%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP104^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:35 AM UTC 2026
% Result : Theorem 6.29s 2.17s
% Output : Refutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 85 ( 37 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 268 ( 19 ~; 13 |; 0 &; 228 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 18 ( 17 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 186 ( 183 usr; 8 con; 0-4 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
list_list_list_a: $tType ).
thf(type_def_6,type,
set_nat: $tType ).
thf(type_def_7,type,
set_list_list_a: $tType ).
thf(type_def_9,type,
list_list_nat: $tType ).
thf(type_def_10,type,
set_list_nat: $tType ).
thf(type_def_11,type,
list_list_a: $tType ).
thf(type_def_12,type,
set_list_a: $tType ).
thf(type_def_13,type,
list_nat: $tType ).
thf(type_def_14,type,
list_a: $tType ).
thf(type_def_15,type,
set_a: $tType ).
thf(type_def_16,type,
list_set_list_a: $tType ).
thf(type_def_17,type,
list_set_nat: $tType ).
thf(type_def_18,type,
list_set_a: $tType ).
thf(type_def_19,type,
nat: $tType ).
thf(type_def_20,type,
list_l2071841302list_a: $tType ).
thf(type_def_21,type,
list_list_list_nat: $tType ).
thf(type_def_22,type,
a: $tType ).
thf(func_def_0,type,
list_l2071841302list_a: $tType ).
thf(func_def_1,type,
list_list_list_nat: $tType ).
thf(func_def_2,type,
list_list_list_a: $tType ).
thf(func_def_3,type,
set_list_list_a: $tType ).
thf(func_def_4,type,
list_set_list_a: $tType ).
thf(func_def_5,type,
list_list_nat: $tType ).
thf(func_def_6,type,
set_list_nat: $tType ).
thf(func_def_7,type,
list_set_nat: $tType ).
thf(func_def_8,type,
list_list_a: $tType ).
thf(func_def_9,type,
set_list_a: $tType ).
thf(func_def_10,type,
list_set_a: $tType ).
thf(func_def_11,type,
list_nat: $tType ).
thf(func_def_12,type,
set_nat: $tType ).
thf(func_def_13,type,
list_a: $tType ).
thf(func_def_14,type,
set_a: $tType ).
thf(func_def_15,type,
nat: $tType ).
thf(func_def_16,type,
a: $tType ).
thf(func_def_17,type,
f_image_list_list_a: list_list_list_a > set_nat > set_list_list_a ).
thf(func_def_18,type,
f_image_list_nat: list_list_nat > set_nat > set_list_nat ).
thf(func_def_19,type,
f_image_list_a: list_list_a > set_nat > set_list_a ).
thf(func_def_20,type,
f_image_nat: list_nat > set_nat > set_nat ).
thf(func_def_21,type,
f_image_a: list_a > set_nat > set_a ).
thf(func_def_22,type,
list_asc_nat: list_nat > $o ).
thf(func_def_23,type,
list_asc_set_list_a: list_set_list_a > $o ).
thf(func_def_24,type,
list_asc_set_nat: list_set_nat > $o ).
thf(func_def_25,type,
list_asc_set_a: list_set_a > $o ).
thf(func_def_26,type,
list_desc_nat: list_nat > $o ).
thf(func_def_27,type,
list_desc_set_list_a: list_set_list_a > $o ).
thf(func_def_28,type,
list_desc_set_nat: list_set_nat > $o ).
thf(func_def_29,type,
list_desc_set_a: list_set_a > $o ).
thf(func_def_30,type,
list_strict_asc_nat: list_nat > $o ).
thf(func_def_31,type,
list_strict_desc_nat: list_nat > $o ).
thf(func_def_32,type,
listSl769338732list_a: list_list_list_a > nat > list_l2071841302list_a ).
thf(func_def_33,type,
listSl2099749758st_nat: list_list_nat > nat > list_list_list_nat ).
thf(func_def_34,type,
listSl703198822list_a: list_list_a > nat > list_list_list_a ).
thf(func_def_35,type,
listSl882585454e2_nat: list_nat > nat > list_list_nat ).
thf(func_def_36,type,
listSl1174287072ice2_a: list_a > nat > list_list_a ).
thf(func_def_37,type,
listSl2102238196list_a: list_list_list_a > nat > list_l2071841302list_a ).
thf(func_def_38,type,
listSl729562870st_nat: list_list_nat > nat > list_list_list_nat ).
thf(func_def_39,type,
listSl162220270list_a: list_list_a > nat > list_list_list_a ).
thf(func_def_40,type,
listSl1630398182ce_nat: list_nat > nat > list_list_nat ).
thf(func_def_41,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(func_def_42,type,
listSl902632890list_a: list_list_list_a > nat > nat > list_l2071841302list_a ).
thf(func_def_43,type,
listSl1506485424st_nat: list_list_nat > nat > nat > list_list_list_nat ).
thf(func_def_44,type,
listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
thf(func_def_45,type,
listSl1794011552ux_nat: list_nat > nat > nat > list_list_nat ).
thf(func_def_46,type,
listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
thf(func_def_47,type,
butlast_list_list_a: list_list_list_a > list_list_list_a ).
thf(func_def_48,type,
butlast_list_nat: list_list_nat > list_list_nat ).
thf(func_def_49,type,
butlast_list_a: list_list_a > list_list_a ).
thf(func_def_50,type,
butlast_nat: list_nat > list_nat ).
thf(func_def_51,type,
butlast_a: list_a > list_a ).
thf(func_def_52,type,
distinct_list_list_a: list_list_list_a > $o ).
thf(func_def_53,type,
distinct_list_nat: list_list_nat > $o ).
thf(func_def_54,type,
distinct_list_a: list_list_a > $o ).
thf(func_def_55,type,
distinct_nat: list_nat > $o ).
thf(func_def_56,type,
distinct_a: list_a > $o ).
thf(func_def_57,type,
set_list_list_a2: list_list_list_a > set_list_list_a ).
thf(func_def_58,type,
set_list_nat2: list_list_nat > set_list_nat ).
thf(func_def_59,type,
set_list_a2: list_list_a > set_list_a ).
thf(func_def_60,type,
set_nat2: list_nat > set_nat ).
thf(func_def_61,type,
set_a2: list_a > set_a ).
thf(func_def_62,type,
list_ex_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
thf(func_def_63,type,
list_ex_list_nat: ( list_nat > $o ) > list_list_nat > $o ).
thf(func_def_64,type,
list_ex_list_a: ( list_a > $o ) > list_list_a > $o ).
thf(func_def_65,type,
list_ex_nat: ( nat > $o ) > list_nat > $o ).
thf(func_def_66,type,
list_ex_a: ( a > $o ) > list_a > $o ).
thf(func_def_67,type,
list_u1330012152list_a: list_list_list_a > nat > list_list_a > list_list_list_a ).
thf(func_def_68,type,
list_update_list_nat: list_list_nat > nat > list_nat > list_list_nat ).
thf(func_def_69,type,
list_update_list_a: list_list_a > nat > list_a > list_list_a ).
thf(func_def_70,type,
list_update_nat: list_nat > nat > nat > list_nat ).
thf(func_def_71,type,
list_update_a: list_a > nat > a > list_a ).
thf(func_def_72,type,
nth_list_list_list_a: list_l2071841302list_a > nat > list_list_list_a ).
thf(func_def_73,type,
nth_list_list_nat: list_list_list_nat > nat > list_list_nat ).
thf(func_def_74,type,
nth_list_list_a: list_list_list_a > nat > list_list_a ).
thf(func_def_75,type,
nth_list_nat: list_list_nat > nat > list_nat ).
thf(func_def_76,type,
nth_list_a: list_list_a > nat > list_a ).
thf(func_def_77,type,
nth_nat: list_nat > nat > nat ).
thf(func_def_78,type,
nth_set_list_a: list_set_list_a > nat > set_list_a ).
thf(func_def_79,type,
nth_set_nat: list_set_nat > nat > set_nat ).
thf(func_def_80,type,
nth_set_a: list_set_a > nat > set_a ).
thf(func_def_81,type,
nth_a: list_a > nat > a ).
thf(func_def_82,type,
size_s1764310658list_a: list_l2071841302list_a > nat ).
thf(func_def_83,type,
size_s1321307156st_nat: list_list_list_nat > nat ).
thf(func_def_84,type,
size_s575106428list_a: list_list_list_a > nat ).
thf(func_def_85,type,
size_s1898481668st_nat: list_list_nat > nat ).
thf(func_def_86,type,
size_s1427607542list_a: list_list_a > nat ).
thf(func_def_87,type,
size_size_list_nat: list_nat > nat ).
thf(func_def_88,type,
size_s1635937238list_a: list_set_list_a > nat ).
thf(func_def_89,type,
size_s577819178et_nat: list_set_nat > nat ).
thf(func_def_90,type,
size_size_list_set_a: list_set_a > nat ).
thf(func_def_91,type,
size_size_list_a: list_a > nat ).
thf(func_def_92,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_93,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_94,type,
ord_le1756736906list_a: set_list_list_a > set_list_list_a > $o ).
thf(func_def_95,type,
ord_le1747345782st_nat: set_list_nat > set_list_nat > $o ).
thf(func_def_96,type,
ord_le1301786372list_a: set_list_a > set_list_a > $o ).
thf(func_def_97,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_98,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_99,type,
top_top_set_nat: set_nat ).
thf(func_def_100,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_101,type,
collect_list_a: ( list_a > $o ) > set_list_a ).
thf(func_def_102,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_103,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_104,type,
member_list_list_a: list_list_a > set_list_list_a > $o ).
thf(func_def_105,type,
member_list_nat: list_nat > set_list_nat > $o ).
thf(func_def_106,type,
member_list_a: list_a > set_list_a > $o ).
thf(func_def_107,type,
member_nat: nat > set_nat > $o ).
thf(func_def_108,type,
member_a: a > set_a > $o ).
thf(func_def_109,type,
k: nat ).
thf(func_def_110,type,
m: nat ).
thf(func_def_111,type,
xs: list_a ).
thf(func_def_126,type,
sP0: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_127,type,
sP1: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_128,type,
sP2: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_129,type,
sP3: nat > nat > nat > $o ).
thf(func_def_130,type,
sP4: nat > nat > nat > $o ).
thf(func_def_131,type,
sP5: nat > nat > nat > $o ).
thf(func_def_132,type,
sP6: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_133,type,
sK7: nat > nat ).
thf(func_def_134,type,
sK8: ( nat > nat ) > nat ).
thf(func_def_135,type,
sK9: ( nat > nat ) > nat ).
thf(func_def_136,type,
sK10: ( nat > nat ) > nat ).
thf(func_def_137,type,
sK11: ( nat > nat ) > nat ).
thf(func_def_138,type,
sK12: ( nat > nat > $o ) > nat ).
thf(func_def_139,type,
sK13: ( nat > nat > $o ) > nat ).
thf(func_def_140,type,
sK14: ( nat > nat > $o ) > nat ).
thf(func_def_141,type,
sK15: ( nat > nat > $o ) > nat ).
thf(func_def_142,type,
sK16: nat > nat ).
thf(func_def_143,type,
sK17: nat > nat ).
thf(func_def_144,type,
sK18: nat > nat ).
thf(func_def_145,type,
sK19: ( nat > $o ) > nat ).
thf(func_def_146,type,
sK20: ( nat > $o ) > nat ).
thf(func_def_147,type,
sK21: ( nat > $o ) > nat > nat ).
thf(func_def_148,type,
sK22: ( nat > $o ) > nat > nat ).
thf(func_def_149,type,
sK23: nat > nat ).
thf(func_def_150,type,
sK24: ( nat > nat ) > nat ).
thf(func_def_151,type,
sK25: ( nat > nat ) > nat ).
thf(func_def_152,type,
sK26: ( nat > nat ) > nat ).
thf(func_def_153,type,
sK27: ( nat > nat ) > nat ).
thf(func_def_154,type,
sK28: nat > nat ).
thf(func_def_155,type,
sK29: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_156,type,
sK30: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_157,type,
sK31: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_158,type,
sK32: nat > list_list_a ).
thf(func_def_159,type,
sK33: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_160,type,
sK34: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_161,type,
sK35: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_162,type,
sK36: ( nat > nat ) > nat ).
thf(func_def_163,type,
sK37: ( nat > nat ) > nat ).
thf(func_def_164,type,
sK38: nat > nat ).
thf(func_def_165,type,
sK39: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_166,type,
sK40: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_167,type,
sK41: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_168,type,
sK42: nat > nat ).
thf(func_def_169,type,
sK43: ( nat > nat ) > nat ).
thf(func_def_170,type,
sK44: ( nat > nat ) > nat ).
thf(func_def_171,type,
sK45: list_list_a > list_list_a > nat ).
thf(func_def_172,type,
sK46: ( nat > nat ) > nat ).
thf(func_def_173,type,
sK47: ( nat > nat ) > nat ).
thf(func_def_174,type,
sK48: nat > list_a ).
thf(func_def_175,type,
sK49: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_176,type,
sK50: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_177,type,
sK51: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_178,type,
sK52: ( nat > nat ) > nat ).
thf(func_def_179,type,
sK53: ( nat > nat ) > nat ).
thf(func_def_180,type,
sK54: ( nat > nat ) > nat ).
thf(func_def_181,type,
sK55: ( nat > nat ) > nat ).
thf(func_def_182,type,
sK56: ( nat > nat ) > nat ).
thf(func_def_183,type,
sK57: ( nat > nat ) > nat ).
thf(func_def_184,type,
sK58: ( list_list_a > $o ) > list_list_a ).
thf(func_def_185,type,
sK59: ( nat > nat ) > nat ).
thf(func_def_186,type,
sK60: ( nat > nat ) > nat ).
thf(func_def_187,type,
sK61: nat > nat ).
thf(func_def_188,type,
sK62: nat > ( nat > list_a > $o ) > list_a ).
thf(func_def_189,type,
sK63: list_list_a > ( nat > list_a > $o ) > nat > nat ).
thf(func_def_190,type,
sK64: ( nat > list_a > $o ) > nat > list_list_a ).
thf(func_def_191,type,
sK65: ( nat > list_a > $o ) > nat > nat ).
thf(func_def_192,type,
sK66: nat > nat ).
thf(func_def_193,type,
sK67: nat > nat > ( nat > $o ) > nat ).
thf(func_def_194,type,
sK68: nat > nat > ( nat > $o ) > nat ).
thf(func_def_195,type,
sK69: nat > nat ).
thf(func_def_196,type,
sK70: ( nat > nat ) > nat ).
thf(func_def_197,type,
sK71: ( nat > nat ) > nat ).
thf(func_def_198,type,
sK72: nat > ( nat > $o ) > nat ).
thf(func_def_199,type,
sK73: ( nat > $o ) > nat ).
thf(func_def_200,type,
sK74: ( nat > $o ) > nat ).
thf(func_def_201,type,
sK75: nat > nat ).
thf(func_def_202,type,
sK76: ( nat > nat ) > nat ).
thf(func_def_203,type,
sK77: ( nat > nat ) > nat ).
thf(func_def_204,type,
sK78: ( list_a > $o ) > list_a ).
thf(func_def_205,type,
sK79: ( nat > nat > $o ) > nat ).
thf(func_def_206,type,
sK80: ( nat > nat > $o ) > nat ).
thf(func_def_207,type,
sK81: ( nat > nat > $o ) > nat ).
thf(func_def_208,type,
sK82: ( nat > nat > $o ) > nat ).
thf(func_def_209,type,
sK83: ( nat > nat > $o ) > nat ).
thf(func_def_210,type,
sK84: nat > nat ).
thf(func_def_212,type,
ph86:
!>[X0: $tType] : X0 ).
thf(f1603,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1597,f1598,f1602]) ).
thf(f1602,plain,
( ~ spl85_2
| spl85_1 ),
inference(avatar_split_clause,[status(thm)],[f1601,f1590,f1594]) ).
thf(f1594,definition,
( spl85_2
<=> ( ( ord_less_nat @ m @ ( size_s1427607542list_a @ ( listSl97544552lice_a @ xs @ k ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl85_2])],[avatar_definition]) ).
thf(f1590,definition,
( spl85_1
<=> ( k
= ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) ) ) ),
introduced(definition,[new_symbols(naming,[spl85_1])],[avatar_definition]) ).
thf(f1601,plain,
( ( ( ord_less_nat @ m @ ( size_s1427607542list_a @ ( listSl97544552lice_a @ xs @ k ) ) )
!= $true )
| spl85_1 ),
inference(forward_demodulation,[status(thm)],[f1600,f1406]) ).
thf(f1406,plain,
! [X0: nat,X1: list_a] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ X1 @ X0 ) )
= ( divide_divide_nat @ ( size_size_list_a @ X1 ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f979]) ).
thf(f979,plain,
! [X0: nat,X1: list_a] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ X1 @ X0 ) )
= ( divide_divide_nat @ ( size_size_list_a @ X1 ) @ X0 ) ),
inference(rectify,[status(thm)],[f53]) ).
thf(f53,axiom,
! [X3: nat,X0: list_a] :
( ( divide_divide_nat @ ( size_size_list_a @ X0 ) @ X3 )
= ( size_s1427607542list_a @ ( listSl97544552lice_a @ X0 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',fact_52_list__slice__length) ).
thf(f1600,plain,
( ( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) )
!= $true )
| spl85_1 ),
inference(trivial_inequality_removal,[status(thm)],[f1599]) ).
thf(f1599,plain,
( ( k != k )
| ( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) )
!= $true )
| spl85_1 ),
inference(superposition,[status(thm)],[f1592,f1377]) ).
thf(f1377,plain,
! [X2: nat,X0: nat,X1: list_a] :
( ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X1 @ X0 ) @ X2 ) )
= X0 )
| ( $true
!= ( ord_less_nat @ X2 @ ( divide_divide_nat @ ( size_size_list_a @ X1 ) @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1008]) ).
thf(f1008,plain,
! [X0: nat,X1: list_a,X2: nat] :
( ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X1 @ X0 ) @ X2 ) )
= X0 )
| ( $true
!= ( ord_less_nat @ X2 @ ( divide_divide_nat @ ( size_size_list_a @ X1 ) @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f418]) ).
thf(f418,plain,
! [X0: nat,X1: list_a,X2: nat] :
( ( $true
= ( ord_less_nat @ X2 @ ( divide_divide_nat @ ( size_size_list_a @ X1 ) @ X0 ) ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X1 @ X0 ) @ X2 ) )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f417]) ).
thf(f417,plain,
! [X0: nat,X1: list_a,X2: nat] :
( ( ord_less_nat @ X2 @ ( divide_divide_nat @ ( size_size_list_a @ X1 ) @ X0 ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X1 @ X0 ) @ X2 ) )
= X0 ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,axiom,
! [X3: nat,X0: list_a,X11: nat] :
( ( ord_less_nat @ X11 @ ( divide_divide_nat @ ( size_size_list_a @ X0 ) @ X3 ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X0 @ X3 ) @ X11 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',fact_30_list__slice__nth__length) ).
thf(f1592,plain,
( ( k
!= ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) ) )
| spl85_1 ),
inference(avatar_component_clause,[status(thm)],[f1590]) ).
thf(f1598,plain,
spl85_2,
inference(avatar_split_clause,[status(thm)],[f1586,f1594]) ).
thf(f1586,plain,
( ( ord_less_nat @ m @ ( size_s1427607542list_a @ ( listSl97544552lice_a @ xs @ k ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1360,f1406]) ).
thf(f1360,plain,
( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f828]) ).
thf(f828,plain,
( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) )
= $true ),
inference(fool_elimination,[status(thm)],[f827]) ).
thf(f827,plain,
ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
inference(rectify,[status(thm)],[f349]) ).
thf(f349,axiom,
ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',conj_0) ).
thf(f1597,plain,
( ~ spl85_1
| ~ spl85_2 ),
inference(avatar_split_clause,[status(thm)],[f1588,f1594,f1590]) ).
thf(f1588,plain,
( ( ( ord_less_nat @ m @ ( size_s1427607542list_a @ ( listSl97544552lice_a @ xs @ k ) ) )
!= $true )
| ( k
!= ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1587,f1406]) ).
thf(f1587,plain,
( ( k
!= ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) ) )
| ( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) )
!= $true ) ),
inference(superposition,[status(thm)],[f1475,f1490]) ).
thf(f1490,plain,
! [X2: list_a,X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ ( divide_divide_nat @ ( size_size_list_a @ X2 ) @ X0 ) )
!= $true )
| ( ( nth_list_a @ ( listSl97544552lice_a @ X2 @ X0 ) @ X1 )
= ( nth_list_a @ ( listSl1174287072ice2_a @ X2 @ X0 ) @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f1125]) ).
thf(f1125,plain,
! [X0: nat,X1: nat,X2: list_a] :
( ( ( ord_less_nat @ X1 @ ( divide_divide_nat @ ( size_size_list_a @ X2 ) @ X0 ) )
!= $true )
| ( ( nth_list_a @ ( listSl97544552lice_a @ X2 @ X0 ) @ X1 )
= ( nth_list_a @ ( listSl1174287072ice2_a @ X2 @ X0 ) @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f870]) ).
thf(f870,plain,
! [X0: nat,X1: nat,X2: list_a] :
( ( ( ord_less_nat @ X1 @ ( divide_divide_nat @ ( size_size_list_a @ X2 ) @ X0 ) )
= $true )
=> ( ( nth_list_a @ ( listSl97544552lice_a @ X2 @ X0 ) @ X1 )
= ( nth_list_a @ ( listSl1174287072ice2_a @ X2 @ X0 ) @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f869]) ).
thf(f869,plain,
! [X0: nat,X1: nat,X2: list_a] :
( ( ord_less_nat @ X1 @ ( divide_divide_nat @ ( size_size_list_a @ X2 ) @ X0 ) )
=> ( ( nth_list_a @ ( listSl97544552lice_a @ X2 @ X0 ) @ X1 )
= ( nth_list_a @ ( listSl1174287072ice2_a @ X2 @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,axiom,
! [X3: nat,X11: nat,X0: list_a] :
( ( ord_less_nat @ X11 @ ( divide_divide_nat @ ( size_size_list_a @ X0 ) @ X3 ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ X0 @ X3 ) @ X11 )
= ( nth_list_a @ ( listSl97544552lice_a @ X0 @ X3 ) @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',fact_19_list__slice2__list__slice__nth) ).
thf(f1475,plain,
( k
!= ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) ) ),
inference(cnf_transformation,[status(thm)],[f957]) ).
thf(f957,plain,
( k
!= ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) ) ),
inference(flattening,[status(thm)],[f351]) ).
thf(f351,negated_conjecture,
( k
!= ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) ) ),
inference(negated_conjecture,[status(cth)],[f350]) ).
thf(f350,conjecture,
( k
= ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP104^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:27:48 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP104^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer ListSlice problem prob_199__5618146_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : ListSlice/prob_199__5618146_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 462 ( 122 unt; 112 typ; 0 def)
% 0.30/0.46 % Number of atoms : 1046 ( 371 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 12 ( 2 avg)
% 0.30/0.46 % Number of connectives : 3415 ( 124 ~; 18 |; 67 &;2673 @)
% 0.30/0.46 % ( 0 <=>; 533 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 18 ( 7 avg)
% 0.30/0.46 % Number of types : 18 ( 17 usr)
% 0.30/0.46 % Number of type conns : 235 ( 235 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 96 ( 95 usr; 4 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 1096 ( 94 ^; 941 !; 61 ?;1096 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:28.219
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (17)
% 0.30/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.30/0.46 list_l2071841302list_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
% 0.30/0.46 list_list_list_nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.30/0.46 list_list_list_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.30/0.46 set_list_list_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.30/0.46 list_set_list_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.30/0.46 list_list_nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.30/0.46 set_list_nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.30/0.46 list_set_nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 list_list_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 set_list_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.30/0.46 list_set_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 list_nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.46 set_nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.30/0.46 list_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 set_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.30/0.46 nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (95)
% 0.30/0.46 thf(sy_c_List2_Of__image_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 f_image_list_list_a: list_list_list_a > set_nat > set_list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Of__image_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 f_image_list_nat: list_list_nat > set_nat > set_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Of__image_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 f_image_list_a: list_list_a > set_nat > set_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Of__image_001t__Nat__Onat,type,
% 0.30/0.46 f_image_nat: list_nat > set_nat > set_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Of__image_001tf__a,type,
% 0.30/0.46 f_image_a: list_a > set_nat > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__asc_001t__Nat__Onat,type,
% 0.30/0.46 list_asc_nat: list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__asc_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 list_asc_set_list_a: list_set_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__asc_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.46 list_asc_set_nat: list_set_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__asc_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 list_asc_set_a: list_set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__desc_001t__Nat__Onat,type,
% 0.30/0.46 list_desc_nat: list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__desc_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 list_desc_set_list_a: list_set_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__desc_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.46 list_desc_set_nat: list_set_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__desc_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 list_desc_set_a: list_set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__strict__asc_001t__Nat__Onat,type,
% 0.30/0.46 list_strict_asc_nat: list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List2_Olist__strict__desc_001t__Nat__Onat,type,
% 0.30/0.46 list_strict_desc_nat: list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 listSl769338732list_a: list_list_list_a > nat > list_l2071841302list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 listSl2099749758st_nat: list_list_nat > nat > list_list_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 listSl703198822list_a: list_list_a > nat > list_list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__Nat__Onat,type,
% 0.30/0.46 listSl882585454e2_nat: list_nat > nat > list_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001tf__a,type,
% 0.30/0.46 listSl1174287072ice2_a: list_a > nat > list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 listSl2102238196list_a: list_list_list_a > nat > list_l2071841302list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 listSl729562870st_nat: list_list_nat > nat > list_list_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 listSl162220270list_a: list_list_a > nat > list_list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__Nat__Onat,type,
% 0.30/0.46 listSl1630398182ce_nat: list_nat > nat > list_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001tf__a,type,
% 0.30/0.46 listSl97544552lice_a: list_a > nat > list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 listSl902632890list_a: list_list_list_a > nat > nat > list_l2071841302list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 listSl1506485424st_nat: list_list_nat > nat > nat > list_list_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__Nat__Onat,type,
% 0.30/0.46 listSl1794011552ux_nat: list_nat > nat > nat > list_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001tf__a,type,
% 0.30/0.46 listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Obutlast_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 butlast_list_list_a: list_list_list_a > list_list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Obutlast_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 butlast_list_nat: list_list_nat > list_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 butlast_list_a: list_list_a > list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 0.30/0.46 butlast_nat: list_nat > list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Obutlast_001tf__a,type,
% 0.30/0.46 butlast_a: list_a > list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Odistinct_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 distinct_list_list_a: list_list_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Odistinct_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 distinct_list_nat: list_list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Odistinct_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 distinct_list_a: list_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 0.30/0.46 distinct_nat: list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Odistinct_001tf__a,type,
% 0.30/0.46 distinct_a: list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 set_list_list_a2: list_list_list_a > set_list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 set_list_nat2: list_list_nat > set_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 set_list_a2: list_list_a > set_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 0.30/0.46 set_nat2: list_nat > set_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_Oset_001tf__a,type,
% 0.30/0.46 set_a2: list_a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__ex_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 list_ex_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__ex_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 list_ex_list_nat: ( list_nat > $o ) > list_list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__ex_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 list_ex_list_a: ( list_a > $o ) > list_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__ex_001t__Nat__Onat,type,
% 0.30/0.46 list_ex_nat: ( nat > $o ) > list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__ex_001tf__a,type,
% 0.30/0.46 list_ex_a: ( a > $o ) > list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__update_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 list_u1330012152list_a: list_list_list_a > nat > list_list_a > list_list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__update_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 list_update_list_nat: list_list_nat > nat > list_nat > list_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__update_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 list_update_list_a: list_list_a > nat > list_a > list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 0.30/0.46 list_update_nat: list_nat > nat > nat > list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__update_001tf__a,type,
% 0.30/0.46 list_update_a: list_a > nat > a > list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.30/0.46 nth_list_list_list_a: list_l2071841302list_a > nat > list_list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.30/0.46 nth_list_list_nat: list_list_list_nat > nat > list_list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 nth_list_list_a: list_list_list_a > nat > list_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 nth_list_nat: list_list_nat > nat > list_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 nth_list_a: list_list_a > nat > list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 0.30/0.46 nth_nat: list_nat > nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 nth_set_list_a: list_set_list_a > nat > set_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.46 nth_set_nat: list_set_nat > nat > set_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 nth_set_a: list_set_a > nat > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth_001tf__a,type,
% 0.30/0.46 nth_a: list_a > nat > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.30/0.46 size_s1764310658list_a: list_l2071841302list_a > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
% 0.30/0.46 size_s1321307156st_nat: list_list_list_nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.30/0.46 size_s575106428list_a: list_list_list_a > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.30/0.46 size_s1898481668st_nat: list_list_nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 size_s1427607542list_a: list_list_a > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 size_size_list_nat: list_nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.30/0.46 size_s1635937238list_a: list_set_list_a > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.30/0.46 size_s577819178et_nat: list_set_nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.30/0.46 size_size_list_set_a: list_set_a > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 size_size_list_a: list_a > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.30/0.46 ord_less_nat: nat > nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.30/0.46 ord_less_eq_nat: nat > nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.30/0.46 ord_le1756736906list_a: set_list_list_a > set_list_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.30/0.46 ord_le1747345782st_nat: set_list_nat > set_list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 ord_le1301786372list_a: set_list_a > set_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.46 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.46 top_top_set_nat: set_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 0.30/0.46 divide_divide_nat: nat > nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 collect_list_a: ( list_a > $o ) > set_list_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.30/0.46 collect_nat: ( nat > $o ) > set_nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.30/0.46 collect_a: ( a > $o ) > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.30/0.46 member_list_list_a: list_list_a > set_list_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.46 member_list_nat: list_nat > set_list_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__List__Olist_Itf__a_J,type,
% 0.30/0.46 member_list_a: list_a > set_list_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Nat__Onat,type,
% 0.30/0.46 member_nat: nat > set_nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001tf__a,type,
% 0.30/0.46 member_a: a > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_k,type,
% 0.30/0.46 k: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_m,type,
% 0.30/0.46 m: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_xs,type,
% 0.30/0.46 xs: list_a ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (348)
% 0.30/0.46 thf(fact_0_nth__equalityI,axiom,
% 0.30/0.46 ! [Xs: list_list_nat,Ys: list_list_nat] :
% 0.30/0.46 ( ( ( size_s1898481668st_nat @ Xs )
% 0.30/0.46 = ( size_s1898481668st_nat @ Ys ) )
% 0.30/0.46 => ( ! [I: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.46 => ( ( nth_list_nat @ Xs @ I )
% 0.30/0.46 = ( nth_list_nat @ Ys @ I ) ) )
% 0.30/0.46 => ( Xs = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nth_equalityI
% 0.30/0.46 thf(fact_1_nth__equalityI,axiom,
% 0.30/0.46 ! [Xs: list_list_list_a,Ys: list_list_list_a] :
% 0.30/0.46 ( ( ( size_s575106428list_a @ Xs )
% 0.30/0.46 = ( size_s575106428list_a @ Ys ) )
% 0.30/0.46 => ( ! [I: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.46 => ( ( nth_list_list_a @ Xs @ I )
% 0.30/0.46 = ( nth_list_list_a @ Ys @ I ) ) )
% 0.30/0.46 => ( Xs = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nth_equalityI
% 0.30/0.46 thf(fact_2_nth__equalityI,axiom,
% 0.30/0.46 ! [Xs: list_nat,Ys: list_nat] :
% 0.30/0.46 ( ( ( size_size_list_nat @ Xs )
% 0.30/0.46 = ( size_size_list_nat @ Ys ) )
% 0.30/0.46 => ( ! [I: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.30/0.46 => ( ( nth_nat @ Xs @ I )
% 0.30/0.46 = ( nth_nat @ Ys @ I ) ) )
% 0.30/0.46 => ( Xs = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nth_equalityI
% 0.30/0.46 thf(fact_3_nth__equalityI,axiom,
% 0.30/0.46 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.30/0.46 ( ( ( size_s1427607542list_a @ Xs )
% 0.30/0.46 = ( size_s1427607542list_a @ Ys ) )
% 0.30/0.46 => ( ! [I: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.46 => ( ( nth_list_a @ Xs @ I )
% 0.30/0.46 = ( nth_list_a @ Ys @ I ) ) )
% 0.30/0.46 => ( Xs = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nth_equalityI
% 0.30/0.46 thf(fact_4_nth__equalityI,axiom,
% 0.30/0.46 ! [Xs: list_a,Ys: list_a] :
% 0.30/0.46 ( ( ( size_size_list_a @ Xs )
% 0.30/0.46 = ( size_size_list_a @ Ys ) )
% 0.30/0.46 => ( ! [I: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 0.30/0.46 => ( ( nth_a @ Xs @ I )
% 0.30/0.46 = ( nth_a @ Ys @ I ) ) )
% 0.30/0.46 => ( Xs = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nth_equalityI
% 0.30/0.46 thf(fact_5_Skolem__list__nth,axiom,
% 0.30/0.46 ! [K: nat,P: nat > list_nat > $o] :
% 0.30/0.46 ( ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ? [X: list_nat] : ( P @ I2 @ X ) ) )
% 0.30/0.46 = ( ? [Xs2: list_list_nat] :
% 0.30/0.46 ( ( ( size_s1898481668st_nat @ Xs2 )
% 0.30/0.46 = K )
% 0.30/0.46 & ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ( P @ I2 @ ( nth_list_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Skolem_list_nth
% 0.30/0.46 thf(fact_6_Skolem__list__nth,axiom,
% 0.30/0.46 ! [K: nat,P: nat > list_list_a > $o] :
% 0.30/0.46 ( ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ? [X: list_list_a] : ( P @ I2 @ X ) ) )
% 0.30/0.46 = ( ? [Xs2: list_list_list_a] :
% 0.30/0.46 ( ( ( size_s575106428list_a @ Xs2 )
% 0.30/0.46 = K )
% 0.30/0.46 & ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ( P @ I2 @ ( nth_list_list_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Skolem_list_nth
% 0.30/0.46 thf(fact_7_Skolem__list__nth,axiom,
% 0.30/0.46 ! [K: nat,P: nat > nat > $o] :
% 0.30/0.46 ( ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ? [X: nat] : ( P @ I2 @ X ) ) )
% 0.30/0.46 = ( ? [Xs2: list_nat] :
% 0.30/0.46 ( ( ( size_size_list_nat @ Xs2 )
% 0.30/0.46 = K )
% 0.30/0.46 & ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ( P @ I2 @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Skolem_list_nth
% 0.30/0.46 thf(fact_8_Skolem__list__nth,axiom,
% 0.30/0.46 ! [K: nat,P: nat > list_a > $o] :
% 0.30/0.46 ( ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ? [X: list_a] : ( P @ I2 @ X ) ) )
% 0.30/0.46 = ( ? [Xs2: list_list_a] :
% 0.30/0.46 ( ( ( size_s1427607542list_a @ Xs2 )
% 0.30/0.46 = K )
% 0.30/0.46 & ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ( P @ I2 @ ( nth_list_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Skolem_list_nth
% 0.30/0.46 thf(fact_9_Skolem__list__nth,axiom,
% 0.30/0.46 ! [K: nat,P: nat > a > $o] :
% 0.30/0.46 ( ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ? [X: a] : ( P @ I2 @ X ) ) )
% 0.30/0.46 = ( ? [Xs2: list_a] :
% 0.30/0.46 ( ( ( size_size_list_a @ Xs2 )
% 0.30/0.46 = K )
% 0.30/0.46 & ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.30/0.46 => ( P @ I2 @ ( nth_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Skolem_list_nth
% 0.30/0.46 thf(fact_10_list__eq__iff__nth__eq,axiom,
% 0.30/0.46 ( ( ^ [Y: list_list_nat,Z: list_list_nat] : ( Y = Z ) )
% 0.30/0.47 = ( ^ [Xs2: list_list_nat,Ys2: list_list_nat] :
% 0.30/0.47 ( ( ( size_s1898481668st_nat @ Xs2 )
% 0.30/0.47 = ( size_s1898481668st_nat @ Ys2 ) )
% 0.30/0.47 & ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_s1898481668st_nat @ Xs2 ) )
% 0.30/0.47 => ( ( nth_list_nat @ Xs2 @ I2 )
% 0.30/0.47 = ( nth_list_nat @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_eq_iff_nth_eq
% 0.30/0.47 thf(fact_11_list__eq__iff__nth__eq,axiom,
% 0.30/0.47 ( ( ^ [Y: list_list_list_a,Z: list_list_list_a] : ( Y = Z ) )
% 0.30/0.47 = ( ^ [Xs2: list_list_list_a,Ys2: list_list_list_a] :
% 0.30/0.47 ( ( ( size_s575106428list_a @ Xs2 )
% 0.30/0.47 = ( size_s575106428list_a @ Ys2 ) )
% 0.30/0.47 & ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_s575106428list_a @ Xs2 ) )
% 0.30/0.47 => ( ( nth_list_list_a @ Xs2 @ I2 )
% 0.30/0.47 = ( nth_list_list_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_eq_iff_nth_eq
% 0.30/0.47 thf(fact_12_list__eq__iff__nth__eq,axiom,
% 0.30/0.47 ( ( ^ [Y: list_nat,Z: list_nat] : ( Y = Z ) )
% 0.30/0.47 = ( ^ [Xs2: list_nat,Ys2: list_nat] :
% 0.30/0.47 ( ( ( size_size_list_nat @ Xs2 )
% 0.30/0.47 = ( size_size_list_nat @ Ys2 ) )
% 0.30/0.47 & ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 => ( ( nth_nat @ Xs2 @ I2 )
% 0.30/0.47 = ( nth_nat @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_eq_iff_nth_eq
% 0.30/0.47 thf(fact_13_list__eq__iff__nth__eq,axiom,
% 0.30/0.47 ( ( ^ [Y: list_list_a,Z: list_list_a] : ( Y = Z ) )
% 0.30/0.47 = ( ^ [Xs2: list_list_a,Ys2: list_list_a] :
% 0.30/0.47 ( ( ( size_s1427607542list_a @ Xs2 )
% 0.30/0.47 = ( size_s1427607542list_a @ Ys2 ) )
% 0.30/0.47 & ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
% 0.30/0.47 => ( ( nth_list_a @ Xs2 @ I2 )
% 0.30/0.47 = ( nth_list_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_eq_iff_nth_eq
% 0.30/0.47 thf(fact_14_list__eq__iff__nth__eq,axiom,
% 0.30/0.47 ( ( ^ [Y: list_a,Z: list_a] : ( Y = Z ) )
% 0.30/0.47 = ( ^ [Xs2: list_a,Ys2: list_a] :
% 0.30/0.47 ( ( ( size_size_list_a @ Xs2 )
% 0.30/0.47 = ( size_size_list_a @ Ys2 ) )
% 0.30/0.47 & ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
% 0.30/0.47 => ( ( nth_a @ Xs2 @ I2 )
% 0.30/0.47 = ( nth_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_eq_iff_nth_eq
% 0.30/0.47 thf(fact_15_list__slice2__list__slice__nth,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_list_nat,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs ) @ K ) )
% 0.30/0.47 => ( ( nth_list_list_nat @ ( listSl2099749758st_nat @ Xs @ K ) @ M )
% 0.30/0.47 = ( nth_list_list_nat @ ( listSl729562870st_nat @ Xs @ K ) @ M ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice2_list_slice_nth
% 0.30/0.47 thf(fact_16_list__slice2__list__slice__nth,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_list_list_a,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s575106428list_a @ Xs ) @ K ) )
% 0.30/0.47 => ( ( nth_list_list_list_a @ ( listSl769338732list_a @ Xs @ K ) @ M )
% 0.30/0.47 = ( nth_list_list_list_a @ ( listSl2102238196list_a @ Xs @ K ) @ M ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice2_list_slice_nth
% 0.30/0.47 thf(fact_17_list__slice2__list__slice__nth,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_list_a,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1427607542list_a @ Xs ) @ K ) )
% 0.30/0.47 => ( ( nth_list_list_a @ ( listSl703198822list_a @ Xs @ K ) @ M )
% 0.30/0.47 = ( nth_list_list_a @ ( listSl162220270list_a @ Xs @ K ) @ M ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice2_list_slice_nth
% 0.30/0.47 thf(fact_18_list__slice2__list__slice__nth,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_nat,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_nat @ Xs ) @ K ) )
% 0.30/0.47 => ( ( nth_list_nat @ ( listSl882585454e2_nat @ Xs @ K ) @ M )
% 0.30/0.47 = ( nth_list_nat @ ( listSl1630398182ce_nat @ Xs @ K ) @ M ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice2_list_slice_nth
% 0.30/0.47 thf(fact_19_list__slice2__list__slice__nth,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_a,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
% 0.30/0.47 => ( ( nth_list_a @ ( listSl1174287072ice2_a @ Xs @ K ) @ M )
% 0.30/0.47 = ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice2_list_slice_nth
% 0.30/0.47 thf(fact_20_length__induct,axiom,
% 0.30/0.47 ! [P: list_list_nat > $o,Xs: list_list_nat] :
% 0.30/0.47 ( ! [Xs3: list_list_nat] :
% 0.30/0.47 ( ! [Ys3: list_list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ ( size_s1898481668st_nat @ Ys3 ) @ ( size_s1898481668st_nat @ Xs3 ) )
% 0.30/0.47 => ( P @ Ys3 ) )
% 0.30/0.47 => ( P @ Xs3 ) )
% 0.30/0.47 => ( P @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_induct
% 0.30/0.47 thf(fact_21_length__induct,axiom,
% 0.30/0.47 ! [P: list_list_list_a > $o,Xs: list_list_list_a] :
% 0.30/0.47 ( ! [Xs3: list_list_list_a] :
% 0.30/0.47 ( ! [Ys3: list_list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ ( size_s575106428list_a @ Ys3 ) @ ( size_s575106428list_a @ Xs3 ) )
% 0.30/0.47 => ( P @ Ys3 ) )
% 0.30/0.47 => ( P @ Xs3 ) )
% 0.30/0.47 => ( P @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_induct
% 0.30/0.47 thf(fact_22_length__induct,axiom,
% 0.30/0.47 ! [P: list_list_a > $o,Xs: list_list_a] :
% 0.30/0.47 ( ! [Xs3: list_list_a] :
% 0.30/0.47 ( ! [Ys3: list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ ( size_s1427607542list_a @ Ys3 ) @ ( size_s1427607542list_a @ Xs3 ) )
% 0.30/0.47 => ( P @ Ys3 ) )
% 0.30/0.47 => ( P @ Xs3 ) )
% 0.30/0.47 => ( P @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_induct
% 0.30/0.47 thf(fact_23_length__induct,axiom,
% 0.30/0.47 ! [P: list_nat > $o,Xs: list_nat] :
% 0.30/0.47 ( ! [Xs3: list_nat] :
% 0.30/0.47 ( ! [Ys3: list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ ( size_size_list_nat @ Ys3 ) @ ( size_size_list_nat @ Xs3 ) )
% 0.30/0.47 => ( P @ Ys3 ) )
% 0.30/0.47 => ( P @ Xs3 ) )
% 0.30/0.47 => ( P @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_induct
% 0.30/0.47 thf(fact_24_length__induct,axiom,
% 0.30/0.47 ! [P: list_a > $o,Xs: list_a] :
% 0.30/0.47 ( ! [Xs3: list_a] :
% 0.30/0.47 ( ! [Ys3: list_a] :
% 0.30/0.47 ( ( ord_less_nat @ ( size_size_list_a @ Ys3 ) @ ( size_size_list_a @ Xs3 ) )
% 0.30/0.47 => ( P @ Ys3 ) )
% 0.30/0.47 => ( P @ Xs3 ) )
% 0.30/0.47 => ( P @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_induct
% 0.30/0.47 thf(fact_25_list__strict__desc__trans,axiom,
% 0.30/0.47 ( list_strict_desc_nat
% 0.30/0.47 = ( ^ [Xs2: list_nat] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_strict_desc_trans
% 0.30/0.47 thf(fact_26_list__slice__nth__length,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_list_nat,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs ) @ K ) )
% 0.30/0.47 => ( ( size_s1898481668st_nat @ ( nth_list_list_nat @ ( listSl729562870st_nat @ Xs @ K ) @ M ) )
% 0.30/0.47 = K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_nth_length
% 0.30/0.47 thf(fact_27_list__slice__nth__length,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_list_list_a,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s575106428list_a @ Xs ) @ K ) )
% 0.30/0.47 => ( ( size_s575106428list_a @ ( nth_list_list_list_a @ ( listSl2102238196list_a @ Xs @ K ) @ M ) )
% 0.30/0.47 = K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_nth_length
% 0.30/0.47 thf(fact_28_list__slice__nth__length,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_list_a,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1427607542list_a @ Xs ) @ K ) )
% 0.30/0.47 => ( ( size_s1427607542list_a @ ( nth_list_list_a @ ( listSl162220270list_a @ Xs @ K ) @ M ) )
% 0.30/0.47 = K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_nth_length
% 0.30/0.47 thf(fact_29_list__slice__nth__length,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_nat,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_nat @ Xs ) @ K ) )
% 0.30/0.47 => ( ( size_size_list_nat @ ( nth_list_nat @ ( listSl1630398182ce_nat @ Xs @ K ) @ M ) )
% 0.30/0.47 = K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_nth_length
% 0.30/0.47 thf(fact_30_list__slice__nth__length,axiom,
% 0.30/0.47 ! [M: nat,Xs: list_a,K: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
% 0.30/0.47 => ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) )
% 0.30/0.47 = K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_nth_length
% 0.30/0.47 thf(fact_31_list__strict__asc__trans,axiom,
% 0.30/0.47 ( list_strict_asc_nat
% 0.30/0.47 = ( ^ [Xs2: list_nat] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_strict_asc_trans
% 0.30/0.47 thf(fact_32_Ex__list__of__length,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ? [Xs3: list_list_nat] :
% 0.30/0.47 ( ( size_s1898481668st_nat @ Xs3 )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % Ex_list_of_length
% 0.30/0.47 thf(fact_33_Ex__list__of__length,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ? [Xs3: list_list_list_a] :
% 0.30/0.47 ( ( size_s575106428list_a @ Xs3 )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % Ex_list_of_length
% 0.30/0.47 thf(fact_34_Ex__list__of__length,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ? [Xs3: list_list_a] :
% 0.30/0.47 ( ( size_s1427607542list_a @ Xs3 )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % Ex_list_of_length
% 0.30/0.47 thf(fact_35_Ex__list__of__length,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ? [Xs3: list_nat] :
% 0.30/0.47 ( ( size_size_list_nat @ Xs3 )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % Ex_list_of_length
% 0.30/0.47 thf(fact_36_Ex__list__of__length,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ? [Xs3: list_a] :
% 0.30/0.47 ( ( size_size_list_a @ Xs3 )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % Ex_list_of_length
% 0.30/0.47 thf(fact_37_neq__if__length__neq,axiom,
% 0.30/0.47 ! [Xs: list_list_nat,Ys: list_list_nat] :
% 0.30/0.47 ( ( ( size_s1898481668st_nat @ Xs )
% 0.30/0.47 != ( size_s1898481668st_nat @ Ys ) )
% 0.30/0.47 => ( Xs != Ys ) ) ).
