 => ( ord_less_set_nat @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_240_strict__mono__on__def,axiom,
% 3.05/1.60 ( strict592849515lle_tv
% 3.05/1.60 = ( ^ [F2: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,A2: set_se800614875lle_tv] :
% 3.05/1.60 ! [R3: set_Pa1764573435lle_tv,S3: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( ( member1875402276lle_tv @ R3 @ A2 )
% 3.05/1.60 & ( member1875402276lle_tv @ S3 @ A2 )
% 3.05/1.60 & ( ord_le727057319lle_tv @ R3 @ S3 ) )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F2 @ R3 ) @ ( F2 @ S3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_241_ord__eq__less__subst,axiom,
% 3.05/1.60 ! [A4: nat,F: nat > nat,B2: nat,C: nat] :
% 3.05/1.60 ( ( A4
% 3.05/1.60 = ( F @ B2 ) )
% 3.05/1.60 => ( ( ord_less_nat @ B2 @ C )
% 3.05/1.60 => ( ! [X3: nat,Y2: nat] :
% 3.05/1.60 ( ( ord_less_nat @ X3 @ Y2 )
% 3.05/1.60 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 3.05/1.60 => ( ord_less_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_242_ord__eq__less__subst,axiom,
% 3.05/1.60 ! [A4: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 3.05/1.60 ( ( A4
% 3.05/1.60 = ( F @ B2 ) )
% 3.05/1.60 => ( ( ord_less_nat @ B2 @ C )
% 3.05/1.60 => ( ! [X3: nat,Y2: nat] :
% 3.05/1.60 ( ( ord_less_nat @ X3 @ Y2 )
% 3.05/1.60 => ( ord_less_set_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 3.05/1.60 => ( ord_less_set_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_243_ord__eq__less__subst,axiom,
% 3.05/1.60 ! [A4: set_Pa1764573435lle_tv,F: nat > set_Pa1764573435lle_tv,B2: nat,C: nat] :
% 3.05/1.60 ( ( A4
% 3.05/1.60 = ( F @ B2 ) )
% 3.05/1.60 => ( ( ord_less_nat @ B2 @ C )
% 3.05/1.60 => ( ! [X3: nat,Y2: nat] :
% 3.05/1.60 ( ( ord_less_nat @ X3 @ Y2 )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 3.05/1.60 => ( ord_le727057319lle_tv @ A4 @ ( F @ C ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_244_ord__eq__less__subst,axiom,
% 3.05/1.60 ! [A4: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 3.05/1.60 ( ( A4
% 3.05/1.60 = ( F @ B2 ) )
% 3.05/1.60 => ( ( ord_less_set_nat @ B2 @ C )
% 3.05/1.60 => ( ! [X3: set_nat,Y2: set_nat] :
% 3.05/1.60 ( ( ord_less_set_nat @ X3 @ Y2 )
% 3.05/1.60 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 3.05/1.60 => ( ord_less_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_245_ord__eq__less__subst,axiom,
% 3.05/1.60 ! [A4: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 3.05/1.60 ( ( A4
% 3.05/1.60 = ( F @ B2 ) )
% 3.05/1.60 => ( ( ord_less_set_nat @ B2 @ C )
% 3.05/1.60 => ( ! [X3: set_nat,Y2: set_nat] :
% 3.05/1.60 ( ( ord_less_set_nat @ X3 @ Y2 )
% 3.05/1.60 => ( ord_less_set_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 3.05/1.60 => ( ord_less_set_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_246_ord__eq__less__subst,axiom,
% 3.05/1.60 ! [A4: set_Pa1764573435lle_tv,F: set_nat > set_Pa1764573435lle_tv,B2: set_nat,C: set_nat] :
% 3.05/1.60 ( ( A4
% 3.05/1.60 = ( F @ B2 ) )
% 3.05/1.60 => ( ( ord_less_set_nat @ B2 @ C )
% 3.05/1.60 => ( ! [X3: set_nat,Y2: set_nat] :
% 3.05/1.60 ( ( ord_less_set_nat @ X3 @ Y2 )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 3.05/1.60 => ( ord_le727057319lle_tv @ A4 @ ( F @ C ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_247_ord__eq__less__subst,axiom,
% 3.05/1.60 ! [A4: nat,F: set_Pa1764573435lle_tv > nat,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( A4
% 3.05/1.60 = ( F @ B2 ) )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ B2 @ C )
% 3.05/1.60 => ( ! [X3: set_Pa1764573435lle_tv,Y2: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( ord_le727057319lle_tv @ X3 @ Y2 )
% 3.05/1.60 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 3.05/1.60 => ( ord_less_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_248_ord__eq__less__subst,axiom,
% 3.05/1.60 ! [A4: set_nat,F: set_Pa1764573435lle_tv > set_nat,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( A4
% 3.05/1.60 = ( F @ B2 ) )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ B2 @ C )
% 3.05/1.60 => ( ! [X3: set_Pa1764573435lle_tv,Y2: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( ord_le727057319lle_tv @ X3 @ Y2 )
% 3.05/1.60 => ( ord_less_set_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 3.05/1.60 => ( ord_less_set_nat @ A4 @ ( F @ C ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_249_ord__eq__less__subst,axiom,
% 3.05/1.60 ! [A4: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,B2: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( A4
% 3.05/1.60 = ( F @ B2 ) )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ B2 @ C )
% 3.05/1.60 => ( ! [X3: set_Pa1764573435lle_tv,Y2: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( ord_le727057319lle_tv @ X3 @ Y2 )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 3.05/1.60 => ( ord_le727057319lle_tv @ A4 @ ( F @ C ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_250_mem__Collect__eq,axiom,
% 3.05/1.60 ! [A4: nat,P: nat > $o] :
% 3.05/1.60 ( ( member_nat @ A4 @ ( collect_nat @ P ) )
% 3.05/1.60 = ( P @ A4 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_251_mem__Collect__eq,axiom,
% 3.05/1.60 ! [A4: paraco1605129243lle_tv,P: paraco1605129243lle_tv > $o] :
% 3.05/1.60 ( ( member266900804lle_tv @ A4 @ ( collec1111687558lle_tv @ P ) )
% 3.05/1.60 = ( P @ A4 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_252_Collect__mem__eq,axiom,
% 3.05/1.60 ! [A: set_nat] :
% 3.05/1.60 ( ( collect_nat
% 3.05/1.60 @ ^ [X2: nat] : ( member_nat @ X2 @ A ) )
% 3.05/1.60 = A ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_253_Collect__mem__eq,axiom,
% 3.05/1.60 ! [A: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( collec1111687558lle_tv
% 3.05/1.60 @ ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ A ) )
% 3.05/1.60 = A ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_254_Collect__cong,axiom,
% 3.05/1.60 ! [P: nat > $o,Q: nat > $o] :
% 3.05/1.60 ( ! [X3: nat] :
% 3.05/1.60 ( ( P @ X3 )
% 3.05/1.60 = ( Q @ X3 ) )
% 3.05/1.60 => ( ( collect_nat @ P )
% 3.05/1.60 = ( collect_nat @ Q ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_255_Collect__cong,axiom,
% 3.05/1.60 ! [P: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv > $o] :
% 3.05/1.60 ( ! [X3: paraco1605129243lle_tv] :
% 3.05/1.60 ( ( P @ X3 )
% 3.05/1.60 = ( Q @ X3 ) )
% 3.05/1.60 => ( ( collec1111687558lle_tv @ P )
% 3.05/1.60 = ( collec1111687558lle_tv @ Q ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_256_inj__on__strict__subset,axiom,
% 3.05/1.60 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.60 ( ( inj_on772319074lle_tv @ F @ B )
% 3.05/1.60 => ( ( ord_le727057319lle_tv @ A @ B )
% 3.05/1.60 => ( ord_le727057319lle_tv @ ( image_335818702lle_tv @ F @ A ) @ ( image_335818702lle_tv @ F @ B ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_257_inj__on__strict__subset,axiom,
% 3.05/1.60 ! [F: nat > nat,B: set_nat,A: set_nat] :
% 3.05/1.60 ( ( inj_on_nat_nat @ F @ B )
% 3.05/1.61 => ( ( ord_less_set_nat @ A @ B )
% 3.05/1.61 => ( ord_less_set_nat @ ( image_nat_nat @ F @ A ) @ ( image_nat_nat @ F @ B ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_258_inj__on__the__inv__into,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.61 => ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ A @ F ) @ ( image_335818702lle_tv @ F @ A ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_259_inj__on__the__inv__into,axiom,
% 3.05/1.61 ! [F: nat > nat,A: set_nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.61 => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A @ F ) @ ( image_nat_nat @ F @ A ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_260_f__the__inv__into__f,axiom,
% 3.05/1.61 ! [F: nat > nat,A: set_nat,Y: nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.61 => ( ( member_nat @ Y @ ( image_nat_nat @ F @ A ) )
% 3.05/1.61 => ( ( F @ ( the_inv_into_nat_nat @ A @ F @ Y ) )
% 3.05/1.61 = Y ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_261_f__the__inv__into__f,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.61 => ( ( member266900804lle_tv @ Y @ ( image_335818702lle_tv @ F @ A ) )
% 3.05/1.61 => ( ( F @ ( the_in452116896lle_tv @ A @ F @ Y ) )
% 3.05/1.61 = Y ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_262_strict__mono__inv,axiom,
% 3.05/1.61 ! [F: nat > nat,G: nat > nat] :
% 3.05/1.61 ( ( order_769474267at_nat @ F )
% 3.05/1.61 => ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ! [X3: nat] :
% 3.05/1.61 ( ( G @ ( F @ X3 ) )
% 3.05/1.61 = X3 )
% 3.05/1.61 => ( order_769474267at_nat @ G ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_263_surjD,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ? [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( Y
% 3.05/1.61 = ( F @ X3 ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_264_surjD,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat,Y: nat] :
% 3.05/1.61 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ? [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( Y
% 3.05/1.61 = ( F @ X3 ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_265_surjD,axiom,
% 3.05/1.61 ! [F: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ? [X3: nat] :
% 3.05/1.61 ( Y
% 3.05/1.61 = ( F @ X3 ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_266_surjD,axiom,
% 3.05/1.61 ! [F: nat > nat,Y: nat] :
% 3.05/1.61 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ? [X3: nat] :
% 3.05/1.61 ( Y
% 3.05/1.61 = ( F @ X3 ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_267_surjE,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ~ ! [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( Y
% 3.05/1.61 != ( F @ X3 ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_268_surjE,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat,Y: nat] :
% 3.05/1.61 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ~ ! [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( Y
% 3.05/1.61 != ( F @ X3 ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_269_surjE,axiom,
% 3.05/1.61 ! [F: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ~ ! [X3: nat] :
% 3.05/1.61 ( Y
% 3.05/1.61 != ( F @ X3 ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_270_surjE,axiom,
% 3.05/1.61 ! [F: nat > nat,Y: nat] :
% 3.05/1.61 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ~ ! [X3: nat] :
% 3.05/1.61 ( Y
% 3.05/1.61 != ( F @ X3 ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_271_surjI,axiom,
% 3.05/1.61 ! [G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.61 ( ! [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( G @ ( F @ X3 ) )
% 3.05/1.61 = X3 )
% 3.05/1.61 => ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_272_surjI,axiom,
% 3.05/1.61 ! [G: paraco1605129243lle_tv > nat,F: nat > paraco1605129243lle_tv] :
% 3.05/1.61 ( ! [X3: nat] :
% 3.05/1.61 ( ( G @ ( F @ X3 ) )
% 3.05/1.61 = X3 )
% 3.05/1.61 => ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_273_surjI,axiom,
% 3.05/1.61 ! [G: nat > paraco1605129243lle_tv,F: paraco1605129243lle_tv > nat] :
% 3.05/1.61 ( ! [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( G @ ( F @ X3 ) )
% 3.05/1.61 = X3 )
% 3.05/1.61 => ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 3.05/1.61 = top_to1057771083lle_tv ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_274_surjI,axiom,
% 3.05/1.61 ! [G: nat > nat,F: nat > nat] :
% 3.05/1.61 ( ! [X3: nat] :
% 3.05/1.61 ( ( G @ ( F @ X3 ) )
% 3.05/1.61 = X3 )
% 3.05/1.61 => ( ( image_nat_nat @ G @ top_top_set_nat )
% 3.05/1.61 = top_top_set_nat ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_275_rangeI,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat,X: paraco1605129243lle_tv] : ( member_nat @ ( F @ X ) @ ( image_376325286tv_nat @ F @ top_to1057771083lle_tv ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_276_rangeI,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] : ( member266900804lle_tv @ ( F @ X ) @ ( image_335818702lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_277_rangeI,axiom,