% 0.30/0.47
% 0.30/0.47 % neq_if_length_neq
% 0.30/0.47 thf(fact_38_neq__if__length__neq,axiom,
% 0.30/0.47 ! [Xs: list_list_list_a,Ys: list_list_list_a] :
% 0.30/0.47 ( ( ( size_s575106428list_a @ Xs )
% 0.30/0.47 != ( size_s575106428list_a @ Ys ) )
% 0.30/0.47 => ( Xs != Ys ) ) ).
% 0.30/0.47
% 0.30/0.47 % neq_if_length_neq
% 0.30/0.47 thf(fact_39_neq__if__length__neq,axiom,
% 0.30/0.47 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.30/0.47 ( ( ( size_s1427607542list_a @ Xs )
% 0.30/0.47 != ( size_s1427607542list_a @ Ys ) )
% 0.30/0.47 => ( Xs != Ys ) ) ).
% 0.30/0.47
% 0.30/0.47 % neq_if_length_neq
% 0.30/0.47 thf(fact_40_neq__if__length__neq,axiom,
% 0.30/0.47 ! [Xs: list_nat,Ys: list_nat] :
% 0.30/0.47 ( ( ( size_size_list_nat @ Xs )
% 0.30/0.47 != ( size_size_list_nat @ Ys ) )
% 0.30/0.47 => ( Xs != Ys ) ) ).
% 0.30/0.47
% 0.30/0.47 % neq_if_length_neq
% 0.30/0.47 thf(fact_41_neq__if__length__neq,axiom,
% 0.30/0.47 ! [Xs: list_a,Ys: list_a] :
% 0.30/0.47 ( ( ( size_size_list_a @ Xs )
% 0.30/0.47 != ( size_size_list_a @ Ys ) )
% 0.30/0.47 => ( Xs != Ys ) ) ).
% 0.30/0.47
% 0.30/0.47 % neq_if_length_neq
% 0.30/0.47 thf(fact_42_size__neq__size__imp__neq,axiom,
% 0.30/0.47 ! [X2: list_list_nat,Y2: list_list_nat] :
% 0.30/0.47 ( ( ( size_s1898481668st_nat @ X2 )
% 0.30/0.47 != ( size_s1898481668st_nat @ Y2 ) )
% 0.30/0.47 => ( X2 != Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % size_neq_size_imp_neq
% 0.30/0.47 thf(fact_43_size__neq__size__imp__neq,axiom,
% 0.30/0.47 ! [X2: list_list_list_a,Y2: list_list_list_a] :
% 0.30/0.47 ( ( ( size_s575106428list_a @ X2 )
% 0.30/0.47 != ( size_s575106428list_a @ Y2 ) )
% 0.30/0.47 => ( X2 != Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % size_neq_size_imp_neq
% 0.30/0.47 thf(fact_44_size__neq__size__imp__neq,axiom,
% 0.30/0.47 ! [X2: list_a,Y2: list_a] :
% 0.30/0.47 ( ( ( size_size_list_a @ X2 )
% 0.30/0.47 != ( size_size_list_a @ Y2 ) )
% 0.30/0.47 => ( X2 != Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % size_neq_size_imp_neq
% 0.30/0.47 thf(fact_45_size__neq__size__imp__neq,axiom,
% 0.30/0.47 ! [X2: list_list_a,Y2: list_list_a] :
% 0.30/0.47 ( ( ( size_s1427607542list_a @ X2 )
% 0.30/0.47 != ( size_s1427607542list_a @ Y2 ) )
% 0.30/0.47 => ( X2 != Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % size_neq_size_imp_neq
% 0.30/0.47 thf(fact_46_size__neq__size__imp__neq,axiom,
% 0.30/0.47 ! [X2: list_nat,Y2: list_nat] :
% 0.30/0.47 ( ( ( size_size_list_nat @ X2 )
% 0.30/0.47 != ( size_size_list_nat @ Y2 ) )
% 0.30/0.47 => ( X2 != Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % size_neq_size_imp_neq
% 0.30/0.47 thf(fact_47_nat__neq__iff,axiom,
% 0.30/0.47 ! [M: nat,N: nat] :
% 0.30/0.47 ( ( M != N )
% 0.30/0.47 = ( ( ord_less_nat @ M @ N )
% 0.30/0.47 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nat_neq_iff
% 0.30/0.47 thf(fact_48_list__slice__length,axiom,
% 0.30/0.47 ! [Xs: list_list_nat,K: nat] :
% 0.30/0.47 ( ( size_s1321307156st_nat @ ( listSl729562870st_nat @ Xs @ K ) )
% 0.30/0.47 = ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs ) @ K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_length
% 0.30/0.47 thf(fact_49_list__slice__length,axiom,
% 0.30/0.47 ! [Xs: list_list_list_a,K: nat] :
% 0.30/0.47 ( ( size_s1764310658list_a @ ( listSl2102238196list_a @ Xs @ K ) )
% 0.30/0.47 = ( divide_divide_nat @ ( size_s575106428list_a @ Xs ) @ K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_length
% 0.30/0.47 thf(fact_50_list__slice__length,axiom,
% 0.30/0.47 ! [Xs: list_list_a,K: nat] :
% 0.30/0.47 ( ( size_s575106428list_a @ ( listSl162220270list_a @ Xs @ K ) )
% 0.30/0.47 = ( divide_divide_nat @ ( size_s1427607542list_a @ Xs ) @ K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_length
% 0.30/0.47 thf(fact_51_list__slice__length,axiom,
% 0.30/0.47 ! [Xs: list_nat,K: nat] :
% 0.30/0.47 ( ( size_s1898481668st_nat @ ( listSl1630398182ce_nat @ Xs @ K ) )
% 0.30/0.47 = ( divide_divide_nat @ ( size_size_list_nat @ Xs ) @ K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_length
% 0.30/0.47 thf(fact_52_list__slice__length,axiom,
% 0.30/0.47 ! [Xs: list_a,K: nat] :
% 0.30/0.47 ( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
% 0.30/0.47 = ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_length
% 0.30/0.47 thf(fact_53_linorder__neqE__nat,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( X2 != Y2 )
% 0.30/0.47 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_neqE_nat
% 0.30/0.47 thf(fact_54_infinite__descent,axiom,
% 0.30/0.47 ! [P: nat > $o,N: nat] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ~ ( P @ N2 )
% 0.30/0.47 => ? [M2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.30/0.47 & ~ ( P @ M2 ) ) )
% 0.30/0.47 => ( P @ N ) ) ).
% 0.30/0.47
% 0.30/0.47 % infinite_descent
% 0.30/0.47 thf(fact_55_nat__less__induct,axiom,
% 0.30/0.47 ! [P: nat > $o,N: nat] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ! [M2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.30/0.47 => ( P @ M2 ) )
% 0.30/0.47 => ( P @ N2 ) )
% 0.30/0.47 => ( P @ N ) ) ).
% 0.30/0.47
% 0.30/0.47 % nat_less_induct
% 0.30/0.47 thf(fact_56_less__irrefl__nat,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/0.47
% 0.30/0.47 % less_irrefl_nat
% 0.30/0.47 thf(fact_57_less__not__refl3,axiom,
% 0.30/0.47 ! [S: nat,T: nat] :
% 0.30/0.47 ( ( ord_less_nat @ S @ T )
% 0.30/0.47 => ( S != T ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_not_refl3
% 0.30/0.47 thf(fact_58_less__not__refl2,axiom,
% 0.30/0.47 ! [N: nat,M: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N @ M )
% 0.30/0.47 => ( M != N ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_not_refl2
% 0.30/0.47 thf(fact_59_less__not__refl,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/0.47
% 0.30/0.47 % less_not_refl
% 0.30/0.47 thf(fact_60_list__slice__def,axiom,
% 0.30/0.47 ( listSl729562870st_nat
% 0.30/0.47 = ( ^ [Xs2: list_list_nat,K2: nat] : ( listSl1506485424st_nat @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs2 ) @ K2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_def
% 0.30/0.47 thf(fact_61_list__slice__def,axiom,
% 0.30/0.47 ( listSl2102238196list_a
% 0.30/0.47 = ( ^ [Xs2: list_list_list_a,K2: nat] : ( listSl902632890list_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_s575106428list_a @ Xs2 ) @ K2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_def
% 0.30/0.47 thf(fact_62_list__slice__def,axiom,
% 0.30/0.47 ( listSl162220270list_a
% 0.30/0.47 = ( ^ [Xs2: list_list_a,K2: nat] : ( listSl856612276list_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_s1427607542list_a @ Xs2 ) @ K2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_def
% 0.30/0.47 thf(fact_63_list__slice__def,axiom,
% 0.30/0.47 ( listSl1630398182ce_nat
% 0.30/0.47 = ( ^ [Xs2: list_nat,K2: nat] : ( listSl1794011552ux_nat @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_nat @ Xs2 ) @ K2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_def
% 0.30/0.47 thf(fact_64_list__slice__def,axiom,
% 0.30/0.47 ( listSl97544552lice_a
% 0.30/0.47 = ( ^ [Xs2: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs2 ) @ K2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_def
% 0.30/0.47 thf(fact_65_list__strict__desc__imp__list__desc,axiom,
% 0.30/0.47 ! [Xs: list_nat] :
% 0.30/0.47 ( ( list_strict_desc_nat @ Xs )
% 0.30/0.47 => ( list_desc_nat @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_strict_desc_imp_list_desc
% 0.30/0.47 thf(fact_66_list__ex__length,axiom,
% 0.30/0.47 ( list_ex_list_nat
% 0.30/0.47 = ( ^ [P2: list_nat > $o,Xs2: list_list_nat] :
% 0.30/0.47 ? [N3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N3 @ ( size_s1898481668st_nat @ Xs2 ) )
% 0.30/0.47 & ( P2 @ ( nth_list_nat @ Xs2 @ N3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex_length
% 0.30/0.47 thf(fact_67_list__ex__length,axiom,
% 0.30/0.47 ( list_ex_list_list_a
% 0.30/0.47 = ( ^ [P2: list_list_a > $o,Xs2: list_list_list_a] :
% 0.30/0.47 ? [N3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N3 @ ( size_s575106428list_a @ Xs2 ) )
% 0.30/0.47 & ( P2 @ ( nth_list_list_a @ Xs2 @ N3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex_length
% 0.30/0.47 thf(fact_68_list__ex__length,axiom,
% 0.30/0.47 ( list_ex_a
% 0.30/0.47 = ( ^ [P2: a > $o,Xs2: list_a] :
% 0.30/0.47 ? [N3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N3 @ ( size_size_list_a @ Xs2 ) )
% 0.30/0.47 & ( P2 @ ( nth_a @ Xs2 @ N3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex_length
% 0.30/0.47 thf(fact_69_list__ex__length,axiom,
% 0.30/0.47 ( list_ex_list_a
% 0.30/0.47 = ( ^ [P2: list_a > $o,Xs2: list_list_a] :
% 0.30/0.47 ? [N3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N3 @ ( size_s1427607542list_a @ Xs2 ) )
% 0.30/0.47 & ( P2 @ ( nth_list_a @ Xs2 @ N3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex_length
% 0.30/0.47 thf(fact_70_list__ex__length,axiom,
% 0.30/0.47 ( list_ex_nat
% 0.30/0.47 = ( ^ [P2: nat > $o,Xs2: list_nat] :
% 0.30/0.47 ? [N3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N3 @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 & ( P2 @ ( nth_nat @ Xs2 @ N3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex_length
% 0.30/0.47 thf(fact_71_f__image__eqI,axiom,
% 0.30/0.47 ! [X2: list_nat,Xs: list_list_nat,N: nat,A: set_nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_list_nat @ Xs @ N ) )
% 0.30/0.47 => ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_eqI
% 0.30/0.47 thf(fact_72_f__image__eqI,axiom,
% 0.30/0.47 ! [X2: list_list_a,Xs: list_list_list_a,N: nat,A: set_nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_list_list_a @ Xs @ N ) )
% 0.30/0.47 => ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_eqI
% 0.30/0.47 thf(fact_73_f__image__eqI,axiom,
% 0.30/0.47 ! [X2: a,Xs: list_a,N: nat,A: set_nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_a @ Xs @ N ) )
% 0.30/0.47 => ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( member_a @ X2 @ ( f_image_a @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_eqI
% 0.30/0.47 thf(fact_74_f__image__eqI,axiom,
% 0.30/0.47 ! [X2: list_a,Xs: list_list_a,N: nat,A: set_nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_list_a @ Xs @ N ) )
% 0.30/0.47 => ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_eqI
% 0.30/0.47 thf(fact_75_f__image__eqI,axiom,
% 0.30/0.47 ! [X2: nat,Xs: list_nat,N: nat,A: set_nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_nat @ Xs @ N ) )
% 0.30/0.47 => ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_eqI
% 0.30/0.47 thf(fact_76_list__strict__asc__imp__list__asc,axiom,
% 0.30/0.47 ! [Xs: list_nat] :
% 0.30/0.47 ( ( list_strict_asc_nat @ Xs )
% 0.30/0.47 => ( list_asc_nat @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_strict_asc_imp_list_asc
% 0.30/0.47 thf(fact_77_nth__list__update__eq,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_nat,X2: list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ I3 )
% 0.30/0.47 = X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_eq
% 0.30/0.47 thf(fact_78_nth__list__update__eq,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_list_a,X2: list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ I3 )
% 0.30/0.47 = X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_eq
% 0.30/0.47 thf(fact_79_nth__list__update__eq,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_a,X2: a] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I3 )
% 0.30/0.47 = X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_eq
% 0.30/0.47 thf(fact_80_nth__list__update__eq,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_a,X2: list_a] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I3 )
% 0.30/0.47 = X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_eq
% 0.30/0.47 thf(fact_81_nth__list__update__eq,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_nat,X2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I3 )
% 0.30/0.47 = X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_eq
% 0.30/0.47 thf(fact_82_rev__f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_list_nat,X2: list_nat] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( ( X2
% 0.30/0.47 = ( nth_list_nat @ Xs @ N ) )
% 0.30/0.47 => ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rev_f_imageI
% 0.30/0.47 thf(fact_83_rev__f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_list_list_a,X2: list_list_a] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( ( X2
% 0.30/0.47 = ( nth_list_list_a @ Xs @ N ) )
% 0.30/0.47 => ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rev_f_imageI
% 0.30/0.47 thf(fact_84_rev__f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_a,X2: a] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( X2
% 0.30/0.47 = ( nth_a @ Xs @ N ) )
% 0.30/0.47 => ( member_a @ X2 @ ( f_image_a @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rev_f_imageI
% 0.30/0.47 thf(fact_85_rev__f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_list_a,X2: list_a] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( X2
% 0.30/0.47 = ( nth_list_a @ Xs @ N ) )
% 0.30/0.47 => ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rev_f_imageI
% 0.30/0.47 thf(fact_86_rev__f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_nat,X2: nat] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( X2
% 0.30/0.47 = ( nth_nat @ Xs @ N ) )
% 0.30/0.47 => ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rev_f_imageI
% 0.30/0.47 thf(fact_87_f__image__iff,axiom,
% 0.30/0.47 ! [X2: list_nat,Xs: list_list_nat,A: set_nat] :
% 0.30/0.47 ( ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) )
% 0.30/0.47 = ( ? [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 & ( ord_less_nat @ X3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 & ( X2
% 0.30/0.47 = ( nth_list_nat @ Xs @ X3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_iff
% 0.30/0.47 thf(fact_88_f__image__iff,axiom,
% 0.30/0.47 ! [X2: list_list_a,Xs: list_list_list_a,A: set_nat] :
% 0.30/0.47 ( ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) )
% 0.30/0.47 = ( ? [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 & ( ord_less_nat @ X3 @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 & ( X2
% 0.30/0.47 = ( nth_list_list_a @ Xs @ X3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_iff
% 0.30/0.47 thf(fact_89_f__image__iff,axiom,
% 0.30/0.47 ! [X2: a,Xs: list_a,A: set_nat] :
% 0.30/0.47 ( ( member_a @ X2 @ ( f_image_a @ Xs @ A ) )
% 0.30/0.47 = ( ? [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 & ( ord_less_nat @ X3 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 & ( X2
% 0.30/0.47 = ( nth_a @ Xs @ X3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_iff
% 0.30/0.47 thf(fact_90_f__image__iff,axiom,
% 0.30/0.47 ! [X2: list_a,Xs: list_list_a,A: set_nat] :
% 0.30/0.47 ( ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) )
% 0.30/0.47 = ( ? [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 & ( ord_less_nat @ X3 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 & ( X2
% 0.30/0.47 = ( nth_list_a @ Xs @ X3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_iff
% 0.30/0.47 thf(fact_91_f__image__iff,axiom,
% 0.30/0.47 ! [X2: nat,Xs: list_nat,A: set_nat] :
% 0.30/0.47 ( ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) )
% 0.30/0.47 = ( ? [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 & ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 & ( X2
% 0.30/0.47 = ( nth_nat @ Xs @ X3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_iff
% 0.30/0.47 thf(fact_92_nth__butlast,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ ( butlast_list_nat @ Xs ) ) )
% 0.30/0.47 => ( ( nth_list_nat @ ( butlast_list_nat @ Xs ) @ N )
% 0.30/0.47 = ( nth_list_nat @ Xs @ N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_butlast
% 0.30/0.47 thf(fact_93_nth__butlast,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_s575106428list_a @ ( butlast_list_list_a @ Xs ) ) )
% 0.30/0.47 => ( ( nth_list_list_a @ ( butlast_list_list_a @ Xs ) @ N )
% 0.30/0.47 = ( nth_list_list_a @ Xs @ N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_butlast
% 0.30/0.47 thf(fact_94_nth__butlast,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ ( butlast_a @ Xs ) ) )
% 0.30/0.47 => ( ( nth_a @ ( butlast_a @ Xs ) @ N )
% 0.30/0.47 = ( nth_a @ Xs @ N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_butlast
% 0.30/0.47 thf(fact_95_nth__butlast,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ ( butlast_list_a @ Xs ) ) )
% 0.30/0.47 => ( ( nth_list_a @ ( butlast_list_a @ Xs ) @ N )
% 0.30/0.47 = ( nth_list_a @ Xs @ N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_butlast
% 0.30/0.47 thf(fact_96_nth__butlast,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ ( butlast_nat @ Xs ) ) )
% 0.30/0.47 => ( ( nth_nat @ ( butlast_nat @ Xs ) @ N )
% 0.30/0.47 = ( nth_nat @ Xs @ N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_butlast
% 0.30/0.47 thf(fact_97_f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_list_nat] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( member_list_nat @ ( nth_list_nat @ Xs @ N ) @ ( f_image_list_nat @ Xs @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageI
% 0.30/0.47 thf(fact_98_f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_list_list_a] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( member_list_list_a @ ( nth_list_list_a @ Xs @ N ) @ ( f_image_list_list_a @ Xs @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageI
% 0.30/0.47 thf(fact_99_f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_a] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( member_a @ ( nth_a @ Xs @ N ) @ ( f_image_a @ Xs @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageI
% 0.30/0.47 thf(fact_100_f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_list_a] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ N ) @ ( f_image_list_a @ Xs @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageI
% 0.30/0.47 thf(fact_101_f__imageI,axiom,
% 0.30/0.47 ! [N: nat,A: set_nat,Xs: list_nat] :
% 0.30/0.47 ( ( member_nat @ N @ A )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( f_image_nat @ Xs @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageI
% 0.30/0.47 thf(fact_102_f__imageE,axiom,
% 0.30/0.47 ! [X2: list_nat,Xs: list_list_nat,A: set_nat] :
% 0.30/0.47 ( ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_list_nat @ Xs @ N2 ) )
% 0.30/0.47 => ( ( member_nat @ N2 @ A )
% 0.30/0.47 => ~ ( ord_less_nat @ N2 @ ( size_s1898481668st_nat @ Xs ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageE
% 0.30/0.47 thf(fact_103_f__imageE,axiom,
% 0.30/0.47 ! [X2: list_list_a,Xs: list_list_list_a,A: set_nat] :
% 0.30/0.47 ( ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_list_list_a @ Xs @ N2 ) )
% 0.30/0.47 => ( ( member_nat @ N2 @ A )
% 0.30/0.47 => ~ ( ord_less_nat @ N2 @ ( size_s575106428list_a @ Xs ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageE
% 0.30/0.47 thf(fact_104_f__imageE,axiom,
% 0.30/0.47 ! [X2: a,Xs: list_a,A: set_nat] :
% 0.30/0.47 ( ( member_a @ X2 @ ( f_image_a @ Xs @ A ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_a @ Xs @ N2 ) )
% 0.30/0.47 => ( ( member_nat @ N2 @ A )
% 0.30/0.47 => ~ ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageE
% 0.30/0.47 thf(fact_105_f__imageE,axiom,
% 0.30/0.47 ! [X2: list_a,Xs: list_list_a,A: set_nat] :
% 0.30/0.47 ( ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_list_a @ Xs @ N2 ) )
% 0.30/0.47 => ( ( member_nat @ N2 @ A )
% 0.30/0.47 => ~ ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageE
% 0.30/0.47 thf(fact_106_f__imageE,axiom,
% 0.30/0.47 ! [X2: nat,Xs: list_nat,A: set_nat] :
% 0.30/0.47 ( ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_nat @ Xs @ N2 ) )
% 0.30/0.47 => ( ( member_nat @ N2 @ A )
% 0.30/0.47 => ~ ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_imageE
% 0.30/0.47 thf(fact_107_list__update__overwrite,axiom,
% 0.30/0.47 ! [Xs: list_nat,I3: nat,X2: nat,Y2: nat] :
% 0.30/0.47 ( ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I3 @ Y2 )
% 0.30/0.47 = ( list_update_nat @ Xs @ I3 @ Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_overwrite
% 0.30/0.47 thf(fact_108_list__update__overwrite,axiom,
% 0.30/0.47 ! [Xs: list_list_a,I3: nat,X2: list_a,Y2: list_a] :
% 0.30/0.47 ( ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I3 @ Y2 )
% 0.30/0.47 = ( list_update_list_a @ Xs @ I3 @ Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_overwrite
% 0.30/0.47 thf(fact_109_list__update__overwrite,axiom,
% 0.30/0.47 ! [Xs: list_a,I3: nat,X2: a,Y2: a] :
% 0.30/0.47 ( ( list_update_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I3 @ Y2 )
% 0.30/0.47 = ( list_update_a @ Xs @ I3 @ Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_overwrite
% 0.30/0.47 thf(fact_110_length__list__update,axiom,
% 0.30/0.47 ! [Xs: list_list_nat,I3: nat,X2: list_nat] :
% 0.30/0.47 ( ( size_s1898481668st_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) )
% 0.30/0.47 = ( size_s1898481668st_nat @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_list_update
% 0.30/0.47 thf(fact_111_length__list__update,axiom,
% 0.30/0.47 ! [Xs: list_list_list_a,I3: nat,X2: list_list_a] :
% 0.30/0.47 ( ( size_s575106428list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) )
% 0.30/0.47 = ( size_s575106428list_a @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_list_update
% 0.30/0.47 thf(fact_112_length__list__update,axiom,
% 0.30/0.47 ! [Xs: list_a,I3: nat,X2: a] :
% 0.30/0.47 ( ( size_size_list_a @ ( list_update_a @ Xs @ I3 @ X2 ) )
% 0.30/0.47 = ( size_size_list_a @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_list_update
% 0.30/0.47 thf(fact_113_length__list__update,axiom,
% 0.30/0.47 ! [Xs: list_list_a,I3: nat,X2: list_a] :
% 0.30/0.47 ( ( size_s1427607542list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) )
% 0.30/0.47 = ( size_s1427607542list_a @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_list_update
% 0.30/0.47 thf(fact_114_length__list__update,axiom,
% 0.30/0.47 ! [Xs: list_nat,I3: nat,X2: nat] :
% 0.30/0.47 ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) )
% 0.30/0.47 = ( size_size_list_nat @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % length_list_update
% 0.30/0.47 thf(fact_115_list__update__id,axiom,
% 0.30/0.47 ! [Xs: list_list_nat,I3: nat] :
% 0.30/0.47 ( ( list_update_list_nat @ Xs @ I3 @ ( nth_list_nat @ Xs @ I3 ) )
% 0.30/0.47 = Xs ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_id
% 0.30/0.47 thf(fact_116_list__update__id,axiom,
% 0.30/0.47 ! [Xs: list_list_list_a,I3: nat] :
% 0.30/0.47 ( ( list_u1330012152list_a @ Xs @ I3 @ ( nth_list_list_a @ Xs @ I3 ) )
% 0.30/0.47 = Xs ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_id
% 0.30/0.47 thf(fact_117_list__update__id,axiom,
% 0.30/0.47 ! [Xs: list_list_a,I3: nat] :
% 0.30/0.47 ( ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ I3 ) )
% 0.30/0.47 = Xs ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_id
% 0.30/0.47 thf(fact_118_list__update__id,axiom,
% 0.30/0.47 ! [Xs: list_a,I3: nat] :
% 0.30/0.47 ( ( list_update_a @ Xs @ I3 @ ( nth_a @ Xs @ I3 ) )
% 0.30/0.47 = Xs ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_id
% 0.30/0.47 thf(fact_119_list__update__id,axiom,
% 0.30/0.47 ! [Xs: list_nat,I3: nat] :
% 0.30/0.47 ( ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ I3 ) )
% 0.30/0.47 = Xs ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_id
% 0.30/0.47 thf(fact_120_nth__list__update__neq,axiom,
% 0.30/0.47 ! [I3: nat,J2: nat,Xs: list_list_nat,X2: list_nat] :
% 0.30/0.47 ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_list_nat @ Xs @ J2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_neq
% 0.30/0.47 thf(fact_121_nth__list__update__neq,axiom,
% 0.30/0.47 ! [I3: nat,J2: nat,Xs: list_list_list_a,X2: list_list_a] :
% 0.30/0.47 ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_list_list_a @ Xs @ J2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_neq
% 0.30/0.47 thf(fact_122_nth__list__update__neq,axiom,
% 0.30/0.47 ! [I3: nat,J2: nat,Xs: list_list_a,X2: list_a] :
% 0.30/0.47 ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_list_a @ Xs @ J2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_neq
% 0.30/0.47 thf(fact_123_nth__list__update__neq,axiom,
% 0.30/0.47 ! [I3: nat,J2: nat,Xs: list_a,X2: a] :
% 0.30/0.47 ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_a @ Xs @ J2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_neq
% 0.30/0.47 thf(fact_124_nth__list__update__neq,axiom,
% 0.30/0.47 ! [I3: nat,J2: nat,Xs: list_nat,X2: nat] :
% 0.30/0.47 ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_nat @ Xs @ J2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update_neq
% 0.30/0.47 thf(fact_125_list__update__swap,axiom,
% 0.30/0.47 ! [I3: nat,I4: nat,Xs: list_nat,X2: nat,X4: nat] :
% 0.30/0.47 ( ( I3 != I4 )
% 0.30/0.47 => ( ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I4 @ X4 )
% 0.30/0.47 = ( list_update_nat @ ( list_update_nat @ Xs @ I4 @ X4 ) @ I3 @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_swap
% 0.30/0.47 thf(fact_126_list__update__swap,axiom,
% 0.30/0.47 ! [I3: nat,I4: nat,Xs: list_list_a,X2: list_a,X4: list_a] :
% 0.30/0.47 ( ( I3 != I4 )
% 0.30/0.47 => ( ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I4 @ X4 )
% 0.30/0.47 = ( list_update_list_a @ ( list_update_list_a @ Xs @ I4 @ X4 ) @ I3 @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_swap
% 0.30/0.47 thf(fact_127_list__update__swap,axiom,
% 0.30/0.47 ! [I3: nat,I4: nat,Xs: list_a,X2: a,X4: a] :
% 0.30/0.47 ( ( I3 != I4 )
% 0.30/0.47 => ( ( list_update_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I4 @ X4 )
% 0.30/0.47 = ( list_update_a @ ( list_update_a @ Xs @ I4 @ X4 ) @ I3 @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_swap
% 0.30/0.47 thf(fact_128_list__slice__aux__length,axiom,
% 0.30/0.47 ! [Xs: list_nat,K: nat,N: nat] :
% 0.30/0.47 ( ( size_s1898481668st_nat @ ( listSl1794011552ux_nat @ Xs @ K @ N ) )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_aux_length
% 0.30/0.47 thf(fact_129_list__slice__aux__length,axiom,
% 0.30/0.47 ! [Xs: list_list_a,K: nat,N: nat] :
% 0.30/0.47 ( ( size_s575106428list_a @ ( listSl856612276list_a @ Xs @ K @ N ) )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_aux_length
% 0.30/0.47 thf(fact_130_list__slice__aux__length,axiom,
% 0.30/0.47 ! [Xs: list_a,K: nat,N: nat] :
% 0.30/0.47 ( ( size_s1427607542list_a @ ( listSl1495374126_aux_a @ Xs @ K @ N ) )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % list_slice_aux_length
% 0.30/0.47 thf(fact_131_nth__list__update,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_nat,J2: nat,X2: list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( ( ( I3 = J2 )
% 0.30/0.47 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = X2 ) )
% 0.30/0.47 & ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_list_nat @ Xs @ J2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update
% 0.30/0.47 thf(fact_132_nth__list__update,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_list_a,J2: nat,X2: list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( ( ( I3 = J2 )
% 0.30/0.47 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = X2 ) )
% 0.30/0.47 & ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_list_list_a @ Xs @ J2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update
% 0.30/0.47 thf(fact_133_nth__list__update,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_a,J2: nat,X2: a] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( ( I3 = J2 )
% 0.30/0.47 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = X2 ) )
% 0.30/0.47 & ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_a @ Xs @ J2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update
% 0.30/0.47 thf(fact_134_nth__list__update,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_a,J2: nat,X2: list_a] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( ( I3 = J2 )
% 0.30/0.47 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = X2 ) )
% 0.30/0.47 & ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_list_a @ Xs @ J2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update
% 0.30/0.47 thf(fact_135_nth__list__update,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_nat,J2: nat,X2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( ( I3 = J2 )
% 0.30/0.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = X2 ) )
% 0.30/0.47 & ( ( I3 != J2 )
% 0.30/0.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.30/0.47 = ( nth_nat @ Xs @ J2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_list_update
% 0.30/0.47 thf(fact_136_list__update__same__conv,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_nat,X2: list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( ( ( list_update_list_nat @ Xs @ I3 @ X2 )
% 0.30/0.47 = Xs )
% 0.30/0.47 = ( ( nth_list_nat @ Xs @ I3 )
% 0.30/0.47 = X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_same_conv
% 0.30/0.47 thf(fact_137_list__update__same__conv,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_list_a,X2: list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( ( ( list_u1330012152list_a @ Xs @ I3 @ X2 )
% 0.30/0.47 = Xs )
% 0.30/0.47 = ( ( nth_list_list_a @ Xs @ I3 )
% 0.30/0.47 = X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_same_conv
% 0.30/0.47 thf(fact_138_list__update__same__conv,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_a,X2: a] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( ( list_update_a @ Xs @ I3 @ X2 )
% 0.30/0.47 = Xs )
% 0.30/0.47 = ( ( nth_a @ Xs @ I3 )
% 0.30/0.47 = X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_same_conv
% 0.30/0.47 thf(fact_139_list__update__same__conv,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_a,X2: list_a] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( ( list_update_list_a @ Xs @ I3 @ X2 )
% 0.30/0.47 = Xs )
% 0.30/0.47 = ( ( nth_list_a @ Xs @ I3 )
% 0.30/0.47 = X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_same_conv
% 0.30/0.47 thf(fact_140_list__update__same__conv,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_nat,X2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( ( list_update_nat @ Xs @ I3 @ X2 )
% 0.30/0.47 = Xs )
% 0.30/0.47 = ( ( nth_nat @ Xs @ I3 )
% 0.30/0.47 = X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_same_conv
% 0.30/0.47 thf(fact_141_set__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_nat,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( ( set_list_nat2 @ ( list_update_list_nat @ ( list_update_list_nat @ Xs @ I3 @ ( nth_list_nat @ Xs @ J2 ) ) @ J2 @ ( nth_list_nat @ Xs @ I3 ) ) )
% 0.30/0.47 = ( set_list_nat2 @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_swap
% 0.30/0.47 thf(fact_142_set__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_list_a,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( ( set_list_list_a2 @ ( list_u1330012152list_a @ ( list_u1330012152list_a @ Xs @ I3 @ ( nth_list_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_list_a @ Xs @ I3 ) ) )
% 0.30/0.47 = ( set_list_list_a2 @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_swap
% 0.30/0.47 thf(fact_143_set__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_a,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( set_a2 @ ( list_update_a @ ( list_update_a @ Xs @ I3 @ ( nth_a @ Xs @ J2 ) ) @ J2 @ ( nth_a @ Xs @ I3 ) ) )
% 0.30/0.47 = ( set_a2 @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_swap
% 0.30/0.47 thf(fact_144_set__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_a,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( set_list_a2 @ ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_a @ Xs @ I3 ) ) )
% 0.30/0.47 = ( set_list_a2 @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_swap
% 0.30/0.47 thf(fact_145_set__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_nat,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ J2 ) ) @ J2 @ ( nth_nat @ Xs @ I3 ) ) )
% 0.30/0.47 = ( set_nat2 @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_swap
% 0.30/0.47 thf(fact_146_list__desc__trans,axiom,
% 0.30/0.47 ( list_desc_set_nat
% 0.30/0.47 = ( ^ [Xs2: list_set_nat] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_s577819178et_nat @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_eq_set_nat @ ( nth_set_nat @ Xs2 @ J ) @ ( nth_set_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_desc_trans
% 0.30/0.47 thf(fact_147_list__desc__trans,axiom,
% 0.30/0.47 ( list_desc_set_list_a
% 0.30/0.47 = ( ^ [Xs2: list_set_list_a] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_s1635937238list_a @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_le1301786372list_a @ ( nth_set_list_a @ Xs2 @ J ) @ ( nth_set_list_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_desc_trans
% 0.30/0.47 thf(fact_148_list__desc__trans,axiom,
% 0.30/0.47 ( list_desc_set_a
% 0.30/0.47 = ( ^ [Xs2: list_set_a] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_set_a @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_eq_set_a @ ( nth_set_a @ Xs2 @ J ) @ ( nth_set_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_desc_trans
% 0.30/0.47 thf(fact_149_list__desc__trans,axiom,
% 0.30/0.47 ( list_desc_nat
% 0.30/0.47 = ( ^ [Xs2: list_nat] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_desc_trans
% 0.30/0.47 thf(fact_150_list__asc__trans,axiom,
% 0.30/0.47 ( list_asc_set_nat
% 0.30/0.47 = ( ^ [Xs2: list_set_nat] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_s577819178et_nat @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_eq_set_nat @ ( nth_set_nat @ Xs2 @ I2 ) @ ( nth_set_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_asc_trans