% 3.05/1.61 ! [F: nat > nat,X: nat] : ( member_nat @ ( F @ X ) @ ( image_nat_nat @ F @ top_top_set_nat ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_278_rangeI,axiom,
% 3.05/1.61 ! [F: nat > paraco1605129243lle_tv,X: nat] : ( member266900804lle_tv @ ( F @ X ) @ ( image_1151963140lle_tv @ F @ top_top_set_nat ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_279_surj__def,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 = ( ! [Y3: paraco1605129243lle_tv] :
% 3.05/1.61 ? [X2: paraco1605129243lle_tv] :
% 3.05/1.61 ( Y3
% 3.05/1.61 = ( F @ X2 ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_280_surj__def,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat] :
% 3.05/1.61 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 = ( ! [Y3: nat] :
% 3.05/1.61 ? [X2: paraco1605129243lle_tv] :
% 3.05/1.61 ( Y3
% 3.05/1.61 = ( F @ X2 ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_281_surj__def,axiom,
% 3.05/1.61 ! [F: nat > paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 = ( ! [Y3: paraco1605129243lle_tv] :
% 3.05/1.61 ? [X2: nat] :
% 3.05/1.61 ( Y3
% 3.05/1.61 = ( F @ X2 ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_282_surj__def,axiom,
% 3.05/1.61 ! [F: nat > nat] :
% 3.05/1.61 ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 = ( ! [Y3: nat] :
% 3.05/1.61 ? [X2: nat] :
% 3.05/1.61 ( Y3
% 3.05/1.61 = ( F @ X2 ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_283_range__eqI,axiom,
% 3.05/1.61 ! [B2: nat,F: paraco1605129243lle_tv > nat,X: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( B2
% 3.05/1.61 = ( F @ X ) )
% 3.05/1.61 => ( member_nat @ B2 @ ( image_376325286tv_nat @ F @ top_to1057771083lle_tv ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_284_range__eqI,axiom,
% 3.05/1.61 ! [B2: paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( B2
% 3.05/1.61 = ( F @ X ) )
% 3.05/1.61 => ( member266900804lle_tv @ B2 @ ( image_335818702lle_tv @ F @ top_to1057771083lle_tv ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_285_range__eqI,axiom,
% 3.05/1.61 ! [B2: nat,F: nat > nat,X: nat] :
% 3.05/1.61 ( ( B2
% 3.05/1.61 = ( F @ X ) )
% 3.05/1.61 => ( member_nat @ B2 @ ( image_nat_nat @ F @ top_top_set_nat ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_286_range__eqI,axiom,
% 3.05/1.61 ! [B2: paraco1605129243lle_tv,F: nat > paraco1605129243lle_tv,X: nat] :
% 3.05/1.61 ( ( B2
% 3.05/1.61 = ( F @ X ) )
% 3.05/1.61 => ( member266900804lle_tv @ B2 @ ( image_1151963140lle_tv @ F @ top_top_set_nat ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_287_inj__on__image__iff,axiom,
% 3.05/1.61 ! [A: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.61 ( ! [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( member266900804lle_tv @ X3 @ A )
% 3.05/1.61 => ! [Xa: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( member266900804lle_tv @ Xa @ A )
% 3.05/1.61 => ( ( ( G @ ( F @ X3 ) )
% 3.05/1.61 = ( G @ ( F @ Xa ) ) )
% 3.05/1.61 = ( ( G @ X3 )
% 3.05/1.61 = ( G @ Xa ) ) ) ) )
% 3.05/1.61 => ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.61 => ( ( inj_on772319074lle_tv @ G @ ( image_335818702lle_tv @ F @ A ) )
% 3.05/1.61 = ( inj_on772319074lle_tv @ G @ A ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_288_inj__on__image__iff,axiom,
% 3.05/1.61 ! [A: set_nat,G: nat > nat,F: nat > nat] :
% 3.05/1.61 ( ! [X3: nat] :
% 3.05/1.61 ( ( member_nat @ X3 @ A )
% 3.05/1.61 => ! [Xa: nat] :
% 3.05/1.61 ( ( member_nat @ Xa @ A )
% 3.05/1.61 => ( ( ( G @ ( F @ X3 ) )
% 3.05/1.61 = ( G @ ( F @ Xa ) ) )
% 3.05/1.61 = ( ( G @ X3 )
% 3.05/1.61 = ( G @ Xa ) ) ) ) )
% 3.05/1.61 => ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.61 => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A ) )
% 3.05/1.61 = ( inj_on_nat_nat @ G @ A ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_289_top_Oextremum__strict,axiom,
% 3.05/1.61 ! [A4: set_Pa1764573435lle_tv] :
% 3.05/1.61 ~ ( ord_le727057319lle_tv @ top_to1057771083lle_tv @ A4 ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_290_top_Oextremum__strict,axiom,
% 3.05/1.61 ! [A4: set_nat] :
% 3.05/1.61 ~ ( ord_less_set_nat @ top_top_set_nat @ A4 ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_291_top_Onot__eq__extremum,axiom,
% 3.05/1.61 ! [A4: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( A4 != top_to1057771083lle_tv )
% 3.05/1.61 = ( ord_le727057319lle_tv @ A4 @ top_to1057771083lle_tv ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_292_top_Onot__eq__extremum,axiom,
% 3.05/1.61 ! [A4: set_nat] :
% 3.05/1.61 ( ( A4 != top_top_set_nat )
% 3.05/1.61 = ( ord_less_set_nat @ A4 @ top_top_set_nat ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_293_inj__on__add,axiom,
% 3.05/1.61 ! [A4: nat,A: set_nat] : ( inj_on_nat_nat @ ( plus_plus_nat @ A4 ) @ A ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_294_the__inv__into__f__f,axiom,
% 3.05/1.61 ! [F: nat > nat,A: set_nat,X: nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.61 => ( ( member_nat @ X @ A )
% 3.05/1.61 => ( ( the_inv_into_nat_nat @ A @ F @ ( F @ X ) )
% 3.05/1.61 = X ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_295_the__inv__into__f__f,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.61 => ( ( member266900804lle_tv @ X @ A )
% 3.05/1.61 => ( ( the_in452116896lle_tv @ A @ F @ ( F @ X ) )
% 3.05/1.61 = X ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_296_the__inv__into__f__eq,axiom,
% 3.05/1.61 ! [F: nat > nat,A: set_nat,X: nat,Y: nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.61 => ( ( ( F @ X )
% 3.05/1.61 = Y )
% 3.05/1.61 => ( ( member_nat @ X @ A )
% 3.05/1.61 => ( ( the_inv_into_nat_nat @ A @ F @ Y )
% 3.05/1.61 = X ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_297_the__inv__into__f__eq,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.61 => ( ( ( F @ X )
% 3.05/1.61 = Y )
% 3.05/1.61 => ( ( member266900804lle_tv @ X @ A )
% 3.05/1.61 => ( ( the_in452116896lle_tv @ A @ F @ Y )
% 3.05/1.61 = X ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_298_psubsetD,axiom,
% 3.05/1.61 ! [A: set_nat,B: set_nat,C: nat] :
% 3.05/1.61 ( ( ord_less_set_nat @ A @ B )
% 3.05/1.61 => ( ( member_nat @ C @ A )
% 3.05/1.61 => ( member_nat @ C @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_299_psubsetD,axiom,
% 3.05/1.61 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ord_le727057319lle_tv @ A @ B )
% 3.05/1.61 => ( ( member266900804lle_tv @ C @ A )
% 3.05/1.61 => ( member266900804lle_tv @ C @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_300_the__inv__into__into,axiom,
% 3.05/1.61 ! [F: nat > nat,A: set_nat,X: nat,B: set_nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.61 => ( ( member_nat @ X @ ( image_nat_nat @ F @ A ) )
% 3.05/1.61 => ( ( ord_less_eq_set_nat @ A @ B )
% 3.05/1.61 => ( member_nat @ ( the_inv_into_nat_nat @ A @ F @ X ) @ B ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_301_the__inv__into__into,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat,A: set_Pa1764573435lle_tv,X: nat,B: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( inj_on1179712058tv_nat @ F @ A )
% 3.05/1.61 => ( ( member_nat @ X @ ( image_376325286tv_nat @ F @ A ) )
% 3.05/1.61 => ( ( ord_le241064091lle_tv @ A @ B )
% 3.05/1.61 => ( member266900804lle_tv @ ( the_in1509933432tv_nat @ A @ F @ X ) @ B ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_302_the__inv__into__into,axiom,
% 3.05/1.61 ! [F: nat > paraco1605129243lle_tv,A: set_nat,X: paraco1605129243lle_tv,B: set_nat] :
% 3.05/1.61 ( ( inj_on1955349912lle_tv @ F @ A )
% 3.05/1.61 => ( ( member266900804lle_tv @ X @ ( image_1151963140lle_tv @ F @ A ) )
% 3.05/1.61 => ( ( ord_less_eq_set_nat @ A @ B )
% 3.05/1.61 => ( member_nat @ ( the_in138087638lle_tv @ A @ F @ X ) @ B ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_303_the__inv__into__into,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.61 => ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F @ A ) )
% 3.05/1.61 => ( ( ord_le241064091lle_tv @ A @ B )
% 3.05/1.61 => ( member266900804lle_tv @ ( the_in452116896lle_tv @ A @ F @ X ) @ B ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_304_prod_Oinj__map,axiom,
% 3.05/1.61 ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 3.05/1.61 => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 3.05/1.61 => ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ F1 @ F22 ) @ top_to1871154984lle_tv ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_305_prod_Oinj__map,axiom,
% 3.05/1.61 ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: nat > nat] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 3.05/1.61 => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 3.05/1.61 => ( inj_on552895452tv_nat @ ( produc42536895at_nat @ F1 @ F22 ) @ top_to975729152tv_nat ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_306_prod_Oinj__map,axiom,
% 3.05/1.61 ! [F1: nat > nat,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 3.05/1.61 => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 3.05/1.61 => ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ F1 @ F22 ) @ top_to1411004326lle_tv ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_307_prod_Oinj__map,axiom,
% 3.05/1.61 ! [F1: nat > nat,F22: nat > nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 3.05/1.61 => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 3.05/1.61 => ( inj_on26176689at_nat @ ( produc505105722at_nat @ F1 @ F22 ) @ top_to1555900337at_nat ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_308_subsetI,axiom,
% 3.05/1.61 ! [A: set_nat,B: set_nat] :
% 3.05/1.61 ( ! [X3: nat] :
% 3.05/1.61 ( ( member_nat @ X3 @ A )
% 3.05/1.61 => ( member_nat @ X3 @ B ) )
% 3.05/1.61 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_309_subsetI,axiom,
% 3.05/1.61 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ! [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( member266900804lle_tv @ X3 @ A )
% 3.05/1.61 => ( member266900804lle_tv @ X3 @ B ) )
% 3.05/1.61 => ( ord_le241064091lle_tv @ A @ B ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_310_image__subsetI,axiom,
% 3.05/1.61 ! [A: set_nat,F: nat > nat,B: set_nat] :
% 3.05/1.61 ( ! [X3: nat] :
% 3.05/1.61 ( ( member_nat @ X3 @ A )
% 3.05/1.61 => ( member_nat @ ( F @ X3 ) @ B ) )
% 3.05/1.61 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A ) @ B ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_311_image__subsetI,axiom,
% 3.05/1.61 ! [A: set_nat,F: nat > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ! [X3: nat] :
% 3.05/1.61 ( ( member_nat @ X3 @ A )
% 3.05/1.61 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 3.05/1.61 => ( ord_le241064091lle_tv @ ( image_1151963140lle_tv @ F @ A ) @ B ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_312_image__subsetI,axiom,
% 3.05/1.61 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > nat,B: set_nat] :
% 3.05/1.61 ( ! [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( member266900804lle_tv @ X3 @ A )
% 3.05/1.61 => ( member_nat @ ( F @ X3 ) @ B ) )
% 3.05/1.61 => ( ord_less_eq_set_nat @ ( image_376325286tv_nat @ F @ A ) @ B ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_313_image__subsetI,axiom,
% 3.05/1.61 ! [A: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ! [X3: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( member266900804lle_tv @ X3 @ A )
% 3.05/1.61 => ( member266900804lle_tv @ ( F @ X3 ) @ B ) )
% 3.05/1.61 => ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ A ) @ B ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_314_top_Oextremum__uniqueI,axiom,
% 3.05/1.61 ! [A4: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A4 )
% 3.05/1.61 => ( A4 = top_to1057771083lle_tv ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_315_top_Oextremum__uniqueI,axiom,
% 3.05/1.61 ! [A4: set_nat] :
% 3.05/1.61 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A4 )
% 3.05/1.61 => ( A4 = top_top_set_nat ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_316_top_Oextremum__unique,axiom,