% 0.30/0.47 thf(fact_151_list__asc__trans,axiom,
% 0.30/0.47 ( list_asc_set_list_a
% 0.30/0.47 = ( ^ [Xs2: list_set_list_a] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_s1635937238list_a @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_le1301786372list_a @ ( nth_set_list_a @ Xs2 @ I2 ) @ ( nth_set_list_a @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_asc_trans
% 0.30/0.47 thf(fact_152_list__asc__trans,axiom,
% 0.30/0.47 ( list_asc_set_a
% 0.30/0.47 = ( ^ [Xs2: list_set_a] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_set_a @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_eq_set_a @ ( nth_set_a @ Xs2 @ I2 ) @ ( nth_set_a @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_asc_trans
% 0.30/0.47 thf(fact_153_list__asc__trans,axiom,
% 0.30/0.47 ( list_asc_nat
% 0.30/0.47 = ( ^ [Xs2: list_nat] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_asc_trans
% 0.30/0.47 thf(fact_154_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A2: nat,P: nat > $o] :
% 0.30/0.47 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_155_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A2: list_a,P: list_a > $o] :
% 0.30/0.47 ( ( member_list_a @ A2 @ ( collect_list_a @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_156_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A2: a,P: a > $o] :
% 0.30/0.47 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_157_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A: set_nat] :
% 0.30/0.47 ( ( collect_nat
% 0.30/0.47 @ ^ [X3: nat] : ( member_nat @ X3 @ A ) )
% 0.30/0.47 = A ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_158_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A: set_list_a] :
% 0.30/0.47 ( ( collect_list_a
% 0.30/0.47 @ ^ [X3: list_a] : ( member_list_a @ X3 @ A ) )
% 0.30/0.47 = A ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_159_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A: set_a] :
% 0.30/0.47 ( ( collect_a
% 0.30/0.47 @ ^ [X3: a] : ( member_a @ X3 @ A ) )
% 0.30/0.47 = A ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_160_distinct__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_nat,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( ( distinct_list_nat @ ( list_update_list_nat @ ( list_update_list_nat @ Xs @ I3 @ ( nth_list_nat @ Xs @ J2 ) ) @ J2 @ ( nth_list_nat @ Xs @ I3 ) ) )
% 0.30/0.47 = ( distinct_list_nat @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_swap
% 0.30/0.47 thf(fact_161_distinct__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_list_a,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( ( distinct_list_list_a @ ( list_u1330012152list_a @ ( list_u1330012152list_a @ Xs @ I3 @ ( nth_list_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_list_a @ Xs @ I3 ) ) )
% 0.30/0.47 = ( distinct_list_list_a @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_swap
% 0.30/0.47 thf(fact_162_distinct__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_a,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( distinct_a @ ( list_update_a @ ( list_update_a @ Xs @ I3 @ ( nth_a @ Xs @ J2 ) ) @ J2 @ ( nth_a @ Xs @ I3 ) ) )
% 0.30/0.47 = ( distinct_a @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_swap
% 0.30/0.47 thf(fact_163_distinct__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_list_a,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( distinct_list_a @ ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_a @ Xs @ I3 ) ) )
% 0.30/0.47 = ( distinct_list_a @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_swap
% 0.30/0.47 thf(fact_164_distinct__swap,axiom,
% 0.30/0.47 ! [I3: nat,Xs: list_nat,J2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ J2 ) ) @ J2 @ ( nth_nat @ Xs @ I3 ) ) )
% 0.30/0.47 = ( distinct_nat @ Xs ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_swap
% 0.30/0.47 thf(fact_165_f__rangeE,axiom,
% 0.30/0.47 ! [X2: list_nat,Xs: list_list_nat] :
% 0.30/0.47 ( ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ top_top_set_nat ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N2 @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( X2
% 0.30/0.47 != ( nth_list_nat @ Xs @ N2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeE
% 0.30/0.47 thf(fact_166_f__rangeE,axiom,
% 0.30/0.47 ! [X2: list_list_a,Xs: list_list_list_a] :
% 0.30/0.47 ( ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ top_top_set_nat ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N2 @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( X2
% 0.30/0.47 != ( nth_list_list_a @ Xs @ N2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeE
% 0.30/0.47 thf(fact_167_f__rangeE,axiom,
% 0.30/0.47 ! [X2: a,Xs: list_a] :
% 0.30/0.47 ( ( member_a @ X2 @ ( f_image_a @ Xs @ top_top_set_nat ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( X2
% 0.30/0.47 != ( nth_a @ Xs @ N2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeE
% 0.30/0.47 thf(fact_168_f__rangeE,axiom,
% 0.30/0.47 ! [X2: list_a,Xs: list_list_a] :
% 0.30/0.47 ( ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ top_top_set_nat ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( X2
% 0.30/0.47 != ( nth_list_a @ Xs @ N2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeE
% 0.30/0.47 thf(fact_169_f__rangeE,axiom,
% 0.30/0.47 ! [X2: nat,Xs: list_nat] :
% 0.30/0.47 ( ( member_nat @ X2 @ ( f_image_nat @ Xs @ top_top_set_nat ) )
% 0.30/0.47 => ~ ! [N2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( X2
% 0.30/0.47 != ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeE
% 0.30/0.47 thf(fact_170_f__rangeI,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( member_list_nat @ ( nth_list_nat @ Xs @ N ) @ ( f_image_list_nat @ Xs @ top_top_set_nat ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeI
% 0.30/0.47 thf(fact_171_f__rangeI,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( member_list_list_a @ ( nth_list_list_a @ Xs @ N ) @ ( f_image_list_list_a @ Xs @ top_top_set_nat ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeI
% 0.30/0.47 thf(fact_172_f__rangeI,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( member_a @ ( nth_a @ Xs @ N ) @ ( f_image_a @ Xs @ top_top_set_nat ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeI
% 0.30/0.47 thf(fact_173_f__rangeI,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ N ) @ ( f_image_list_a @ Xs @ top_top_set_nat ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeI
% 0.30/0.47 thf(fact_174_f__rangeI,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( f_image_nat @ Xs @ top_top_set_nat ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_rangeI
% 0.30/0.47 thf(fact_175_f__range__eqI,axiom,
% 0.30/0.47 ! [X2: list_nat,Xs: list_list_nat,N: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_list_nat @ Xs @ N ) )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.30/0.47 => ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_range_eqI
% 0.30/0.47 thf(fact_176_f__range__eqI,axiom,
% 0.30/0.47 ! [X2: list_list_a,Xs: list_list_list_a,N: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_list_list_a @ Xs @ N ) )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.30/0.47 => ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_range_eqI
% 0.30/0.47 thf(fact_177_f__range__eqI,axiom,
% 0.30/0.47 ! [X2: a,Xs: list_a,N: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_a @ Xs @ N ) )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( member_a @ X2 @ ( f_image_a @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_range_eqI
% 0.30/0.47 thf(fact_178_f__range__eqI,axiom,
% 0.30/0.47 ! [X2: list_a,Xs: list_list_a,N: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_list_a @ Xs @ N ) )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_range_eqI
% 0.30/0.47 thf(fact_179_f__range__eqI,axiom,
% 0.30/0.47 ! [X2: nat,Xs: list_nat,N: nat] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( nth_nat @ Xs @ N ) )
% 0.30/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( member_nat @ X2 @ ( f_image_nat @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_range_eqI
% 0.30/0.47 thf(fact_180_f__image__subsetI,axiom,
% 0.30/0.47 ! [A: set_nat,Xs: list_list_nat,B: set_list_nat] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ( ( member_nat @ N2 @ A )
% 0.30/0.47 & ( ord_less_nat @ N2 @ ( size_s1898481668st_nat @ Xs ) ) )
% 0.30/0.47 => ( member_list_nat @ ( nth_list_nat @ Xs @ N2 ) @ B ) )
% 0.30/0.47 => ( ord_le1747345782st_nat @ ( f_image_list_nat @ Xs @ A ) @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_subsetI
% 0.30/0.47 thf(fact_181_f__image__subsetI,axiom,
% 0.30/0.47 ! [A: set_nat,Xs: list_list_list_a,B: set_list_list_a] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ( ( member_nat @ N2 @ A )
% 0.30/0.47 & ( ord_less_nat @ N2 @ ( size_s575106428list_a @ Xs ) ) )
% 0.30/0.47 => ( member_list_list_a @ ( nth_list_list_a @ Xs @ N2 ) @ B ) )
% 0.30/0.47 => ( ord_le1756736906list_a @ ( f_image_list_list_a @ Xs @ A ) @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_subsetI
% 0.30/0.47 thf(fact_182_f__image__subsetI,axiom,
% 0.30/0.47 ! [A: set_nat,Xs: list_a,B: set_a] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ( ( member_nat @ N2 @ A )
% 0.30/0.47 & ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) ) )
% 0.30/0.47 => ( member_a @ ( nth_a @ Xs @ N2 ) @ B ) )
% 0.30/0.47 => ( ord_less_eq_set_a @ ( f_image_a @ Xs @ A ) @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_subsetI
% 0.30/0.47 thf(fact_183_f__image__subsetI,axiom,
% 0.30/0.47 ! [A: set_nat,Xs: list_list_a,B: set_list_a] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ( ( member_nat @ N2 @ A )
% 0.30/0.47 & ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) ) )
% 0.30/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ N2 ) @ B ) )
% 0.30/0.47 => ( ord_le1301786372list_a @ ( f_image_list_a @ Xs @ A ) @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_subsetI
% 0.30/0.47 thf(fact_184_f__image__subsetI,axiom,
% 0.30/0.47 ! [A: set_nat,Xs: list_nat,B: set_nat] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ( ( member_nat @ N2 @ A )
% 0.30/0.47 & ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) ) )
% 0.30/0.47 => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ B ) )
% 0.30/0.47 => ( ord_less_eq_set_nat @ ( f_image_nat @ Xs @ A ) @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_subsetI
% 0.30/0.47 thf(fact_185_f__image__subset__iff,axiom,
% 0.30/0.47 ! [Xs: list_a,A: set_nat,B: set_a] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ ( f_image_a @ Xs @ A ) @ B )
% 0.30/0.47 = ( ! [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 => ( ( ord_less_nat @ X3 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( member_a @ ( nth_a @ Xs @ X3 ) @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_subset_iff
% 0.30/0.47 thf(fact_186_f__image__subset__iff,axiom,
% 0.30/0.47 ! [Xs: list_list_a,A: set_nat,B: set_list_a] :
% 0.30/0.47 ( ( ord_le1301786372list_a @ ( f_image_list_a @ Xs @ A ) @ B )
% 0.30/0.47 = ( ! [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 => ( ( ord_less_nat @ X3 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ X3 ) @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_subset_iff
% 0.30/0.47 thf(fact_187_f__image__subset__iff,axiom,
% 0.30/0.47 ! [Xs: list_nat,A: set_nat,B: set_nat] :
% 0.30/0.47 ( ( ord_less_eq_set_nat @ ( f_image_nat @ Xs @ A ) @ B )
% 0.30/0.47 = ( ! [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ A )
% 0.30/0.47 => ( ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( member_nat @ ( nth_nat @ Xs @ X3 ) @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_subset_iff
% 0.30/0.47 thf(fact_188_list__update__beyond,axiom,
% 0.30/0.47 ! [Xs: list_a,I3: nat,X2: a] :
% 0.30/0.47 ( ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ I3 )
% 0.30/0.47 => ( ( list_update_a @ Xs @ I3 @ X2 )
% 0.30/0.47 = Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_beyond
% 0.30/0.47 thf(fact_189_list__update__beyond,axiom,
% 0.30/0.47 ! [Xs: list_list_a,I3: nat,X2: list_a] :
% 0.30/0.47 ( ( ord_less_eq_nat @ ( size_s1427607542list_a @ Xs ) @ I3 )
% 0.30/0.47 => ( ( list_update_list_a @ Xs @ I3 @ X2 )
% 0.30/0.47 = Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_beyond
% 0.30/0.47 thf(fact_190_list__update__beyond,axiom,
% 0.30/0.47 ! [Xs: list_nat,I3: nat,X2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I3 )
% 0.30/0.47 => ( ( list_update_nat @ Xs @ I3 @ X2 )
% 0.30/0.47 = Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_update_beyond
% 0.30/0.47 thf(fact_191_less__mono__imp__le__mono,axiom,
% 0.30/0.47 ! [F: nat > nat,I3: nat,J2: nat] :
% 0.30/0.47 ( ! [I: nat,J3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I @ J3 )
% 0.30/0.47 => ( ord_less_nat @ ( F @ I ) @ ( F @ J3 ) ) )
% 0.30/0.47 => ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.30/0.47 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( F @ J2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_mono_imp_le_mono
% 0.30/0.47 thf(fact_192_le__neq__implies__less,axiom,
% 0.30/0.47 ! [M: nat,N: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.47 => ( ( M != N )
% 0.30/0.47 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_neq_implies_less
% 0.30/0.47 thf(fact_193_less__or__eq__imp__le,axiom,
% 0.30/0.47 ! [M: nat,N: nat] :
% 0.30/0.47 ( ( ( ord_less_nat @ M @ N )
% 0.30/0.47 | ( M = N ) )
% 0.30/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_or_eq_imp_le
% 0.30/0.47 thf(fact_194_le__eq__less__or__eq,axiom,
% 0.30/0.47 ( ord_less_eq_nat
% 0.30/0.47 = ( ^ [M3: nat,N3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.30/0.47 | ( M3 = N3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_eq_less_or_eq
% 0.30/0.47 thf(fact_195_less__imp__le__nat,axiom,
% 0.30/0.47 ! [M: nat,N: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M @ N )
% 0.30/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_le_nat
% 0.30/0.47 thf(fact_196_nat__less__le,axiom,
% 0.30/0.47 ( ord_less_nat
% 0.30/0.47 = ( ^ [M3: nat,N3: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ M3 @ N3 )
% 0.30/0.47 & ( M3 != N3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nat_less_le
% 0.30/0.47 thf(fact_197_distinct__Ex1,axiom,
% 0.30/0.47 ! [Xs: list_a,X2: a] :
% 0.30/0.47 ( ( distinct_a @ Xs )
% 0.30/0.47 => ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
% 0.30/0.47 => ? [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 & ( ( nth_a @ Xs @ X5 )
% 0.30/0.47 = X2 )
% 0.30/0.47 & ! [Y3: nat] :
% 0.30/0.47 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 & ( ( nth_a @ Xs @ Y3 )
% 0.30/0.47 = X2 ) )
% 0.30/0.47 => ( Y3 = X5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_Ex1
% 0.30/0.47 thf(fact_198_distinct__Ex1,axiom,
% 0.30/0.47 ! [Xs: list_list_a,X2: list_a] :
% 0.30/0.47 ( ( distinct_list_a @ Xs )
% 0.30/0.47 => ( ( member_list_a @ X2 @ ( set_list_a2 @ Xs ) )
% 0.30/0.47 => ? [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 & ( ( nth_list_a @ Xs @ X5 )
% 0.30/0.47 = X2 )
% 0.30/0.47 & ! [Y3: nat] :
% 0.30/0.47 ( ( ( ord_less_nat @ Y3 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 & ( ( nth_list_a @ Xs @ Y3 )
% 0.30/0.47 = X2 ) )
% 0.30/0.47 => ( Y3 = X5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_Ex1
% 0.30/0.47 thf(fact_199_distinct__Ex1,axiom,
% 0.30/0.47 ! [Xs: list_nat,X2: nat] :
% 0.30/0.47 ( ( distinct_nat @ Xs )
% 0.30/0.47 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.30/0.47 => ? [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 & ( ( nth_nat @ Xs @ X5 )
% 0.30/0.47 = X2 )
% 0.30/0.47 & ! [Y3: nat] :
% 0.30/0.47 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 & ( ( nth_nat @ Xs @ Y3 )
% 0.30/0.47 = X2 ) )
% 0.30/0.47 => ( Y3 = X5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_Ex1
% 0.30/0.47 thf(fact_200_list__strict__asc__distinct,axiom,
% 0.30/0.47 ! [Xs: list_nat] :
% 0.30/0.47 ( ( list_strict_asc_nat @ Xs )
% 0.30/0.47 => ( distinct_nat @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_strict_asc_distinct
% 0.30/0.47 thf(fact_201_list__strict__desc__distinct,axiom,
% 0.30/0.47 ! [Xs: list_nat] :
% 0.30/0.47 ( ( list_strict_desc_nat @ Xs )
% 0.30/0.47 => ( distinct_nat @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_strict_desc_distinct
% 0.30/0.47 thf(fact_202_list__strict__asc__trans__le,axiom,
% 0.30/0.47 ! [Xs: list_nat] :
% 0.30/0.47 ( ( list_strict_asc_nat @ Xs )
% 0.30/0.47 => ! [J4: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J4 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ! [I5: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ I5 @ J4 )
% 0.30/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I5 ) @ ( nth_nat @ Xs @ J4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_strict_asc_trans_le
% 0.30/0.47 thf(fact_203_list__asc__trans__le,axiom,
% 0.30/0.47 ( list_asc_nat
% 0.30/0.47 = ( ^ [Xs2: list_nat] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_asc_trans_le
% 0.30/0.47 thf(fact_204_list__desc__trans__le,axiom,
% 0.30/0.47 ( list_desc_nat
% 0.30/0.47 = ( ^ [Xs2: list_nat] :
% 0.30/0.47 ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 => ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ I2 @ J )
% 0.30/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_desc_trans_le
% 0.30/0.47 thf(fact_205_nth__eq__iff__index__eq,axiom,
% 0.30/0.47 ! [Xs: list_a,I3: nat,J2: nat] :
% 0.30/0.47 ( ( distinct_a @ Xs )
% 0.30/0.47 => ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ( ( nth_a @ Xs @ I3 )
% 0.30/0.47 = ( nth_a @ Xs @ J2 ) )
% 0.30/0.47 = ( I3 = J2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_eq_iff_index_eq
% 0.30/0.47 thf(fact_206_nth__eq__iff__index__eq,axiom,
% 0.30/0.47 ! [Xs: list_list_a,I3: nat,J2: nat] :
% 0.30/0.47 ( ( distinct_list_a @ Xs )
% 0.30/0.47 => ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ( ( nth_list_a @ Xs @ I3 )
% 0.30/0.47 = ( nth_list_a @ Xs @ J2 ) )
% 0.30/0.47 = ( I3 = J2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_eq_iff_index_eq
% 0.30/0.47 thf(fact_207_nth__eq__iff__index__eq,axiom,
% 0.30/0.47 ! [Xs: list_nat,I3: nat,J2: nat] :
% 0.30/0.47 ( ( distinct_nat @ Xs )
% 0.30/0.47 => ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ( ( nth_nat @ Xs @ I3 )
% 0.30/0.47 = ( nth_nat @ Xs @ J2 ) )
% 0.30/0.47 = ( I3 = J2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_eq_iff_index_eq
% 0.30/0.47 thf(fact_208_distinct__conv__nth,axiom,
% 0.30/0.47 ( distinct_a
% 0.30/0.47 = ( ^ [Xs2: list_a] :
% 0.30/0.47 ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
% 0.30/0.47 => ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_a @ Xs2 ) )
% 0.30/0.47 => ( ( I2 != J )
% 0.30/0.47 => ( ( nth_a @ Xs2 @ I2 )
% 0.30/0.47 != ( nth_a @ Xs2 @ J ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_conv_nth
% 0.30/0.47 thf(fact_209_distinct__conv__nth,axiom,
% 0.30/0.47 ( distinct_list_a
% 0.30/0.47 = ( ^ [Xs2: list_list_a] :
% 0.30/0.47 ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
% 0.30/0.47 => ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_s1427607542list_a @ Xs2 ) )
% 0.30/0.47 => ( ( I2 != J )
% 0.30/0.47 => ( ( nth_list_a @ Xs2 @ I2 )
% 0.30/0.47 != ( nth_list_a @ Xs2 @ J ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_conv_nth
% 0.30/0.47 thf(fact_210_distinct__conv__nth,axiom,
% 0.30/0.47 ( distinct_nat
% 0.30/0.47 = ( ^ [Xs2: list_nat] :
% 0.30/0.47 ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 => ! [J: nat] :
% 0.30/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.47 => ( ( I2 != J )
% 0.30/0.47 => ( ( nth_nat @ Xs2 @ I2 )
% 0.30/0.47 != ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % distinct_conv_nth
% 0.30/0.47 thf(fact_211_all__set__conv__all__nth,axiom,
% 0.30/0.47 ! [Xs: list_a,P: a > $o] :
% 0.30/0.47 ( ( ! [X3: a] :
% 0.30/0.47 ( ( member_a @ X3 @ ( set_a2 @ Xs ) )
% 0.30/0.47 => ( P @ X3 ) ) )
% 0.30/0.47 = ( ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( P @ ( nth_a @ Xs @ I2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_set_conv_all_nth
% 0.30/0.47 thf(fact_212_all__set__conv__all__nth,axiom,
% 0.30/0.47 ! [Xs: list_list_a,P: list_a > $o] :
% 0.30/0.47 ( ( ! [X3: list_a] :
% 0.30/0.47 ( ( member_list_a @ X3 @ ( set_list_a2 @ Xs ) )
% 0.30/0.47 => ( P @ X3 ) ) )
% 0.30/0.47 = ( ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( P @ ( nth_list_a @ Xs @ I2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_set_conv_all_nth
% 0.30/0.47 thf(fact_213_all__set__conv__all__nth,axiom,
% 0.30/0.47 ! [Xs: list_nat,P: nat > $o] :
% 0.30/0.47 ( ( ! [X3: nat] :
% 0.30/0.47 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.30/0.47 => ( P @ X3 ) ) )
% 0.30/0.47 = ( ! [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( P @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_set_conv_all_nth
% 0.30/0.47 thf(fact_214_all__nth__imp__all__set,axiom,
% 0.30/0.47 ! [Xs: list_a,P: a > $o,X2: a] :
% 0.30/0.47 ( ! [I: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( P @ ( nth_a @ Xs @ I ) ) )
% 0.30/0.47 => ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
% 0.30/0.47 => ( P @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_nth_imp_all_set
% 0.30/0.47 thf(fact_215_all__nth__imp__all__set,axiom,
% 0.30/0.47 ! [Xs: list_list_a,P: list_a > $o,X2: list_a] :
% 0.30/0.47 ( ! [I: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( P @ ( nth_list_a @ Xs @ I ) ) )
% 0.30/0.47 => ( ( member_list_a @ X2 @ ( set_list_a2 @ Xs ) )
% 0.30/0.47 => ( P @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_nth_imp_all_set
% 0.30/0.47 thf(fact_216_all__nth__imp__all__set,axiom,
% 0.30/0.47 ! [Xs: list_nat,P: nat > $o,X2: nat] :
% 0.30/0.47 ( ! [I: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( P @ ( nth_nat @ Xs @ I ) ) )
% 0.30/0.47 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.30/0.47 => ( P @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_nth_imp_all_set
% 0.30/0.47 thf(fact_217_in__set__conv__nth,axiom,
% 0.30/0.47 ! [X2: a,Xs: list_a] :
% 0.30/0.47 ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
% 0.30/0.47 = ( ? [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 & ( ( nth_a @ Xs @ I2 )
% 0.30/0.47 = X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_set_conv_nth
% 0.30/0.47 thf(fact_218_in__set__conv__nth,axiom,
% 0.30/0.47 ! [X2: list_a,Xs: list_list_a] :
% 0.30/0.47 ( ( member_list_a @ X2 @ ( set_list_a2 @ Xs ) )
% 0.30/0.47 = ( ? [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 & ( ( nth_list_a @ Xs @ I2 )
% 0.30/0.47 = X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_set_conv_nth
% 0.30/0.47 thf(fact_219_in__set__conv__nth,axiom,
% 0.30/0.47 ! [X2: nat,Xs: list_nat] :
% 0.30/0.47 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.30/0.47 = ( ? [I2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 & ( ( nth_nat @ Xs @ I2 )
% 0.30/0.47 = X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_set_conv_nth
% 0.30/0.47 thf(fact_220_list__ball__nth,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_a,P: a > $o] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( ! [X5: a] :
% 0.30/0.47 ( ( member_a @ X5 @ ( set_a2 @ Xs ) )
% 0.30/0.47 => ( P @ X5 ) )
% 0.30/0.47 => ( P @ ( nth_a @ Xs @ N ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_ball_nth
% 0.30/0.47 thf(fact_221_list__ball__nth,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_list_a,P: list_a > $o] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( ! [X5: list_a] :
% 0.30/0.47 ( ( member_list_a @ X5 @ ( set_list_a2 @ Xs ) )
% 0.30/0.47 => ( P @ X5 ) )
% 0.30/0.47 => ( P @ ( nth_list_a @ Xs @ N ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_ball_nth
% 0.30/0.47 thf(fact_222_list__ball__nth,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( ! [X5: nat] :
% 0.30/0.47 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 0.30/0.47 => ( P @ X5 ) )
% 0.30/0.47 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list_ball_nth
% 0.30/0.47 thf(fact_223_nth__mem,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( member_a @ ( nth_a @ Xs @ N ) @ ( set_a2 @ Xs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_mem
% 0.30/0.47 thf(fact_224_nth__mem,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_list_a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ N ) @ ( set_list_a2 @ Xs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_mem
% 0.30/0.47 thf(fact_225_nth__mem,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_nat] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nth_mem
% 0.30/0.47 thf(fact_226_set__update__memI,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_a,X2: a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( member_a @ X2 @ ( set_a2 @ ( list_update_a @ Xs @ N @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_update_memI
% 0.30/0.47 thf(fact_227_set__update__memI,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_list_a,X2: list_a] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( member_list_a @ X2 @ ( set_list_a2 @ ( list_update_list_a @ Xs @ N @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_update_memI
% 0.30/0.47 thf(fact_228_set__update__memI,axiom,
% 0.30/0.47 ! [N: nat,Xs: list_nat,X2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_update_memI
% 0.30/0.47 thf(fact_229_f__image__eq__set,axiom,
% 0.30/0.47 ! [Xs: list_a,A: set_nat] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) )
% 0.30/0.47 => ( member_nat @ N2 @ A ) )
% 0.30/0.47 => ( ( f_image_a @ Xs @ A )
% 0.30/0.47 = ( set_a2 @ Xs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_eq_set
% 0.30/0.47 thf(fact_230_f__image__eq__set,axiom,
% 0.30/0.47 ! [Xs: list_list_a,A: set_nat] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) )
% 0.30/0.47 => ( member_nat @ N2 @ A ) )
% 0.30/0.47 => ( ( f_image_list_a @ Xs @ A )
% 0.30/0.47 = ( set_list_a2 @ Xs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_eq_set
% 0.30/0.47 thf(fact_231_f__image__eq__set,axiom,
% 0.30/0.47 ! [Xs: list_nat,A: set_nat] :
% 0.30/0.47 ( ! [N2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.30/0.47 => ( member_nat @ N2 @ A ) )
% 0.30/0.47 => ( ( f_image_nat @ Xs @ A )
% 0.30/0.47 = ( set_nat2 @ Xs ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f_image_eq_set
% 0.30/0.47 thf(fact_232_order__refl,axiom,
% 0.30/0.47 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.30/0.47
% 0.30/0.47 % order_refl
% 0.30/0.47 thf(fact_233_Nat_Oex__has__greatest__nat,axiom,
% 0.30/0.47 ! [P: nat > $o,K: nat,B2: nat] :
% 0.30/0.47 ( ( P @ K )
% 0.30/0.47 => ( ! [Y4: nat] :
% 0.30/0.47 ( ( P @ Y4 )
% 0.30/0.47 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 0.30/0.47 => ? [X5: nat] :
% 0.30/0.47 ( ( P @ X5 )
% 0.30/0.47 & ! [Y3: nat] :
% 0.30/0.47 ( ( P @ Y3 )
% 0.30/0.47 => ( ord_less_eq_nat @ Y3 @ X5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Nat.ex_has_greatest_nat
% 0.30/0.47 thf(fact_234_nat__le__linear,axiom,
% 0.30/0.47 ! [M: nat,N: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.47 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.30/0.47
% 0.30/0.47 % nat_le_linear
% 0.30/0.47 thf(fact_235_le__antisym,axiom,
% 0.30/0.47 ! [M: nat,N: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.47 => ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.47 => ( M = N ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_antisym
% 0.30/0.47 thf(fact_236_eq__imp__le,axiom,
% 0.30/0.47 ! [M: nat,N: nat] :
% 0.30/0.47 ( ( M = N )
% 0.30/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_imp_le
% 0.30/0.47 thf(fact_237_le__trans,axiom,
% 0.30/0.47 ! [I3: nat,J2: nat,K: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ J2 @ K )
% 0.30/0.47 => ( ord_less_eq_nat @ I3 @ K ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_trans
% 0.30/0.47 thf(fact_238_le__refl,axiom,
% 0.30/0.47 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.30/0.47
% 0.30/0.47 % le_refl
% 0.30/0.47 thf(fact_239_dual__order_Oantisym,axiom,
% 0.30/0.47 ! [B2: nat,A2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( A2 = B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.antisym
% 0.30/0.47 thf(fact_240_dual__order_Oeq__iff,axiom,
% 0.30/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.30/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.30/0.47 & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.eq_iff
% 0.30/0.47 thf(fact_241_dual__order_Otrans,axiom,
% 0.30/0.47 ! [B2: nat,A2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ C @ B2 )
% 0.30/0.47 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.trans
% 0.30/0.47 thf(fact_242_linorder__wlog,axiom,
% 0.30/0.47 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 0.30/0.47 ( ! [A4: nat,B4: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A4 @ B4 )
% 0.30/0.47 => ( P @ A4 @ B4 ) )
% 0.30/0.47 => ( ! [A4: nat,B4: nat] :
% 0.30/0.47 ( ( P @ B4 @ A4 )
% 0.30/0.47 => ( P @ A4 @ B4 ) )
% 0.30/0.47 => ( P @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_wlog
% 0.30/0.47 thf(fact_243_dual__order_Orefl,axiom,
% 0.30/0.47 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.refl
% 0.30/0.47 thf(fact_244_order__trans,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.30/0.47 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_trans
% 0.30/0.47 thf(fact_245_order__class_Oorder_Oantisym,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.30/0.47 => ( A2 = B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_class.order.antisym
% 0.30/0.47 thf(fact_246_ord__le__eq__trans,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( B2 = C )
% 0.30/0.47 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_le_eq_trans
% 0.30/0.47 thf(fact_247_ord__eq__le__trans,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( A2 = B2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.30/0.47 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_le_trans
% 0.30/0.47 thf(fact_248_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.30/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.30/0.47 & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_class.order.eq_iff
% 0.30/0.47 thf(fact_249_antisym__conv,axiom,
% 0.30/0.47 ! [Y2: nat,X2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 = ( X2 = Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym_conv
% 0.30/0.47 thf(fact_250_le__cases3,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.30/0.47 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 0.30/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.30/0.47 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 0.30/0.47 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.30/0.47 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 0.30/0.47 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 0.30/0.47 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 0.30/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.30/0.47 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 0.30/0.47 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 0.30/0.47 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_cases3
% 0.30/0.47 thf(fact_251_order_Otrans,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.30/0.47 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.trans
% 0.30/0.47 thf(fact_252_le__cases,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_cases
% 0.30/0.47 thf(fact_253_eq__refl,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( X2 = Y2 )
% 0.30/0.47 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_refl
% 0.30/0.47 thf(fact_254_linear,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % linear
% 0.30/0.47 thf(fact_255_antisym,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.30/0.47 => ( X2 = Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym
% 0.30/0.47 thf(fact_256_eq__iff,axiom,
% 0.30/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.30/0.47 = ( ^ [X3: nat,Y5: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 0.30/0.47 & ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_iff
% 0.30/0.47 thf(fact_257_ord__le__eq__subst,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ( F @ B2 )
% 0.30/0.47 = C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_le_eq_subst
% 0.30/0.47 thf(fact_258_ord__eq__le__subst,axiom,
% 0.30/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( A2
% 0.30/0.47 = ( F @ B2 ) )
% 0.30/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_le_subst
% 0.30/0.47 thf(fact_259_order__subst2,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_subst2
% 0.30/0.47 thf(fact_260_order__subst1,axiom,
% 0.30/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 0.30/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_subst1
% 0.30/0.47 thf(fact_261_ord__eq__less__subst,axiom,
% 0.30/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( A2
% 0.30/0.47 = ( F @ B2 ) )
% 0.30/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_less_subst
% 0.30/0.47 thf(fact_262_ord__less__eq__subst,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ( F @ B2 )
% 0.30/0.47 = C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_less_eq_subst
% 0.30/0.47 thf(fact_263_order__less__subst1,axiom,
% 0.30/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ ( F @ B2 ) )
% 0.30/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_subst1
% 0.30/0.47 thf(fact_264_order__less__subst2,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_subst2
% 0.30/0.47 thf(fact_265_gt__ex,axiom,
% 0.30/0.47 ! [X2: nat] :
% 0.30/0.47 ? [X_1: nat] : ( ord_less_nat @ X2 @ X_1 ) ).
% 0.30/0.47
% 0.30/0.47 % gt_ex
% 0.30/0.47 thf(fact_266_neqE,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( X2 != Y2 )
% 0.30/0.47 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neqE
% 0.30/0.47 thf(fact_267_neq__iff,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( X2 != Y2 )
% 0.30/0.47 = ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 | ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neq_iff
% 0.30/0.47 thf(fact_268_order_Oasym,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.asym
% 0.30/0.47 thf(fact_269_less__imp__neq,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( X2 != Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_neq
% 0.30/0.47 thf(fact_270_less__asym,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_asym
% 0.30/0.47 thf(fact_271_less__asym_H,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_asym'
% 0.30/0.47 thf(fact_272_less__trans,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( ord_less_nat @ Y2 @ Z2 )
% 0.30/0.47 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_trans
% 0.30/0.47 thf(fact_273_less__linear,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 | ( X2 = Y2 )
% 0.30/0.47 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_linear
% 0.30/0.47 thf(fact_274_less__irrefl,axiom,
% 0.30/0.47 ! [X2: nat] :
% 0.30/0.47 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 0.30/0.47
% 0.30/0.47 % less_irrefl
% 0.30/0.47 thf(fact_275_ord__eq__less__trans,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( A2 = B2 )
% 0.30/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.30/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_less_trans
% 0.30/0.47 thf(fact_276_ord__less__eq__trans,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( B2 = C )
% 0.30/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_less_eq_trans
% 0.30/0.47 thf(fact_277_dual__order_Oasym,axiom,
% 0.30/0.47 ! [B2: nat,A2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.30/0.47 => ~ ( ord_less_nat @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.asym
% 0.30/0.47 thf(fact_278_less__imp__not__eq,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( X2 != Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_eq
% 0.30/0.47 thf(fact_279_less__not__sym,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_not_sym
% 0.30/0.47 thf(fact_280_less__induct,axiom,
% 0.30/0.47 ! [P: nat > $o,A2: nat] :
% 0.30/0.47 ( ! [X5: nat] :
% 0.30/0.47 ( ! [Y3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Y3 @ X5 )
% 0.30/0.47 => ( P @ Y3 ) )
% 0.30/0.47 => ( P @ X5 ) )
% 0.30/0.47 => ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_induct
% 0.30/0.47 thf(fact_281_antisym__conv3,axiom,
% 0.30/0.47 ! [Y2: nat,X2: nat] :
% 0.30/0.47 ( ~ ( ord_less_nat @ Y2 @ X2 )
% 0.30/0.47 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.30/0.47 = ( X2 = Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym_conv3
% 0.30/0.47 thf(fact_282_less__imp__not__eq2,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( Y2 != X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_eq2
% 0.30/0.47 thf(fact_283_less__imp__triv,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat,P: $o] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( ord_less_nat @ Y2 @ X2 )
% 0.30/0.47 => P ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_triv
% 0.30/0.47 thf(fact_284_linorder__cases,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( X2 != Y2 )
% 0.30/0.47 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_cases
% 0.30/0.47 thf(fact_285_dual__order_Oirrefl,axiom,
% 0.30/0.47 ! [A2: nat] :
% 0.30/0.47 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.irrefl
% 0.30/0.47 thf(fact_286_order_Ostrict__trans,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.30/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_trans
% 0.30/0.47 thf(fact_287_less__imp__not__less,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_less
% 0.30/0.47 thf(fact_288_exists__least__iff,axiom,
% 0.30/0.47 ( ( ^ [P3: nat > $o] :
% 0.30/0.47 ? [X: nat] : ( P3 @ X ) )
% 0.30/0.47 = ( ^ [P2: nat > $o] :
% 0.30/0.47 ? [N3: nat] :
% 0.30/0.47 ( ( P2 @ N3 )
% 0.30/0.47 & ! [M3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.30/0.47 => ~ ( P2 @ M3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % exists_least_iff
% 0.30/0.47 thf(fact_289_linorder__less__wlog,axiom,
% 0.30/0.47 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 0.30/0.47 ( ! [A4: nat,B4: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A4 @ B4 )
% 0.30/0.47 => ( P @ A4 @ B4 ) )
% 0.30/0.47 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 0.30/0.47 => ( ! [A4: nat,B4: nat] :
% 0.30/0.47 ( ( P @ B4 @ A4 )
% 0.30/0.47 => ( P @ A4 @ B4 ) )
% 0.30/0.47 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_less_wlog
% 0.30/0.47 thf(fact_290_dual__order_Ostrict__trans,axiom,
% 0.30/0.47 ! [B2: nat,A2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.30/0.47 => ( ( ord_less_nat @ C @ B2 )
% 0.30/0.47 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans
% 0.30/0.47 thf(fact_291_not__less__iff__gr__or__eq,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.30/0.47 = ( ( ord_less_nat @ Y2 @ X2 )
% 0.30/0.47 | ( X2 = Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_less_iff_gr_or_eq
% 0.30/0.47 thf(fact_292_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ( A2 != B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_implies_not_eq
% 0.30/0.47 thf(fact_293_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.47 ! [B2: nat,A2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.30/0.47 => ( A2 != B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_implies_not_eq
% 0.30/0.47 thf(fact_294_order_Onot__eq__order__implies__strict,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat] :
% 0.30/0.47 ( ( A2 != B2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.not_eq_order_implies_strict
% 0.30/0.47 thf(fact_295_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.47 ! [B2: nat,A2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.30/0.47 => ( ord_less_eq_nat @ B2 @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_implies_order
% 0.30/0.47 thf(fact_296_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.47 ( ord_less_nat
% 0.30/0.47 = ( ^ [B3: nat,A3: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.30/0.47 & ( A3 != B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_iff_order
% 0.30/0.47 thf(fact_297_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.47 ( ord_less_eq_nat
% 0.30/0.47 = ( ^ [B3: nat,A3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ B3 @ A3 )
% 0.30/0.47 | ( A3 = B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.order_iff_strict
% 0.30/0.47 thf(fact_298_order_Ostrict__implies__order,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_implies_order
% 0.30/0.47 thf(fact_299_dual__order_Ostrict__trans2,axiom,
% 0.30/0.47 ! [B2: nat,A2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ C @ B2 )
% 0.30/0.47 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans2
% 0.30/0.47 thf(fact_300_dual__order_Ostrict__trans1,axiom,
% 0.30/0.47 ! [B2: nat,A2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.30/0.47 => ( ( ord_less_nat @ C @ B2 )
% 0.30/0.47 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans1
% 0.30/0.47 thf(fact_301_order_Ostrict__iff__order,axiom,
% 0.30/0.47 ( ord_less_nat
% 0.30/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.30/0.47 & ( A3 != B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_iff_order
% 0.30/0.47 thf(fact_302_order_Oorder__iff__strict,axiom,
% 0.30/0.47 ( ord_less_eq_nat
% 0.30/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A3 @ B3 )
% 0.30/0.47 | ( A3 = B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.order_iff_strict
% 0.30/0.47 thf(fact_303_order_Ostrict__trans2,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.30/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_trans2
% 0.30/0.47 thf(fact_304_order_Ostrict__trans1,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.30/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_trans1
% 0.30/0.47 thf(fact_305_not__le__imp__less,axiom,
% 0.30/0.47 ! [Y2: nat,X2: nat] :
% 0.30/0.47 ( ~ ( ord_less_eq_nat @ Y2 @ X2 )
% 0.30/0.47 => ( ord_less_nat @ X2 @ Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_le_imp_less
% 0.30/0.47 thf(fact_306_less__le__not__le,axiom,
% 0.30/0.47 ( ord_less_nat
% 0.30/0.47 = ( ^ [X3: nat,Y5: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 0.30/0.47 & ~ ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_le_not_le
% 0.30/0.47 thf(fact_307_le__imp__less__or__eq,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 | ( X2 = Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_imp_less_or_eq
% 0.30/0.47 thf(fact_308_le__less__linear,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_less_linear
% 0.30/0.47 thf(fact_309_less__le__trans,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.30/0.47 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_le_trans
% 0.30/0.47 thf(fact_310_le__less__trans,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( ord_less_nat @ Y2 @ Z2 )
% 0.30/0.47 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_less_trans
% 0.30/0.47 thf(fact_311_less__imp__le,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_le
% 0.30/0.47 thf(fact_312_antisym__conv2,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.30/0.47 = ( X2 = Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym_conv2
% 0.30/0.47 thf(fact_313_antisym__conv1,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.30/0.47 = ( X2 = Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym_conv1
% 0.30/0.47 thf(fact_314_le__neq__trans,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( A2 != B2 )
% 0.30/0.47 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_neq_trans
% 0.30/0.47 thf(fact_315_not__less,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.30/0.47 = ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_less
% 0.30/0.47 thf(fact_316_not__le,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ( ~ ( ord_less_eq_nat @ X2 @ Y2 ) )
% 0.30/0.47 = ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_le
% 0.30/0.47 thf(fact_317_order__less__le__subst2,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_le_subst2
% 0.30/0.47 thf(fact_318_order__less__le__subst1,axiom,
% 0.30/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ ( F @ B2 ) )
% 0.30/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_le_subst1
% 0.30/0.47 thf(fact_319_order__le__less__subst2,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_le_less_subst2
% 0.30/0.47 thf(fact_320_order__le__less__subst1,axiom,
% 0.30/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 0.30/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.30/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.30/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.47 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_le_less_subst1
% 0.30/0.47 thf(fact_321_less__le,axiom,
% 0.30/0.47 ( ord_less_nat
% 0.30/0.47 = ( ^ [X3: nat,Y5: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 0.30/0.47 & ( X3 != Y5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_le
% 0.30/0.47 thf(fact_322_le__less,axiom,
% 0.30/0.47 ( ord_less_eq_nat
% 0.30/0.47 = ( ^ [X3: nat,Y5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X3 @ Y5 )
% 0.30/0.47 | ( X3 = Y5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_less
% 0.30/0.47 thf(fact_323_leI,axiom,
% 0.30/0.47 ! [X2: nat,Y2: nat] :
% 0.30/0.47 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % leI
% 0.30/0.47 thf(fact_324_leD,axiom,
% 0.30/0.47 ! [Y2: nat,X2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.30/0.47 => ~ ( ord_less_nat @ X2 @ Y2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % leD
% 0.30/0.47 thf(fact_325_div__gr__imp__gr__divisor,axiom,
% 0.30/0.47 ! [X2: nat,N: nat,M: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X2 @ ( divide_divide_nat @ N @ M ) )
% 0.30/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.47
% 0.30/0.47 % div_gr_imp_gr_divisor
% 0.30/0.47 thf(fact_326_div__le__mono,axiom,
% 0.30/0.47 ! [M: nat,N: nat,K: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.47 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % div_le_mono
% 0.30/0.47 thf(fact_327_div__le__dividend,axiom,
% 0.30/0.47 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 0.30/0.47
% 0.30/0.47 % div_le_dividend
% 0.30/0.47 thf(fact_328_nat__descend__induct,axiom,
% 0.30/0.47 ! [N: nat,P: nat > $o,M: nat] :
% 0.30/0.47 ( ! [K3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ N @ K3 )
% 0.30/0.47 => ( P @ K3 ) )
% 0.30/0.47 => ( ! [K3: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ K3 @ N )
% 0.30/0.47 => ( ! [I5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ K3 @ I5 )
% 0.30/0.47 => ( P @ I5 ) )
% 0.30/0.47 => ( P @ K3 ) ) )
% 0.30/0.47 => ( P @ M ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nat_descend_induct
% 0.30/0.47 thf(fact_329_minf_I8_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.30/0.47 => ~ ( ord_less_eq_nat @ T @ X6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(8)
% 0.30/0.47 thf(fact_330_minf_I7_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.30/0.47 => ~ ( ord_less_nat @ T @ X6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(7)
% 0.30/0.47 thf(fact_331_minf_I5_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.30/0.47 => ( ord_less_nat @ X6 @ T ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(5)
% 0.30/0.47 thf(fact_332_minf_I4_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.30/0.47 => ( X6 != T ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(4)
% 0.30/0.47 thf(fact_333_minf_I3_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.30/0.47 => ( X6 != T ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(3)
% 0.30/0.47 thf(fact_334_minf_I2_J,axiom,
% 0.30/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.30/0.47 ( ? [Z4: nat] :
% 0.30/0.47 ! [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Z4 )
% 0.30/0.47 => ( ( P @ X5 )
% 0.30/0.47 = ( P4 @ X5 ) ) )
% 0.30/0.47 => ( ? [Z4: nat] :
% 0.30/0.47 ! [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Z4 )
% 0.30/0.47 => ( ( Q @ X5 )
% 0.30/0.47 = ( Q2 @ X5 ) ) )
% 0.30/0.47 => ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.30/0.47 => ( ( ( P @ X6 )
% 0.30/0.47 | ( Q @ X6 ) )
% 0.30/0.47 = ( ( P4 @ X6 )
% 0.30/0.47 | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(2)
% 0.30/0.47 thf(fact_335_minf_I1_J,axiom,
% 0.30/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.30/0.47 ( ? [Z4: nat] :
% 0.30/0.47 ! [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Z4 )
% 0.30/0.47 => ( ( P @ X5 )
% 0.30/0.47 = ( P4 @ X5 ) ) )
% 0.30/0.47 => ( ? [Z4: nat] :
% 0.30/0.47 ! [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X5 @ Z4 )
% 0.30/0.47 => ( ( Q @ X5 )
% 0.30/0.47 = ( Q2 @ X5 ) ) )
% 0.30/0.47 => ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.30/0.47 => ( ( ( P @ X6 )
% 0.30/0.47 & ( Q @ X6 ) )
% 0.30/0.47 = ( ( P4 @ X6 )
% 0.30/0.47 & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(1)
% 0.30/0.47 thf(fact_336_pinf_I7_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.30/0.47 => ( ord_less_nat @ T @ X6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(7)
% 0.30/0.47 thf(fact_337_pinf_I5_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.30/0.47 => ~ ( ord_less_nat @ X6 @ T ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(5)
% 0.30/0.47 thf(fact_338_pinf_I4_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.30/0.47 => ( X6 != T ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(4)
% 0.30/0.47 thf(fact_339_pinf_I3_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.30/0.47 => ( X6 != T ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(3)
% 0.30/0.47 thf(fact_340_pinf_I2_J,axiom,
% 0.30/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.30/0.47 ( ? [Z4: nat] :
% 0.30/0.47 ! [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z4 @ X5 )
% 0.30/0.47 => ( ( P @ X5 )
% 0.30/0.47 = ( P4 @ X5 ) ) )
% 0.30/0.47 => ( ? [Z4: nat] :
% 0.30/0.47 ! [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z4 @ X5 )
% 0.30/0.47 => ( ( Q @ X5 )
% 0.30/0.47 = ( Q2 @ X5 ) ) )
% 0.30/0.47 => ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.30/0.47 => ( ( ( P @ X6 )
% 0.30/0.47 | ( Q @ X6 ) )
% 0.30/0.47 = ( ( P4 @ X6 )
% 0.30/0.47 | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(2)
% 0.30/0.47 thf(fact_341_pinf_I1_J,axiom,
% 0.30/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.30/0.47 ( ? [Z4: nat] :
% 0.30/0.47 ! [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z4 @ X5 )
% 0.30/0.47 => ( ( P @ X5 )
% 0.30/0.47 = ( P4 @ X5 ) ) )
% 0.30/0.47 => ( ? [Z4: nat] :
% 0.30/0.47 ! [X5: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z4 @ X5 )
% 0.30/0.47 => ( ( Q @ X5 )
% 0.30/0.47 = ( Q2 @ X5 ) ) )
% 0.30/0.47 => ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.30/0.47 => ( ( ( P @ X6 )
% 0.30/0.47 & ( Q @ X6 ) )
% 0.30/0.47 = ( ( P4 @ X6 )
% 0.30/0.47 & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(1)
% 0.30/0.47 thf(fact_342_pinf_I6_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.30/0.47 => ~ ( ord_less_eq_nat @ X6 @ T ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(6)
% 0.30/0.47 thf(fact_343_pinf_I8_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.30/0.47 => ( ord_less_eq_nat @ T @ X6 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(8)
% 0.30/0.47 thf(fact_344_minf_I6_J,axiom,
% 0.30/0.47 ! [T: nat] :
% 0.30/0.47 ? [Z3: nat] :
% 0.30/0.47 ! [X6: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.30/0.47 => ( ord_less_eq_nat @ X6 @ T ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(6)
% 0.30/0.47 thf(fact_345_complete__interval,axiom,
% 0.30/0.47 ! [A2: nat,B2: nat,P: nat > $o] :
% 0.30/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.47 => ( ( P @ A2 )
% 0.30/0.47 => ( ~ ( P @ B2 )
% 0.30/0.47 => ? [C2: nat] :
% 0.30/0.47 ( ( ord_less_eq_nat @ A2 @ C2 )
% 0.30/0.47 & ( ord_less_eq_nat @ C2 @ B2 )
% 0.30/0.47 & ! [X6: nat] :
% 0.30/0.47 ( ( ( ord_less_eq_nat @ A2 @ X6 )
% 0.30/0.47 & ( ord_less_nat @ X6 @ C2 ) )
% 0.30/0.47 => ( P @ X6 ) )
% 0.30/0.47 & ! [D: nat] :
% 0.30/0.47 ( ! [X5: nat] :
% 0.30/0.47 ( ( ( ord_less_eq_nat @ A2 @ X5 )
% 0.30/0.47 & ( ord_less_nat @ X5 @ D ) )
% 0.30/0.47 => ( P @ X5 ) )
% 0.30/0.47 => ( ord_less_eq_nat @ D @ C2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % complete_interval
% 0.30/0.47 thf(fact_346_le__greater__neq__conv,axiom,
% 0.30/0.47 ( ord_less_eq_nat
% 0.30/0.47 = ( ^ [N3: nat,A3: nat] :
% 0.30/0.47 ! [X3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ A3 @ X3 )
% 0.30/0.47 => ( N3 != X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_greater_neq_conv
% 0.30/0.47 thf(fact_347_ge__less__neq__conv,axiom,
% 0.30/0.47 ( ord_less_eq_nat
% 0.30/0.47 = ( ^ [A3: nat,N3: nat] :
% 0.30/0.47 ! [X3: nat] :
% 0.30/0.47 ( ( ord_less_nat @ X3 @ A3 )
% 0.30/0.47 => ( N3 != X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ge_less_neq_conv
% 0.30/0.47
% 0.30/0.47 % Conjectures (2)
% 0.30/0.47 thf(conj_0,hypothesis,
% 0.30/0.47 ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) ).
% 0.30/0.47
% 0.30/0.47 thf(conj_1,conjecture,
% 0.30/0.47 ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
% 0.30/0.47 = k ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 2.95/1.53 ---- Embedded in THF ---
% 2.95/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.95/1.53 %%% Generated on Tue Feb 24 08:27:49 EST 2026
% 2.95/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.95/1.53 %%% Logic specification used:
% 2.95/1.53 %%% thf(spec, logic, $$dhol).
% 2.95/1.53
% 2.95/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2DTF26969.p
% See solution above
% 2.95/1.53 ------------------------
% 2.95/1.59 ---- Cleaned THF ---
% 2.95/1.59 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 2.95/1.59 list_l2071841302list_a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
% 2.95/1.59 list_list_list_nat: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 2.95/1.59 list_list_list_a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 2.95/1.59 set_list_list_a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 2.95/1.59 list_set_list_a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 2.95/1.59 list_list_nat: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 2.95/1.59 set_list_nat: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 2.95/1.59 list_set_nat: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 list_list_a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 set_list_a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 2.95/1.59 list_set_a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 list_nat: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.95/1.59 set_nat: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 2.95/1.59 list_a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.95/1.59 set_a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_t__Nat__Onat,type,
% 2.95/1.59 nat: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(ty_n_tf__a,type,
% 2.95/1.59 a: $tType ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Of__image_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 f_image_list_list_a: list_list_list_a > set_nat > set_list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Of__image_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 f_image_list_nat: list_list_nat > set_nat > set_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Of__image_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 f_image_list_a: list_list_a > set_nat > set_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Of__image_001t__Nat__Onat,type,
% 2.95/1.59 f_image_nat: list_nat > set_nat > set_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Of__image_001tf__a,type,
% 2.95/1.59 f_image_a: list_a > set_nat > set_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__asc_001t__Nat__Onat,type,
% 2.95/1.59 list_asc_nat: list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__asc_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 list_asc_set_list_a: list_set_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__asc_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.95/1.59 list_asc_set_nat: list_set_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__asc_001t__Set__Oset_Itf__a_J,type,
% 2.95/1.59 list_asc_set_a: list_set_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__desc_001t__Nat__Onat,type,
% 2.95/1.59 list_desc_nat: list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__desc_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 list_desc_set_list_a: list_set_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__desc_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.95/1.59 list_desc_set_nat: list_set_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__desc_001t__Set__Oset_Itf__a_J,type,
% 2.95/1.59 list_desc_set_a: list_set_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__strict__asc_001t__Nat__Onat,type,
% 2.95/1.59 list_strict_asc_nat: list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List2_Olist__strict__desc_001t__Nat__Onat,type,
% 2.95/1.59 list_strict_desc_nat: list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 listSl769338732list_a: list_list_list_a > nat > list_l2071841302list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 listSl2099749758st_nat: list_list_nat > nat > list_list_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 listSl703198822list_a: list_list_a > nat > list_list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__Nat__Onat,type,
% 2.95/1.59 listSl882585454e2_nat: list_nat > nat > list_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001tf__a,type,
% 2.95/1.59 listSl1174287072ice2_a: list_a > nat > list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 listSl2102238196list_a: list_list_list_a > nat > list_l2071841302list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 listSl729562870st_nat: list_list_nat > nat > list_list_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 listSl162220270list_a: list_list_a > nat > list_list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__Nat__Onat,type,
% 2.95/1.59 listSl1630398182ce_nat: list_nat > nat > list_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001tf__a,type,
% 2.95/1.59 listSl97544552lice_a: list_a > nat > list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 listSl902632890list_a: list_list_list_a > nat > nat > list_l2071841302list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 listSl1506485424st_nat: list_list_nat > nat > nat > list_list_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__Nat__Onat,type,
% 2.95/1.59 listSl1794011552ux_nat: list_nat > nat > nat > list_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001tf__a,type,
% 2.95/1.59 listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Obutlast_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 butlast_list_list_a: list_list_list_a > list_list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Obutlast_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 butlast_list_nat: list_list_nat > list_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 butlast_list_a: list_list_a > list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 2.95/1.59 butlast_nat: list_nat > list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Obutlast_001tf__a,type,
% 2.95/1.59 butlast_a: list_a > list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Odistinct_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 distinct_list_list_a: list_list_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Odistinct_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 distinct_list_nat: list_list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Odistinct_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 distinct_list_a: list_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 2.95/1.59 distinct_nat: list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Odistinct_001tf__a,type,
% 2.95/1.59 distinct_a: list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 set_list_list_a2: list_list_list_a > set_list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 set_list_nat2: list_list_nat > set_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 set_list_a2: list_list_a > set_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 2.95/1.59 set_nat2: list_nat > set_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist_Oset_001tf__a,type,
% 2.95/1.59 set_a2: list_a > set_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__ex_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 list_ex_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__ex_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 list_ex_list_nat: ( list_nat > $o ) > list_list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__ex_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 list_ex_list_a: ( list_a > $o ) > list_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__ex_001t__Nat__Onat,type,
% 2.95/1.59 list_ex_nat: ( nat > $o ) > list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__ex_001tf__a,type,
% 2.95/1.59 list_ex_a: ( a > $o ) > list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__update_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 list_u1330012152list_a: list_list_list_a > nat > list_list_a > list_list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__update_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 list_update_list_nat: list_list_nat > nat > list_nat > list_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__update_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 list_update_list_a: list_list_a > nat > list_a > list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 2.95/1.59 list_update_nat: list_nat > nat > nat > list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Olist__update_001tf__a,type,
% 2.95/1.59 list_update_a: list_a > nat > a > list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 2.95/1.59 nth_list_list_list_a: list_l2071841302list_a > nat > list_list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 2.95/1.59 nth_list_list_nat: list_list_list_nat > nat > list_list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 nth_list_list_a: list_list_list_a > nat > list_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 nth_list_nat: list_list_nat > nat > list_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 nth_list_a: list_list_a > nat > list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 2.95/1.59 nth_nat: list_nat > nat > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 nth_set_list_a: list_set_list_a > nat > set_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.95/1.59 nth_set_nat: list_set_nat > nat > set_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001t__Set__Oset_Itf__a_J,type,
% 2.95/1.59 nth_set_a: list_set_a > nat > set_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_List_Onth_001tf__a,type,
% 2.95/1.59 nth_a: list_a > nat > a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 2.95/1.59 size_s1764310658list_a: list_l2071841302list_a > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
% 2.95/1.59 size_s1321307156st_nat: list_list_list_nat > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 2.95/1.59 size_s575106428list_a: list_list_list_a > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 2.95/1.59 size_s1898481668st_nat: list_list_nat > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 size_s1427607542list_a: list_list_a > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 size_size_list_nat: list_nat > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 2.95/1.59 size_s1635937238list_a: list_set_list_a > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 2.95/1.59 size_s577819178et_nat: list_set_nat > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 2.95/1.59 size_size_list_set_a: list_set_a > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 size_size_list_a: list_a > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 2.95/1.59 ord_less_nat: nat > nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.95/1.59 ord_less_eq_nat: nat > nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 2.95/1.59 ord_le1756736906list_a: set_list_list_a > set_list_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 2.95/1.59 ord_le1747345782st_nat: set_list_nat > set_list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 ord_le1301786372list_a: set_list_a > set_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.95/1.59 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 2.95/1.59 ord_less_eq_set_a: set_a > set_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.95/1.59 top_top_set_nat: set_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 2.95/1.59 divide_divide_nat: nat > nat > nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Set_OCollect_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 collect_list_a: ( list_a > $o ) > set_list_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 2.95/1.59 collect_nat: ( nat > $o ) > set_nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.95/1.59 collect_a: ( a > $o ) > set_a ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_member_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.95/1.59 member_list_list_a: list_list_a > set_list_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 2.95/1.59 member_list_nat: list_nat > set_list_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_member_001t__List__Olist_Itf__a_J,type,
% 2.95/1.59 member_list_a: list_a > set_list_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_member_001t__Nat__Onat,type,
% 2.95/1.59 member_nat: nat > set_nat > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_c_member_001tf__a,type,
% 2.95/1.59 member_a: a > set_a > $o ).
% 2.95/1.59
% 2.95/1.59 thf(sy_v_k,type,
% 2.95/1.59 k: nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_v_m,type,
% 2.95/1.59 m: nat ).
% 2.95/1.59
% 2.95/1.59 thf(sy_v_xs,type,
% 2.95/1.59 xs: list_a ).