% 3.05/1.61 ! [A4: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A4 )
% 3.05/1.61 = ( A4 = top_to1057771083lle_tv ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_317_top_Oextremum__unique,axiom,
% 3.05/1.61 ! [A4: set_nat] :
% 3.05/1.61 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A4 )
% 3.05/1.61 = ( A4 = top_top_set_nat ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_318_top__greatest,axiom,
% 3.05/1.61 ! [A4: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A4 @ top_to1057771083lle_tv ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_319_top__greatest,axiom,
% 3.05/1.61 ! [A4: set_nat] : ( ord_less_eq_set_nat @ A4 @ top_top_set_nat ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_320_subset__UNIV,axiom,
% 3.05/1.61 ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_321_subset__UNIV,axiom,
% 3.05/1.61 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_322_subset__inj__on,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ B )
% 3.05/1.61 => ( ( ord_le241064091lle_tv @ A @ B )
% 3.05/1.61 => ( inj_on772319074lle_tv @ F @ A ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_323_subset__inj__on,axiom,
% 3.05/1.61 ! [F: nat > nat,B: set_nat,A: set_nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ B )
% 3.05/1.61 => ( ( ord_less_eq_set_nat @ A @ B )
% 3.05/1.61 => ( inj_on_nat_nat @ F @ A ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_324_inj__on__subset,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ A )
% 3.05/1.61 => ( ( ord_le241064091lle_tv @ B @ A )
% 3.05/1.61 => ( inj_on772319074lle_tv @ F @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_325_inj__on__subset,axiom,
% 3.05/1.61 ! [F: nat > nat,A: set_nat,B: set_nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ A )
% 3.05/1.61 => ( ( ord_less_eq_set_nat @ B @ A )
% 3.05/1.61 => ( inj_on_nat_nat @ F @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_326_in__mono,axiom,
% 3.05/1.61 ! [A: set_nat,B: set_nat,X: nat] :
% 3.05/1.61 ( ( ord_less_eq_set_nat @ A @ B )
% 3.05/1.61 => ( ( member_nat @ X @ A )
% 3.05/1.61 => ( member_nat @ X @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_327_in__mono,axiom,
% 3.05/1.61 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ord_le241064091lle_tv @ A @ B )
% 3.05/1.61 => ( ( member266900804lle_tv @ X @ A )
% 3.05/1.61 => ( member266900804lle_tv @ X @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_328_subsetD,axiom,
% 3.05/1.61 ! [A: set_nat,B: set_nat,C: nat] :
% 3.05/1.61 ( ( ord_less_eq_set_nat @ A @ B )
% 3.05/1.61 => ( ( member_nat @ C @ A )
% 3.05/1.61 => ( member_nat @ C @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_329_subsetD,axiom,
% 3.05/1.61 ! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ord_le241064091lle_tv @ A @ B )
% 3.05/1.61 => ( ( member266900804lle_tv @ C @ A )
% 3.05/1.61 => ( member266900804lle_tv @ C @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_330_subset__eq,axiom,
% 3.05/1.61 ( ord_less_eq_set_nat
% 3.05/1.61 = ( ^ [A2: set_nat,B3: set_nat] :
% 3.05/1.61 ! [X2: nat] :
% 3.05/1.61 ( ( member_nat @ X2 @ A2 )
% 3.05/1.61 => ( member_nat @ X2 @ B3 ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_331_subset__eq,axiom,
% 3.05/1.61 ( ord_le241064091lle_tv
% 3.05/1.61 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 3.05/1.61 ! [X2: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( member266900804lle_tv @ X2 @ A2 )
% 3.05/1.61 => ( member266900804lle_tv @ X2 @ B3 ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_332_subset__iff,axiom,
% 3.05/1.61 ( ord_less_eq_set_nat
% 3.05/1.61 = ( ^ [A2: set_nat,B3: set_nat] :
% 3.05/1.61 ! [T: nat] :
% 3.05/1.61 ( ( member_nat @ T @ A2 )
% 3.05/1.61 => ( member_nat @ T @ B3 ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_333_subset__iff,axiom,
% 3.05/1.61 ( ord_le241064091lle_tv
% 3.05/1.61 = ( ^ [A2: set_Pa1764573435lle_tv,B3: set_Pa1764573435lle_tv] :
% 3.05/1.61 ! [T: paraco1605129243lle_tv] :
% 3.05/1.61 ( ( member266900804lle_tv @ T @ A2 )
% 3.05/1.61 => ( member266900804lle_tv @ T @ B3 ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_334_linorder__inj__onI,axiom,
% 3.05/1.61 ! [A: set_nat,F: nat > nat] :
% 3.05/1.61 ( ! [X3: nat,Y2: nat] :
% 3.05/1.61 ( ( ord_less_nat @ X3 @ Y2 )
% 3.05/1.61 => ( ( member_nat @ X3 @ A )
% 3.05/1.61 => ( ( member_nat @ Y2 @ A )
% 3.05/1.61 => ( ( F @ X3 )
% 3.05/1.61 != ( F @ Y2 ) ) ) ) )
% 3.05/1.61 => ( ! [X3: nat,Y2: nat] :
% 3.05/1.61 ( ( member_nat @ X3 @ A )
% 3.05/1.61 => ( ( member_nat @ Y2 @ A )
% 3.05/1.61 => ( ( ord_less_eq_nat @ X3 @ Y2 )
% 3.05/1.61 | ( ord_less_eq_nat @ Y2 @ X3 ) ) ) )
% 3.05/1.61 => ( inj_on_nat_nat @ F @ A ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_335_inj__on__image__mem__iff,axiom,
% 3.05/1.61 ! [F: nat > nat,B: set_nat,A4: nat,A: set_nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ B )
% 3.05/1.61 => ( ( member_nat @ A4 @ B )
% 3.05/1.61 => ( ( ord_less_eq_set_nat @ A @ B )
% 3.05/1.61 => ( ( member_nat @ ( F @ A4 ) @ ( image_nat_nat @ F @ A ) )
% 3.05/1.61 = ( member_nat @ A4 @ A ) ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_336_inj__on__image__mem__iff,axiom,
% 3.05/1.61 ! [F: nat > paraco1605129243lle_tv,B: set_nat,A4: nat,A: set_nat] :
% 3.05/1.61 ( ( inj_on1955349912lle_tv @ F @ B )
% 3.05/1.61 => ( ( member_nat @ A4 @ B )
% 3.05/1.61 => ( ( ord_less_eq_set_nat @ A @ B )
% 3.05/1.61 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_1151963140lle_tv @ F @ A ) )
% 3.05/1.61 = ( member_nat @ A4 @ A ) ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_337_inj__on__image__mem__iff,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv,A4: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( inj_on1179712058tv_nat @ F @ B )
% 3.05/1.61 => ( ( member266900804lle_tv @ A4 @ B )
% 3.05/1.61 => ( ( ord_le241064091lle_tv @ A @ B )
% 3.05/1.61 => ( ( member_nat @ ( F @ A4 ) @ ( image_376325286tv_nat @ F @ A ) )
% 3.05/1.61 = ( member266900804lle_tv @ A4 @ A ) ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_338_inj__on__image__mem__iff,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,A4: paraco1605129243lle_tv,A: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ B )
% 3.05/1.61 => ( ( member266900804lle_tv @ A4 @ B )
% 3.05/1.61 => ( ( ord_le241064091lle_tv @ A @ B )
% 3.05/1.61 => ( ( member266900804lle_tv @ ( F @ A4 ) @ ( image_335818702lle_tv @ F @ A ) )
% 3.05/1.61 = ( member266900804lle_tv @ A4 @ A ) ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_339_inj__on__image__eq__iff,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,C2: set_Pa1764573435lle_tv,A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ C2 )
% 3.05/1.61 => ( ( ord_le241064091lle_tv @ A @ C2 )
% 3.05/1.61 => ( ( ord_le241064091lle_tv @ B @ C2 )
% 3.05/1.61 => ( ( ( image_335818702lle_tv @ F @ A )
% 3.05/1.61 = ( image_335818702lle_tv @ F @ B ) )
% 3.05/1.61 = ( A = B ) ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_340_inj__on__image__eq__iff,axiom,
% 3.05/1.61 ! [F: nat > nat,C2: set_nat,A: set_nat,B: set_nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ C2 )
% 3.05/1.61 => ( ( ord_less_eq_set_nat @ A @ C2 )
% 3.05/1.61 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 3.05/1.61 => ( ( ( image_nat_nat @ F @ A )
% 3.05/1.61 = ( image_nat_nat @ F @ B ) )
% 3.05/1.61 = ( A = B ) ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_341_inj__image__subset__iff,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.61 => ( ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ F @ A ) @ ( image_335818702lle_tv @ F @ B ) )
% 3.05/1.61 = ( ord_le241064091lle_tv @ A @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_342_inj__image__subset__iff,axiom,
% 3.05/1.61 ! [F: nat > nat,A: set_nat,B: set_nat] :
% 3.05/1.61 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.05/1.61 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A ) @ ( image_nat_nat @ F @ B ) )
% 3.05/1.61 = ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_343_map__prod__surj,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ F @ G ) @ top_to1871154984lle_tv )
% 3.05/1.61 = top_to1871154984lle_tv ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_344_map__prod__surj,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 3.05/1.61 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ( image_1796815776tv_nat @ ( produc1500159719tv_nat @ F @ G ) @ top_to1871154984lle_tv )
% 3.05/1.61 = top_to975729152tv_nat ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_345_map__prod__surj,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( image_228488944lle_tv @ ( produc1521089895lle_tv @ F @ G ) @ top_to975729152tv_nat )
% 3.05/1.61 = top_to1871154984lle_tv ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_346_map__prod__surj,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: nat > nat] :
% 3.05/1.61 ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ( image_1104296520tv_nat @ ( produc42536895at_nat @ F @ G ) @ top_to975729152tv_nat )
% 3.05/1.61 = top_to975729152tv_nat ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_347_map__prod__surj,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( image_1892891680lle_tv @ ( produc1095080935lle_tv @ F @ G ) @ top_to1871154984lle_tv )
% 3.05/1.61 = top_to1411004326lle_tv ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_348_map__prod__surj,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat,G: paraco1605129243lle_tv > nat] :
% 3.05/1.61 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ( image_901203832at_nat @ ( produc51277375tv_nat @ F @ G ) @ top_to1871154984lle_tv )
% 3.05/1.61 = top_to1555900337at_nat ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_349_map__prod__surj,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat,G: nat > paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ F @ G ) @ top_to975729152tv_nat )
% 3.05/1.61 = top_to1411004326lle_tv ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_350_map__prod__surj,axiom,
% 3.05/1.61 ! [F: paraco1605129243lle_tv > nat,G: nat > nat] :
% 3.05/1.61 ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ( image_1805124128at_nat @ ( produc386540311at_nat @ F @ G ) @ top_to975729152tv_nat )
% 3.05/1.61 = top_to1555900337at_nat ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_351_map__prod__surj,axiom,
% 3.05/1.61 ! [F: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.05/1.61 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ F @ G ) @ top_to1411004326lle_tv )
% 3.05/1.61 = top_to1871154984lle_tv ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_352_map__prod__surj,axiom,
% 3.05/1.61 ! [F: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 3.05/1.61 ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 3.05/1.61 = top_to1057771083lle_tv )
% 3.05/1.61 => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 3.05/1.61 = top_top_set_nat )
% 3.05/1.61 => ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ F @ G ) @ top_to1411004326lle_tv )
% 3.05/1.61 = top_to975729152tv_nat ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_353_subset__image__inj,axiom,
% 3.05/1.61 ! [S4: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,T2: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( ord_le241064091lle_tv @ S4 @ ( image_335818702lle_tv @ F @ T2 ) )
% 3.05/1.61 = ( ? [U: set_Pa1764573435lle_tv] :
% 3.05/1.61 ( ( ord_le241064091lle_tv @ U @ T2 )
% 3.05/1.61 & ( inj_on772319074lle_tv @ F @ U )
% 3.05/1.61 & ( S4
% 3.05/1.61 = ( image_335818702lle_tv @ F @ U ) ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(fact_354_subset__image__inj,axiom,
% 3.05/1.61 ! [S4: set_nat,F: nat > nat,T2: set_nat] :
% 3.05/1.61 ( ( ord_less_eq_set_nat @ S4 @ ( image_nat_nat @ F @ T2 ) )
% 3.05/1.61 = ( ? [U: set_nat] :
% 3.05/1.61 ( ( ord_less_eq_set_nat @ U @ T2 )
% 3.05/1.61 & ( inj_on_nat_nat @ F @ U )
% 3.05/1.61 & ( S4
% 3.05/1.61 = ( image_nat_nat @ F @ U ) ) ) ) ) ).