% 2.95/1.59
% 2.95/1.59 thf(fact_0_nth__equalityI,axiom,
% 2.95/1.59 ! [Xs: list_list_nat,Ys: list_list_nat] :
% 2.95/1.59 ( ( ( size_s1898481668st_nat @ Xs )
% 2.95/1.59 = ( size_s1898481668st_nat @ Ys ) )
% 2.95/1.59 => ( ! [I: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( ( nth_list_nat @ Xs @ I )
% 2.95/1.59 = ( nth_list_nat @ Ys @ I ) ) )
% 2.95/1.59 => ( Xs = Ys ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_1_nth__equalityI,axiom,
% 2.95/1.59 ! [Xs: list_list_list_a,Ys: list_list_list_a] :
% 2.95/1.59 ( ( ( size_s575106428list_a @ Xs )
% 2.95/1.59 = ( size_s575106428list_a @ Ys ) )
% 2.95/1.59 => ( ! [I: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( ( nth_list_list_a @ Xs @ I )
% 2.95/1.59 = ( nth_list_list_a @ Ys @ I ) ) )
% 2.95/1.59 => ( Xs = Ys ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_2_nth__equalityI,axiom,
% 2.95/1.59 ! [Xs: list_nat,Ys: list_nat] :
% 2.95/1.59 ( ( ( size_size_list_nat @ Xs )
% 2.95/1.59 = ( size_size_list_nat @ Ys ) )
% 2.95/1.59 => ( ! [I: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( nth_nat @ Xs @ I )
% 2.95/1.59 = ( nth_nat @ Ys @ I ) ) )
% 2.95/1.59 => ( Xs = Ys ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_3_nth__equalityI,axiom,
% 2.95/1.59 ! [Xs: list_list_a,Ys: list_list_a] :
% 2.95/1.59 ( ( ( size_s1427607542list_a @ Xs )
% 2.95/1.59 = ( size_s1427607542list_a @ Ys ) )
% 2.95/1.59 => ( ! [I: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( nth_list_a @ Xs @ I )
% 2.95/1.59 = ( nth_list_a @ Ys @ I ) ) )
% 2.95/1.59 => ( Xs = Ys ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_4_nth__equalityI,axiom,
% 2.95/1.59 ! [Xs: list_a,Ys: list_a] :
% 2.95/1.59 ( ( ( size_size_list_a @ Xs )
% 2.95/1.59 = ( size_size_list_a @ Ys ) )
% 2.95/1.59 => ( ! [I: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( nth_a @ Xs @ I )
% 2.95/1.59 = ( nth_a @ Ys @ I ) ) )
% 2.95/1.59 => ( Xs = Ys ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_5_Skolem__list__nth,axiom,
% 2.95/1.59 ! [K: nat,P: nat > list_nat > $o] :
% 2.95/1.59 ( ( ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ? [X: list_nat] : ( P @ I2 @ X ) ) )
% 2.95/1.59 = ( ? [Xs2: list_list_nat] :
% 2.95/1.59 ( ( ( size_s1898481668st_nat @ Xs2 )
% 2.95/1.59 = K )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ( P @ I2 @ ( nth_list_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_6_Skolem__list__nth,axiom,
% 2.95/1.59 ! [K: nat,P: nat > list_list_a > $o] :
% 2.95/1.59 ( ( ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ? [X: list_list_a] : ( P @ I2 @ X ) ) )
% 2.95/1.59 = ( ? [Xs2: list_list_list_a] :
% 2.95/1.59 ( ( ( size_s575106428list_a @ Xs2 )
% 2.95/1.59 = K )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ( P @ I2 @ ( nth_list_list_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_7_Skolem__list__nth,axiom,
% 2.95/1.59 ! [K: nat,P: nat > nat > $o] :
% 2.95/1.59 ( ( ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ? [X: nat] : ( P @ I2 @ X ) ) )
% 2.95/1.59 = ( ? [Xs2: list_nat] :
% 2.95/1.59 ( ( ( size_size_list_nat @ Xs2 )
% 2.95/1.59 = K )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ( P @ I2 @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_8_Skolem__list__nth,axiom,
% 2.95/1.59 ! [K: nat,P: nat > list_a > $o] :
% 2.95/1.59 ( ( ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ? [X: list_a] : ( P @ I2 @ X ) ) )
% 2.95/1.59 = ( ? [Xs2: list_list_a] :
% 2.95/1.59 ( ( ( size_s1427607542list_a @ Xs2 )
% 2.95/1.59 = K )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ( P @ I2 @ ( nth_list_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_9_Skolem__list__nth,axiom,
% 2.95/1.59 ! [K: nat,P: nat > a > $o] :
% 2.95/1.59 ( ( ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ? [X: a] : ( P @ I2 @ X ) ) )
% 2.95/1.59 = ( ? [Xs2: list_a] :
% 2.95/1.59 ( ( ( size_size_list_a @ Xs2 )
% 2.95/1.59 = K )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ K )
% 2.95/1.59 => ( P @ I2 @ ( nth_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_10_list__eq__iff__nth__eq,axiom,
% 2.95/1.59 ( ( ^ [Y: list_list_nat,Z: list_list_nat] : ( Y = Z ) )
% 2.95/1.59 = ( ^ [Xs2: list_list_nat,Ys2: list_list_nat] :
% 2.95/1.59 ( ( ( size_s1898481668st_nat @ Xs2 )
% 2.95/1.59 = ( size_s1898481668st_nat @ Ys2 ) )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_s1898481668st_nat @ Xs2 ) )
% 2.95/1.59 => ( ( nth_list_nat @ Xs2 @ I2 )
% 2.95/1.59 = ( nth_list_nat @ Ys2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_11_list__eq__iff__nth__eq,axiom,
% 2.95/1.59 ( ( ^ [Y: list_list_list_a,Z: list_list_list_a] : ( Y = Z ) )
% 2.95/1.59 = ( ^ [Xs2: list_list_list_a,Ys2: list_list_list_a] :
% 2.95/1.59 ( ( ( size_s575106428list_a @ Xs2 )
% 2.95/1.59 = ( size_s575106428list_a @ Ys2 ) )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_s575106428list_a @ Xs2 ) )
% 2.95/1.59 => ( ( nth_list_list_a @ Xs2 @ I2 )
% 2.95/1.59 = ( nth_list_list_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_12_list__eq__iff__nth__eq,axiom,
% 2.95/1.59 ( ( ^ [Y: list_nat,Z: list_nat] : ( Y = Z ) )
% 2.95/1.59 = ( ^ [Xs2: list_nat,Ys2: list_nat] :
% 2.95/1.59 ( ( ( size_size_list_nat @ Xs2 )
% 2.95/1.59 = ( size_size_list_nat @ Ys2 ) )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 => ( ( nth_nat @ Xs2 @ I2 )
% 2.95/1.59 = ( nth_nat @ Ys2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_13_list__eq__iff__nth__eq,axiom,
% 2.95/1.59 ( ( ^ [Y: list_list_a,Z: list_list_a] : ( Y = Z ) )
% 2.95/1.59 = ( ^ [Xs2: list_list_a,Ys2: list_list_a] :
% 2.95/1.59 ( ( ( size_s1427607542list_a @ Xs2 )
% 2.95/1.59 = ( size_s1427607542list_a @ Ys2 ) )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
% 2.95/1.59 => ( ( nth_list_a @ Xs2 @ I2 )
% 2.95/1.59 = ( nth_list_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_14_list__eq__iff__nth__eq,axiom,
% 2.95/1.59 ( ( ^ [Y: list_a,Z: list_a] : ( Y = Z ) )
% 2.95/1.59 = ( ^ [Xs2: list_a,Ys2: list_a] :
% 2.95/1.59 ( ( ( size_size_list_a @ Xs2 )
% 2.95/1.59 = ( size_size_list_a @ Ys2 ) )
% 2.95/1.59 & ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
% 2.95/1.59 => ( ( nth_a @ Xs2 @ I2 )
% 2.95/1.59 = ( nth_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_15_list__slice2__list__slice__nth,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_list_nat,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs ) @ K ) )
% 2.95/1.59 => ( ( nth_list_list_nat @ ( listSl2099749758st_nat @ Xs @ K ) @ M )
% 2.95/1.59 = ( nth_list_list_nat @ ( listSl729562870st_nat @ Xs @ K ) @ M ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_16_list__slice2__list__slice__nth,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_list_list_a,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s575106428list_a @ Xs ) @ K ) )
% 2.95/1.59 => ( ( nth_list_list_list_a @ ( listSl769338732list_a @ Xs @ K ) @ M )
% 2.95/1.59 = ( nth_list_list_list_a @ ( listSl2102238196list_a @ Xs @ K ) @ M ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_17_list__slice2__list__slice__nth,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_list_a,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1427607542list_a @ Xs ) @ K ) )
% 2.95/1.59 => ( ( nth_list_list_a @ ( listSl703198822list_a @ Xs @ K ) @ M )
% 2.95/1.59 = ( nth_list_list_a @ ( listSl162220270list_a @ Xs @ K ) @ M ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_18_list__slice2__list__slice__nth,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_nat,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_nat @ Xs ) @ K ) )
% 2.95/1.59 => ( ( nth_list_nat @ ( listSl882585454e2_nat @ Xs @ K ) @ M )
% 2.95/1.59 = ( nth_list_nat @ ( listSl1630398182ce_nat @ Xs @ K ) @ M ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_19_list__slice2__list__slice__nth,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_a,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
% 2.95/1.59 => ( ( nth_list_a @ ( listSl1174287072ice2_a @ Xs @ K ) @ M )
% 2.95/1.59 = ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_20_length__induct,axiom,
% 2.95/1.59 ! [P: list_list_nat > $o,Xs: list_list_nat] :
% 2.95/1.59 ( ! [Xs3: list_list_nat] :
% 2.95/1.59 ( ! [Ys3: list_list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ ( size_s1898481668st_nat @ Ys3 ) @ ( size_s1898481668st_nat @ Xs3 ) )
% 2.95/1.59 => ( P @ Ys3 ) )
% 2.95/1.59 => ( P @ Xs3 ) )
% 2.95/1.59 => ( P @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_21_length__induct,axiom,
% 2.95/1.59 ! [P: list_list_list_a > $o,Xs: list_list_list_a] :
% 2.95/1.59 ( ! [Xs3: list_list_list_a] :
% 2.95/1.59 ( ! [Ys3: list_list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ ( size_s575106428list_a @ Ys3 ) @ ( size_s575106428list_a @ Xs3 ) )
% 2.95/1.59 => ( P @ Ys3 ) )
% 2.95/1.59 => ( P @ Xs3 ) )
% 2.95/1.59 => ( P @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_22_length__induct,axiom,
% 2.95/1.59 ! [P: list_list_a > $o,Xs: list_list_a] :
% 2.95/1.59 ( ! [Xs3: list_list_a] :
% 2.95/1.59 ( ! [Ys3: list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ ( size_s1427607542list_a @ Ys3 ) @ ( size_s1427607542list_a @ Xs3 ) )
% 2.95/1.59 => ( P @ Ys3 ) )
% 2.95/1.59 => ( P @ Xs3 ) )
% 2.95/1.59 => ( P @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_23_length__induct,axiom,
% 2.95/1.59 ! [P: list_nat > $o,Xs: list_nat] :
% 2.95/1.59 ( ! [Xs3: list_nat] :
% 2.95/1.59 ( ! [Ys3: list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ ( size_size_list_nat @ Ys3 ) @ ( size_size_list_nat @ Xs3 ) )
% 2.95/1.59 => ( P @ Ys3 ) )
% 2.95/1.59 => ( P @ Xs3 ) )
% 2.95/1.59 => ( P @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_24_length__induct,axiom,
% 2.95/1.59 ! [P: list_a > $o,Xs: list_a] :
% 2.95/1.59 ( ! [Xs3: list_a] :
% 2.95/1.59 ( ! [Ys3: list_a] :
% 2.95/1.59 ( ( ord_less_nat @ ( size_size_list_a @ Ys3 ) @ ( size_size_list_a @ Xs3 ) )
% 2.95/1.59 => ( P @ Ys3 ) )
% 2.95/1.59 => ( P @ Xs3 ) )
% 2.95/1.59 => ( P @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_25_list__strict__desc__trans,axiom,
% 2.95/1.59 ( list_strict_desc_nat
% 2.95/1.59 = ( ^ [Xs2: list_nat] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_26_list__slice__nth__length,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_list_nat,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs ) @ K ) )
% 2.95/1.59 => ( ( size_s1898481668st_nat @ ( nth_list_list_nat @ ( listSl729562870st_nat @ Xs @ K ) @ M ) )
% 2.95/1.59 = K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_27_list__slice__nth__length,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_list_list_a,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s575106428list_a @ Xs ) @ K ) )
% 2.95/1.59 => ( ( size_s575106428list_a @ ( nth_list_list_list_a @ ( listSl2102238196list_a @ Xs @ K ) @ M ) )
% 2.95/1.59 = K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_28_list__slice__nth__length,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_list_a,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1427607542list_a @ Xs ) @ K ) )
% 2.95/1.59 => ( ( size_s1427607542list_a @ ( nth_list_list_a @ ( listSl162220270list_a @ Xs @ K ) @ M ) )
% 2.95/1.59 = K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_29_list__slice__nth__length,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_nat,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_nat @ Xs ) @ K ) )
% 2.95/1.59 => ( ( size_size_list_nat @ ( nth_list_nat @ ( listSl1630398182ce_nat @ Xs @ K ) @ M ) )
% 2.95/1.59 = K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_30_list__slice__nth__length,axiom,
% 2.95/1.59 ! [M: nat,Xs: list_a,K: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
% 2.95/1.59 => ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) )
% 2.95/1.59 = K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_31_list__strict__asc__trans,axiom,
% 2.95/1.59 ( list_strict_asc_nat
% 2.95/1.59 = ( ^ [Xs2: list_nat] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_32_Ex__list__of__length,axiom,
% 2.95/1.59 ! [N: nat] :
% 2.95/1.59 ? [Xs3: list_list_nat] :
% 2.95/1.59 ( ( size_s1898481668st_nat @ Xs3 )
% 2.95/1.59 = N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_33_Ex__list__of__length,axiom,
% 2.95/1.59 ! [N: nat] :
% 2.95/1.59 ? [Xs3: list_list_list_a] :
% 2.95/1.59 ( ( size_s575106428list_a @ Xs3 )
% 2.95/1.59 = N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_34_Ex__list__of__length,axiom,
% 2.95/1.59 ! [N: nat] :
% 2.95/1.59 ? [Xs3: list_list_a] :
% 2.95/1.59 ( ( size_s1427607542list_a @ Xs3 )
% 2.95/1.59 = N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_35_Ex__list__of__length,axiom,
% 2.95/1.59 ! [N: nat] :
% 2.95/1.59 ? [Xs3: list_nat] :
% 2.95/1.59 ( ( size_size_list_nat @ Xs3 )
% 2.95/1.59 = N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_36_Ex__list__of__length,axiom,
% 2.95/1.59 ! [N: nat] :
% 2.95/1.59 ? [Xs3: list_a] :
% 2.95/1.59 ( ( size_size_list_a @ Xs3 )
% 2.95/1.59 = N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_37_neq__if__length__neq,axiom,
% 2.95/1.59 ! [Xs: list_list_nat,Ys: list_list_nat] :
% 2.95/1.59 ( ( ( size_s1898481668st_nat @ Xs )
% 2.95/1.59 != ( size_s1898481668st_nat @ Ys ) )
% 2.95/1.59 => ( Xs != Ys ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_38_neq__if__length__neq,axiom,
% 2.95/1.59 ! [Xs: list_list_list_a,Ys: list_list_list_a] :
% 2.95/1.59 ( ( ( size_s575106428list_a @ Xs )
% 2.95/1.59 != ( size_s575106428list_a @ Ys ) )
% 2.95/1.59 => ( Xs != Ys ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_39_neq__if__length__neq,axiom,
% 2.95/1.59 ! [Xs: list_list_a,Ys: list_list_a] :
% 2.95/1.59 ( ( ( size_s1427607542list_a @ Xs )
% 2.95/1.59 != ( size_s1427607542list_a @ Ys ) )
% 2.95/1.59 => ( Xs != Ys ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_40_neq__if__length__neq,axiom,
% 2.95/1.59 ! [Xs: list_nat,Ys: list_nat] :
% 2.95/1.59 ( ( ( size_size_list_nat @ Xs )
% 2.95/1.59 != ( size_size_list_nat @ Ys ) )
% 2.95/1.59 => ( Xs != Ys ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_41_neq__if__length__neq,axiom,
% 2.95/1.59 ! [Xs: list_a,Ys: list_a] :
% 2.95/1.59 ( ( ( size_size_list_a @ Xs )
% 2.95/1.59 != ( size_size_list_a @ Ys ) )
% 2.95/1.59 => ( Xs != Ys ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_42_size__neq__size__imp__neq,axiom,
% 2.95/1.59 ! [X2: list_list_nat,Y2: list_list_nat] :
% 2.95/1.59 ( ( ( size_s1898481668st_nat @ X2 )
% 2.95/1.59 != ( size_s1898481668st_nat @ Y2 ) )
% 2.95/1.59 => ( X2 != Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_43_size__neq__size__imp__neq,axiom,
% 2.95/1.59 ! [X2: list_list_list_a,Y2: list_list_list_a] :
% 2.95/1.59 ( ( ( size_s575106428list_a @ X2 )
% 2.95/1.59 != ( size_s575106428list_a @ Y2 ) )
% 2.95/1.59 => ( X2 != Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_44_size__neq__size__imp__neq,axiom,
% 2.95/1.59 ! [X2: list_a,Y2: list_a] :
% 2.95/1.59 ( ( ( size_size_list_a @ X2 )
% 2.95/1.59 != ( size_size_list_a @ Y2 ) )
% 2.95/1.59 => ( X2 != Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_45_size__neq__size__imp__neq,axiom,
% 2.95/1.59 ! [X2: list_list_a,Y2: list_list_a] :
% 2.95/1.59 ( ( ( size_s1427607542list_a @ X2 )
% 2.95/1.59 != ( size_s1427607542list_a @ Y2 ) )
% 2.95/1.59 => ( X2 != Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_46_size__neq__size__imp__neq,axiom,
% 2.95/1.59 ! [X2: list_nat,Y2: list_nat] :
% 2.95/1.59 ( ( ( size_size_list_nat @ X2 )
% 2.95/1.59 != ( size_size_list_nat @ Y2 ) )
% 2.95/1.59 => ( X2 != Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_47_nat__neq__iff,axiom,
% 2.95/1.59 ! [M: nat,N: nat] :
% 2.95/1.59 ( ( M != N )
% 2.95/1.59 = ( ( ord_less_nat @ M @ N )
% 2.95/1.59 | ( ord_less_nat @ N @ M ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_48_list__slice__length,axiom,
% 2.95/1.59 ! [Xs: list_list_nat,K: nat] :
% 2.95/1.59 ( ( size_s1321307156st_nat @ ( listSl729562870st_nat @ Xs @ K ) )
% 2.95/1.59 = ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs ) @ K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_49_list__slice__length,axiom,
% 2.95/1.59 ! [Xs: list_list_list_a,K: nat] :
% 2.95/1.59 ( ( size_s1764310658list_a @ ( listSl2102238196list_a @ Xs @ K ) )
% 2.95/1.59 = ( divide_divide_nat @ ( size_s575106428list_a @ Xs ) @ K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_50_list__slice__length,axiom,
% 2.95/1.59 ! [Xs: list_list_a,K: nat] :
% 2.95/1.59 ( ( size_s575106428list_a @ ( listSl162220270list_a @ Xs @ K ) )
% 2.95/1.59 = ( divide_divide_nat @ ( size_s1427607542list_a @ Xs ) @ K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_51_list__slice__length,axiom,
% 2.95/1.59 ! [Xs: list_nat,K: nat] :
% 2.95/1.59 ( ( size_s1898481668st_nat @ ( listSl1630398182ce_nat @ Xs @ K ) )
% 2.95/1.59 = ( divide_divide_nat @ ( size_size_list_nat @ Xs ) @ K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_52_list__slice__length,axiom,
% 2.95/1.59 ! [Xs: list_a,K: nat] :
% 2.95/1.59 ( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
% 2.95/1.59 = ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_53_linorder__neqE__nat,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ( X2 != Y2 )
% 2.95/1.59 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.59 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_54_infinite__descent,axiom,
% 2.95/1.59 ! [P: nat > $o,N: nat] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ~ ( P @ N2 )
% 2.95/1.59 => ? [M2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M2 @ N2 )
% 2.95/1.59 & ~ ( P @ M2 ) ) )
% 2.95/1.59 => ( P @ N ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_55_nat__less__induct,axiom,
% 2.95/1.59 ! [P: nat > $o,N: nat] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ! [M2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M2 @ N2 )
% 2.95/1.59 => ( P @ M2 ) )
% 2.95/1.59 => ( P @ N2 ) )
% 2.95/1.59 => ( P @ N ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_56_less__irrefl__nat,axiom,
% 2.95/1.59 ! [N: nat] :
% 2.95/1.59 ~ ( ord_less_nat @ N @ N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_57_less__not__refl3,axiom,
% 2.95/1.59 ! [S: nat,T: nat] :
% 2.95/1.59 ( ( ord_less_nat @ S @ T )
% 2.95/1.59 => ( S != T ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_58_less__not__refl2,axiom,
% 2.95/1.59 ! [N: nat,M: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N @ M )
% 2.95/1.59 => ( M != N ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_59_less__not__refl,axiom,
% 2.95/1.59 ! [N: nat] :
% 2.95/1.59 ~ ( ord_less_nat @ N @ N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_60_list__slice__def,axiom,
% 2.95/1.59 ( listSl729562870st_nat
% 2.95/1.59 = ( ^ [Xs2: list_list_nat,K2: nat] : ( listSl1506485424st_nat @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs2 ) @ K2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_61_list__slice__def,axiom,
% 2.95/1.59 ( listSl2102238196list_a
% 2.95/1.59 = ( ^ [Xs2: list_list_list_a,K2: nat] : ( listSl902632890list_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_s575106428list_a @ Xs2 ) @ K2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_62_list__slice__def,axiom,
% 2.95/1.59 ( listSl162220270list_a
% 2.95/1.59 = ( ^ [Xs2: list_list_a,K2: nat] : ( listSl856612276list_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_s1427607542list_a @ Xs2 ) @ K2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_63_list__slice__def,axiom,
% 2.95/1.59 ( listSl1630398182ce_nat
% 2.95/1.59 = ( ^ [Xs2: list_nat,K2: nat] : ( listSl1794011552ux_nat @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_nat @ Xs2 ) @ K2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_64_list__slice__def,axiom,
% 2.95/1.59 ( listSl97544552lice_a
% 2.95/1.59 = ( ^ [Xs2: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs2 ) @ K2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_65_list__strict__desc__imp__list__desc,axiom,
% 2.95/1.59 ! [Xs: list_nat] :
% 2.95/1.59 ( ( list_strict_desc_nat @ Xs )
% 2.95/1.59 => ( list_desc_nat @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_66_list__ex__length,axiom,
% 2.95/1.59 ( list_ex_list_nat
% 2.95/1.59 = ( ^ [P2: list_nat > $o,Xs2: list_list_nat] :
% 2.95/1.59 ? [N3: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N3 @ ( size_s1898481668st_nat @ Xs2 ) )
% 2.95/1.59 & ( P2 @ ( nth_list_nat @ Xs2 @ N3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_67_list__ex__length,axiom,
% 2.95/1.59 ( list_ex_list_list_a
% 2.95/1.59 = ( ^ [P2: list_list_a > $o,Xs2: list_list_list_a] :
% 2.95/1.59 ? [N3: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N3 @ ( size_s575106428list_a @ Xs2 ) )
% 2.95/1.59 & ( P2 @ ( nth_list_list_a @ Xs2 @ N3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_68_list__ex__length,axiom,
% 2.95/1.59 ( list_ex_a
% 2.95/1.59 = ( ^ [P2: a > $o,Xs2: list_a] :
% 2.95/1.59 ? [N3: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N3 @ ( size_size_list_a @ Xs2 ) )
% 2.95/1.59 & ( P2 @ ( nth_a @ Xs2 @ N3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_69_list__ex__length,axiom,
% 2.95/1.59 ( list_ex_list_a
% 2.95/1.59 = ( ^ [P2: list_a > $o,Xs2: list_list_a] :
% 2.95/1.59 ? [N3: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N3 @ ( size_s1427607542list_a @ Xs2 ) )
% 2.95/1.59 & ( P2 @ ( nth_list_a @ Xs2 @ N3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_70_list__ex__length,axiom,
% 2.95/1.59 ( list_ex_nat
% 2.95/1.59 = ( ^ [P2: nat > $o,Xs2: list_nat] :
% 2.95/1.59 ? [N3: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N3 @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 & ( P2 @ ( nth_nat @ Xs2 @ N3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_71_f__image__eqI,axiom,
% 2.95/1.59 ! [X2: list_nat,Xs: list_list_nat,N: nat,A: set_nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_list_nat @ Xs @ N ) )
% 2.95/1.59 => ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_72_f__image__eqI,axiom,
% 2.95/1.59 ! [X2: list_list_a,Xs: list_list_list_a,N: nat,A: set_nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_list_list_a @ Xs @ N ) )
% 2.95/1.59 => ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_73_f__image__eqI,axiom,
% 2.95/1.59 ! [X2: a,Xs: list_a,N: nat,A: set_nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_a @ Xs @ N ) )
% 2.95/1.59 => ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( member_a @ X2 @ ( f_image_a @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_74_f__image__eqI,axiom,
% 2.95/1.59 ! [X2: list_a,Xs: list_list_a,N: nat,A: set_nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_list_a @ Xs @ N ) )
% 2.95/1.59 => ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_75_f__image__eqI,axiom,
% 2.95/1.59 ! [X2: nat,Xs: list_nat,N: nat,A: set_nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_nat @ Xs @ N ) )
% 2.95/1.59 => ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_76_list__strict__asc__imp__list__asc,axiom,
% 2.95/1.59 ! [Xs: list_nat] :
% 2.95/1.59 ( ( list_strict_asc_nat @ Xs )
% 2.95/1.59 => ( list_asc_nat @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_77_nth__list__update__eq,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_nat,X2: list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ I3 )
% 2.95/1.59 = X2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_78_nth__list__update__eq,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_list_a,X2: list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ I3 )
% 2.95/1.59 = X2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_79_nth__list__update__eq,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_a,X2: a] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I3 )
% 2.95/1.59 = X2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_80_nth__list__update__eq,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_a,X2: list_a] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I3 )
% 2.95/1.59 = X2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_81_nth__list__update__eq,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_nat,X2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I3 )
% 2.95/1.59 = X2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_82_rev__f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_list_nat,X2: list_nat] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( ( X2
% 2.95/1.59 = ( nth_list_nat @ Xs @ N ) )
% 2.95/1.59 => ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_83_rev__f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_list_list_a,X2: list_list_a] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( ( X2
% 2.95/1.59 = ( nth_list_list_a @ Xs @ N ) )
% 2.95/1.59 => ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_84_rev__f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_a,X2: a] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( X2
% 2.95/1.59 = ( nth_a @ Xs @ N ) )
% 2.95/1.59 => ( member_a @ X2 @ ( f_image_a @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_85_rev__f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_list_a,X2: list_a] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( X2
% 2.95/1.59 = ( nth_list_a @ Xs @ N ) )
% 2.95/1.59 => ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_86_rev__f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_nat,X2: nat] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( X2
% 2.95/1.59 = ( nth_nat @ Xs @ N ) )
% 2.95/1.59 => ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_87_f__image__iff,axiom,
% 2.95/1.59 ! [X2: list_nat,Xs: list_list_nat,A: set_nat] :
% 2.95/1.59 ( ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) )
% 2.95/1.59 = ( ? [X3: nat] :
% 2.95/1.59 ( ( member_nat @ X3 @ A )
% 2.95/1.59 & ( ord_less_nat @ X3 @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 & ( X2
% 2.95/1.59 = ( nth_list_nat @ Xs @ X3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_88_f__image__iff,axiom,
% 2.95/1.59 ! [X2: list_list_a,Xs: list_list_list_a,A: set_nat] :
% 2.95/1.59 ( ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) )
% 2.95/1.59 = ( ? [X3: nat] :
% 2.95/1.59 ( ( member_nat @ X3 @ A )
% 2.95/1.59 & ( ord_less_nat @ X3 @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 & ( X2
% 2.95/1.59 = ( nth_list_list_a @ Xs @ X3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_89_f__image__iff,axiom,
% 2.95/1.59 ! [X2: a,Xs: list_a,A: set_nat] :
% 2.95/1.59 ( ( member_a @ X2 @ ( f_image_a @ Xs @ A ) )
% 2.95/1.59 = ( ? [X3: nat] :
% 2.95/1.59 ( ( member_nat @ X3 @ A )
% 2.95/1.59 & ( ord_less_nat @ X3 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 & ( X2
% 2.95/1.59 = ( nth_a @ Xs @ X3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_90_f__image__iff,axiom,
% 2.95/1.59 ! [X2: list_a,Xs: list_list_a,A: set_nat] :
% 2.95/1.59 ( ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) )
% 2.95/1.59 = ( ? [X3: nat] :
% 2.95/1.59 ( ( member_nat @ X3 @ A )
% 2.95/1.59 & ( ord_less_nat @ X3 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 & ( X2
% 2.95/1.59 = ( nth_list_a @ Xs @ X3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_91_f__image__iff,axiom,
% 2.95/1.59 ! [X2: nat,Xs: list_nat,A: set_nat] :
% 2.95/1.59 ( ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) )
% 2.95/1.59 = ( ? [X3: nat] :
% 2.95/1.59 ( ( member_nat @ X3 @ A )
% 2.95/1.59 & ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 & ( X2
% 2.95/1.59 = ( nth_nat @ Xs @ X3 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_92_nth__butlast,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ ( butlast_list_nat @ Xs ) ) )
% 2.95/1.59 => ( ( nth_list_nat @ ( butlast_list_nat @ Xs ) @ N )
% 2.95/1.59 = ( nth_list_nat @ Xs @ N ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_93_nth__butlast,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_s575106428list_a @ ( butlast_list_list_a @ Xs ) ) )
% 2.95/1.59 => ( ( nth_list_list_a @ ( butlast_list_list_a @ Xs ) @ N )
% 2.95/1.59 = ( nth_list_list_a @ Xs @ N ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_94_nth__butlast,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_a @ ( butlast_a @ Xs ) ) )
% 2.95/1.59 => ( ( nth_a @ ( butlast_a @ Xs ) @ N )
% 2.95/1.59 = ( nth_a @ Xs @ N ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_95_nth__butlast,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ ( butlast_list_a @ Xs ) ) )
% 2.95/1.59 => ( ( nth_list_a @ ( butlast_list_a @ Xs ) @ N )
% 2.95/1.59 = ( nth_list_a @ Xs @ N ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_96_nth__butlast,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_nat @ ( butlast_nat @ Xs ) ) )
% 2.95/1.59 => ( ( nth_nat @ ( butlast_nat @ Xs ) @ N )
% 2.95/1.59 = ( nth_nat @ Xs @ N ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_97_f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_list_nat] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( member_list_nat @ ( nth_list_nat @ Xs @ N ) @ ( f_image_list_nat @ Xs @ A ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_98_f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_list_list_a] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( member_list_list_a @ ( nth_list_list_a @ Xs @ N ) @ ( f_image_list_list_a @ Xs @ A ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_99_f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_a] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( member_a @ ( nth_a @ Xs @ N ) @ ( f_image_a @ Xs @ A ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_100_f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_list_a] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( member_list_a @ ( nth_list_a @ Xs @ N ) @ ( f_image_list_a @ Xs @ A ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_101_f__imageI,axiom,
% 2.95/1.59 ! [N: nat,A: set_nat,Xs: list_nat] :
% 2.95/1.59 ( ( member_nat @ N @ A )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( f_image_nat @ Xs @ A ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_102_f__imageE,axiom,
% 2.95/1.59 ! [X2: list_nat,Xs: list_list_nat,A: set_nat] :
% 2.95/1.59 ( ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_list_nat @ Xs @ N2 ) )
% 2.95/1.59 => ( ( member_nat @ N2 @ A )
% 2.95/1.59 => ~ ( ord_less_nat @ N2 @ ( size_s1898481668st_nat @ Xs ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_103_f__imageE,axiom,
% 2.95/1.59 ! [X2: list_list_a,Xs: list_list_list_a,A: set_nat] :
% 2.95/1.59 ( ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_list_list_a @ Xs @ N2 ) )
% 2.95/1.59 => ( ( member_nat @ N2 @ A )
% 2.95/1.59 => ~ ( ord_less_nat @ N2 @ ( size_s575106428list_a @ Xs ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_104_f__imageE,axiom,
% 2.95/1.59 ! [X2: a,Xs: list_a,A: set_nat] :
% 2.95/1.59 ( ( member_a @ X2 @ ( f_image_a @ Xs @ A ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_a @ Xs @ N2 ) )
% 2.95/1.59 => ( ( member_nat @ N2 @ A )
% 2.95/1.59 => ~ ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_105_f__imageE,axiom,
% 2.95/1.59 ! [X2: list_a,Xs: list_list_a,A: set_nat] :
% 2.95/1.59 ( ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_list_a @ Xs @ N2 ) )
% 2.95/1.59 => ( ( member_nat @ N2 @ A )
% 2.95/1.59 => ~ ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_106_f__imageE,axiom,
% 2.95/1.59 ! [X2: nat,Xs: list_nat,A: set_nat] :
% 2.95/1.59 ( ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_nat @ Xs @ N2 ) )
% 2.95/1.59 => ( ( member_nat @ N2 @ A )
% 2.95/1.59 => ~ ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_107_list__update__overwrite,axiom,
% 2.95/1.59 ! [Xs: list_nat,I3: nat,X2: nat,Y2: nat] :
% 2.95/1.59 ( ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I3 @ Y2 )
% 2.95/1.59 = ( list_update_nat @ Xs @ I3 @ Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_108_list__update__overwrite,axiom,
% 2.95/1.59 ! [Xs: list_list_a,I3: nat,X2: list_a,Y2: list_a] :
% 2.95/1.59 ( ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I3 @ Y2 )
% 2.95/1.59 = ( list_update_list_a @ Xs @ I3 @ Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_109_list__update__overwrite,axiom,
% 2.95/1.59 ! [Xs: list_a,I3: nat,X2: a,Y2: a] :
% 2.95/1.59 ( ( list_update_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I3 @ Y2 )
% 2.95/1.59 = ( list_update_a @ Xs @ I3 @ Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_110_length__list__update,axiom,
% 2.95/1.59 ! [Xs: list_list_nat,I3: nat,X2: list_nat] :
% 2.95/1.59 ( ( size_s1898481668st_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) )
% 2.95/1.59 = ( size_s1898481668st_nat @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_111_length__list__update,axiom,
% 2.95/1.59 ! [Xs: list_list_list_a,I3: nat,X2: list_list_a] :
% 2.95/1.59 ( ( size_s575106428list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) )
% 2.95/1.59 = ( size_s575106428list_a @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_112_length__list__update,axiom,
% 2.95/1.59 ! [Xs: list_a,I3: nat,X2: a] :
% 2.95/1.59 ( ( size_size_list_a @ ( list_update_a @ Xs @ I3 @ X2 ) )
% 2.95/1.59 = ( size_size_list_a @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_113_length__list__update,axiom,
% 2.95/1.59 ! [Xs: list_list_a,I3: nat,X2: list_a] :
% 2.95/1.59 ( ( size_s1427607542list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) )
% 2.95/1.59 = ( size_s1427607542list_a @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_114_length__list__update,axiom,
% 2.95/1.59 ! [Xs: list_nat,I3: nat,X2: nat] :
% 2.95/1.59 ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) )
% 2.95/1.59 = ( size_size_list_nat @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_115_list__update__id,axiom,
% 2.95/1.59 ! [Xs: list_list_nat,I3: nat] :
% 2.95/1.59 ( ( list_update_list_nat @ Xs @ I3 @ ( nth_list_nat @ Xs @ I3 ) )
% 2.95/1.59 = Xs ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_116_list__update__id,axiom,
% 2.95/1.59 ! [Xs: list_list_list_a,I3: nat] :
% 2.95/1.59 ( ( list_u1330012152list_a @ Xs @ I3 @ ( nth_list_list_a @ Xs @ I3 ) )
% 2.95/1.59 = Xs ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_117_list__update__id,axiom,
% 2.95/1.59 ! [Xs: list_list_a,I3: nat] :
% 2.95/1.59 ( ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ I3 ) )
% 2.95/1.59 = Xs ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_118_list__update__id,axiom,
% 2.95/1.59 ! [Xs: list_a,I3: nat] :
% 2.95/1.59 ( ( list_update_a @ Xs @ I3 @ ( nth_a @ Xs @ I3 ) )
% 2.95/1.59 = Xs ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_119_list__update__id,axiom,
% 2.95/1.59 ! [Xs: list_nat,I3: nat] :
% 2.95/1.59 ( ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ I3 ) )
% 2.95/1.59 = Xs ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_120_nth__list__update__neq,axiom,
% 2.95/1.59 ! [I3: nat,J2: nat,Xs: list_list_nat,X2: list_nat] :
% 2.95/1.59 ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_list_nat @ Xs @ J2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_121_nth__list__update__neq,axiom,
% 2.95/1.59 ! [I3: nat,J2: nat,Xs: list_list_list_a,X2: list_list_a] :
% 2.95/1.59 ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_list_list_a @ Xs @ J2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_122_nth__list__update__neq,axiom,
% 2.95/1.59 ! [I3: nat,J2: nat,Xs: list_list_a,X2: list_a] :
% 2.95/1.59 ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_list_a @ Xs @ J2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_123_nth__list__update__neq,axiom,
% 2.95/1.59 ! [I3: nat,J2: nat,Xs: list_a,X2: a] :
% 2.95/1.59 ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_a @ Xs @ J2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_124_nth__list__update__neq,axiom,
% 2.95/1.59 ! [I3: nat,J2: nat,Xs: list_nat,X2: nat] :
% 2.95/1.59 ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_nat @ Xs @ J2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_125_list__update__swap,axiom,
% 2.95/1.59 ! [I3: nat,I4: nat,Xs: list_nat,X2: nat,X4: nat] :
% 2.95/1.59 ( ( I3 != I4 )
% 2.95/1.59 => ( ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I4 @ X4 )
% 2.95/1.59 = ( list_update_nat @ ( list_update_nat @ Xs @ I4 @ X4 ) @ I3 @ X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_126_list__update__swap,axiom,
% 2.95/1.59 ! [I3: nat,I4: nat,Xs: list_list_a,X2: list_a,X4: list_a] :
% 2.95/1.59 ( ( I3 != I4 )
% 2.95/1.59 => ( ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I4 @ X4 )
% 2.95/1.59 = ( list_update_list_a @ ( list_update_list_a @ Xs @ I4 @ X4 ) @ I3 @ X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_127_list__update__swap,axiom,
% 2.95/1.59 ! [I3: nat,I4: nat,Xs: list_a,X2: a,X4: a] :
% 2.95/1.59 ( ( I3 != I4 )
% 2.95/1.59 => ( ( list_update_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I4 @ X4 )
% 2.95/1.59 = ( list_update_a @ ( list_update_a @ Xs @ I4 @ X4 ) @ I3 @ X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_128_list__slice__aux__length,axiom,
% 2.95/1.59 ! [Xs: list_nat,K: nat,N: nat] :
% 2.95/1.59 ( ( size_s1898481668st_nat @ ( listSl1794011552ux_nat @ Xs @ K @ N ) )
% 2.95/1.59 = N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_129_list__slice__aux__length,axiom,
% 2.95/1.59 ! [Xs: list_list_a,K: nat,N: nat] :
% 2.95/1.59 ( ( size_s575106428list_a @ ( listSl856612276list_a @ Xs @ K @ N ) )
% 2.95/1.59 = N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_130_list__slice__aux__length,axiom,
% 2.95/1.59 ! [Xs: list_a,K: nat,N: nat] :
% 2.95/1.59 ( ( size_s1427607542list_a @ ( listSl1495374126_aux_a @ Xs @ K @ N ) )
% 2.95/1.59 = N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_131_nth__list__update,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_nat,J2: nat,X2: list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( ( ( I3 = J2 )
% 2.95/1.59 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = X2 ) )
% 2.95/1.59 & ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_list_nat @ Xs @ J2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_132_nth__list__update,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_list_a,J2: nat,X2: list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( ( ( I3 = J2 )
% 2.95/1.59 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = X2 ) )
% 2.95/1.59 & ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_list_list_a @ Xs @ J2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_133_nth__list__update,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_a,J2: nat,X2: a] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( ( I3 = J2 )
% 2.95/1.59 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = X2 ) )
% 2.95/1.59 & ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_a @ Xs @ J2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_134_nth__list__update,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_a,J2: nat,X2: list_a] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( ( I3 = J2 )
% 2.95/1.59 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = X2 ) )
% 2.95/1.59 & ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_list_a @ Xs @ J2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_135_nth__list__update,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_nat,J2: nat,X2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( ( I3 = J2 )
% 2.95/1.59 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = X2 ) )
% 2.95/1.59 & ( ( I3 != J2 )
% 2.95/1.59 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J2 )
% 2.95/1.59 = ( nth_nat @ Xs @ J2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_136_list__update__same__conv,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_nat,X2: list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( ( ( list_update_list_nat @ Xs @ I3 @ X2 )
% 2.95/1.59 = Xs )
% 2.95/1.59 = ( ( nth_list_nat @ Xs @ I3 )
% 2.95/1.59 = X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_137_list__update__same__conv,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_list_a,X2: list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( ( ( list_u1330012152list_a @ Xs @ I3 @ X2 )
% 2.95/1.59 = Xs )
% 2.95/1.59 = ( ( nth_list_list_a @ Xs @ I3 )
% 2.95/1.59 = X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_138_list__update__same__conv,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_a,X2: a] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( ( list_update_a @ Xs @ I3 @ X2 )
% 2.95/1.59 = Xs )
% 2.95/1.59 = ( ( nth_a @ Xs @ I3 )
% 2.95/1.59 = X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_139_list__update__same__conv,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_a,X2: list_a] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( ( list_update_list_a @ Xs @ I3 @ X2 )
% 2.95/1.59 = Xs )
% 2.95/1.59 = ( ( nth_list_a @ Xs @ I3 )
% 2.95/1.59 = X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_140_list__update__same__conv,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_nat,X2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( ( list_update_nat @ Xs @ I3 @ X2 )
% 2.95/1.59 = Xs )
% 2.95/1.59 = ( ( nth_nat @ Xs @ I3 )
% 2.95/1.59 = X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_141_set__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_nat,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( ( set_list_nat2 @ ( list_update_list_nat @ ( list_update_list_nat @ Xs @ I3 @ ( nth_list_nat @ Xs @ J2 ) ) @ J2 @ ( nth_list_nat @ Xs @ I3 ) ) )
% 2.95/1.59 = ( set_list_nat2 @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_142_set__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_list_a,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( ( set_list_list_a2 @ ( list_u1330012152list_a @ ( list_u1330012152list_a @ Xs @ I3 @ ( nth_list_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_list_a @ Xs @ I3 ) ) )
% 2.95/1.59 = ( set_list_list_a2 @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_143_set__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_a,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( set_a2 @ ( list_update_a @ ( list_update_a @ Xs @ I3 @ ( nth_a @ Xs @ J2 ) ) @ J2 @ ( nth_a @ Xs @ I3 ) ) )
% 2.95/1.59 = ( set_a2 @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_144_set__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_a,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( set_list_a2 @ ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_a @ Xs @ I3 ) ) )
% 2.95/1.59 = ( set_list_a2 @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_145_set__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_nat,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ J2 ) ) @ J2 @ ( nth_nat @ Xs @ I3 ) ) )
% 2.95/1.59 = ( set_nat2 @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_146_list__desc__trans,axiom,
% 2.95/1.59 ( list_desc_set_nat
% 2.95/1.59 = ( ^ [Xs2: list_set_nat] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_s577819178et_nat @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_eq_set_nat @ ( nth_set_nat @ Xs2 @ J ) @ ( nth_set_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_147_list__desc__trans,axiom,
% 2.95/1.59 ( list_desc_set_list_a
% 2.95/1.59 = ( ^ [Xs2: list_set_list_a] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_s1635937238list_a @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_le1301786372list_a @ ( nth_set_list_a @ Xs2 @ J ) @ ( nth_set_list_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_148_list__desc__trans,axiom,
% 2.95/1.59 ( list_desc_set_a
% 2.95/1.59 = ( ^ [Xs2: list_set_a] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_set_a @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_eq_set_a @ ( nth_set_a @ Xs2 @ J ) @ ( nth_set_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_149_list__desc__trans,axiom,
% 2.95/1.59 ( list_desc_nat
% 2.95/1.59 = ( ^ [Xs2: list_nat] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_150_list__asc__trans,axiom,
% 2.95/1.59 ( list_asc_set_nat
% 2.95/1.59 = ( ^ [Xs2: list_set_nat] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_s577819178et_nat @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_eq_set_nat @ ( nth_set_nat @ Xs2 @ I2 ) @ ( nth_set_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_151_list__asc__trans,axiom,
% 2.95/1.59 ( list_asc_set_list_a
% 2.95/1.59 = ( ^ [Xs2: list_set_list_a] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_s1635937238list_a @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_le1301786372list_a @ ( nth_set_list_a @ Xs2 @ I2 ) @ ( nth_set_list_a @ Xs2 @ J ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_152_list__asc__trans,axiom,
% 2.95/1.59 ( list_asc_set_a
% 2.95/1.59 = ( ^ [Xs2: list_set_a] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_set_a @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_eq_set_a @ ( nth_set_a @ Xs2 @ I2 ) @ ( nth_set_a @ Xs2 @ J ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_153_list__asc__trans,axiom,
% 2.95/1.59 ( list_asc_nat
% 2.95/1.59 = ( ^ [Xs2: list_nat] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_154_mem__Collect__eq,axiom,
% 2.95/1.59 ! [A2: nat,P: nat > $o] :
% 2.95/1.59 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 2.95/1.59 = ( P @ A2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_155_mem__Collect__eq,axiom,
% 2.95/1.59 ! [A2: list_a,P: list_a > $o] :
% 2.95/1.59 ( ( member_list_a @ A2 @ ( collect_list_a @ P ) )
% 2.95/1.59 = ( P @ A2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_156_mem__Collect__eq,axiom,
% 2.95/1.59 ! [A2: a,P: a > $o] :
% 2.95/1.59 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 2.95/1.59 = ( P @ A2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_157_Collect__mem__eq,axiom,
% 2.95/1.59 ! [A: set_nat] :
% 2.95/1.59 ( ( collect_nat
% 2.95/1.59 @ ^ [X3: nat] : ( member_nat @ X3 @ A ) )
% 2.95/1.59 = A ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_158_Collect__mem__eq,axiom,
% 2.95/1.59 ! [A: set_list_a] :
% 2.95/1.59 ( ( collect_list_a
% 2.95/1.59 @ ^ [X3: list_a] : ( member_list_a @ X3 @ A ) )
% 2.95/1.59 = A ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_159_Collect__mem__eq,axiom,
% 2.95/1.59 ! [A: set_a] :
% 2.95/1.59 ( ( collect_a
% 2.95/1.59 @ ^ [X3: a] : ( member_a @ X3 @ A ) )
% 2.95/1.59 = A ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_160_distinct__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_nat,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( ( distinct_list_nat @ ( list_update_list_nat @ ( list_update_list_nat @ Xs @ I3 @ ( nth_list_nat @ Xs @ J2 ) ) @ J2 @ ( nth_list_nat @ Xs @ I3 ) ) )
% 2.95/1.59 = ( distinct_list_nat @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_161_distinct__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_list_a,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( ( distinct_list_list_a @ ( list_u1330012152list_a @ ( list_u1330012152list_a @ Xs @ I3 @ ( nth_list_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_list_a @ Xs @ I3 ) ) )
% 2.95/1.59 = ( distinct_list_list_a @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_162_distinct__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_a,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( distinct_a @ ( list_update_a @ ( list_update_a @ Xs @ I3 @ ( nth_a @ Xs @ J2 ) ) @ J2 @ ( nth_a @ Xs @ I3 ) ) )
% 2.95/1.59 = ( distinct_a @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_163_distinct__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_list_a,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( distinct_list_a @ ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_a @ Xs @ I3 ) ) )
% 2.95/1.59 = ( distinct_list_a @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_164_distinct__swap,axiom,
% 2.95/1.59 ! [I3: nat,Xs: list_nat,J2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ J2 ) ) @ J2 @ ( nth_nat @ Xs @ I3 ) ) )
% 2.95/1.59 = ( distinct_nat @ Xs ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_165_f__rangeE,axiom,
% 2.95/1.59 ! [X2: list_nat,Xs: list_list_nat] :
% 2.95/1.59 ( ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ top_top_set_nat ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N2 @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( X2
% 2.95/1.59 != ( nth_list_nat @ Xs @ N2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_166_f__rangeE,axiom,
% 2.95/1.59 ! [X2: list_list_a,Xs: list_list_list_a] :
% 2.95/1.59 ( ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ top_top_set_nat ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N2 @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( X2
% 2.95/1.59 != ( nth_list_list_a @ Xs @ N2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_167_f__rangeE,axiom,
% 2.95/1.59 ! [X2: a,Xs: list_a] :
% 2.95/1.59 ( ( member_a @ X2 @ ( f_image_a @ Xs @ top_top_set_nat ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( X2
% 2.95/1.59 != ( nth_a @ Xs @ N2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_168_f__rangeE,axiom,
% 2.95/1.59 ! [X2: list_a,Xs: list_list_a] :
% 2.95/1.59 ( ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ top_top_set_nat ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( X2
% 2.95/1.59 != ( nth_list_a @ Xs @ N2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_169_f__rangeE,axiom,
% 2.95/1.59 ! [X2: nat,Xs: list_nat] :
% 2.95/1.59 ( ( member_nat @ X2 @ ( f_image_nat @ Xs @ top_top_set_nat ) )
% 2.95/1.59 => ~ ! [N2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( X2
% 2.95/1.59 != ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_170_f__rangeI,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( member_list_nat @ ( nth_list_nat @ Xs @ N ) @ ( f_image_list_nat @ Xs @ top_top_set_nat ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_171_f__rangeI,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( member_list_list_a @ ( nth_list_list_a @ Xs @ N ) @ ( f_image_list_list_a @ Xs @ top_top_set_nat ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_172_f__rangeI,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( member_a @ ( nth_a @ Xs @ N ) @ ( f_image_a @ Xs @ top_top_set_nat ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_173_f__rangeI,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( member_list_a @ ( nth_list_a @ Xs @ N ) @ ( f_image_list_a @ Xs @ top_top_set_nat ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_174_f__rangeI,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( f_image_nat @ Xs @ top_top_set_nat ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_175_f__range__eqI,axiom,
% 2.95/1.59 ! [X2: list_nat,Xs: list_list_nat,N: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_list_nat @ Xs @ N ) )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 2.95/1.59 => ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ top_top_set_nat ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_176_f__range__eqI,axiom,
% 2.95/1.59 ! [X2: list_list_a,Xs: list_list_list_a,N: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_list_list_a @ Xs @ N ) )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 2.95/1.59 => ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ top_top_set_nat ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_177_f__range__eqI,axiom,
% 2.95/1.59 ! [X2: a,Xs: list_a,N: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_a @ Xs @ N ) )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( member_a @ X2 @ ( f_image_a @ Xs @ top_top_set_nat ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_178_f__range__eqI,axiom,
% 2.95/1.59 ! [X2: list_a,Xs: list_list_a,N: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_list_a @ Xs @ N ) )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ top_top_set_nat ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_179_f__range__eqI,axiom,
% 2.95/1.59 ! [X2: nat,Xs: list_nat,N: nat] :
% 2.95/1.59 ( ( X2
% 2.95/1.59 = ( nth_nat @ Xs @ N ) )
% 2.95/1.59 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( member_nat @ X2 @ ( f_image_nat @ Xs @ top_top_set_nat ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_180_f__image__subsetI,axiom,
% 2.95/1.59 ! [A: set_nat,Xs: list_list_nat,B: set_list_nat] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ( ( member_nat @ N2 @ A )
% 2.95/1.59 & ( ord_less_nat @ N2 @ ( size_s1898481668st_nat @ Xs ) ) )
% 2.95/1.59 => ( member_list_nat @ ( nth_list_nat @ Xs @ N2 ) @ B ) )
% 2.95/1.59 => ( ord_le1747345782st_nat @ ( f_image_list_nat @ Xs @ A ) @ B ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_181_f__image__subsetI,axiom,
% 2.95/1.59 ! [A: set_nat,Xs: list_list_list_a,B: set_list_list_a] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ( ( member_nat @ N2 @ A )
% 2.95/1.59 & ( ord_less_nat @ N2 @ ( size_s575106428list_a @ Xs ) ) )
% 2.95/1.59 => ( member_list_list_a @ ( nth_list_list_a @ Xs @ N2 ) @ B ) )
% 2.95/1.59 => ( ord_le1756736906list_a @ ( f_image_list_list_a @ Xs @ A ) @ B ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_182_f__image__subsetI,axiom,
% 2.95/1.59 ! [A: set_nat,Xs: list_a,B: set_a] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ( ( member_nat @ N2 @ A )
% 2.95/1.59 & ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) ) )
% 2.95/1.59 => ( member_a @ ( nth_a @ Xs @ N2 ) @ B ) )
% 2.95/1.59 => ( ord_less_eq_set_a @ ( f_image_a @ Xs @ A ) @ B ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_183_f__image__subsetI,axiom,
% 2.95/1.59 ! [A: set_nat,Xs: list_list_a,B: set_list_a] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ( ( member_nat @ N2 @ A )
% 2.95/1.59 & ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) ) )
% 2.95/1.59 => ( member_list_a @ ( nth_list_a @ Xs @ N2 ) @ B ) )
% 2.95/1.59 => ( ord_le1301786372list_a @ ( f_image_list_a @ Xs @ A ) @ B ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_184_f__image__subsetI,axiom,
% 2.95/1.59 ! [A: set_nat,Xs: list_nat,B: set_nat] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ( ( member_nat @ N2 @ A )
% 2.95/1.59 & ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) ) )
% 2.95/1.59 => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ B ) )
% 2.95/1.59 => ( ord_less_eq_set_nat @ ( f_image_nat @ Xs @ A ) @ B ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_185_f__image__subset__iff,axiom,
% 2.95/1.59 ! [Xs: list_a,A: set_nat,B: set_a] :
% 2.95/1.59 ( ( ord_less_eq_set_a @ ( f_image_a @ Xs @ A ) @ B )
% 2.95/1.59 = ( ! [X3: nat] :
% 2.95/1.59 ( ( member_nat @ X3 @ A )
% 2.95/1.59 => ( ( ord_less_nat @ X3 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( member_a @ ( nth_a @ Xs @ X3 ) @ B ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_186_f__image__subset__iff,axiom,
% 2.95/1.59 ! [Xs: list_list_a,A: set_nat,B: set_list_a] :
% 2.95/1.59 ( ( ord_le1301786372list_a @ ( f_image_list_a @ Xs @ A ) @ B )
% 2.95/1.59 = ( ! [X3: nat] :
% 2.95/1.59 ( ( member_nat @ X3 @ A )
% 2.95/1.59 => ( ( ord_less_nat @ X3 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( member_list_a @ ( nth_list_a @ Xs @ X3 ) @ B ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_187_f__image__subset__iff,axiom,
% 2.95/1.59 ! [Xs: list_nat,A: set_nat,B: set_nat] :
% 2.95/1.59 ( ( ord_less_eq_set_nat @ ( f_image_nat @ Xs @ A ) @ B )
% 2.95/1.59 = ( ! [X3: nat] :
% 2.95/1.59 ( ( member_nat @ X3 @ A )
% 2.95/1.59 => ( ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( member_nat @ ( nth_nat @ Xs @ X3 ) @ B ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_188_list__update__beyond,axiom,
% 2.95/1.59 ! [Xs: list_a,I3: nat,X2: a] :
% 2.95/1.59 ( ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ I3 )
% 2.95/1.59 => ( ( list_update_a @ Xs @ I3 @ X2 )
% 2.95/1.59 = Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_189_list__update__beyond,axiom,
% 2.95/1.59 ! [Xs: list_list_a,I3: nat,X2: list_a] :
% 2.95/1.59 ( ( ord_less_eq_nat @ ( size_s1427607542list_a @ Xs ) @ I3 )
% 2.95/1.59 => ( ( list_update_list_a @ Xs @ I3 @ X2 )
% 2.95/1.59 = Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_190_list__update__beyond,axiom,
% 2.95/1.59 ! [Xs: list_nat,I3: nat,X2: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I3 )
% 2.95/1.59 => ( ( list_update_nat @ Xs @ I3 @ X2 )
% 2.95/1.59 = Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_191_less__mono__imp__le__mono,axiom,
% 2.95/1.59 ! [F: nat > nat,I3: nat,J2: nat] :
% 2.95/1.59 ( ! [I: nat,J3: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I @ J3 )
% 2.95/1.59 => ( ord_less_nat @ ( F @ I ) @ ( F @ J3 ) ) )
% 2.95/1.59 => ( ( ord_less_eq_nat @ I3 @ J2 )
% 2.95/1.59 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( F @ J2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_192_le__neq__implies__less,axiom,
% 2.95/1.59 ! [M: nat,N: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ M @ N )
% 2.95/1.59 => ( ( M != N )
% 2.95/1.59 => ( ord_less_nat @ M @ N ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_193_less__or__eq__imp__le,axiom,
% 2.95/1.59 ! [M: nat,N: nat] :
% 2.95/1.59 ( ( ( ord_less_nat @ M @ N )
% 2.95/1.59 | ( M = N ) )
% 2.95/1.59 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_194_le__eq__less__or__eq,axiom,
% 2.95/1.59 ( ord_less_eq_nat
% 2.95/1.59 = ( ^ [M3: nat,N3: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M3 @ N3 )
% 2.95/1.59 | ( M3 = N3 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_195_less__imp__le__nat,axiom,
% 2.95/1.59 ! [M: nat,N: nat] :
% 2.95/1.59 ( ( ord_less_nat @ M @ N )
% 2.95/1.59 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_196_nat__less__le,axiom,
% 2.95/1.59 ( ord_less_nat
% 2.95/1.59 = ( ^ [M3: nat,N3: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ M3 @ N3 )
% 2.95/1.59 & ( M3 != N3 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_197_distinct__Ex1,axiom,
% 2.95/1.59 ! [Xs: list_a,X2: a] :
% 2.95/1.59 ( ( distinct_a @ Xs )
% 2.95/1.59 => ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
% 2.95/1.59 => ? [X5: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X5 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 & ( ( nth_a @ Xs @ X5 )
% 2.95/1.59 = X2 )
% 2.95/1.59 & ! [Y3: nat] :
% 2.95/1.59 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 & ( ( nth_a @ Xs @ Y3 )
% 2.95/1.59 = X2 ) )
% 2.95/1.59 => ( Y3 = X5 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_198_distinct__Ex1,axiom,
% 2.95/1.59 ! [Xs: list_list_a,X2: list_a] :
% 2.95/1.59 ( ( distinct_list_a @ Xs )
% 2.95/1.59 => ( ( member_list_a @ X2 @ ( set_list_a2 @ Xs ) )
% 2.95/1.59 => ? [X5: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X5 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 & ( ( nth_list_a @ Xs @ X5 )
% 2.95/1.59 = X2 )
% 2.95/1.59 & ! [Y3: nat] :
% 2.95/1.59 ( ( ( ord_less_nat @ Y3 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 & ( ( nth_list_a @ Xs @ Y3 )
% 2.95/1.59 = X2 ) )
% 2.95/1.59 => ( Y3 = X5 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_199_distinct__Ex1,axiom,
% 2.95/1.59 ! [Xs: list_nat,X2: nat] :
% 2.95/1.59 ( ( distinct_nat @ Xs )
% 2.95/1.59 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 2.95/1.59 => ? [X5: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X5 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 & ( ( nth_nat @ Xs @ X5 )
% 2.95/1.59 = X2 )
% 2.95/1.59 & ! [Y3: nat] :
% 2.95/1.59 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 & ( ( nth_nat @ Xs @ Y3 )
% 2.95/1.59 = X2 ) )
% 2.95/1.59 => ( Y3 = X5 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_200_list__strict__asc__distinct,axiom,
% 2.95/1.59 ! [Xs: list_nat] :
% 2.95/1.59 ( ( list_strict_asc_nat @ Xs )
% 2.95/1.59 => ( distinct_nat @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_201_list__strict__desc__distinct,axiom,
% 2.95/1.59 ! [Xs: list_nat] :
% 2.95/1.59 ( ( list_strict_desc_nat @ Xs )
% 2.95/1.59 => ( distinct_nat @ Xs ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_202_list__strict__asc__trans__le,axiom,
% 2.95/1.59 ! [Xs: list_nat] :
% 2.95/1.59 ( ( list_strict_asc_nat @ Xs )
% 2.95/1.59 => ! [J4: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J4 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ! [I5: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ I5 @ J4 )
% 2.95/1.59 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I5 ) @ ( nth_nat @ Xs @ J4 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_203_list__asc__trans__le,axiom,
% 2.95/1.59 ( list_asc_nat
% 2.95/1.59 = ( ^ [Xs2: list_nat] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_204_list__desc__trans__le,axiom,
% 2.95/1.59 ( list_desc_nat
% 2.95/1.59 = ( ^ [Xs2: list_nat] :
% 2.95/1.59 ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 => ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ I2 @ J )
% 2.95/1.59 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_205_nth__eq__iff__index__eq,axiom,
% 2.95/1.59 ! [Xs: list_a,I3: nat,J2: nat] :
% 2.95/1.59 ( ( distinct_a @ Xs )
% 2.95/1.59 => ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ( ( nth_a @ Xs @ I3 )
% 2.95/1.59 = ( nth_a @ Xs @ J2 ) )
% 2.95/1.59 = ( I3 = J2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_206_nth__eq__iff__index__eq,axiom,
% 2.95/1.59 ! [Xs: list_list_a,I3: nat,J2: nat] :
% 2.95/1.59 ( ( distinct_list_a @ Xs )
% 2.95/1.59 => ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ( ( nth_list_a @ Xs @ I3 )
% 2.95/1.59 = ( nth_list_a @ Xs @ J2 ) )
% 2.95/1.59 = ( I3 = J2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_207_nth__eq__iff__index__eq,axiom,
% 2.95/1.59 ! [Xs: list_nat,I3: nat,J2: nat] :
% 2.95/1.59 ( ( distinct_nat @ Xs )
% 2.95/1.59 => ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ( ( nth_nat @ Xs @ I3 )
% 2.95/1.59 = ( nth_nat @ Xs @ J2 ) )
% 2.95/1.59 = ( I3 = J2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_208_distinct__conv__nth,axiom,
% 2.95/1.59 ( distinct_a
% 2.95/1.59 = ( ^ [Xs2: list_a] :
% 2.95/1.59 ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
% 2.95/1.59 => ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_a @ Xs2 ) )
% 2.95/1.59 => ( ( I2 != J )
% 2.95/1.59 => ( ( nth_a @ Xs2 @ I2 )
% 2.95/1.59 != ( nth_a @ Xs2 @ J ) ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_209_distinct__conv__nth,axiom,
% 2.95/1.59 ( distinct_list_a
% 2.95/1.59 = ( ^ [Xs2: list_list_a] :
% 2.95/1.59 ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
% 2.95/1.59 => ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_s1427607542list_a @ Xs2 ) )
% 2.95/1.59 => ( ( I2 != J )
% 2.95/1.59 => ( ( nth_list_a @ Xs2 @ I2 )
% 2.95/1.59 != ( nth_list_a @ Xs2 @ J ) ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_210_distinct__conv__nth,axiom,
% 2.95/1.59 ( distinct_nat
% 2.95/1.59 = ( ^ [Xs2: list_nat] :
% 2.95/1.59 ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 => ! [J: nat] :
% 2.95/1.59 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.95/1.59 => ( ( I2 != J )
% 2.95/1.59 => ( ( nth_nat @ Xs2 @ I2 )
% 2.95/1.59 != ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_211_all__set__conv__all__nth,axiom,
% 2.95/1.59 ! [Xs: list_a,P: a > $o] :
% 2.95/1.59 ( ( ! [X3: a] :
% 2.95/1.59 ( ( member_a @ X3 @ ( set_a2 @ Xs ) )
% 2.95/1.59 => ( P @ X3 ) ) )
% 2.95/1.59 = ( ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( P @ ( nth_a @ Xs @ I2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_212_all__set__conv__all__nth,axiom,
% 2.95/1.59 ! [Xs: list_list_a,P: list_a > $o] :
% 2.95/1.59 ( ( ! [X3: list_a] :
% 2.95/1.59 ( ( member_list_a @ X3 @ ( set_list_a2 @ Xs ) )
% 2.95/1.59 => ( P @ X3 ) ) )
% 2.95/1.59 = ( ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( P @ ( nth_list_a @ Xs @ I2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_213_all__set__conv__all__nth,axiom,
% 2.95/1.59 ! [Xs: list_nat,P: nat > $o] :
% 2.95/1.59 ( ( ! [X3: nat] :
% 2.95/1.59 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 2.95/1.59 => ( P @ X3 ) ) )
% 2.95/1.59 = ( ! [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( P @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_214_all__nth__imp__all__set,axiom,
% 2.95/1.59 ! [Xs: list_a,P: a > $o,X2: a] :
% 2.95/1.59 ( ! [I: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( P @ ( nth_a @ Xs @ I ) ) )
% 2.95/1.59 => ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
% 2.95/1.59 => ( P @ X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_215_all__nth__imp__all__set,axiom,
% 2.95/1.59 ! [Xs: list_list_a,P: list_a > $o,X2: list_a] :
% 2.95/1.59 ( ! [I: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( P @ ( nth_list_a @ Xs @ I ) ) )
% 2.95/1.59 => ( ( member_list_a @ X2 @ ( set_list_a2 @ Xs ) )
% 2.95/1.59 => ( P @ X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_216_all__nth__imp__all__set,axiom,
% 2.95/1.59 ! [Xs: list_nat,P: nat > $o,X2: nat] :
% 2.95/1.59 ( ! [I: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( P @ ( nth_nat @ Xs @ I ) ) )
% 2.95/1.59 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 2.95/1.59 => ( P @ X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_217_in__set__conv__nth,axiom,
% 2.95/1.59 ! [X2: a,Xs: list_a] :
% 2.95/1.59 ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
% 2.95/1.59 = ( ? [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 & ( ( nth_a @ Xs @ I2 )
% 2.95/1.59 = X2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_218_in__set__conv__nth,axiom,
% 2.95/1.59 ! [X2: list_a,Xs: list_list_a] :
% 2.95/1.59 ( ( member_list_a @ X2 @ ( set_list_a2 @ Xs ) )
% 2.95/1.59 = ( ? [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 & ( ( nth_list_a @ Xs @ I2 )
% 2.95/1.59 = X2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_219_in__set__conv__nth,axiom,
% 2.95/1.59 ! [X2: nat,Xs: list_nat] :
% 2.95/1.59 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 2.95/1.59 = ( ? [I2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 & ( ( nth_nat @ Xs @ I2 )
% 2.95/1.59 = X2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_220_list__ball__nth,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_a,P: a > $o] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( ! [X5: a] :
% 2.95/1.59 ( ( member_a @ X5 @ ( set_a2 @ Xs ) )
% 2.95/1.59 => ( P @ X5 ) )
% 2.95/1.59 => ( P @ ( nth_a @ Xs @ N ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_221_list__ball__nth,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_list_a,P: list_a > $o] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( ! [X5: list_a] :
% 2.95/1.59 ( ( member_list_a @ X5 @ ( set_list_a2 @ Xs ) )
% 2.95/1.59 => ( P @ X5 ) )
% 2.95/1.59 => ( P @ ( nth_list_a @ Xs @ N ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_222_list__ball__nth,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( ! [X5: nat] :
% 2.95/1.59 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 2.95/1.59 => ( P @ X5 ) )
% 2.95/1.59 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_223_nth__mem,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( member_a @ ( nth_a @ Xs @ N ) @ ( set_a2 @ Xs ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_224_nth__mem,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_list_a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( member_list_a @ ( nth_list_a @ Xs @ N ) @ ( set_list_a2 @ Xs ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_225_nth__mem,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_nat] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_226_set__update__memI,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_a,X2: a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( member_a @ X2 @ ( set_a2 @ ( list_update_a @ Xs @ N @ X2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_227_set__update__memI,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_list_a,X2: list_a] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( member_list_a @ X2 @ ( set_list_a2 @ ( list_update_list_a @ Xs @ N @ X2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_228_set__update__memI,axiom,
% 2.95/1.59 ! [N: nat,Xs: list_nat,X2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X2 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_229_f__image__eq__set,axiom,
% 2.95/1.59 ! [Xs: list_a,A: set_nat] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) )
% 2.95/1.59 => ( member_nat @ N2 @ A ) )
% 2.95/1.59 => ( ( f_image_a @ Xs @ A )
% 2.95/1.59 = ( set_a2 @ Xs ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_230_f__image__eq__set,axiom,
% 2.95/1.59 ! [Xs: list_list_a,A: set_nat] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) )
% 2.95/1.59 => ( member_nat @ N2 @ A ) )
% 2.95/1.59 => ( ( f_image_list_a @ Xs @ A )
% 2.95/1.59 = ( set_list_a2 @ Xs ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_231_f__image__eq__set,axiom,
% 2.95/1.59 ! [Xs: list_nat,A: set_nat] :
% 2.95/1.59 ( ! [N2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 2.95/1.59 => ( member_nat @ N2 @ A ) )
% 2.95/1.59 => ( ( f_image_nat @ Xs @ A )
% 2.95/1.59 = ( set_nat2 @ Xs ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_232_order__refl,axiom,
% 2.95/1.59 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_233_Nat_Oex__has__greatest__nat,axiom,
% 2.95/1.59 ! [P: nat > $o,K: nat,B2: nat] :
% 2.95/1.59 ( ( P @ K )
% 2.95/1.59 => ( ! [Y4: nat] :
% 2.95/1.59 ( ( P @ Y4 )
% 2.95/1.59 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 2.95/1.59 => ? [X5: nat] :
% 2.95/1.59 ( ( P @ X5 )
% 2.95/1.59 & ! [Y3: nat] :
% 2.95/1.59 ( ( P @ Y3 )
% 2.95/1.59 => ( ord_less_eq_nat @ Y3 @ X5 ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_234_nat__le__linear,axiom,
% 2.95/1.59 ! [M: nat,N: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ M @ N )
% 2.95/1.59 | ( ord_less_eq_nat @ N @ M ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_235_le__antisym,axiom,
% 2.95/1.59 ! [M: nat,N: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ M @ N )
% 2.95/1.59 => ( ( ord_less_eq_nat @ N @ M )
% 2.95/1.59 => ( M = N ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_236_eq__imp__le,axiom,
% 2.95/1.59 ! [M: nat,N: nat] :
% 2.95/1.59 ( ( M = N )
% 2.95/1.59 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_237_le__trans,axiom,
% 2.95/1.59 ! [I3: nat,J2: nat,K: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ I3 @ J2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ J2 @ K )
% 2.95/1.59 => ( ord_less_eq_nat @ I3 @ K ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_238_le__refl,axiom,
% 2.95/1.59 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_239_dual__order_Oantisym,axiom,
% 2.95/1.59 ! [B2: nat,A2: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.59 => ( A2 = B2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_240_dual__order_Oeq__iff,axiom,
% 2.95/1.59 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.95/1.59 = ( ^ [A3: nat,B3: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ B3 @ A3 )
% 2.95/1.59 & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_241_dual__order_Otrans,axiom,
% 2.95/1.59 ! [B2: nat,A2: nat,C: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ C @ B2 )
% 2.95/1.59 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_242_linorder__wlog,axiom,
% 2.95/1.59 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 2.95/1.59 ( ! [A4: nat,B4: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ A4 @ B4 )
% 2.95/1.59 => ( P @ A4 @ B4 ) )
% 2.95/1.59 => ( ! [A4: nat,B4: nat] :
% 2.95/1.59 ( ( P @ B4 @ A4 )
% 2.95/1.59 => ( P @ A4 @ B4 ) )
% 2.95/1.59 => ( P @ A2 @ B2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_243_dual__order_Orefl,axiom,
% 2.95/1.59 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_244_order__trans,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.95/1.59 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_245_order__class_Oorder_Oantisym,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.95/1.59 => ( A2 = B2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_246_ord__le__eq__trans,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat,C: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.59 => ( ( B2 = C )
% 2.95/1.59 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_247_ord__eq__le__trans,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat,C: nat] :
% 2.95/1.59 ( ( A2 = B2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.95/1.59 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_248_order__class_Oorder_Oeq__iff,axiom,
% 2.95/1.59 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.95/1.59 = ( ^ [A3: nat,B3: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ A3 @ B3 )
% 2.95/1.59 & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_249_antisym__conv,axiom,
% 2.95/1.59 ! [Y2: nat,X2: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.59 = ( X2 = Y2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_250_le__cases3,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.95/1.59 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.59 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 2.95/1.59 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.95/1.59 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 2.95/1.59 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 2.95/1.59 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 2.95/1.59 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 2.95/1.59 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 2.95/1.59 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.95/1.59 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 2.95/1.59 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 2.95/1.59 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_251_order_Otrans,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat,C: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.95/1.59 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_252_le__cases,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.59 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_253_eq__refl,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ( X2 = Y2 )
% 2.95/1.59 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_254_linear,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.59 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_255_antisym,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.95/1.59 => ( X2 = Y2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_256_eq__iff,axiom,
% 2.95/1.59 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.95/1.59 = ( ^ [X3: nat,Y5: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 2.95/1.59 & ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_257_ord__le__eq__subst,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.59 => ( ( ( F @ B2 )
% 2.95/1.59 = C )
% 2.95/1.59 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 2.95/1.59 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_258_ord__eq__le__subst,axiom,
% 2.95/1.59 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 2.95/1.59 ( ( A2
% 2.95/1.59 = ( F @ B2 ) )
% 2.95/1.59 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.95/1.59 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 2.95/1.59 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.59 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_259_order__subst2,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.59 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 2.95/1.59 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 2.95/1.59 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.59 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_260_order__subst1,axiom,
% 2.95/1.59 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 2.95/1.59 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.95/1.59 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.59 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 2.95/1.59 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.59 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_261_ord__eq__less__subst,axiom,
% 2.95/1.59 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 2.95/1.59 ( ( A2
% 2.95/1.59 = ( F @ B2 ) )
% 2.95/1.59 => ( ( ord_less_nat @ B2 @ C )
% 2.95/1.59 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X5 @ Y4 )
% 2.95/1.59 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.59 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_262_ord__less__eq__subst,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 2.95/1.59 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.59 => ( ( ( F @ B2 )
% 2.95/1.59 = C )
% 2.95/1.59 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X5 @ Y4 )
% 2.95/1.59 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.59 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_263_order__less__subst1,axiom,
% 2.95/1.59 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 2.95/1.59 ( ( ord_less_nat @ A2 @ ( F @ B2 ) )
% 2.95/1.59 => ( ( ord_less_nat @ B2 @ C )
% 2.95/1.59 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X5 @ Y4 )
% 2.95/1.59 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.59 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_264_order__less__subst2,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 2.95/1.59 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.59 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 2.95/1.59 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X5 @ Y4 )
% 2.95/1.59 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.59 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_265_gt__ex,axiom,
% 2.95/1.59 ! [X2: nat] :
% 2.95/1.59 ? [X_1: nat] : ( ord_less_nat @ X2 @ X_1 ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_266_neqE,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ( X2 != Y2 )
% 2.95/1.59 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.59 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_267_neq__iff,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ( X2 != Y2 )
% 2.95/1.59 = ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.59 | ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_268_order_Oasym,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.59 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_269_less__imp__neq,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.59 => ( X2 != Y2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_270_less__asym,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.59 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_271_less__asym_H,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.59 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_272_less__trans,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.59 => ( ( ord_less_nat @ Y2 @ Z2 )
% 2.95/1.59 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_273_less__linear,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.59 | ( X2 = Y2 )
% 2.95/1.59 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_274_less__irrefl,axiom,
% 2.95/1.59 ! [X2: nat] :
% 2.95/1.59 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_275_ord__eq__less__trans,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat,C: nat] :
% 2.95/1.59 ( ( A2 = B2 )
% 2.95/1.59 => ( ( ord_less_nat @ B2 @ C )
% 2.95/1.59 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_276_ord__less__eq__trans,axiom,
% 2.95/1.59 ! [A2: nat,B2: nat,C: nat] :
% 2.95/1.59 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.59 => ( ( B2 = C )
% 2.95/1.59 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_277_dual__order_Oasym,axiom,
% 2.95/1.59 ! [B2: nat,A2: nat] :
% 2.95/1.59 ( ( ord_less_nat @ B2 @ A2 )
% 2.95/1.59 => ~ ( ord_less_nat @ A2 @ B2 ) ) ).