% 3.05/1.61
% 3.05/1.61 thf(conj_0,conjecture,
% 3.05/1.61 inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv ).
% 3.05/1.61 ------------------------
% 3.05/1.63 % (11304)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_11108 for (2999ds/4Mi)
% 3.05/1.63 % (11303)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/183Mi)
% 3.05/1.64 % (11307)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_11108 for (2999ds/2Mi)
% 3.05/1.64 % (11305)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_11108 for (2999ds/27Mi)
% 3.05/1.64 % (11306)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/2Mi)
% 3.05/1.64 % (11307)Instruction limit reached!
% 3.05/1.64 % (11307)------------------------------
% 3.05/1.64 % (11307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.64 % (11307)Termination reason: Unknown
% 3.05/1.64 % (11307)Termination phase: shuffling
% 3.05/1.64
% 3.05/1.64 % (11307)Memory used [KB]: 1535
% 3.05/1.64 % (11307)Time elapsed: 0.003 s
% 3.05/1.64 % (11307)Instructions burned: 3 (million)
% 3.05/1.64 % (11307)------------------------------
% 3.05/1.64 % (11307)------------------------------
% 3.05/1.64 % (11310)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/18Mi)
% 3.05/1.64 % (11306)Instruction limit reached!
% 3.05/1.64 % (11306)------------------------------
% 3.05/1.64 % (11306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.64 % (11306)Termination reason: Unknown
% 3.05/1.64 % (11306)Termination phase: shuffling
% 3.05/1.64
% 3.05/1.64 % (11306)Memory used [KB]: 1535
% 3.05/1.64 % (11306)Time elapsed: 0.003 s
% 3.05/1.64 % (11306)Instructions burned: 2 (million)
% 3.05/1.64 % (11306)------------------------------
% 3.05/1.64 % (11306)------------------------------
% 3.05/1.64 % (11308)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_11108 for (2999ds/275Mi)
% 3.05/1.64 % (11304)Instruction limit reached!
% 3.05/1.64 % (11304)------------------------------
% 3.05/1.64 % (11304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.64 % (11304)Termination reason: Unknown
% 3.05/1.64 % (11304)Termination phase: shuffling
% 3.05/1.64
% 3.05/1.64 % (11304)Memory used [KB]: 1663
% 3.05/1.64 % (11304)Time elapsed: 0.004 s
% 3.05/1.64 % (11304)Instructions burned: 5 (million)
% 3.05/1.64 % (11304)------------------------------
% 3.05/1.64 % (11304)------------------------------
% 3.05/1.65 % (11310)Instruction limit reached!
% 3.05/1.65 % (11310)------------------------------
% 3.05/1.65 % (11310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (11310)Termination reason: Unknown
% 3.05/1.65 % (11310)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (11310)Memory used [KB]: 1918
% 3.05/1.65 % (11310)Time elapsed: 0.012 s
% 3.05/1.65 % (11310)Instructions burned: 18 (million)
% 3.05/1.65 % (11310)------------------------------
% 3.05/1.65 % (11310)------------------------------
% 3.05/1.65 % (11305)Instruction limit reached!
% 3.05/1.65 % (11305)------------------------------
% 3.05/1.65 % (11305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (11305)Termination reason: Unknown
% 3.05/1.65 % (11305)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (11305)Memory used [KB]: 2046
% 3.05/1.65 % (11305)Time elapsed: 0.016 s
% 3.05/1.65 % (11305)Instructions burned: 28 (million)
% 3.05/1.65 % (11305)------------------------------
% 3.05/1.65 % (11305)------------------------------
% 3.05/1.65 % (11311)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/3Mi)
% 3.05/1.65 % (11312)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_11108 for (2999ds/37Mi)
% 3.05/1.65 % (11311)Instruction limit reached!
% 3.05/1.65 % (11311)------------------------------
% 3.05/1.65 % (11311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (11311)Termination reason: Unknown
% 3.05/1.65 % (11311)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (11311)Memory used [KB]: 1535
% 3.05/1.65 % (11311)Time elapsed: 0.003 s
% 3.05/1.65 % (11311)Instructions burned: 3 (million)
% 3.05/1.65 % (11311)------------------------------
% 3.05/1.65 % (11311)------------------------------
% 3.05/1.66 % (11313)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_11108 for (2999ds/15Mi)
% 3.05/1.66 % (11314)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/3Mi)
% 3.05/1.67 % (11314)Instruction limit reached!
% 3.05/1.67 % (11314)------------------------------
% 3.05/1.67 % (11314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (11314)Termination reason: Unknown
% 3.05/1.67 % (11314)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (11314)Memory used [KB]: 1535
% 3.05/1.67 % (11314)Time elapsed: 0.004 s
% 3.05/1.67 % (11314)Instructions burned: 4 (million)
% 3.05/1.67 % (11314)------------------------------
% 3.05/1.67 % (11314)------------------------------
% 3.05/1.67 % (11316)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/1041Mi)
% 3.05/1.67 % (11308)Refutation not found, incomplete strategy
% 3.05/1.67 % (11308)------------------------------
% 3.05/1.67 % (11308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (11308)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.67
% 3.05/1.67
% 3.05/1.67 % (11308)Memory used [KB]: 6652
% 3.05/1.67 % (11308)Time elapsed: 0.028 s
% 3.05/1.67 % (11308)Instructions burned: 60 (million)
% 3.05/1.67 % (11308)------------------------------
% 3.05/1.67 % (11308)------------------------------
% 3.05/1.67 % (11313)Instruction limit reached!
% 3.05/1.67 % (11313)------------------------------
% 3.05/1.67 % (11313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (11313)Termination reason: Unknown
% 3.05/1.67 % (11313)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (11313)Memory used [KB]: 1791
% 3.05/1.67 % (11313)Time elapsed: 0.010 s
% 3.05/1.67 % (11313)Instructions burned: 15 (million)
% 3.05/1.67 % (11313)------------------------------
% 3.05/1.67 % (11313)------------------------------
% 3.05/1.67 % (11317)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/7Mi)
% 3.05/1.67 % (11312)Instruction limit reached!
% 3.05/1.67 % (11312)------------------------------
% 3.05/1.67 % (11312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (11312)Termination reason: Unknown
% 3.05/1.67 % (11312)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (11312)Memory used [KB]: 2302
% 3.05/1.67 % (11312)Time elapsed: 0.019 s
% 3.05/1.67 % (11312)Instructions burned: 38 (million)
% 3.05/1.67 % (11312)------------------------------
% 3.05/1.67 % (11312)------------------------------
% 3.05/1.68 % (11317)Instruction limit reached!
% 3.05/1.68 % (11317)------------------------------
% 3.05/1.68 % (11317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.68 % (11317)Termination reason: Unknown
% 3.05/1.68 % (11317)Termination phase: shuffling
% 3.05/1.68
% 3.05/1.68 % (11317)Memory used [KB]: 1663
% 3.05/1.68 % (11317)Time elapsed: 0.006 s
% 3.05/1.68 % (11317)Instructions burned: 8 (million)
% 3.05/1.68 % (11317)------------------------------
% 3.05/1.68 % (11317)------------------------------
% 3.05/1.68 % (11318)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/16Mi)
% 3.05/1.68 % (11319)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/3Mi)
% 3.05/1.68 % (11319)Instruction limit reached!
% 3.05/1.68 % (11319)------------------------------
% 3.05/1.68 % (11319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.68 % (11319)Termination reason: Unknown
% 3.05/1.68 % (11319)Termination phase: shuffling
% 3.05/1.68
% 3.05/1.68 % (11319)Memory used [KB]: 1535
% 3.05/1.68 % (11319)Time elapsed: 0.003 s
% 3.05/1.68 % (11319)Instructions burned: 4 (million)
% 3.05/1.68 % (11319)------------------------------
% 3.05/1.68 % (11319)------------------------------
% 3.05/1.69 % (11320)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/3Mi)
% 3.05/1.69 % (11321)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/7Mi)
% 3.05/1.69 % (11320)Instruction limit reached!
% 3.05/1.69 % (11320)------------------------------
% 3.05/1.69 % (11320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (11320)Termination reason: Unknown
% 3.05/1.69 % (11320)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (11320)Memory used [KB]: 1535
% 3.05/1.69 % (11320)Time elapsed: 0.004 s
% 3.05/1.69 % (11320)Instructions burned: 4 (million)
% 3.05/1.69 % (11320)------------------------------
% 3.05/1.69 % (11320)------------------------------
% 3.05/1.69 % (11318)Instruction limit reached!
% 3.05/1.69 % (11318)------------------------------
% 3.05/1.69 % (11318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (11318)Termination reason: Unknown
% 3.05/1.69 % (11318)Termination phase: shuffling
% 3.05/1.69 % (11322)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/3Mi)
% 3.05/1.69
% 3.05/1.69 % (11318)Memory used [KB]: 1791
% 3.05/1.69 % (11318)Time elapsed: 0.010 s
% 3.05/1.69 % (11318)Instructions burned: 17 (million)
% 3.05/1.69 % (11318)------------------------------
% 3.05/1.69 % (11318)------------------------------
% 3.05/1.69 % (11321)Instruction limit reached!
% 3.05/1.69 % (11321)------------------------------
% 3.05/1.69 % (11321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (11321)Termination reason: Unknown
% 3.05/1.69 % (11321)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (11321)Memory used [KB]: 1663
% 3.05/1.69 % (11321)Time elapsed: 0.006 s
% 3.05/1.69 % (11321)Instructions burned: 8 (million)
% 3.05/1.69 % (11321)------------------------------
% 3.05/1.69 % (11321)------------------------------
% 3.05/1.69 % (11322)Instruction limit reached!
% 3.05/1.69 % (11322)------------------------------
% 3.05/1.69 % (11322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (11322)Termination reason: Unknown
% 3.05/1.69 % (11322)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (11322)Memory used [KB]: 1535
% 3.05/1.69 % (11322)Time elapsed: 0.003 s
% 3.05/1.69 % (11322)Instructions burned: 3 (million)
% 3.05/1.69 % (11322)------------------------------
% 3.05/1.69 % (11322)------------------------------
% 3.05/1.69 % (11303)Instruction limit reached!
% 3.05/1.69 % (11303)------------------------------
% 3.05/1.69 % (11303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (11303)Termination reason: Unknown
% 3.05/1.69 % (11303)Termination phase: Saturation
% 3.05/1.69
% 3.05/1.69 % (11303)Memory used [KB]: 7419
% 3.05/1.69 % (11303)Time elapsed: 0.062 s
% 3.05/1.69 % (11303)Instructions burned: 183 (million)
% 3.05/1.69 % (11303)------------------------------
% 3.05/1.69 % (11303)------------------------------
% 3.05/1.70 % (11324)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/4Mi)
% 3.11/1.70 % (11324)Instruction limit reached!
% 3.11/1.70 % (11324)------------------------------
% 3.11/1.70 % (11324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.70 % (11324)Termination reason: Unknown
% 3.11/1.70 % (11324)Termination phase: shuffling
% 3.11/1.70
% 3.11/1.70 % (11324)Memory used [KB]: 1535
% 3.11/1.70 % (11324)Time elapsed: 0.004 s
% 3.11/1.70 % (11324)Instructions burned: 6 (million)
% 3.11/1.70 % (11324)------------------------------
% 3.11/1.70 % (11324)------------------------------
% 3.11/1.71 % (11325)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/18Mi)
% 3.11/1.71 % (11326)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/710Mi)
% 3.11/1.71 % (11330)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/5Mi)
% 3.11/1.71 % (11327)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/6Mi)
% 3.11/1.71 % (11328)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/902Mi)
% 3.11/1.71 % (11330)Instruction limit reached!
% 3.11/1.71 % (11330)------------------------------
% 3.11/1.71 % (11330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.71 % (11330)Termination reason: Unknown
% 3.11/1.71 % (11330)Termination phase: shuffling
% 3.11/1.71
% 3.11/1.71 % (11330)Memory used [KB]: 1663
% 3.11/1.71 % (11330)Time elapsed: 0.003 s
% 3.11/1.71 % (11330)Instructions burned: 6 (million)
% 3.11/1.71 % (11330)------------------------------
% 3.11/1.71 % (11330)------------------------------
% 3.11/1.71 % (11329)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/21Mi)
% 3.11/1.71 % (11327)Instruction limit reached!
% 3.11/1.71 % (11327)------------------------------
% 3.11/1.71 % (11327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.71 % (11327)Termination reason: Unknown
% 3.11/1.71 % (11327)Termination phase: shuffling
% 3.11/1.71
% 3.11/1.71 % (11327)Memory used [KB]: 1663
% 3.11/1.71 % (11327)Time elapsed: 0.005 s
% 3.11/1.71 % (11327)Instructions burned: 7 (million)
% 3.11/1.71 % (11327)------------------------------
% 3.11/1.71 % (11327)------------------------------
% 3.11/1.72 % (11325)Instruction limit reached!
% 3.11/1.72 % (11325)------------------------------
% 3.11/1.72 % (11325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.72 % (11325)Termination reason: Unknown
% 3.11/1.72 % (11325)Termination phase: shuffling
% 3.11/1.72
% 3.11/1.72 % (11325)Memory used [KB]: 1918
% 3.11/1.72 % (11325)Time elapsed: 0.012 s
% 3.11/1.72 % (11325)Instructions burned: 19 (million)
% 3.11/1.72 % (11325)------------------------------
% 3.11/1.72 % (11325)------------------------------
% 3.11/1.72 % (11332)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/6Mi)
% 3.11/1.72 % (11329)Instruction limit reached!
% 3.11/1.72 % (11329)------------------------------
% 3.11/1.72 % (11329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.72 % (11329)Termination reason: Unknown
% 3.11/1.72 % (11329)Termination phase: shuffling
% 3.11/1.72
% 3.11/1.72 % (11329)Memory used [KB]: 1918
% 3.11/1.72 % (11329)Time elapsed: 0.012 s
% 3.11/1.72 % (11329)Instructions burned: 21 (million)
% 3.11/1.72 % (11329)------------------------------
% 3.11/1.72 % (11329)------------------------------
% 3.11/1.72 % (11332)Instruction limit reached!
% 3.11/1.72 % (11332)------------------------------
% 3.11/1.72 % (11332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.72 % (11332)Termination reason: Unknown
% 3.11/1.72 % (11332)Termination phase: shuffling
% 3.11/1.72
% 3.11/1.72 % (11332)Memory used [KB]: 1663
% 3.11/1.72 % (11332)Time elapsed: 0.004 s
% 3.11/1.72 % (11332)Instructions burned: 7 (million)
% 3.11/1.72 % (11332)------------------------------
% 3.11/1.72 % (11332)------------------------------
% 3.11/1.73 % (11336)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_11108 for (2998ds/19Mi)
% 3.11/1.73 % (11333)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/377Mi)
% 3.11/1.73 % (11335)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_11108 for (2999ds/779Mi)
% 3.11/1.74 % (11337)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_11108 for (2998ds/879Mi)
% 3.11/1.74 % (11336)Instruction limit reached!
% 3.11/1.74 % (11336)------------------------------
% 3.11/1.74 % (11336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.74 % (11336)Termination reason: Unknown
% 3.11/1.74 % (11336)Termination phase: shuffling
% 3.11/1.74
% 3.11/1.74 % (11336)Memory used [KB]: 1918
% 3.11/1.74 % (11336)Time elapsed: 0.008 s
% 3.11/1.74 % (11336)Instructions burned: 20 (million)
% 3.11/1.74 % (11336)------------------------------
% 3.11/1.74 % (11336)------------------------------
% 3.11/1.75 % (11338)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_11108 for (2998ds/17Mi)
% 3.11/1.75 % (11338)Instruction limit reached!
% 3.11/1.75 % (11338)------------------------------
% 3.11/1.75 % (11338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.75 % (11338)Termination reason: Unknown
% 3.11/1.75 % (11338)Termination phase: shuffling
% 3.11/1.75
% 3.11/1.75 % (11338)Memory used [KB]: 1791
% 3.11/1.75 % (11338)Time elapsed: 0.008 s
% 3.11/1.75 % (11338)Instructions burned: 18 (million)
% 3.11/1.75 % (11338)------------------------------
% 3.11/1.75 % (11338)------------------------------
% 3.11/1.77 % (11340)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11108 for (2998ds/3Mi)
% 3.11/1.77 % (11340)Instruction limit reached!
% 3.11/1.77 % (11340)------------------------------
% 3.11/1.77 % (11340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.77 % (11340)Termination reason: Unknown
% 3.11/1.77 % (11340)Termination phase: shuffling
% 3.11/1.77
% 3.11/1.77 % (11340)Memory used [KB]: 1535
% 3.11/1.77 % (11340)Time elapsed: 0.002 s
% 3.11/1.77 % (11340)Instructions burned: 3 (million)
% 3.11/1.77 % (11340)------------------------------
% 3.11/1.77 % (11340)------------------------------
% 3.11/1.78 % (11342)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_11108 for (2998ds/30Mi)
% 3.11/1.79 % (11342)Instruction limit reached!
% 3.11/1.79 % (11342)------------------------------
% 3.11/1.79 % (11342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.79 % (11342)Termination reason: Unknown
% 3.11/1.79 % (11342)Termination phase: shuffling
% 3.11/1.79
% 3.11/1.79 % (11342)Memory used [KB]: 2046
% 3.11/1.79 % (11342)Time elapsed: 0.013 s
% 3.11/1.79 % (11342)Instructions burned: 32 (million)
% 3.11/1.79 % (11342)------------------------------
% 3.11/1.79 % (11342)------------------------------
% 3.11/1.80 % (11343)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_11108 for (2998ds/127Mi)
% 3.11/1.87 % (11343)Instruction limit reached!
% 3.11/1.87 % (11343)------------------------------
% 3.11/1.87 % (11343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.87 % (11343)Termination reason: Unknown
% 3.11/1.87 % (11343)Termination phase: Property scanning
% 3.11/1.87
% 3.11/1.87 % (11343)Memory used [KB]: 2814
% 3.11/1.87 % (11343)Time elapsed: 0.066 s
% 3.11/1.87 % (11343)Instructions burned: 127 (million)
% 3.11/1.87 % (11343)------------------------------
% 3.11/1.87 % (11343)------------------------------
% 3.11/1.88 % (11348)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_11108 for (2997ds/100Mi)
% 3.11/1.91 % (11333)Instruction limit reached!
% 3.11/1.91 % (11333)------------------------------
% 3.11/1.91 % (11333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.91 % (11333)Termination reason: Unknown
% 3.11/1.91 % (11333)Termination phase: Saturation
% 3.11/1.91
% 3.11/1.91 % (11333)Memory used [KB]: 8699
% 3.11/1.91 % (11333)Time elapsed: 0.174 s
% 3.11/1.91 % (11333)Instructions burned: 377 (million)
% 3.11/1.91 % (11333)------------------------------
% 3.11/1.91 % (11333)------------------------------
% 3.11/1.93 % (11350)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_11108 for (2997ds/3Mi)
% 3.11/1.93 % (11350)Instruction limit reached!
% 3.11/1.93 % (11350)------------------------------
% 3.11/1.93 % (11350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.93 % (11350)Termination reason: Unknown
% 3.11/1.93 % (11350)Termination phase: shuffling
% 3.11/1.93
% 3.11/1.93 % (11350)Memory used [KB]: 1535
% 3.11/1.93 % (11350)Time elapsed: 0.004 s
% 3.11/1.93 % (11350)Instructions burned: 4 (million)
% 3.11/1.93 % (11350)------------------------------
% 3.11/1.93 % (11350)------------------------------
% 3.11/1.93 % (11348)Instruction limit reached!
% 3.11/1.93 % (11348)------------------------------
% 3.11/1.93 % (11348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.93 % (11348)Termination reason: Unknown
% 3.11/1.93 % (11348)Termination phase: Property scanning
% 3.11/1.93
% 3.11/1.93 % (11348)Memory used [KB]: 2814
% 3.11/1.93 % (11348)Time elapsed: 0.047 s
% 3.11/1.93 % (11348)Instructions burned: 100 (million)
% 3.11/1.93 % (11348)------------------------------
% 3.11/1.93 % (11348)------------------------------
% 3.11/1.94 % (11337)First to succeed.