% 2.95/1.59
% 2.95/1.59 thf(fact_278_less__imp__not__eq,axiom,
% 2.95/1.59 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ( X2 != Y2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_279_less__not__sym,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_280_less__induct,axiom,
% 2.95/1.60 ! [P: nat > $o,A2: nat] :
% 2.95/1.60 ( ! [X5: nat] :
% 2.95/1.60 ( ! [Y3: nat] :
% 2.95/1.60 ( ( ord_less_nat @ Y3 @ X5 )
% 2.95/1.60 => ( P @ Y3 ) )
% 2.95/1.60 => ( P @ X5 ) )
% 2.95/1.60 => ( P @ A2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_281_antisym__conv3,axiom,
% 2.95/1.60 ! [Y2: nat,X2: nat] :
% 2.95/1.60 ( ~ ( ord_less_nat @ Y2 @ X2 )
% 2.95/1.60 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 2.95/1.60 = ( X2 = Y2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_282_less__imp__not__eq2,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ( Y2 != X2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_283_less__imp__triv,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat,P: $o] :
% 2.95/1.60 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ( ( ord_less_nat @ Y2 @ X2 )
% 2.95/1.60 => P ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_284_linorder__cases,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ( ( X2 != Y2 )
% 2.95/1.60 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_285_dual__order_Oirrefl,axiom,
% 2.95/1.60 ! [A2: nat] :
% 2.95/1.60 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_286_order_Ostrict__trans,axiom,
% 2.95/1.60 ! [A2: nat,B2: nat,C: nat] :
% 2.95/1.60 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.60 => ( ( ord_less_nat @ B2 @ C )
% 2.95/1.60 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_287_less__imp__not__less,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_288_exists__least__iff,axiom,
% 2.95/1.60 ( ( ^ [P3: nat > $o] :
% 2.95/1.60 ? [X: nat] : ( P3 @ X ) )
% 2.95/1.60 = ( ^ [P2: nat > $o] :
% 2.95/1.60 ? [N3: nat] :
% 2.95/1.60 ( ( P2 @ N3 )
% 2.95/1.60 & ! [M3: nat] :
% 2.95/1.60 ( ( ord_less_nat @ M3 @ N3 )
% 2.95/1.60 => ~ ( P2 @ M3 ) ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_289_linorder__less__wlog,axiom,
% 2.95/1.60 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 2.95/1.60 ( ! [A4: nat,B4: nat] :
% 2.95/1.60 ( ( ord_less_nat @ A4 @ B4 )
% 2.95/1.60 => ( P @ A4 @ B4 ) )
% 2.95/1.60 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 2.95/1.60 => ( ! [A4: nat,B4: nat] :
% 2.95/1.60 ( ( P @ B4 @ A4 )
% 2.95/1.60 => ( P @ A4 @ B4 ) )
% 2.95/1.60 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_290_dual__order_Ostrict__trans,axiom,
% 2.95/1.60 ! [B2: nat,A2: nat,C: nat] :
% 2.95/1.60 ( ( ord_less_nat @ B2 @ A2 )
% 2.95/1.60 => ( ( ord_less_nat @ C @ B2 )
% 2.95/1.60 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_291_not__less__iff__gr__or__eq,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 2.95/1.60 = ( ( ord_less_nat @ Y2 @ X2 )
% 2.95/1.60 | ( X2 = Y2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_292_order_Ostrict__implies__not__eq,axiom,
% 2.95/1.60 ! [A2: nat,B2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.60 => ( A2 != B2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_293_dual__order_Ostrict__implies__not__eq,axiom,
% 2.95/1.60 ! [B2: nat,A2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ B2 @ A2 )
% 2.95/1.60 => ( A2 != B2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_294_order_Onot__eq__order__implies__strict,axiom,
% 2.95/1.60 ! [A2: nat,B2: nat] :
% 2.95/1.60 ( ( A2 != B2 )
% 2.95/1.60 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.60 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_295_dual__order_Ostrict__implies__order,axiom,
% 2.95/1.60 ! [B2: nat,A2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ B2 @ A2 )
% 2.95/1.60 => ( ord_less_eq_nat @ B2 @ A2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_296_dual__order_Ostrict__iff__order,axiom,
% 2.95/1.60 ( ord_less_nat
% 2.95/1.60 = ( ^ [B3: nat,A3: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ B3 @ A3 )
% 2.95/1.60 & ( A3 != B3 ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_297_dual__order_Oorder__iff__strict,axiom,
% 2.95/1.60 ( ord_less_eq_nat
% 2.95/1.60 = ( ^ [B3: nat,A3: nat] :
% 2.95/1.60 ( ( ord_less_nat @ B3 @ A3 )
% 2.95/1.60 | ( A3 = B3 ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_298_order_Ostrict__implies__order,axiom,
% 2.95/1.60 ! [A2: nat,B2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.60 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_299_dual__order_Ostrict__trans2,axiom,
% 2.95/1.60 ! [B2: nat,A2: nat,C: nat] :
% 2.95/1.60 ( ( ord_less_nat @ B2 @ A2 )
% 2.95/1.60 => ( ( ord_less_eq_nat @ C @ B2 )
% 2.95/1.60 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_300_dual__order_Ostrict__trans1,axiom,
% 2.95/1.60 ! [B2: nat,A2: nat,C: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.95/1.60 => ( ( ord_less_nat @ C @ B2 )
% 2.95/1.60 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_301_order_Ostrict__iff__order,axiom,
% 2.95/1.60 ( ord_less_nat
% 2.95/1.60 = ( ^ [A3: nat,B3: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ A3 @ B3 )
% 2.95/1.60 & ( A3 != B3 ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_302_order_Oorder__iff__strict,axiom,
% 2.95/1.60 ( ord_less_eq_nat
% 2.95/1.60 = ( ^ [A3: nat,B3: nat] :
% 2.95/1.60 ( ( ord_less_nat @ A3 @ B3 )
% 2.95/1.60 | ( A3 = B3 ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_303_order_Ostrict__trans2,axiom,
% 2.95/1.60 ! [A2: nat,B2: nat,C: nat] :
% 2.95/1.60 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.60 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.95/1.60 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_304_order_Ostrict__trans1,axiom,
% 2.95/1.60 ! [A2: nat,B2: nat,C: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.60 => ( ( ord_less_nat @ B2 @ C )
% 2.95/1.60 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_305_not__le__imp__less,axiom,
% 2.95/1.60 ! [Y2: nat,X2: nat] :
% 2.95/1.60 ( ~ ( ord_less_eq_nat @ Y2 @ X2 )
% 2.95/1.60 => ( ord_less_nat @ X2 @ Y2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_306_less__le__not__le,axiom,
% 2.95/1.60 ( ord_less_nat
% 2.95/1.60 = ( ^ [X3: nat,Y5: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 2.95/1.60 & ~ ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_307_le__imp__less__or__eq,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.60 => ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 | ( X2 = Y2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_308_le__less__linear,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.60 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_309_less__le__trans,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.95/1.60 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_310_le__less__trans,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.60 => ( ( ord_less_nat @ Y2 @ Z2 )
% 2.95/1.60 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_311_less__imp__le,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_312_antisym__conv2,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.60 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 2.95/1.60 = ( X2 = Y2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_313_antisym__conv1,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.95/1.60 = ( X2 = Y2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_314_le__neq__trans,axiom,
% 2.95/1.60 ! [A2: nat,B2: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.60 => ( ( A2 != B2 )
% 2.95/1.60 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_315_not__less,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 2.95/1.60 = ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_316_not__le,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ( ~ ( ord_less_eq_nat @ X2 @ Y2 ) )
% 2.95/1.60 = ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_317_order__less__le__subst2,axiom,
% 2.95/1.60 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 2.95/1.60 ( ( ord_less_nat @ A2 @ B2 )
% 2.95/1.60 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 2.95/1.60 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X5 @ Y4 )
% 2.95/1.60 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.60 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_318_order__less__le__subst1,axiom,
% 2.95/1.60 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 2.95/1.60 ( ( ord_less_nat @ A2 @ ( F @ B2 ) )
% 2.95/1.60 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.95/1.60 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 2.95/1.60 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.60 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_319_order__le__less__subst2,axiom,
% 2.95/1.60 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.95/1.60 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 2.95/1.60 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 2.95/1.60 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.60 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_320_order__le__less__subst1,axiom,
% 2.95/1.60 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 2.95/1.60 => ( ( ord_less_nat @ B2 @ C )
% 2.95/1.60 => ( ! [X5: nat,Y4: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X5 @ Y4 )
% 2.95/1.60 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.95/1.60 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_321_less__le,axiom,
% 2.95/1.60 ( ord_less_nat
% 2.95/1.60 = ( ^ [X3: nat,Y5: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 2.95/1.60 & ( X3 != Y5 ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_322_le__less,axiom,
% 2.95/1.60 ( ord_less_eq_nat
% 2.95/1.60 = ( ^ [X3: nat,Y5: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X3 @ Y5 )
% 2.95/1.60 | ( X3 = Y5 ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_323_leI,axiom,
% 2.95/1.60 ! [X2: nat,Y2: nat] :
% 2.95/1.60 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.95/1.60 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_324_leD,axiom,
% 2.95/1.60 ! [Y2: nat,X2: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.95/1.60 => ~ ( ord_less_nat @ X2 @ Y2 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_325_div__gr__imp__gr__divisor,axiom,
% 2.95/1.60 ! [X2: nat,N: nat,M: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X2 @ ( divide_divide_nat @ N @ M ) )
% 2.95/1.60 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_326_div__le__mono,axiom,
% 2.95/1.60 ! [M: nat,N: nat,K: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ M @ N )
% 2.95/1.60 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_327_div__le__dividend,axiom,
% 2.95/1.60 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_328_nat__descend__induct,axiom,
% 2.95/1.60 ! [N: nat,P: nat > $o,M: nat] :
% 2.95/1.60 ( ! [K3: nat] :
% 2.95/1.60 ( ( ord_less_nat @ N @ K3 )
% 2.95/1.60 => ( P @ K3 ) )
% 2.95/1.60 => ( ! [K3: nat] :
% 2.95/1.60 ( ( ord_less_eq_nat @ K3 @ N )
% 2.95/1.60 => ( ! [I5: nat] :
% 2.95/1.60 ( ( ord_less_nat @ K3 @ I5 )
% 2.95/1.60 => ( P @ I5 ) )
% 2.95/1.60 => ( P @ K3 ) ) )
% 2.95/1.60 => ( P @ M ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_329_minf_I8_J,axiom,
% 2.95/1.60 ! [T: nat] :
% 2.95/1.60 ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X6 @ Z3 )
% 2.95/1.60 => ~ ( ord_less_eq_nat @ T @ X6 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_330_minf_I7_J,axiom,
% 2.95/1.60 ! [T: nat] :
% 2.95/1.60 ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X6 @ Z3 )
% 2.95/1.60 => ~ ( ord_less_nat @ T @ X6 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_331_minf_I5_J,axiom,
% 2.95/1.60 ! [T: nat] :
% 2.95/1.60 ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X6 @ Z3 )
% 2.95/1.60 => ( ord_less_nat @ X6 @ T ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_332_minf_I4_J,axiom,
% 2.95/1.60 ! [T: nat] :
% 2.95/1.60 ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X6 @ Z3 )
% 2.95/1.60 => ( X6 != T ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_333_minf_I3_J,axiom,
% 2.95/1.60 ! [T: nat] :
% 2.95/1.60 ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X6 @ Z3 )
% 2.95/1.60 => ( X6 != T ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_334_minf_I2_J,axiom,
% 2.95/1.60 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 2.95/1.60 ( ? [Z4: nat] :
% 2.95/1.60 ! [X5: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X5 @ Z4 )
% 2.95/1.60 => ( ( P @ X5 )
% 2.95/1.60 = ( P4 @ X5 ) ) )
% 2.95/1.60 => ( ? [Z4: nat] :
% 2.95/1.60 ! [X5: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X5 @ Z4 )
% 2.95/1.60 => ( ( Q @ X5 )
% 2.95/1.60 = ( Q2 @ X5 ) ) )
% 2.95/1.60 => ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X6 @ Z3 )
% 2.95/1.60 => ( ( ( P @ X6 )
% 2.95/1.60 | ( Q @ X6 ) )
% 2.95/1.60 = ( ( P4 @ X6 )
% 2.95/1.60 | ( Q2 @ X6 ) ) ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_335_minf_I1_J,axiom,
% 2.95/1.60 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 2.95/1.60 ( ? [Z4: nat] :
% 2.95/1.60 ! [X5: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X5 @ Z4 )
% 2.95/1.60 => ( ( P @ X5 )
% 2.95/1.60 = ( P4 @ X5 ) ) )
% 2.95/1.60 => ( ? [Z4: nat] :
% 2.95/1.60 ! [X5: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X5 @ Z4 )
% 2.95/1.60 => ( ( Q @ X5 )
% 2.95/1.60 = ( Q2 @ X5 ) ) )
% 2.95/1.60 => ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ X6 @ Z3 )
% 2.95/1.60 => ( ( ( P @ X6 )
% 2.95/1.60 & ( Q @ X6 ) )
% 2.95/1.60 = ( ( P4 @ X6 )
% 2.95/1.60 & ( Q2 @ X6 ) ) ) ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_336_pinf_I7_J,axiom,
% 2.95/1.60 ! [T: nat] :
% 2.95/1.60 ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ Z3 @ X6 )
% 2.95/1.60 => ( ord_less_nat @ T @ X6 ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_337_pinf_I5_J,axiom,
% 2.95/1.60 ! [T: nat] :
% 2.95/1.60 ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ Z3 @ X6 )
% 2.95/1.60 => ~ ( ord_less_nat @ X6 @ T ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_338_pinf_I4_J,axiom,
% 2.95/1.60 ! [T: nat] :
% 2.95/1.60 ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ Z3 @ X6 )
% 2.95/1.60 => ( X6 != T ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_339_pinf_I3_J,axiom,
% 2.95/1.60 ! [T: nat] :
% 2.95/1.60 ? [Z3: nat] :
% 2.95/1.60 ! [X6: nat] :
% 2.95/1.60 ( ( ord_less_nat @ Z3 @ X6 )
% 2.95/1.60 => ( X6 != T ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(fact_340_pinf_I2_J,axiom,
% 3.08/1.60 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 3.08/1.60 ( ? [Z4: nat] :
% 3.08/1.60 ! [X5: nat] :
% 3.08/1.60 ( ( ord_less_nat @ Z4 @ X5 )
% 3.08/1.60 => ( ( P @ X5 )
% 3.08/1.60 = ( P4 @ X5 ) ) )
% 3.08/1.60 => ( ? [Z4: nat] :
% 3.08/1.60 ! [X5: nat] :
% 3.08/1.60 ( ( ord_less_nat @ Z4 @ X5 )
% 3.08/1.60 => ( ( Q @ X5 )
% 3.08/1.60 = ( Q2 @ X5 ) ) )
% 3.08/1.60 => ? [Z3: nat] :
% 3.08/1.60 ! [X6: nat] :
% 3.08/1.60 ( ( ord_less_nat @ Z3 @ X6 )
% 3.08/1.60 => ( ( ( P @ X6 )
% 3.08/1.60 | ( Q @ X6 ) )
% 3.08/1.60 = ( ( P4 @ X6 )
% 3.08/1.60 | ( Q2 @ X6 ) ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(fact_341_pinf_I1_J,axiom,
% 3.08/1.60 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 3.08/1.60 ( ? [Z4: nat] :
% 3.08/1.60 ! [X5: nat] :
% 3.08/1.60 ( ( ord_less_nat @ Z4 @ X5 )
% 3.08/1.60 => ( ( P @ X5 )
% 3.08/1.60 = ( P4 @ X5 ) ) )
% 3.08/1.60 => ( ? [Z4: nat] :
% 3.08/1.60 ! [X5: nat] :
% 3.08/1.60 ( ( ord_less_nat @ Z4 @ X5 )
% 3.08/1.60 => ( ( Q @ X5 )
% 3.08/1.60 = ( Q2 @ X5 ) ) )
% 3.08/1.60 => ? [Z3: nat] :
% 3.08/1.60 ! [X6: nat] :
% 3.08/1.60 ( ( ord_less_nat @ Z3 @ X6 )
% 3.08/1.60 => ( ( ( P @ X6 )
% 3.08/1.60 & ( Q @ X6 ) )
% 3.08/1.60 = ( ( P4 @ X6 )
% 3.08/1.60 & ( Q2 @ X6 ) ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(fact_342_pinf_I6_J,axiom,
% 3.08/1.60 ! [T: nat] :
% 3.08/1.60 ? [Z3: nat] :
% 3.08/1.60 ! [X6: nat] :
% 3.08/1.60 ( ( ord_less_nat @ Z3 @ X6 )
% 3.08/1.60 => ~ ( ord_less_eq_nat @ X6 @ T ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(fact_343_pinf_I8_J,axiom,
% 3.08/1.60 ! [T: nat] :
% 3.08/1.60 ? [Z3: nat] :
% 3.08/1.60 ! [X6: nat] :
% 3.08/1.60 ( ( ord_less_nat @ Z3 @ X6 )
% 3.08/1.60 => ( ord_less_eq_nat @ T @ X6 ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(fact_344_minf_I6_J,axiom,
% 3.08/1.60 ! [T: nat] :
% 3.08/1.60 ? [Z3: nat] :
% 3.08/1.60 ! [X6: nat] :
% 3.08/1.60 ( ( ord_less_nat @ X6 @ Z3 )
% 3.08/1.60 => ( ord_less_eq_nat @ X6 @ T ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(fact_345_complete__interval,axiom,
% 3.08/1.60 ! [A2: nat,B2: nat,P: nat > $o] :
% 3.08/1.60 ( ( ord_less_nat @ A2 @ B2 )
% 3.08/1.60 => ( ( P @ A2 )
% 3.08/1.60 => ( ~ ( P @ B2 )
% 3.08/1.60 => ? [C2: nat] :
% 3.08/1.60 ( ( ord_less_eq_nat @ A2 @ C2 )
% 3.08/1.60 & ( ord_less_eq_nat @ C2 @ B2 )
% 3.08/1.60 & ! [X6: nat] :
% 3.08/1.60 ( ( ( ord_less_eq_nat @ A2 @ X6 )
% 3.08/1.60 & ( ord_less_nat @ X6 @ C2 ) )
% 3.08/1.60 => ( P @ X6 ) )
% 3.08/1.60 & ! [D: nat] :
% 3.08/1.60 ( ! [X5: nat] :
% 3.08/1.60 ( ( ( ord_less_eq_nat @ A2 @ X5 )
% 3.08/1.60 & ( ord_less_nat @ X5 @ D ) )
% 3.08/1.60 => ( P @ X5 ) )
% 3.08/1.60 => ( ord_less_eq_nat @ D @ C2 ) ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(fact_346_le__greater__neq__conv,axiom,
% 3.08/1.60 ( ord_less_eq_nat
% 3.08/1.60 = ( ^ [N3: nat,A3: nat] :
% 3.08/1.60 ! [X3: nat] :
% 3.08/1.60 ( ( ord_less_nat @ A3 @ X3 )
% 3.08/1.60 => ( N3 != X3 ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(fact_347_ge__less__neq__conv,axiom,
% 3.08/1.60 ( ord_less_eq_nat
% 3.08/1.60 = ( ^ [A3: nat,N3: nat] :
% 3.08/1.60 ! [X3: nat] :
% 3.08/1.60 ( ( ord_less_nat @ X3 @ A3 )
% 3.08/1.60 => ( N3 != X3 ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(conj_0,hypothesis,
% 3.08/1.60 ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) ).
% 3.08/1.60
% 3.08/1.60 thf(conj_1,conjecture,
% 3.08/1.60 ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
% 3.08/1.60 = k ) ).
% 3.08/1.60 ------------------------
% 3.08/1.63 % (27243)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/18Mi)
% 3.08/1.64 % (27243)Instruction limit reached!
% 3.08/1.64 % (27243)------------------------------
% 3.08/1.64 % (27243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (27243)Termination reason: Unknown
% 3.08/1.64 % (27243)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (27243)Memory used [KB]: 1791
% 3.08/1.64 % (27243)Time elapsed: 0.008 s
% 3.08/1.64 % (27243)Instructions burned: 20 (million)
% 3.08/1.64 % (27243)------------------------------
% 3.08/1.64 % (27243)------------------------------
% 3.08/1.64 % (27238)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_26969 for (2999ds/4Mi)
% 3.08/1.64 % (27237)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/183Mi)
% 3.08/1.64 % (27239)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_26969 for (2999ds/27Mi)
% 3.08/1.64 % (27240)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/2Mi)
% 3.08/1.64 % (27241)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_26969 for (2999ds/2Mi)
% 3.08/1.64 % (27242)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_26969 for (2999ds/275Mi)
% 3.08/1.64 % (27240)Instruction limit reached!
% 3.08/1.64 % (27240)------------------------------
% 3.08/1.64 % (27240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (27240)Termination reason: Unknown
% 3.08/1.64 % (27240)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (27240)Memory used [KB]: 1407
% 3.08/1.64 % (27240)Time elapsed: 0.003 s
% 3.08/1.64 % (27240)Instructions burned: 2 (million)
% 3.08/1.64 % (27240)------------------------------
% 3.08/1.64 % (27240)------------------------------
% 3.08/1.64 % (27241)Instruction limit reached!
% 3.08/1.64 % (27241)------------------------------
% 3.08/1.64 % (27241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (27241)Termination reason: Unknown
% 3.08/1.64 % (27241)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (27241)Memory used [KB]: 1407
% 3.08/1.64 % (27241)Time elapsed: 0.003 s
% 3.08/1.64 % (27241)Instructions burned: 2 (million)
% 3.08/1.64 % (27241)------------------------------
% 3.08/1.64 % (27241)------------------------------
% 3.08/1.64 % (27238)Instruction limit reached!
% 3.08/1.64 % (27238)------------------------------
% 3.08/1.64 % (27238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (27238)Termination reason: Unknown
% 3.08/1.64 % (27238)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (27238)Memory used [KB]: 1535
% 3.08/1.64 % (27238)Time elapsed: 0.005 s
% 3.08/1.64 % (27238)Instructions burned: 4 (million)
% 3.08/1.64 % (27238)------------------------------
% 3.08/1.64 % (27238)------------------------------
% 3.08/1.65 % (27244)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/3Mi)
% 3.08/1.65 % (27244)Instruction limit reached!
% 3.08/1.65 % (27244)------------------------------
% 3.08/1.65 % (27244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.65 % (27244)Termination reason: Unknown
% 3.08/1.65 % (27244)Termination phase: shuffling
% 3.08/1.65
% 3.08/1.65 % (27244)Memory used [KB]: 1535
% 3.08/1.65 % (27244)Time elapsed: 0.003 s
% 3.08/1.65 % (27244)Instructions burned: 4 (million)
% 3.08/1.65 % (27244)------------------------------
% 3.08/1.65 % (27244)------------------------------
% 3.08/1.65 % (27239)Instruction limit reached!
% 3.08/1.65 % (27239)------------------------------
% 3.08/1.65 % (27239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.65 % (27239)Termination reason: Unknown
% 3.08/1.65 % (27239)Termination phase: shuffling
% 3.08/1.65
% 3.08/1.65 % (27239)Memory used [KB]: 1918
% 3.08/1.65 % (27239)Time elapsed: 0.018 s
% 3.08/1.65 % (27239)Instructions burned: 28 (million)
% 3.08/1.65 % (27239)------------------------------
% 3.08/1.65 % (27239)------------------------------
% 3.08/1.65 % (27245)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_26969 for (2999ds/37Mi)
% 3.08/1.66 % (27246)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_26969 for (2999ds/15Mi)
% 3.08/1.66 % (27247)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_26969 for (2999ds/3Mi)
% 3.08/1.66 % (27247)Instruction limit reached!
% 3.08/1.66 % (27247)------------------------------
% 3.08/1.66 % (27247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.66 % (27247)Termination reason: Unknown
% 3.08/1.66 % (27247)Termination phase: shuffling
% 3.08/1.66
% 3.08/1.66 % (27247)Memory used [KB]: 1407
% 3.08/1.66 % (27247)Time elapsed: 0.004 s
% 3.08/1.66 % (27247)Instructions burned: 3 (million)
% 3.08/1.66 % (27247)------------------------------
% 3.08/1.66 % (27247)------------------------------
% 3.08/1.66 % (27248)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_26969 for (2999ds/1041Mi)
% 3.08/1.66 % (27246)Instruction limit reached!
% 3.08/1.66 % (27246)------------------------------
% 3.08/1.66 % (27246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.66 % (27246)Termination reason: Unknown
% 3.08/1.66 % (27246)Termination phase: shuffling
% 3.08/1.66
% 3.08/1.66 % (27246)Memory used [KB]: 1663
% 3.08/1.66 % (27246)Time elapsed: 0.011 s
% 3.08/1.66 % (27246)Instructions burned: 15 (million)
% 3.08/1.66 % (27246)------------------------------
% 3.08/1.66 % (27246)------------------------------
% 3.08/1.67 % (27245)Instruction limit reached!
% 3.08/1.67 % (27245)------------------------------
% 3.08/1.67 % (27245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (27245)Termination reason: Unknown
% 3.08/1.67 % (27245)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (27245)Memory used [KB]: 2174
% 3.08/1.67 % (27245)Time elapsed: 0.015 s
% 3.08/1.67 % (27245)Instructions burned: 37 (million)
% 3.08/1.67 % (27245)------------------------------
% 3.08/1.67 % (27245)------------------------------
% 3.08/1.67 % (27249)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/7Mi)
% 3.08/1.67 % (27249)Instruction limit reached!
% 3.08/1.67 % (27249)------------------------------
% 3.08/1.67 % (27249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (27249)Termination reason: Unknown
% 3.08/1.67 % (27249)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (27249)Memory used [KB]: 1535
% 3.08/1.67 % (27249)Time elapsed: 0.006 s
% 3.08/1.67 % (27249)Instructions burned: 8 (million)
% 3.08/1.67 % (27249)------------------------------
% 3.08/1.67 % (27249)------------------------------
% 3.08/1.68 % (27250)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/16Mi)
% 3.08/1.68 % (27252)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_26969 for (2999ds/3Mi)
% 3.08/1.68 % (27252)Instruction limit reached!
% 3.08/1.68 % (27252)------------------------------
% 3.08/1.68 % (27252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (27252)Termination reason: Unknown
% 3.08/1.68 % (27252)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (27252)Memory used [KB]: 1535
% 3.08/1.68 % (27252)Time elapsed: 0.003 s
% 3.08/1.68 % (27252)Instructions burned: 4 (million)
% 3.08/1.68 % (27252)------------------------------
% 3.08/1.68 % (27252)------------------------------
% 3.08/1.68 % (27251)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_26969 for (2999ds/3Mi)
% 3.08/1.68 % (27251)Instruction limit reached!
% 3.08/1.68 % (27251)------------------------------
% 3.08/1.68 % (27251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (27251)Termination reason: Unknown
% 3.08/1.68 % (27251)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (27251)Memory used [KB]: 1407
% 3.08/1.68 % (27251)Time elapsed: 0.004 s
% 3.08/1.68 % (27251)Instructions burned: 3 (million)
% 3.08/1.68 % (27251)------------------------------
% 3.08/1.68 % (27251)------------------------------
% 3.08/1.68 % (27250)Instruction limit reached!
% 3.08/1.68 % (27250)------------------------------
% 3.08/1.68 % (27250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (27250)Termination reason: Unknown
% 3.08/1.68 % (27250)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (27250)Memory used [KB]: 1791
% 3.08/1.68 % (27250)Time elapsed: 0.011 s
% 3.08/1.68 % (27250)Instructions burned: 16 (million)
% 3.08/1.68 % (27250)------------------------------
% 3.08/1.68 % (27250)------------------------------
% 3.08/1.69 % (27253)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/7Mi)
% 3.08/1.69 % (27254)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/3Mi)
% 3.08/1.69 % (27253)Instruction limit reached!
% 3.08/1.69 % (27253)------------------------------
% 3.08/1.69 % (27253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (27253)Termination reason: Unknown
% 3.08/1.69 % (27253)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (27253)Memory used [KB]: 1535
% 3.08/1.69 % (27253)Time elapsed: 0.004 s
% 3.08/1.69 % (27253)Instructions burned: 7 (million)
% 3.08/1.69 % (27253)------------------------------
% 3.08/1.69 % (27253)------------------------------
% 3.08/1.69 % (27254)Instruction limit reached!
% 3.08/1.69 % (27254)------------------------------
% 3.08/1.69 % (27254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (27254)Termination reason: Unknown
% 3.08/1.69 % (27254)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (27254)Memory used [KB]: 1407
% 3.08/1.69 % (27254)Time elapsed: 0.002 s
% 3.08/1.69 % (27254)Instructions burned: 3 (million)
% 3.08/1.69 % (27254)------------------------------
% 3.08/1.69 % (27254)------------------------------
% 3.08/1.70 % (27256)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/18Mi)
% 3.08/1.70 % (27255)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/4Mi)
% 3.08/1.70 % (27255)Instruction limit reached!
% 3.08/1.70 % (27255)------------------------------
% 3.08/1.70 % (27255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.70 % (27255)Termination reason: Unknown
% 3.08/1.70 % (27255)Termination phase: shuffling
% 3.08/1.70
% 3.08/1.70 % (27255)Memory used [KB]: 1535
% 3.08/1.70 % (27255)Time elapsed: 0.003 s
% 3.08/1.70 % (27255)Instructions burned: 6 (million)
% 3.08/1.70 % (27255)------------------------------
% 3.08/1.70 % (27255)------------------------------
% 3.08/1.70 % (27257)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/710Mi)
% 3.08/1.70 % (27258)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/6Mi)
% 3.08/1.70 % (27258)Instruction limit reached!
% 3.08/1.70 % (27258)------------------------------
% 3.08/1.70 % (27258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.70 % (27258)Termination reason: Unknown
% 3.08/1.70 % (27258)Termination phase: shuffling
% 3.08/1.70
% 3.08/1.70 % (27258)Memory used [KB]: 1535
% 3.08/1.70 % (27258)Time elapsed: 0.003 s
% 3.08/1.70 % (27258)Instructions burned: 6 (million)
% 3.08/1.70 % (27258)------------------------------
% 3.08/1.70 % (27258)------------------------------
% 3.08/1.70 % (27256)Instruction limit reached!
% 3.08/1.70 % (27256)------------------------------
% 3.08/1.70 % (27256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.70 % (27256)Termination reason: Unknown
% 3.08/1.70 % (27256)Termination phase: shuffling
% 3.08/1.70
% 3.08/1.70 % (27256)Memory used [KB]: 1791
% 3.08/1.70 % (27256)Time elapsed: 0.008 s
% 3.08/1.70 % (27256)Instructions burned: 20 (million)
% 3.08/1.70 % (27256)------------------------------
% 3.08/1.70 % (27256)------------------------------
% 3.08/1.71 % (27259)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_26969 for (2999ds/902Mi)
% 3.08/1.71 % (27260)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_26969 for (2999ds/21Mi)
% 3.08/1.71 % (27261)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26969 for (2999ds/5Mi)
% 3.08/1.71 % (27261)Instruction limit reached!
% 3.08/1.71 % (27261)------------------------------
% 3.08/1.71 % (27261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.71 % (27261)Termination reason: Unknown
% 3.08/1.71 % (27261)Termination phase: shuffling
% 3.08/1.71
% 3.08/1.71 % (27261)Memory used [KB]: 1535
% 3.08/1.71 % (27261)Time elapsed: 0.004 s
% 3.08/1.71 % (27261)Instructions burned: 7 (million)
% 3.08/1.71 % (27261)------------------------------
% 3.08/1.71 % (27261)------------------------------
% 3.08/1.72 % (27260)Instruction limit reached!
% 3.08/1.72 % (27260)------------------------------
% 3.08/1.72 % (27260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.72 % (27260)Termination reason: Unknown
% 3.08/1.72 % (27260)Termination phase: shuffling
% 3.08/1.72
% 3.08/1.72 % (27260)Memory used [KB]: 1791
% 3.08/1.72 % (27260)Time elapsed: 0.008 s
% 3.08/1.72 % (27260)Instructions burned: 22 (million)
% 3.08/1.72 % (27260)------------------------------
% 3.08/1.72 % (27260)------------------------------
% 3.08/1.72 % (27237)Instruction limit reached!
% 3.08/1.72 % (27237)------------------------------
% 3.08/1.72 % (27237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.72 % (27237)Termination reason: Unknown
% 3.08/1.72 % (27237)Termination phase: Saturation
% 3.08/1.72
% 3.08/1.72 % (27237)Memory used [KB]: 7419
% 3.08/1.72 % (27237)Time elapsed: 0.087 s
% 3.08/1.72 % (27237)Instructions burned: 184 (million)
% 3.08/1.72 % (27237)------------------------------
% 3.08/1.72 % (27237)------------------------------
% 3.08/1.72 % (27262)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_26969 for (2998ds/6Mi)
% 3.08/1.73 % (27262)Instruction limit reached!
% 3.08/1.73 % (27262)------------------------------
% 3.08/1.73 % (27262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.73 % (27262)Termination reason: Unknown
% 3.08/1.73 % (27262)Termination phase: shuffling
% 3.08/1.73
% 3.08/1.73 % (27262)Memory used [KB]: 1535
% 3.08/1.73 % (27262)Time elapsed: 0.003 s
% 3.08/1.73 % (27262)Instructions burned: 7 (million)
% 3.08/1.73 % (27262)------------------------------
% 3.08/1.73 % (27262)------------------------------
% 3.08/1.73 % (27263)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26969 for (2998ds/377Mi)
% 3.08/1.73 % (27264)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_26969 for (2998ds/779Mi)
% 3.08/1.74 % (27265)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_26969 for (2998ds/19Mi)
% 3.08/1.74 % (27265)Instruction limit reached!
% 3.08/1.74 % (27265)------------------------------
% 3.08/1.74 % (27265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.74 % (27265)Termination reason: Unknown
% 3.08/1.74 % (27265)Termination phase: shuffling
% 3.08/1.74
% 3.08/1.74 % (27265)Memory used [KB]: 1791
% 3.08/1.74 % (27265)Time elapsed: 0.007 s
% 3.08/1.74 % (27265)Instructions burned: 20 (million)
% 3.08/1.74 % (27265)------------------------------
% 3.08/1.74 % (27265)------------------------------
% 3.08/1.75 % (27242)Instruction limit reached!
% 3.08/1.75 % (27242)------------------------------
% 3.08/1.75 % (27242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.75 % (27242)Termination reason: Unknown
% 3.08/1.75 % (27242)Termination phase: Saturation
% 3.08/1.75
% 3.08/1.75 % (27242)Memory used [KB]: 7291
% 3.08/1.75 % (27242)Time elapsed: 0.111 s
% 3.08/1.75 % (27242)Instructions burned: 276 (million)
% 3.08/1.75 % (27242)------------------------------
% 3.08/1.75 % (27242)------------------------------
% 3.08/1.75 % (27266)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26969 for (2998ds/879Mi)
% 3.08/1.76 % (27267)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26969 for (2998ds/17Mi)
% 3.08/1.76 % (27267)Instruction limit reached!
% 3.08/1.76 % (27267)------------------------------
% 3.08/1.76 % (27267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.76 % (27267)Termination reason: Unknown
% 3.08/1.76 % (27267)Termination phase: shuffling
% 3.08/1.76
% 3.08/1.76 % (27267)Memory used [KB]: 1791
% 3.08/1.76 % (27267)Time elapsed: 0.008 s
% 3.08/1.76 % (27267)Instructions burned: 18 (million)
% 3.08/1.76 % (27267)------------------------------
% 3.08/1.76 % (27267)------------------------------
% 3.08/1.77 % (27268)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26969 for (2998ds/3Mi)
% 3.08/1.77 % (27268)Instruction limit reached!
% 3.08/1.77 % (27268)------------------------------
% 3.08/1.77 % (27268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.77 % (27268)Termination reason: Unknown
% 3.08/1.77 % (27268)Termination phase: shuffling
% 3.08/1.77
% 3.08/1.77 % (27268)Memory used [KB]: 1407
% 3.08/1.77 % (27268)Time elapsed: 0.003 s
% 3.08/1.77 % (27268)Instructions burned: 3 (million)
% 3.08/1.77 % (27268)------------------------------
% 3.08/1.77 % (27268)------------------------------
% 3.08/1.78 % (27269)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26969 for (2998ds/30Mi)
% 3.08/1.79 % (27269)Instruction limit reached!
% 3.08/1.79 % (27269)------------------------------
% 3.08/1.79 % (27269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.79 % (27269)Termination reason: Unknown
% 3.08/1.79 % (27269)Termination phase: shuffling
% 3.08/1.79
% 3.08/1.79 % (27269)Memory used [KB]: 1918
% 3.08/1.79 % (27269)Time elapsed: 0.012 s
% 3.08/1.79 % (27269)Instructions burned: 30 (million)
% 3.08/1.79 % (27269)------------------------------
% 3.08/1.79 % (27269)------------------------------
% 3.08/1.80 % (27270)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26969 for (2997ds/127Mi)
% 3.08/1.84 % (27263)Instruction limit reached!
% 3.08/1.84 % (27263)------------------------------
% 3.08/1.84 % (27263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.84 % (27263)Termination reason: Unknown
% 3.08/1.84 % (27263)Termination phase: Saturation
% 3.08/1.84
% 3.08/1.84 % (27263)Memory used [KB]: 8443
% 3.08/1.84 % (27263)Time elapsed: 0.109 s
% 3.08/1.84 % (27263)Instructions burned: 379 (million)
% 3.08/1.84 % (27263)------------------------------
% 3.08/1.84 % (27263)------------------------------
% 3.08/1.84 % (27270)Instruction limit reached!
% 3.08/1.84 % (27270)------------------------------
% 3.08/1.84 % (27270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.84 % (27270)Termination reason: Unknown
% 3.08/1.84 % (27270)Termination phase: Property scanning
% 3.08/1.84
% 3.08/1.84 % (27270)Memory used [KB]: 2686
% 3.08/1.84 % (27270)Time elapsed: 0.040 s
% 3.08/1.84 % (27270)Instructions burned: 127 (million)
% 3.08/1.84 % (27270)------------------------------
% 3.08/1.84 % (27270)------------------------------
% 3.08/1.84 % (27271)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26969 for (2997ds/100Mi)
% 3.08/1.85 % (27272)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_26969 for (2997ds/3Mi)
% 3.08/1.85 % (27272)Instruction limit reached!
% 3.08/1.85 % (27272)------------------------------
% 3.08/1.85 % (27272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.85 % (27272)Termination reason: Unknown
% 3.08/1.85 % (27272)Termination phase: shuffling
% 3.08/1.85
% 3.08/1.85 % (27272)Memory used [KB]: 1407
% 3.08/1.85 % (27272)Time elapsed: 0.003 s
% 3.08/1.85 % (27272)Instructions burned: 4 (million)
% 3.08/1.85 % (27272)------------------------------
% 3.08/1.85 % (27272)------------------------------
% 3.08/1.86 % (27273)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_26969 for (2997ds/20Mi)
% 3.08/1.87 % (27273)Instruction limit reached!
% 3.08/1.87 % (27273)------------------------------
% 3.08/1.87 % (27273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.87 % (27273)Termination reason: Unknown
% 3.08/1.87 % (27273)Termination phase: shuffling
% 3.08/1.87
% 3.08/1.87 % (27273)Memory used [KB]: 1791
% 3.08/1.87 % (27273)Time elapsed: 0.009 s
% 3.08/1.87 % (27273)Instructions burned: 21 (million)
% 3.08/1.87 % (27273)------------------------------
% 3.08/1.87 % (27273)------------------------------
% 3.08/1.87 % (27271)Instruction limit reached!
% 3.08/1.87 % (27271)------------------------------
% 3.08/1.87 % (27271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.87 % (27271)Termination reason: Unknown
% 3.08/1.87 % (27271)Termination phase: Property scanning
% 3.08/1.87
% 3.08/1.87 % (27271)Memory used [KB]: 2558
% 3.08/1.87 % (27271)Time elapsed: 0.027 s
% 3.08/1.87 % (27271)Instructions burned: 101 (million)
% 3.08/1.87 % (27271)------------------------------
% 3.08/1.87 % (27271)------------------------------
% 3.08/1.88 % (27275)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_26969 for (2997ds/107Mi)
% 3.08/1.88 % (27274)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_26969 for (2997ds/86Mi)
% 3.08/1.91 % (27274)Instruction limit reached!
% 3.08/1.91 % (27274)------------------------------
% 3.08/1.91 % (27274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.91 % (27274)Termination reason: Unknown
% 3.08/1.91 % (27274)Termination phase: Property scanning
% 3.08/1.91
% 3.08/1.91 % (27274)Memory used [KB]: 2558
% 3.08/1.91 % (27274)Time elapsed: 0.028 s
% 3.08/1.91 % (27274)Instructions burned: 86 (million)
% 3.08/1.91 % (27274)------------------------------
% 3.08/1.91 % (27274)------------------------------
% 3.08/1.91 % (27275)Instruction limit reached!
% 3.08/1.91 % (27275)------------------------------
% 3.08/1.91 % (27275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.91 % (27275)Termination reason: Unknown
% 3.08/1.91 % (27275)Termination phase: Property scanning
% 3.08/1.91
% 3.08/1.91 % (27275)Memory used [KB]: 2558
% 3.08/1.91 % (27275)Time elapsed: 0.032 s
% 3.08/1.91 % (27275)Instructions burned: 110 (million)
% 3.08/1.91 % (27275)------------------------------
% 3.08/1.91 % (27275)------------------------------
% 3.08/1.92 % (27257)Instruction limit reached!
% 3.08/1.92 % (27257)------------------------------
% 3.08/1.92 % (27257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.92 % (27257)Termination reason: Unknown
% 3.08/1.92 % (27257)Termination phase: Saturation
% 3.08/1.92
% 3.08/1.92 % (27257)Memory used [KB]: 9083
% 3.08/1.92 % (27257)Time elapsed: 0.218 s
% 3.08/1.92 % (27257)Instructions burned: 710 (million)
% 3.08/1.92 % (27257)------------------------------
% 3.08/1.92 % (27257)------------------------------
% 3.08/1.92 % (27276)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/39Mi)
% 3.08/1.92 % (27277)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/448Mi)
% 3.08/1.93 % (27278)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/46Mi)
% 3.08/1.93 % (27276)Instruction limit reached!
% 3.08/1.93 % (27276)------------------------------
% 3.08/1.93 % (27276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.93 % (27276)Termination reason: Unknown
% 3.08/1.93 % (27276)Termination phase: shuffling
% 3.08/1.93
% 3.08/1.93 % (27276)Memory used [KB]: 2174
% 3.08/1.93 % (27276)Time elapsed: 0.014 s
% 3.08/1.93 % (27276)Instructions burned: 42 (million)
% 3.08/1.93 % (27276)------------------------------
% 3.08/1.93 % (27276)------------------------------
% 3.08/1.94 % (27279)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/98Mi)
% 3.08/1.94 % (27278)Instruction limit reached!
% 3.08/1.94 % (27278)------------------------------
% 3.08/1.94 % (27278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.94 % (27278)Termination reason: Unknown
% 3.08/1.94 % (27278)Termination phase: Property scanning
% 3.08/1.94
% 3.08/1.94 % (27278)Memory used [KB]: 2046
% 3.08/1.94 % (27278)Time elapsed: 0.015 s
% 3.08/1.94 % (27278)Instructions burned: 46 (million)
% 3.08/1.94 % (27278)------------------------------
% 3.08/1.94 % (27278)------------------------------
% 3.08/1.95 % (27280)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/507Mi)
% 3.08/1.95 % (27259)Instruction limit reached!