% 3.11/1.94 % (11337)Refutation found. Thanks to Tanya!
% 3.11/1.94 % SZS status Theorem for DTF2THF_11108
% 3.11/1.94 % SZS output start Proof for DTF2THF_11108
% 3.11/1.94 thf(type_def_5, type, nat: $tType).
% 3.11/1.94 thf(type_def_7, type, set_nat: $tType).
% 3.11/1.94 thf(type_def_8, type, paraco1605129243lle_tv: $tType).
% 3.11/1.94 thf(type_def_9, type, set_Pa1764573435lle_tv: $tType).
% 3.11/1.94 thf(type_def_10, type, product_prod_nat_nat: $tType).
% 3.11/1.94 thf(type_def_11, type, set_Pr1986765409at_nat: $tType).
% 3.11/1.94 thf(type_def_12, type, produc270694976lle_tv: $tType).
% 3.11/1.94 thf(type_def_13, type, produc194167194tv_nat: $tType).
% 3.11/1.94 thf(type_def_14, type, set_Pr13445366lle_tv: $tType).
% 3.11/1.94 thf(type_def_15, type, set_Pr1725653840tv_nat: $tType).
% 3.11/1.94 thf(type_def_16, type, produc1647334210lle_tv: $tType).
% 3.11/1.94 thf(type_def_17, type, set_Pr2014382200lle_tv: $tType).
% 3.11/1.94 thf(type_def_18, type, set_set_nat: $tType).
% 3.11/1.94 thf(type_def_19, type, set_se800614875lle_tv: $tType).
% 3.11/1.94 thf(func_def_0, type, set_Pr2014382200lle_tv: $tType).
% 3.11/1.94 thf(func_def_1, type, produc1647334210lle_tv: $tType).
% 3.11/1.94 thf(func_def_2, type, set_Pr1725653840tv_nat: $tType).
% 3.11/1.94 thf(func_def_3, type, set_Pr13445366lle_tv: $tType).
% 3.11/1.94 thf(func_def_4, type, produc194167194tv_nat: $tType).
% 3.11/1.94 thf(func_def_5, type, produc270694976lle_tv: $tType).
% 3.11/1.94 thf(func_def_6, type, set_se800614875lle_tv: $tType).
% 3.11/1.94 thf(func_def_7, type, set_Pr1986765409at_nat: $tType).
% 3.11/1.94 thf(func_def_8, type, set_Pa1764573435lle_tv: $tType).
% 3.11/1.94 thf(func_def_9, type, product_prod_nat_nat: $tType).
% 3.11/1.94 thf(func_def_10, type, paraco1605129243lle_tv: $tType).
% 3.11/1.94 thf(func_def_11, type, set_set_nat: $tType).
% 3.11/1.94 thf(func_def_12, type, set_nat: $tType).
% 3.11/1.94 thf(func_def_13, type, nat: $tType).
% 3.11/1.94 thf(func_def_14, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 3.11/1.94 thf(func_def_15, type, inj_on1955349912lle_tv: (nat > paraco1605129243lle_tv) > set_nat > $o).
% 3.11/1.94 thf(func_def_16, type, inj_on1179712058tv_nat: (paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > $o).
% 3.11/1.94 thf(func_def_17, type, inj_on772319074lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > $o).
% 3.11/1.94 thf(func_def_18, type, inj_on642995232at_nat: (product_prod_nat_nat > nat) > set_Pr1986765409at_nat > $o).
% 3.11/1.94 thf(func_def_19, type, inj_on520021963lle_tv: (product_prod_nat_nat > paraco1605129243lle_tv) > set_Pr1986765409at_nat > $o).
% 3.11/1.94 thf(func_def_20, type, inj_on26176689at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > $o).
% 3.11/1.94 thf(func_def_21, type, inj_on1840679568lle_tv: (product_prod_nat_nat > produc270694976lle_tv) > set_Pr1986765409at_nat > $o).
% 3.11/1.94 thf(func_def_22, type, inj_on1764151786tv_nat: (product_prod_nat_nat > produc194167194tv_nat) > set_Pr1986765409at_nat > $o).
% 3.11/1.94 thf(func_def_23, type, inj_on936843139tv_nat: (produc270694976lle_tv > nat) > set_Pr13445366lle_tv > $o).
% 3.11/1.94 thf(func_def_24, type, inj_on394919723lle_tv: (produc270694976lle_tv > paraco1605129243lle_tv) > set_Pr13445366lle_tv > $o).
% 3.11/1.94 thf(func_def_25, type, inj_on1954136462at_nat: (produc270694976lle_tv > product_prod_nat_nat) > set_Pr13445366lle_tv > $o).
% 3.11/1.94 thf(func_def_26, type, inj_on1745913142lle_tv: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > $o).
% 3.11/1.94 thf(func_def_27, type, inj_on808253149at_nat: (produc194167194tv_nat > nat) > set_Pr1725653840tv_nat > $o).
% 3.11/1.94 thf(func_def_28, type, inj_on1612474245lle_tv: (produc194167194tv_nat > paraco1605129243lle_tv) > set_Pr1725653840tv_nat > $o).
% 3.11/1.94 thf(func_def_29, type, inj_on1971554740at_nat: (produc194167194tv_nat > product_prod_nat_nat) > set_Pr1725653840tv_nat > $o).
% 3.11/1.94 thf(func_def_30, type, inj_on552895452tv_nat: (produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > $o).
% 3.11/1.94 thf(func_def_31, type, inj_on967082628lle_tv: (produc194167194tv_nat > produc1647334210lle_tv) > set_Pr1725653840tv_nat > $o).
% 3.11/1.94 thf(func_def_32, type, inj_on2112487900lle_tv: (produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > $o).
% 3.11/1.94 thf(func_def_33, type, strict2146030304at_nat: (nat > nat) > set_nat > $o).
% 3.11/1.94 thf(func_def_34, type, strict1310998166et_nat: (nat > set_nat) > set_nat > $o).
% 3.11/1.94 thf(func_def_35, type, strict1658340843lle_tv: (nat > set_Pa1764573435lle_tv) > set_nat > $o).
% 3.11/1.94 thf(func_def_36, type, strict1802283670at_nat: (set_nat > nat) > set_set_nat > $o).
% 3.11/1.94 thf(func_def_37, type, strict473775692et_nat: (set_nat > set_nat) > set_set_nat > $o).
% 3.11/1.94 thf(func_def_38, type, strict172559285lle_tv: (set_nat > set_Pa1764573435lle_tv) > set_set_nat > $o).
% 3.11/1.94 thf(func_def_39, type, strict1125660301tv_nat: (set_Pa1764573435lle_tv > nat) > set_se800614875lle_tv > $o).
% 3.11/1.94 thf(func_def_40, type, strict1455779395et_nat: (set_Pa1764573435lle_tv > set_nat) > set_se800614875lle_tv > $o).
% 3.11/1.94 thf(func_def_41, type, strict592849515lle_tv: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_se800614875lle_tv > $o).
% 3.11/1.94 thf(func_def_42, type, the_inv_into_nat_nat: set_nat > (nat > nat) > nat > nat).
% 3.11/1.94 thf(func_def_43, type, the_in138087638lle_tv: set_nat > (nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > nat).
% 3.11/1.94 thf(func_def_44, type, the_in1509933432tv_nat: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > nat) > nat > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_45, type, the_in452116896lle_tv: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_46, type, the_in2068894451at_nat: set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 3.11/1.94 thf(func_def_47, type, the_in744013006lle_tv: set_Pr1986765409at_nat > (product_prod_nat_nat > produc270694976lle_tv) > produc270694976lle_tv > product_prod_nat_nat).
% 3.11/1.94 thf(func_def_48, type, the_in667485224tv_nat: set_Pr1986765409at_nat > (product_prod_nat_nat > produc194167194tv_nat) > produc194167194tv_nat > product_prod_nat_nat).
% 3.11/1.94 thf(func_def_49, type, the_in857469900at_nat: set_Pr13445366lle_tv > (produc270694976lle_tv > product_prod_nat_nat) > product_prod_nat_nat > produc270694976lle_tv).
% 3.11/1.94 thf(func_def_50, type, the_in1388677748lle_tv: set_Pr13445366lle_tv > (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv > produc270694976lle_tv).
% 3.11/1.94 thf(func_def_51, type, the_in874888178at_nat: set_Pr1725653840tv_nat > (produc194167194tv_nat > product_prod_nat_nat) > product_prod_nat_nat > produc194167194tv_nat).
% 3.11/1.94 thf(func_def_52, type, the_in195660058tv_nat: set_Pr1725653840tv_nat > (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat > produc194167194tv_nat).
% 3.11/1.94 thf(func_def_53, type, the_in427240730lle_tv: set_Pr2014382200lle_tv > (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv > produc1647334210lle_tv).
% 3.11/1.94 thf(func_def_54, type, plus_plus_nat: nat > nat > nat).
% 3.11/1.94 thf(func_def_55, type, ord_less_nat: nat > nat > $o).
% 3.11/1.94 thf(func_def_56, type, ord_less_set_nat: set_nat > set_nat > $o).
% 3.11/1.94 thf(func_def_57, type, ord_le727057319lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o).
% 3.11/1.94 thf(func_def_58, type, ord_less_eq_nat: nat > nat > $o).
% 3.11/1.94 thf(func_def_59, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 3.11/1.94 thf(func_def_60, type, ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o).
% 3.11/1.94 thf(func_def_61, type, order_769474267at_nat: (nat > nat) > $o).
% 3.11/1.94 thf(func_def_62, type, top_top_nat_o: nat > $o).
% 3.11/1.94 thf(func_def_63, type, top_to1299250770e_tv_o: paraco1605129243lle_tv > $o).
% 3.11/1.94 thf(func_def_64, type, top_to632227436_nat_o: product_prod_nat_nat > $o).
% 3.11/1.94 thf(func_def_65, type, top_to1889334367e_tv_o: produc270694976lle_tv > $o).
% 3.11/1.94 thf(func_def_66, type, top_to900819589_nat_o: produc194167194tv_nat > $o).
% 3.11/1.94 thf(func_def_68, type, top_top_set_nat: set_nat).
% 3.11/1.94 thf(func_def_69, type, top_to1057771083lle_tv: set_Pa1764573435lle_tv).
% 3.11/1.94 thf(func_def_70, type, top_to1555900337at_nat: set_Pr1986765409at_nat).
% 3.11/1.94 thf(func_def_71, type, top_to1411004326lle_tv: set_Pr13445366lle_tv).
% 3.11/1.94 thf(func_def_72, type, top_to975729152tv_nat: set_Pr1725653840tv_nat).
% 3.11/1.94 thf(func_def_73, type, top_to1871154984lle_tv: set_Pr2014382200lle_tv).
% 3.11/1.94 thf(func_def_74, type, paraco1147068288nge_tv: (nat > nat) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_75, type, paraco793048302_Indet: nat > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_76, type, produc1320959600at_nat: (nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 3.11/1.94 thf(func_def_77, type, produc237097339lle_tv: (nat > nat) > produc194167194tv_nat > produc194167194tv_nat).
% 3.11/1.94 thf(func_def_78, type, produc1608943133tv_nat: (nat > paraco1605129243lle_tv) > product_prod_nat_nat > produc270694976lle_tv).
% 3.11/1.94 thf(func_def_79, type, produc1804670661lle_tv: (nat > paraco1605129243lle_tv) > produc194167194tv_nat > produc1647334210lle_tv).
% 3.11/1.94 thf(func_def_80, type, produc2040316391tv_nat: (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc270694976lle_tv).
% 3.11/1.94 thf(func_def_81, type, produc1408152463lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc1647334210lle_tv > produc1647334210lle_tv).
% 3.11/1.94 thf(func_def_82, type, produc505105722at_nat: (nat > nat) > (nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 3.11/1.94 thf(func_def_83, type, produc2101297531lle_tv: (nat > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc270694976lle_tv).
% 3.11/1.94 thf(func_def_84, type, produc189459613tv_nat: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > produc270694976lle_tv > produc194167194tv_nat).
% 3.11/1.94 thf(func_def_85, type, produc1975500101lle_tv: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc1647334210lle_tv).
% 3.11/1.94 thf(func_def_86, type, produc386540311at_nat: (paraco1605129243lle_tv > nat) > (nat > nat) > produc194167194tv_nat > product_prod_nat_nat).
% 3.11/1.94 thf(func_def_87, type, produc72207551lle_tv: (paraco1605129243lle_tv > nat) > (nat > paraco1605129243lle_tv) > produc194167194tv_nat > produc270694976lle_tv).
% 3.11/1.94 thf(func_def_88, type, produc51277375tv_nat: (paraco1605129243lle_tv > nat) > (paraco1605129243lle_tv > nat) > produc1647334210lle_tv > product_prod_nat_nat).
% 3.11/1.94 thf(func_def_89, type, produc1095080935lle_tv: (paraco1605129243lle_tv > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc1647334210lle_tv > produc270694976lle_tv).
% 3.11/1.94 thf(func_def_90, type, produc42536895at_nat: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (nat > nat) > produc194167194tv_nat > produc194167194tv_nat).
% 3.11/1.94 thf(func_def_91, type, produc1521089895lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > produc194167194tv_nat > produc1647334210lle_tv).
% 3.11/1.94 thf(func_def_92, type, produc1500159719tv_nat: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > produc1647334210lle_tv > produc194167194tv_nat).
% 3.11/1.94 thf(func_def_93, type, produc1345917071lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc1647334210lle_tv > produc1647334210lle_tv).
% 3.11/1.94 thf(func_def_94, type, collect_nat: (nat > $o) > set_nat).
% 3.11/1.94 thf(func_def_95, type, collec1111687558lle_tv: (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv).
% 3.11/1.94 thf(func_def_96, type, collec7649004at_nat: (product_prod_nat_nat > $o) > set_Pr1986765409at_nat).
% 3.11/1.94 thf(func_def_97, type, collec924990229lle_tv: (produc270694976lle_tv > $o) > set_Pr13445366lle_tv).
% 3.11/1.94 thf(func_def_98, type, collec848462447tv_nat: (produc194167194tv_nat > $o) > set_Pr1725653840tv_nat).
% 3.11/1.94 thf(func_def_99, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 3.11/1.94 thf(func_def_100, type, image_1151963140lle_tv: (nat > paraco1605129243lle_tv) > set_nat > set_Pa1764573435lle_tv).
% 3.11/1.94 thf(func_def_101, type, image_376325286tv_nat: (paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > set_nat).
% 3.11/1.94 thf(func_def_102, type, image_335818702lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv).
% 3.11/1.94 thf(func_def_103, type, image_1397137548at_nat: (product_prod_nat_nat > nat) > set_Pr1986765409at_nat > set_nat).
% 3.11/1.94 thf(func_def_104, type, image_1093035615lle_tv: (product_prod_nat_nat > paraco1605129243lle_tv) > set_Pr1986765409at_nat > set_Pa1764573435lle_tv).
% 3.11/1.94 thf(func_def_105, type, image_815163717at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 3.11/1.94 thf(func_def_106, type, image_1674248956lle_tv: (product_prod_nat_nat > produc270694976lle_tv) > set_Pr1986765409at_nat > set_Pr13445366lle_tv).
% 3.11/1.94 thf(func_def_107, type, image_1597721174tv_nat: (product_prod_nat_nat > produc194167194tv_nat) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat).
% 3.11/1.94 thf(func_def_108, type, image_1509856791tv_nat: (produc270694976lle_tv > nat) > set_Pr13445366lle_tv > set_nat).
% 3.11/1.94 thf(func_def_109, type, image_802013119lle_tv: (produc270694976lle_tv > paraco1605129243lle_tv) > set_Pr13445366lle_tv > set_Pa1764573435lle_tv).
% 3.11/1.94 thf(func_def_110, type, image_1787705850at_nat: (produc270694976lle_tv > product_prod_nat_nat) > set_Pr13445366lle_tv > set_Pr1986765409at_nat).
% 3.11/1.94 thf(func_def_111, type, image_149830562lle_tv: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > set_Pr13445366lle_tv).
% 3.11/1.94 thf(func_def_112, type, image_53754658tv_nat: (produc270694976lle_tv > produc194167194tv_nat) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat).
% 3.11/1.94 thf(func_def_113, type, image_988201162lle_tv: (produc270694976lle_tv > produc1647334210lle_tv) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv).
% 3.11/1.94 thf(func_def_114, type, image_1381266801at_nat: (produc194167194tv_nat > nat) > set_Pr1725653840tv_nat > set_nat).
% 3.11/1.94 thf(func_def_115, type, image_2019567641lle_tv: (produc194167194tv_nat > paraco1605129243lle_tv) > set_Pr1725653840tv_nat > set_Pa1764573435lle_tv).
% 3.11/1.94 thf(func_def_116, type, image_1805124128at_nat: (produc194167194tv_nat > product_prod_nat_nat) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat).
% 3.11/1.94 thf(func_def_117, type, image_1200372424lle_tv: (produc194167194tv_nat > produc270694976lle_tv) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv).
% 3.11/1.94 thf(func_def_118, type, image_1104296520tv_nat: (produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > set_Pr1725653840tv_nat).
% 3.11/1.94 thf(func_def_119, type, image_228488944lle_tv: (produc194167194tv_nat > produc1647334210lle_tv) > set_Pr1725653840tv_nat > set_Pr2014382200lle_tv).
% 3.11/1.94 thf(func_def_120, type, image_901203832at_nat: (produc1647334210lle_tv > product_prod_nat_nat) > set_Pr2014382200lle_tv > set_Pr1986765409at_nat).
% 3.11/1.94 thf(func_def_121, type, image_1892891680lle_tv: (produc1647334210lle_tv > produc270694976lle_tv) > set_Pr2014382200lle_tv > set_Pr13445366lle_tv).
% 3.11/1.94 thf(func_def_122, type, image_1796815776tv_nat: (produc1647334210lle_tv > produc194167194tv_nat) > set_Pr2014382200lle_tv > set_Pr1725653840tv_nat).
% 3.11/1.94 thf(func_def_123, type, image_1221801032lle_tv: (produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv).
% 3.11/1.94 thf(func_def_124, type, member_nat: nat > set_nat > $o).
% 3.11/1.94 thf(func_def_125, type, member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o).
% 3.11/1.94 thf(func_def_126, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 3.11/1.94 thf(func_def_127, type, member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o).
% 3.11/1.94 thf(func_def_128, type, member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o).
% 3.11/1.94 thf(func_def_129, type, member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o).
% 3.11/1.94 thf(func_def_130, type, member_set_nat: set_nat > set_set_nat > $o).
% 3.11/1.94 thf(func_def_131, type, member1875402276lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv > $o).
% 3.11/1.94 thf(func_def_132, type, f: nat > nat).
% 3.11/1.94 thf(func_def_147, type, sK0: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_148, type, sK1: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_149, type, sK2: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_150, type, sK3: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_151, type, sK4: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_152, type, sK5: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_153, type, sK6: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_154, type, sK7: paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_155, type, sK8: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_156, type, sK9: set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_158, type, sK11: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv).
% 3.11/1.94 thf(func_def_159, type, sK12: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_160, type, sK13: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_161, type, sK14: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_162, type, sK15: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_163, type, sK16: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_164, type, sK17: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_165, type, sK18: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_166, type, sK19: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_167, type, sK20: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_168, type, sK21: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_169, type, sK22: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_170, type, sK23: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_171, type, sK24: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_172, type, sK25: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_173, type, sK26: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_174, type, sK27: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_175, type, sK28: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_176, type, sK29: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_177, type, sK30: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_178, type, sK31: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_179, type, sK32: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_180, type, sK33: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_181, type, sK34: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_182, type, sK35: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_183, type, sK36: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_184, type, sK37: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_185, type, sK38: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_186, type, sK39: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_187, type, sK40: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_188, type, sK41: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_189, type, sK42: paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_190, type, sK43: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_191, type, sK44: paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_192, type, sK45: paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_193, type, sK46: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_194, type, sK47: paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_195, type, sK48: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_196, type, sK49: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_197, type, sK50: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_198, type, sK51: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_199, type, sK52: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_200, type, sK53: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_201, type, sK54: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_202, type, sK55: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_203, type, sK56: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_204, type, sK57: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_205, type, sK58: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_206, type, sK59: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_207, type, sK60: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_208, type, sK61: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_209, type, sK62: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_210, type, sK63: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_211, type, sK64: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_212, type, sK65: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_213, type, sK66: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_214, type, sK67: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_215, type, sK68: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_216, type, sK69: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_217, type, sK70: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_218, type, sK71: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_219, type, sK72: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_220, type, sK73: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_221, type, sK74: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_222, type, sK75: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_223, type, sK76: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_224, type, sK77: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_225, type, sK78: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_226, type, sK79: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_227, type, sK80: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_228, type, sK81: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_229, type, sK82: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_230, type, sK83: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_231, type, sK84: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_232, type, sK85: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_233, type, sK86: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_234, type, sK87: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_235, type, sK88: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_236, type, sK89: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_237, type, sK90: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_238, type, sK91: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_239, type, sK92: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_240, type, sK93: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_241, type, sK94: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_242, type, sK95: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_243, type, sK96: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_244, type, sK97: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_245, type, sK98: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_246, type, sK99: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_247, type, sK100: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_248, type, sK101: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_249, type, sK102: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_250, type, sK103: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_251, type, sK104: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_252, type, sK105: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_253, type, sK106: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_254, type, sK107: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_255, type, sK108: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_256, type, sK109: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_257, type, sK110: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_258, type, sK111: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_259, type, sK112: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_260, type, sK113: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_261, type, sK114: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_262, type, sK115: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_263, type, sK116: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_264, type, sK117: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_265, type, sK118: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_266, type, sK119: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_267, type, sK120: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_268, type, sK121: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_269, type, sK122: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_270, type, sK123: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_271, type, sK124: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_272, type, sK125: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_273, type, sK126: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_274, type, sK127: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_275, type, sK128: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_276, type, sK129: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_277, type, sK130: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_278, type, sK131: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_279, type, sK132: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_280, type, sK133: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_281, type, sK134: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_282, type, sK135: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_283, type, sK136: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_284, type, sK137: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_285, type, sK138: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_286, type, sK139: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_287, type, sK140: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_288, type, sK141: paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_289, type, sK142: paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_290, type, sK143: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_291, type, sK144: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_292, type, sK145: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_293, type, sK146: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_294, type, sK147: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_295, type, sK148: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_296, type, sK149: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_297, type, sK150: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_298, type, sK151: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_299, type, sK152: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_300, type, sK153: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_301, type, sK154: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.11/1.94 thf(func_def_302, type, ph155: !>[X0: $tType]:(X0)).
% 3.11/1.94 thf(f3167,plain,(
% 3.11/1.94 $false),
% 3.11/1.94 inference(subsumption_resolution,[status(thm)],[f3166,f3011])).
% 3.11/1.94 thf(f3011,plain,(
% 3.11/1.94 (sK141 != sK142)),
% 3.11/1.94 inference(equality_proxy_clausification,[status(thm)],[f3008])).
% 3.11/1.94 thf(f3008,plain,(
% 3.11/1.94 ((sK141 = sK142) = $false)),
% 3.11/1.94 inference(binary_proxy_clausification,[status(thm)],[f3006])).
% 3.11/1.94 thf(f3006,plain,(
% 3.11/1.94 ((((paraco1147068288nge_tv @ f @ sK142) = (paraco1147068288nge_tv @ f @ sK141)) => (sK141 = sK142)) = $false)),
% 3.11/1.94 inference(binary_proxy_clausification,[status(thm)],[f3005])).
% 3.11/1.94 thf(f3005,plain,(
% 3.11/1.94 ($false = ((member266900804lle_tv @ sK142 @ top_to1057771083lle_tv) => (((paraco1147068288nge_tv @ f @ sK142) = (paraco1147068288nge_tv @ f @ sK141)) => (sK141 = sK142))))),
% 3.11/1.94 inference(beta_eta_normalization,[status(thm)],[f3004])).
% 3.11/1.94 thf(f3004,plain,(
% 3.11/1.94 ($false = ((^[Y0 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y0 @ top_to1057771083lle_tv) => (((paraco1147068288nge_tv @ f @ Y0) = (paraco1147068288nge_tv @ f @ sK141)) => (sK141 = Y0)))) @ sK142))),
% 3.11/1.94 inference(sigma_clausification,[status(thm)],[f3002])).
% 3.11/1.94 thf(f3002,plain,(
% 3.11/1.94 ($false = (!! @ paraco1605129243lle_tv @ (^[Y0 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y0 @ top_to1057771083lle_tv) => (((paraco1147068288nge_tv @ f @ Y0) = (paraco1147068288nge_tv @ f @ sK141)) => (sK141 = Y0))))))),
% 3.11/1.94 inference(binary_proxy_clausification,[status(thm)],[f3001])).
% 3.11/1.94 thf(f3001,plain,(
% 3.11/1.94 (((member266900804lle_tv @ sK141 @ top_to1057771083lle_tv) => (!! @ paraco1605129243lle_tv @ (^[Y0 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y0 @ top_to1057771083lle_tv) => (((paraco1147068288nge_tv @ f @ Y0) = (paraco1147068288nge_tv @ f @ sK141)) => (sK141 = Y0)))))) = $false)),
% 3.11/1.94 inference(beta_eta_normalization,[status(thm)],[f3000])).
% 3.11/1.94 thf(f3000,plain,(
% 3.11/1.94 (((^[Y0 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y0 @ top_to1057771083lle_tv) => (!! @ paraco1605129243lle_tv @ (^[Y1 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y1 @ top_to1057771083lle_tv) => (((paraco1147068288nge_tv @ f @ Y1) = (paraco1147068288nge_tv @ f @ Y0)) => (Y0 = Y1))))))) @ sK141) = $false)),
% 3.11/1.94 inference(sigma_clausification,[status(thm)],[f2999])).
% 3.11/1.94 thf(f2999,plain,(
% 3.11/1.94 ((!! @ paraco1605129243lle_tv @ (^[Y0 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y0 @ top_to1057771083lle_tv) => (!! @ paraco1605129243lle_tv @ (^[Y1 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y1 @ top_to1057771083lle_tv) => (((paraco1147068288nge_tv @ f @ Y1) = (paraco1147068288nge_tv @ f @ Y0)) => (Y0 = Y1)))))))) != $true)),
% 3.11/1.94 inference(beta_eta_normalization,[status(thm)],[f1124])).
% 3.11/1.94 thf(f1124,plain,(
% 3.11/1.94 ($true != ((^[Y0 : paraco1605129243lle_tv > paraco1605129243lle_tv]: ((^[Y1 : set_Pa1764573435lle_tv]: (!! @ paraco1605129243lle_tv @ (^[Y2 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y2 @ Y1) => (!! @ paraco1605129243lle_tv @ (^[Y3 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y3 @ Y1) => (((Y0 @ Y3) = (Y0 @ Y2)) => (Y2 = Y3))))))))))) @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv))),
% 3.11/1.94 inference(definition_unfolding,[status(thm)],[f1074,f1105])).
% 3.11/1.94 thf(f1105,plain,(
% 3.11/1.94 (inj_on772319074lle_tv = (^[Y0 : paraco1605129243lle_tv > paraco1605129243lle_tv]: ((^[Y1 : set_Pa1764573435lle_tv]: (!! @ paraco1605129243lle_tv @ (^[Y2 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y2 @ Y1) => (!! @ paraco1605129243lle_tv @ (^[Y3 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y3 @ Y1) => (((Y0 @ Y3) = (Y0 @ Y2)) => (Y2 = Y3))))))))))))),
% 3.11/1.94 inference(cnf_transformation,[status(thm)],[f890])).
% 3.11/1.94 thf(f890,plain,(
% 3.11/1.94 (inj_on772319074lle_tv = (^[Y0 : paraco1605129243lle_tv > paraco1605129243lle_tv]: ((^[Y1 : set_Pa1764573435lle_tv]: (!! @ paraco1605129243lle_tv @ (^[Y2 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y2 @ Y1) => (!! @ paraco1605129243lle_tv @ (^[Y3 : paraco1605129243lle_tv]: ((member266900804lle_tv @ Y3 @ Y1) => (((Y0 @ Y3) = (Y0 @ Y2)) => (Y2 = Y3))))))))))))),
% 3.11/1.94 inference(fool_elimination,[status(thm)],[f889])).
% 3.11/1.94 thf(f889,plain,(
% 3.11/1.94 ((^[X0 : paraco1605129243lle_tv > paraco1605129243lle_tv, X1 : set_Pa1764573435lle_tv] : (! [X2 : paraco1605129243lle_tv] : ((member266900804lle_tv @ X2 @ X1) => ! [X3 : paraco1605129243lle_tv] : ((member266900804lle_tv @ X3 @ X1) => (((X0 @ X3) = (X0 @ X2)) => (X2 = X3)))))) = inj_on772319074lle_tv)),
% 3.11/1.94 inference(rectify,[status(thm)],[f61])).
% 3.11/1.94 thf(f61,axiom,(
% 3.11/1.94 ((^[X10 : paraco1605129243lle_tv > paraco1605129243lle_tv, X11 : set_Pa1764573435lle_tv] : (! [X3 : paraco1605129243lle_tv] : ((member266900804lle_tv @ X3 @ X11) => ! [X8 : paraco1605129243lle_tv] : ((member266900804lle_tv @ X8 @ X11) => (((X10 @ X3) = (X10 @ X8)) => (X3 = X8)))))) = inj_on772319074lle_tv)),
% 3.11/1.94 file('/export/starexec/sandbox2/tmp/tmp.8VRe1TRbh8/DTF2THF_11108.p',fact_60_inj__on__def)).
% 3.11/1.94 thf(f1074,plain,(
% 3.11/1.94 ((inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv) != $true)),
% 3.11/1.94 inference(cnf_transformation,[status(thm)],[f993])).
% 3.11/1.94 thf(f993,plain,(
% 3.11/1.94 ((inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv) != $true)),
% 3.11/1.94 inference(flattening,[status(thm)],[f438])).
% 3.11/1.94 thf(f438,plain,(
% 3.11/1.94 ~((inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv) = $true)),
% 3.11/1.94 inference(fool_elimination,[status(thm)],[f437])).
% 3.11/1.94 thf(f437,plain,(
% 3.11/1.94 ~(inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)),
% 3.11/1.94 inference(rectify,[status(thm)],[f357])).
% 3.11/1.94 thf(f357,negated_conjecture,(
% 3.11/1.94 ~(inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)),
% 3.11/1.94 inference(negated_conjecture,[status(cth)],[f356])).
% 3.11/1.94 thf(f356,conjecture,(
% 3.11/1.94 (inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)),
% 3.11/1.94 file('/export/starexec/sandbox2/tmp/tmp.8VRe1TRbh8/DTF2THF_11108.p',conj_0)).
% 3.11/1.94 thf(f3166,plain,(
% 3.11/1.94 (sK141 = sK142)),
% 3.11/1.94 inference(equality_resolution,[status(thm)],[f3137])).
% 3.11/1.94 thf(f3137,plain,(
% 3.11/1.94 ( ! [X0 : paraco1605129243lle_tv] : (((paraco1147068288nge_tv @ f @ X0) != (paraco1147068288nge_tv @ f @ sK141)) | (sK142 = X0)) )),
% 3.11/1.94 inference(superposition,[status(thm)],[f1084,f3010])).
% 3.11/1.94 thf(f3010,plain,(
% 3.11/1.94 ((paraco1147068288nge_tv @ f @ sK142) = (paraco1147068288nge_tv @ f @ sK141))),
% 3.11/1.94 inference(equality_proxy_clausification,[status(thm)],[f3009])).
% 3.11/1.94 thf(f3009,plain,(
% 3.11/1.94 (((paraco1147068288nge_tv @ f @ sK142) = (paraco1147068288nge_tv @ f @ sK141)) = $true)),
% 3.11/1.94 inference(binary_proxy_clausification,[status(thm)],[f3006])).
% 3.11/1.94 thf(f1084,plain,(
% 3.11/1.94 ( ! [X0 : paraco1605129243lle_tv,X1 : paraco1605129243lle_tv] : (((paraco1147068288nge_tv @ f @ X0) != (paraco1147068288nge_tv @ f @ X1)) | (X0 = X1)) )),
% 3.11/1.94 inference(cnf_transformation,[status(thm)],[f1046])).
% 3.11/1.94 thf(f1046,plain,(
% 3.11/1.94 ! [X0 : paraco1605129243lle_tv,X1 : paraco1605129243lle_tv] : ((X0 = X1) | ((paraco1147068288nge_tv @ f @ X0) != (paraco1147068288nge_tv @ f @ X1)))),
% 3.11/1.94 inference(ennf_transformation,[status(thm)],[f997])).
% 3.11/1.94 thf(f997,plain,(
% 3.11/1.94 ! [X0 : paraco1605129243lle_tv,X1 : paraco1605129243lle_tv] : (((paraco1147068288nge_tv @ f @ X0) = (paraco1147068288nge_tv @ f @ X1)) => (X0 = X1))),
% 3.11/1.94 inference(rectify,[status(thm)],[f1])).
% 3.11/1.94 thf(f1,axiom,(
% 3.11/1.94 ! [X1 : paraco1605129243lle_tv,X0 : paraco1605129243lle_tv] : (((paraco1147068288nge_tv @ f @ X0) = (paraco1147068288nge_tv @ f @ X1)) => (X0 = X1))),
% 3.11/1.94 file('/export/starexec/sandbox2/tmp/tmp.8VRe1TRbh8/DTF2THF_11108.p',fact_0__092_060open_062_092_060And_062tv2_Atv1_O_Achange__tv_Af_Atv1_A_061_Achange__tv_Af_Atv2_A_092_060Longrightarrow_062_Atv1_A_061_Atv2_092_060close_062)).
% 3.11/1.94 % SZS output end Proof for DTF2THF_11108
% 3.11/1.94 % (11337)------------------------------
% 3.11/1.94 % (11337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.94 % (11337)Termination reason: Refutation
% 3.11/1.94
% 3.11/1.94 % (11337)Memory used [KB]: 8059
% 3.11/1.94 % (11337)Time elapsed: 0.205 s
% 3.11/1.94 % (11337)Instructions burned: 519 (million)
% 3.11/1.94 % (11337)------------------------------
% 3.11/1.94 % (11337)------------------------------
% 3.11/1.94 % (11299)Success in time 0.32 s
%------------------------------------------------------------------------------