% 3.08/1.95 % (27259)------------------------------
% 3.08/1.95 % (27259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.95 % (27259)Termination reason: Unknown
% 3.08/1.95 % (27259)Termination phase: Saturation
% 3.08/1.95
% 3.08/1.95 % (27259)Memory used [KB]: 8699
% 3.08/1.95 % (27259)Time elapsed: 0.246 s
% 3.08/1.95 % (27259)Instructions burned: 904 (million)
% 3.08/1.95 % (27259)------------------------------
% 3.08/1.95 % (27259)------------------------------
% 3.08/1.96 % (27281)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/149Mi)
% 3.08/1.97 % (27279)Instruction limit reached!
% 3.08/1.97 % (27279)------------------------------
% 3.08/1.97 % (27279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.97 % (27279)Termination reason: Unknown
% 3.08/1.97 % (27279)Termination phase: Property scanning
% 3.08/1.97
% 3.08/1.97 % (27279)Memory used [KB]: 2558
% 3.08/1.97 % (27279)Time elapsed: 0.030 s
% 3.08/1.97 % (27279)Instructions burned: 101 (million)
% 3.08/1.97 % (27279)------------------------------
% 3.08/1.97 % (27279)------------------------------
% 3.08/1.98 % (27282)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/39Mi)
% 3.08/1.98 % (27248)Instruction limit reached!
% 3.08/1.98 % (27248)------------------------------
% 3.08/1.98 % (27248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.98 % (27248)Termination reason: Unknown
% 3.08/1.98 % (27248)Termination phase: Saturation
% 3.08/1.98
% 3.08/1.98 % (27248)Memory used [KB]: 9978
% 3.08/1.98 % (27248)Time elapsed: 0.322 s
% 3.08/1.98 % (27248)Instructions burned: 1043 (million)
% 3.08/1.98 % (27248)------------------------------
% 3.08/1.98 % (27248)------------------------------
% 3.08/1.98 % (27264)Instruction limit reached!
% 3.08/1.98 % (27264)------------------------------
% 3.08/1.98 % (27264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.98 % (27264)Termination reason: Unknown
% 3.08/1.98 % (27264)Termination phase: Saturation
% 3.08/1.98
% 3.08/1.98 % (27264)Memory used [KB]: 9083
% 3.08/1.98 % (27264)Time elapsed: 0.273 s
% 3.08/1.98 % (27264)Instructions burned: 781 (million)
% 3.08/1.98 % (27264)------------------------------
% 3.08/1.98 % (27264)------------------------------
% 3.08/1.99 % (27283)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/6Mi)
% 3.08/1.99 % (27282)Instruction limit reached!
% 3.08/1.99 % (27282)------------------------------
% 3.08/1.99 % (27282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.99 % (27282)Termination reason: Unknown
% 3.08/1.99 % (27282)Termination phase: Property scanning
% 3.08/1.99
% 3.08/1.99 % (27282)Memory used [KB]: 2046
% 3.08/1.99 % (27282)Time elapsed: 0.013 s
% 3.08/1.99 % (27282)Instructions burned: 40 (million)
% 3.08/1.99 % (27282)------------------------------
% 3.08/1.99 % (27282)------------------------------
% 3.08/1.99 % (27283)Instruction limit reached!
% 3.08/1.99 % (27283)------------------------------
% 3.08/1.99 % (27283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.99 % (27283)Termination reason: Unknown
% 3.08/1.99 % (27283)Termination phase: shuffling
% 3.08/1.99
% 3.08/1.99 % (27283)Memory used [KB]: 1535
% 3.08/1.99 % (27283)Time elapsed: 0.003 s
% 3.08/1.99 % (27283)Instructions burned: 6 (million)
% 3.08/1.99 % (27283)------------------------------
% 3.08/1.99 % (27283)------------------------------
% 3.08/1.99 % (27284)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/1087Mi)
% 3.08/2.00 % (27285)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/47Mi)
% 3.08/2.00 % (27281)Instruction limit reached!
% 3.08/2.00 % (27281)------------------------------
% 3.08/2.00 % (27281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/2.00 % (27281)Termination reason: Unknown
% 3.08/2.00 % (27281)Termination phase: Property scanning
% 3.08/2.00
% 3.08/2.00 % (27281)Memory used [KB]: 2686
% 3.08/2.00 % (27281)Time elapsed: 0.041 s
% 3.08/2.00 % (27281)Instructions burned: 150 (million)
% 3.08/2.00 % (27281)------------------------------
% 3.08/2.00 % (27281)------------------------------
% 3.08/2.01 % (27286)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_26969 for (2996ds/44Mi)
% 5.79/2.01 % (27287)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/432Mi)
% 5.79/2.01 % (27285)Instruction limit reached!
% 5.79/2.01 % (27285)------------------------------
% 5.79/2.01 % (27285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.01 % (27285)Termination reason: Unknown
% 5.79/2.01 % (27285)Termination phase: Property scanning
% 5.79/2.01
% 5.79/2.01 % (27285)Memory used [KB]: 2046
% 5.79/2.01 % (27285)Time elapsed: 0.015 s
% 5.79/2.01 % (27285)Instructions burned: 48 (million)
% 5.79/2.01 % (27285)------------------------------
% 5.79/2.01 % (27285)------------------------------
% 5.79/2.02 % (27288)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/62Mi)
% 5.79/2.03 % (27286)Instruction limit reached!
% 5.79/2.03 % (27286)------------------------------
% 5.79/2.03 % (27286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.03 % (27286)Termination reason: Unknown
% 5.79/2.03 % (27286)Termination phase: shuffling
% 5.79/2.03
% 5.79/2.03 % (27286)Memory used [KB]: 2302
% 5.79/2.03 % (27286)Time elapsed: 0.025 s
% 5.79/2.03 % (27286)Instructions burned: 45 (million)
% 5.79/2.03 % (27286)------------------------------
% 5.79/2.03 % (27286)------------------------------
% 5.79/2.04 % (27288)Instruction limit reached!
% 5.79/2.04 % (27288)------------------------------
% 5.79/2.04 % (27288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.04 % (27288)Termination reason: Unknown
% 5.79/2.04 % (27288)Termination phase: Property scanning
% 5.79/2.04
% 5.79/2.04 % (27288)Memory used [KB]: 2430
% 5.79/2.04 % (27288)Time elapsed: 0.018 s
% 5.79/2.04 % (27288)Instructions burned: 62 (million)
% 5.79/2.04 % (27288)------------------------------
% 5.79/2.04 % (27288)------------------------------
% 5.79/2.05 % (27289)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/31Mi)
% 5.79/2.05 % (27290)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/96Mi)
% 5.79/2.05 % (27277)Instruction limit reached!
% 5.79/2.05 % (27277)------------------------------
% 5.79/2.05 % (27277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.05 % (27277)Termination reason: Unknown
% 5.79/2.05 % (27277)Termination phase: Saturation
% 5.79/2.05
% 5.79/2.05 % (27277)Memory used [KB]: 8187
% 5.79/2.05 % (27277)Time elapsed: 0.132 s
% 5.79/2.05 % (27277)Instructions burned: 448 (million)
% 5.79/2.05 % (27277)------------------------------
% 5.79/2.05 % (27277)------------------------------
% 5.79/2.05 % (27266)Instruction limit reached!
% 5.79/2.05 % (27266)------------------------------
% 5.79/2.05 % (27266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.05 % (27266)Termination reason: Unknown
% 5.79/2.05 % (27266)Termination phase: Saturation
% 5.79/2.05
% 5.79/2.05 % (27266)Memory used [KB]: 8827
% 5.79/2.05 % (27266)Time elapsed: 0.325 s
% 5.79/2.05 % (27266)Instructions burned: 881 (million)
% 5.79/2.05 % (27266)------------------------------
% 5.79/2.05 % (27266)------------------------------
% 5.79/2.06 % (27291)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/453Mi)
% 5.79/2.06 % (27292)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/71Mi)
% 5.79/2.07 % (27289)Instruction limit reached!
% 5.79/2.07 % (27289)------------------------------
% 5.79/2.07 % (27289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.07 % (27289)Termination reason: Unknown
% 5.79/2.07 % (27289)Termination phase: Property scanning
% 5.79/2.07
% 5.79/2.07 % (27289)Memory used [KB]: 2046
% 5.79/2.07 % (27289)Time elapsed: 0.021 s
% 5.79/2.07 % (27289)Instructions burned: 32 (million)
% 5.79/2.07 % (27289)------------------------------
% 5.79/2.07 % (27289)------------------------------
% 5.79/2.08 % (27290)Instruction limit reached!
% 5.79/2.08 % (27290)------------------------------
% 5.79/2.08 % (27290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.08 % (27290)Termination reason: Unknown
% 5.79/2.08 % (27290)Termination phase: Function definition elimination
% 5.79/2.08
% 5.79/2.08 % (27290)Memory used [KB]: 2686
% 5.79/2.08 % (27290)Time elapsed: 0.028 s
% 5.79/2.08 % (27290)Instructions burned: 97 (million)
% 5.79/2.08 % (27290)------------------------------
% 5.79/2.08 % (27290)------------------------------
% 5.79/2.08 % (27293)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/83Mi)
% 5.79/2.08 % (27292)Instruction limit reached!
% 5.79/2.08 % (27292)------------------------------
% 5.79/2.08 % (27292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.08 % (27292)Termination reason: Unknown
% 5.79/2.08 % (27292)Termination phase: Property scanning
% 5.79/2.08
% 5.79/2.08 % (27292)Memory used [KB]: 2558
% 5.79/2.08 % (27292)Time elapsed: 0.022 s
% 5.79/2.08 % (27292)Instructions burned: 72 (million)
% 5.79/2.08 % (27292)------------------------------
% 5.79/2.08 % (27292)------------------------------
% 5.79/2.08 % (27294)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/11Mi)
% 5.79/2.09 % (27294)Instruction limit reached!
% 5.79/2.09 % (27294)------------------------------
% 5.79/2.09 % (27294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.09 % (27294)Termination reason: Unknown
% 5.79/2.09 % (27294)Termination phase: shuffling
% 5.79/2.09
% 5.79/2.09 % (27294)Memory used [KB]: 1663
% 5.79/2.09 % (27294)Time elapsed: 0.005 s
% 5.79/2.09 % (27294)Instructions burned: 14 (million)
% 5.79/2.09 % (27294)------------------------------
% 5.79/2.09 % (27294)------------------------------
% 5.79/2.09 % (27295)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/41Mi)
% 5.79/2.10 % (27280)Instruction limit reached!
% 5.79/2.10 % (27280)------------------------------
% 5.79/2.10 % (27280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.10 % (27280)Termination reason: Unknown
% 5.79/2.10 % (27280)Termination phase: Saturation
% 5.79/2.10
% 5.79/2.10 % (27280)Memory used [KB]: 8699
% 5.79/2.10 % (27280)Time elapsed: 0.149 s
% 5.79/2.10 % (27280)Instructions burned: 507 (million)
% 5.79/2.10 % (27280)------------------------------
% 5.79/2.10 % (27280)------------------------------
% 5.79/2.10 % (27296)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/6Mi)
% 5.79/2.10 % (27296)Instruction limit reached!
% 5.79/2.10 % (27296)------------------------------
% 5.79/2.10 % (27296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.10 % (27296)Termination reason: Unknown
% 5.79/2.10 % (27296)Termination phase: shuffling
% 5.79/2.10
% 5.79/2.10 % (27296)Memory used [KB]: 1535
% 5.79/2.10 % (27296)Time elapsed: 0.004 s
% 5.79/2.10 % (27296)Instructions burned: 8 (million)
% 5.79/2.10 % (27296)------------------------------
% 5.79/2.10 % (27296)------------------------------
% 5.79/2.11 % (27295)Instruction limit reached!
% 5.79/2.11 % (27295)------------------------------
% 5.79/2.11 % (27295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.79/2.11 % (27295)Termination reason: Unknown
% 5.79/2.11 % (27295)Termination phase: shuffling
% 5.79/2.11
% 5.79/2.11 % (27295)Memory used [KB]: 2302
% 5.79/2.11 % (27295)Time elapsed: 0.013 s
% 5.79/2.11 % (27295)Instructions burned: 44 (million)
% 5.79/2.11 % (27295)------------------------------
% 5.79/2.11 % (27295)------------------------------
% 5.79/2.11 % (27297)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/150Mi)
% 5.79/2.11 % (27298)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_26969 for (2995ds/343Mi)
% 6.29/2.12 % (27299)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_26969 for (2994ds/109Mi)
% 6.29/2.12 % (27293)Instruction limit reached!
% 6.29/2.12 % (27293)------------------------------
% 6.29/2.12 % (27293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.12 % (27293)Termination reason: Unknown
% 6.29/2.12 % (27293)Termination phase: Saturation
% 6.29/2.12
% 6.29/2.12 % (27293)Memory used [KB]: 6652
% 6.29/2.12 % (27293)Time elapsed: 0.035 s
% 6.29/2.12 % (27293)Instructions burned: 84 (million)
% 6.29/2.12 % (27293)------------------------------
% 6.29/2.12 % (27293)------------------------------
% 6.29/2.13 % (27300)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_26969 for (2994ds/253Mi)
% 6.29/2.13 % (27287)Instruction limit reached!
% 6.29/2.13 % (27287)------------------------------
% 6.29/2.13 % (27287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.13 % (27287)Termination reason: Unknown
% 6.29/2.13 % (27287)Termination phase: Saturation
% 6.29/2.13
% 6.29/2.13 % (27287)Memory used [KB]: 4605
% 6.29/2.13 % (27287)Time elapsed: 0.122 s
% 6.29/2.13 % (27287)Instructions burned: 434 (million)
% 6.29/2.13 % (27287)------------------------------
% 6.29/2.13 % (27287)------------------------------
% 6.29/2.14 % (27301)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_26969 for (2994ds/140Mi)
% 6.29/2.15 % (27299)Instruction limit reached!
% 6.29/2.15 % (27299)------------------------------
% 6.29/2.15 % (27299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.15 % (27299)Termination reason: Unknown
% 6.29/2.15 % (27299)Termination phase: Property scanning
% 6.29/2.15
% 6.29/2.15 % (27299)Memory used [KB]: 2558
% 6.29/2.15 % (27299)Time elapsed: 0.033 s
% 6.29/2.15 % (27299)Instructions burned: 111 (million)
% 6.29/2.15 % (27299)------------------------------
% 6.29/2.15 % (27299)------------------------------
% 6.29/2.15 % (27297)Instruction limit reached!
% 6.29/2.15 % (27297)------------------------------
% 6.29/2.15 % (27297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.15 % (27297)Termination reason: Unknown
% 6.29/2.15 % (27297)Termination phase: Property scanning
% 6.29/2.15
% 6.29/2.15 % (27297)Memory used [KB]: 2942
% 6.29/2.15 % (27297)Time elapsed: 0.042 s
% 6.29/2.15 % (27297)Instructions burned: 151 (million)
% 6.29/2.15 % (27297)------------------------------
% 6.29/2.15 % (27297)------------------------------
% 6.29/2.16 % (27302)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_26969 for (2994ds/614Mi)
% 6.29/2.16 % (27303)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_26969 for (2994ds/202Mi)
% 6.29/2.16 % (27300)First to succeed.
% 6.29/2.17 % (27300)Refutation found. Thanks to Tanya!
% 6.29/2.17 % SZS status Theorem for DTF2THF_26969
% 6.29/2.17 % SZS output start Proof for DTF2THF_26969
% 6.29/2.17 thf(type_def_5, type, list_list_list_a: $tType).
% 6.29/2.17 thf(type_def_6, type, set_nat: $tType).
% 6.29/2.17 thf(type_def_7, type, set_list_list_a: $tType).
% 6.29/2.17 thf(type_def_9, type, list_list_nat: $tType).
% 6.29/2.17 thf(type_def_10, type, set_list_nat: $tType).
% 6.29/2.17 thf(type_def_11, type, list_list_a: $tType).
% 6.29/2.17 thf(type_def_12, type, set_list_a: $tType).
% 6.29/2.17 thf(type_def_13, type, list_nat: $tType).
% 6.29/2.17 thf(type_def_14, type, list_a: $tType).
% 6.29/2.17 thf(type_def_15, type, set_a: $tType).
% 6.29/2.17 thf(type_def_16, type, list_set_list_a: $tType).
% 6.29/2.17 thf(type_def_17, type, list_set_nat: $tType).
% 6.29/2.17 thf(type_def_18, type, list_set_a: $tType).
% 6.29/2.17 thf(type_def_19, type, nat: $tType).
% 6.29/2.17 thf(type_def_20, type, list_l2071841302list_a: $tType).
% 6.29/2.17 thf(type_def_21, type, list_list_list_nat: $tType).
% 6.29/2.17 thf(type_def_22, type, a: $tType).
% 6.29/2.17 thf(func_def_0, type, list_l2071841302list_a: $tType).
% 6.29/2.17 thf(func_def_1, type, list_list_list_nat: $tType).
% 6.29/2.17 thf(func_def_2, type, list_list_list_a: $tType).
% 6.29/2.17 thf(func_def_3, type, set_list_list_a: $tType).
% 6.29/2.17 thf(func_def_4, type, list_set_list_a: $tType).
% 6.29/2.17 thf(func_def_5, type, list_list_nat: $tType).
% 6.29/2.17 thf(func_def_6, type, set_list_nat: $tType).
% 6.29/2.17 thf(func_def_7, type, list_set_nat: $tType).
% 6.29/2.17 thf(func_def_8, type, list_list_a: $tType).
% 6.29/2.17 thf(func_def_9, type, set_list_a: $tType).
% 6.29/2.17 thf(func_def_10, type, list_set_a: $tType).
% 6.29/2.17 thf(func_def_11, type, list_nat: $tType).
% 6.29/2.17 thf(func_def_12, type, set_nat: $tType).
% 6.29/2.17 thf(func_def_13, type, list_a: $tType).
% 6.29/2.17 thf(func_def_14, type, set_a: $tType).
% 6.29/2.17 thf(func_def_15, type, nat: $tType).
% 6.29/2.17 thf(func_def_16, type, a: $tType).
% 6.29/2.17 thf(func_def_17, type, f_image_list_list_a: list_list_list_a > set_nat > set_list_list_a).
% 6.29/2.17 thf(func_def_18, type, f_image_list_nat: list_list_nat > set_nat > set_list_nat).
% 6.29/2.17 thf(func_def_19, type, f_image_list_a: list_list_a > set_nat > set_list_a).
% 6.29/2.17 thf(func_def_20, type, f_image_nat: list_nat > set_nat > set_nat).
% 6.29/2.17 thf(func_def_21, type, f_image_a: list_a > set_nat > set_a).
% 6.29/2.17 thf(func_def_22, type, list_asc_nat: list_nat > $o).
% 6.29/2.17 thf(func_def_23, type, list_asc_set_list_a: list_set_list_a > $o).
% 6.29/2.17 thf(func_def_24, type, list_asc_set_nat: list_set_nat > $o).
% 6.29/2.17 thf(func_def_25, type, list_asc_set_a: list_set_a > $o).
% 6.29/2.17 thf(func_def_26, type, list_desc_nat: list_nat > $o).
% 6.29/2.17 thf(func_def_27, type, list_desc_set_list_a: list_set_list_a > $o).
% 6.29/2.17 thf(func_def_28, type, list_desc_set_nat: list_set_nat > $o).
% 6.29/2.17 thf(func_def_29, type, list_desc_set_a: list_set_a > $o).
% 6.29/2.17 thf(func_def_30, type, list_strict_asc_nat: list_nat > $o).
% 6.29/2.17 thf(func_def_31, type, list_strict_desc_nat: list_nat > $o).
% 6.29/2.17 thf(func_def_32, type, listSl769338732list_a: list_list_list_a > nat > list_l2071841302list_a).
% 6.29/2.17 thf(func_def_33, type, listSl2099749758st_nat: list_list_nat > nat > list_list_list_nat).
% 6.29/2.17 thf(func_def_34, type, listSl703198822list_a: list_list_a > nat > list_list_list_a).
% 6.29/2.17 thf(func_def_35, type, listSl882585454e2_nat: list_nat > nat > list_list_nat).
% 6.29/2.17 thf(func_def_36, type, listSl1174287072ice2_a: list_a > nat > list_list_a).
% 6.29/2.17 thf(func_def_37, type, listSl2102238196list_a: list_list_list_a > nat > list_l2071841302list_a).
% 6.29/2.17 thf(func_def_38, type, listSl729562870st_nat: list_list_nat > nat > list_list_list_nat).
% 6.29/2.17 thf(func_def_39, type, listSl162220270list_a: list_list_a > nat > list_list_list_a).
% 6.29/2.17 thf(func_def_40, type, listSl1630398182ce_nat: list_nat > nat > list_list_nat).
% 6.29/2.17 thf(func_def_41, type, listSl97544552lice_a: list_a > nat > list_list_a).
% 6.29/2.17 thf(func_def_42, type, listSl902632890list_a: list_list_list_a > nat > nat > list_l2071841302list_a).
% 6.29/2.17 thf(func_def_43, type, listSl1506485424st_nat: list_list_nat > nat > nat > list_list_list_nat).
% 6.29/2.17 thf(func_def_44, type, listSl856612276list_a: list_list_a > nat > nat > list_list_list_a).
% 6.29/2.17 thf(func_def_45, type, listSl1794011552ux_nat: list_nat > nat > nat > list_list_nat).
% 6.29/2.17 thf(func_def_46, type, listSl1495374126_aux_a: list_a > nat > nat > list_list_a).
% 6.29/2.17 thf(func_def_47, type, butlast_list_list_a: list_list_list_a > list_list_list_a).
% 6.29/2.17 thf(func_def_48, type, butlast_list_nat: list_list_nat > list_list_nat).
% 6.29/2.17 thf(func_def_49, type, butlast_list_a: list_list_a > list_list_a).
% 6.29/2.17 thf(func_def_50, type, butlast_nat: list_nat > list_nat).
% 6.29/2.17 thf(func_def_51, type, butlast_a: list_a > list_a).
% 6.29/2.17 thf(func_def_52, type, distinct_list_list_a: list_list_list_a > $o).
% 6.29/2.17 thf(func_def_53, type, distinct_list_nat: list_list_nat > $o).
% 6.29/2.17 thf(func_def_54, type, distinct_list_a: list_list_a > $o).
% 6.29/2.17 thf(func_def_55, type, distinct_nat: list_nat > $o).
% 6.29/2.17 thf(func_def_56, type, distinct_a: list_a > $o).
% 6.29/2.17 thf(func_def_57, type, set_list_list_a2: list_list_list_a > set_list_list_a).
% 6.29/2.17 thf(func_def_58, type, set_list_nat2: list_list_nat > set_list_nat).
% 6.29/2.17 thf(func_def_59, type, set_list_a2: list_list_a > set_list_a).
% 6.29/2.17 thf(func_def_60, type, set_nat2: list_nat > set_nat).
% 6.29/2.17 thf(func_def_61, type, set_a2: list_a > set_a).
% 6.29/2.17 thf(func_def_62, type, list_ex_list_list_a: (list_list_a > $o) > list_list_list_a > $o).
% 6.29/2.17 thf(func_def_63, type, list_ex_list_nat: (list_nat > $o) > list_list_nat > $o).
% 6.29/2.17 thf(func_def_64, type, list_ex_list_a: (list_a > $o) > list_list_a > $o).
% 6.29/2.17 thf(func_def_65, type, list_ex_nat: (nat > $o) > list_nat > $o).
% 6.29/2.17 thf(func_def_66, type, list_ex_a: (a > $o) > list_a > $o).
% 6.29/2.17 thf(func_def_67, type, list_u1330012152list_a: list_list_list_a > nat > list_list_a > list_list_list_a).
% 6.29/2.17 thf(func_def_68, type, list_update_list_nat: list_list_nat > nat > list_nat > list_list_nat).
% 6.29/2.17 thf(func_def_69, type, list_update_list_a: list_list_a > nat > list_a > list_list_a).
% 6.29/2.17 thf(func_def_70, type, list_update_nat: list_nat > nat > nat > list_nat).
% 6.29/2.17 thf(func_def_71, type, list_update_a: list_a > nat > a > list_a).
% 6.29/2.17 thf(func_def_72, type, nth_list_list_list_a: list_l2071841302list_a > nat > list_list_list_a).
% 6.29/2.17 thf(func_def_73, type, nth_list_list_nat: list_list_list_nat > nat > list_list_nat).
% 6.29/2.17 thf(func_def_74, type, nth_list_list_a: list_list_list_a > nat > list_list_a).
% 6.29/2.17 thf(func_def_75, type, nth_list_nat: list_list_nat > nat > list_nat).
% 6.29/2.17 thf(func_def_76, type, nth_list_a: list_list_a > nat > list_a).
% 6.29/2.17 thf(func_def_77, type, nth_nat: list_nat > nat > nat).
% 6.29/2.17 thf(func_def_78, type, nth_set_list_a: list_set_list_a > nat > set_list_a).
% 6.29/2.17 thf(func_def_79, type, nth_set_nat: list_set_nat > nat > set_nat).
% 6.29/2.17 thf(func_def_80, type, nth_set_a: list_set_a > nat > set_a).
% 6.29/2.17 thf(func_def_81, type, nth_a: list_a > nat > a).
% 6.29/2.17 thf(func_def_82, type, size_s1764310658list_a: list_l2071841302list_a > nat).
% 6.29/2.17 thf(func_def_83, type, size_s1321307156st_nat: list_list_list_nat > nat).
% 6.29/2.17 thf(func_def_84, type, size_s575106428list_a: list_list_list_a > nat).
% 6.29/2.17 thf(func_def_85, type, size_s1898481668st_nat: list_list_nat > nat).
% 6.29/2.17 thf(func_def_86, type, size_s1427607542list_a: list_list_a > nat).
% 6.29/2.17 thf(func_def_87, type, size_size_list_nat: list_nat > nat).
% 6.29/2.17 thf(func_def_88, type, size_s1635937238list_a: list_set_list_a > nat).
% 6.29/2.17 thf(func_def_89, type, size_s577819178et_nat: list_set_nat > nat).
% 6.29/2.17 thf(func_def_90, type, size_size_list_set_a: list_set_a > nat).
% 6.29/2.17 thf(func_def_91, type, size_size_list_a: list_a > nat).
% 6.29/2.17 thf(func_def_92, type, ord_less_nat: nat > nat > $o).
% 6.29/2.17 thf(func_def_93, type, ord_less_eq_nat: nat > nat > $o).
% 6.29/2.17 thf(func_def_94, type, ord_le1756736906list_a: set_list_list_a > set_list_list_a > $o).
% 6.29/2.17 thf(func_def_95, type, ord_le1747345782st_nat: set_list_nat > set_list_nat > $o).
% 6.29/2.17 thf(func_def_96, type, ord_le1301786372list_a: set_list_a > set_list_a > $o).
% 6.29/2.17 thf(func_def_97, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 6.29/2.17 thf(func_def_98, type, ord_less_eq_set_a: set_a > set_a > $o).
% 6.29/2.17 thf(func_def_99, type, top_top_set_nat: set_nat).
% 6.29/2.17 thf(func_def_100, type, divide_divide_nat: nat > nat > nat).
% 6.29/2.17 thf(func_def_101, type, collect_list_a: (list_a > $o) > set_list_a).
% 6.29/2.17 thf(func_def_102, type, collect_nat: (nat > $o) > set_nat).
% 6.29/2.17 thf(func_def_103, type, collect_a: (a > $o) > set_a).
% 6.29/2.17 thf(func_def_104, type, member_list_list_a: list_list_a > set_list_list_a > $o).
% 6.29/2.17 thf(func_def_105, type, member_list_nat: list_nat > set_list_nat > $o).
% 6.29/2.17 thf(func_def_106, type, member_list_a: list_a > set_list_a > $o).
% 6.29/2.17 thf(func_def_107, type, member_nat: nat > set_nat > $o).
% 6.29/2.17 thf(func_def_108, type, member_a: a > set_a > $o).
% 6.29/2.17 thf(func_def_109, type, k: nat).
% 6.29/2.17 thf(func_def_110, type, m: nat).
% 6.29/2.17 thf(func_def_111, type, xs: list_a).
% 6.29/2.17 thf(func_def_126, type, sP0: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 6.29/2.17 thf(func_def_127, type, sP1: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 6.29/2.17 thf(func_def_128, type, sP2: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 6.29/2.17 thf(func_def_129, type, sP3: nat > nat > nat > $o).
% 6.29/2.17 thf(func_def_130, type, sP4: nat > nat > nat > $o).
% 6.29/2.17 thf(func_def_131, type, sP5: nat > nat > nat > $o).
% 6.29/2.17 thf(func_def_132, type, sP6: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 6.29/2.17 thf(func_def_133, type, sK7: nat > nat).
% 6.29/2.17 thf(func_def_134, type, sK8: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_135, type, sK9: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_136, type, sK10: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_137, type, sK11: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_138, type, sK12: (nat > nat > $o) > nat).
% 6.29/2.17 thf(func_def_139, type, sK13: (nat > nat > $o) > nat).
% 6.29/2.17 thf(func_def_140, type, sK14: (nat > nat > $o) > nat).
% 6.29/2.17 thf(func_def_141, type, sK15: (nat > nat > $o) > nat).
% 6.29/2.17 thf(func_def_142, type, sK16: nat > nat).
% 6.29/2.17 thf(func_def_143, type, sK17: nat > nat).
% 6.29/2.17 thf(func_def_144, type, sK18: nat > nat).
% 6.29/2.17 thf(func_def_145, type, sK19: (nat > $o) > nat).
% 6.29/2.17 thf(func_def_146, type, sK20: (nat > $o) > nat).
% 6.29/2.17 thf(func_def_147, type, sK21: (nat > $o) > nat > nat).
% 6.29/2.17 thf(func_def_148, type, sK22: (nat > $o) > nat > nat).
% 6.29/2.17 thf(func_def_149, type, sK23: nat > nat).
% 6.29/2.17 thf(func_def_150, type, sK24: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_151, type, sK25: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_152, type, sK26: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_153, type, sK27: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_154, type, sK28: nat > nat).
% 6.29/2.17 thf(func_def_155, type, sK29: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_156, type, sK30: nat > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_157, type, sK31: nat > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_158, type, sK32: nat > list_list_a).
% 6.29/2.17 thf(func_def_159, type, sK33: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_160, type, sK34: nat > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_161, type, sK35: nat > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_162, type, sK36: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_163, type, sK37: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_164, type, sK38: nat > nat).
% 6.29/2.17 thf(func_def_165, type, sK39: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_166, type, sK40: nat > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_167, type, sK41: nat > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_168, type, sK42: nat > nat).
% 6.29/2.17 thf(func_def_169, type, sK43: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_170, type, sK44: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_171, type, sK45: list_list_a > list_list_a > nat).
% 6.29/2.17 thf(func_def_172, type, sK46: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_173, type, sK47: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_174, type, sK48: nat > list_a).
% 6.29/2.17 thf(func_def_175, type, sK49: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_176, type, sK50: nat > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_177, type, sK51: nat > (nat > $o) > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_178, type, sK52: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_179, type, sK53: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_180, type, sK54: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_181, type, sK55: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_182, type, sK56: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_183, type, sK57: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_184, type, sK58: (list_list_a > $o) > list_list_a).
% 6.29/2.17 thf(func_def_185, type, sK59: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_186, type, sK60: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_187, type, sK61: nat > nat).
% 6.29/2.17 thf(func_def_188, type, sK62: nat > (nat > list_a > $o) > list_a).
% 6.29/2.17 thf(func_def_189, type, sK63: list_list_a > (nat > list_a > $o) > nat > nat).
% 6.29/2.17 thf(func_def_190, type, sK64: (nat > list_a > $o) > nat > list_list_a).
% 6.29/2.17 thf(func_def_191, type, sK65: (nat > list_a > $o) > nat > nat).
% 6.29/2.17 thf(func_def_192, type, sK66: nat > nat).
% 6.29/2.17 thf(func_def_193, type, sK67: nat > nat > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_194, type, sK68: nat > nat > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_195, type, sK69: nat > nat).
% 6.29/2.17 thf(func_def_196, type, sK70: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_197, type, sK71: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_198, type, sK72: nat > (nat > $o) > nat).
% 6.29/2.17 thf(func_def_199, type, sK73: (nat > $o) > nat).
% 6.29/2.17 thf(func_def_200, type, sK74: (nat > $o) > nat).
% 6.29/2.17 thf(func_def_201, type, sK75: nat > nat).
% 6.29/2.17 thf(func_def_202, type, sK76: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_203, type, sK77: (nat > nat) > nat).
% 6.29/2.17 thf(func_def_204, type, sK78: (list_a > $o) > list_a).
% 6.29/2.17 thf(func_def_205, type, sK79: (nat > nat > $o) > nat).
% 6.29/2.17 thf(func_def_206, type, sK80: (nat > nat > $o) > nat).
% 6.29/2.17 thf(func_def_207, type, sK81: (nat > nat > $o) > nat).
% 6.29/2.17 thf(func_def_208, type, sK82: (nat > nat > $o) > nat).
% 6.29/2.17 thf(func_def_209, type, sK83: (nat > nat > $o) > nat).
% 6.29/2.17 thf(func_def_210, type, sK84: nat > nat).
% 6.29/2.17 thf(func_def_212, type, ph86: !>[X0: $tType]:(X0)).
% 6.29/2.17 thf(f1603,plain,(
% 6.29/2.17 $false),
% 6.29/2.17 inference(avatar_sat_refutation,[status(thm)],[f1597,f1598,f1602])).
% 6.29/2.17 thf(f1602,plain,(
% 6.29/2.17 ~spl85_2 | spl85_1),
% 6.29/2.17 inference(avatar_split_clause,[status(thm)],[f1601,f1590,f1594])).
% 6.29/2.17 thf(f1594,definition,(
% 6.29/2.17 spl85_2 <=> ((ord_less_nat @ m @ (size_s1427607542list_a @ (listSl97544552lice_a @ xs @ k))) = $true)),
% 6.29/2.17 introduced(definition,[new_symbols(naming,[spl85_2])],[avatar_definition])).
% 6.29/2.17 thf(f1590,definition,(
% 6.29/2.17 spl85_1 <=> (k = (size_size_list_a @ (nth_list_a @ (listSl97544552lice_a @ xs @ k) @ m)))),
% 6.29/2.17 introduced(definition,[new_symbols(naming,[spl85_1])],[avatar_definition])).
% 6.29/2.17 thf(f1601,plain,(
% 6.29/2.17 ((ord_less_nat @ m @ (size_s1427607542list_a @ (listSl97544552lice_a @ xs @ k))) != $true) | spl85_1),
% 6.29/2.17 inference(forward_demodulation,[status(thm)],[f1600,f1406])).
% 6.29/2.17 thf(f1406,plain,(
% 6.29/2.17 ( ! [X0 : nat,X1 : list_a] : (((size_s1427607542list_a @ (listSl97544552lice_a @ X1 @ X0)) = (divide_divide_nat @ (size_size_list_a @ X1) @ X0))) )),
% 6.29/2.17 inference(cnf_transformation,[status(thm)],[f979])).
% 6.29/2.17 thf(f979,plain,(
% 6.29/2.17 ! [X0 : nat,X1 : list_a] : ((size_s1427607542list_a @ (listSl97544552lice_a @ X1 @ X0)) = (divide_divide_nat @ (size_size_list_a @ X1) @ X0))),
% 6.29/2.17 inference(rectify,[status(thm)],[f53])).
% 6.29/2.17 thf(f53,axiom,(
% 6.29/2.17 ! [X3 : nat,X0 : list_a] : ((divide_divide_nat @ (size_size_list_a @ X0) @ X3) = (size_s1427607542list_a @ (listSl97544552lice_a @ X0 @ X3)))),
% 6.29/2.17 file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',fact_52_list__slice__length)).
% 6.29/2.17 thf(f1600,plain,(
% 6.29/2.17 ((ord_less_nat @ m @ (divide_divide_nat @ (size_size_list_a @ xs) @ k)) != $true) | spl85_1),
% 6.29/2.17 inference(trivial_inequality_removal,[status(thm)],[f1599])).
% 6.29/2.17 thf(f1599,plain,(
% 6.29/2.17 (k != k) | ((ord_less_nat @ m @ (divide_divide_nat @ (size_size_list_a @ xs) @ k)) != $true) | spl85_1),
% 6.29/2.17 inference(superposition,[status(thm)],[f1592,f1377])).
% 6.29/2.17 thf(f1377,plain,(
% 6.29/2.17 ( ! [X2 : nat,X0 : nat,X1 : list_a] : (((size_size_list_a @ (nth_list_a @ (listSl97544552lice_a @ X1 @ X0) @ X2)) = X0) | ($true != (ord_less_nat @ X2 @ (divide_divide_nat @ (size_size_list_a @ X1) @ X0)))) )),
% 6.29/2.17 inference(cnf_transformation,[status(thm)],[f1008])).
% 6.29/2.17 thf(f1008,plain,(
% 6.29/2.17 ! [X0 : nat,X1 : list_a,X2 : nat] : (((size_size_list_a @ (nth_list_a @ (listSl97544552lice_a @ X1 @ X0) @ X2)) = X0) | ($true != (ord_less_nat @ X2 @ (divide_divide_nat @ (size_size_list_a @ X1) @ X0))))),
% 6.29/2.17 inference(ennf_transformation,[status(thm)],[f418])).
% 6.29/2.17 thf(f418,plain,(
% 6.29/2.17 ! [X0 : nat,X1 : list_a,X2 : nat] : (($true = (ord_less_nat @ X2 @ (divide_divide_nat @ (size_size_list_a @ X1) @ X0))) => ((size_size_list_a @ (nth_list_a @ (listSl97544552lice_a @ X1 @ X0) @ X2)) = X0))),
% 6.29/2.17 inference(fool_elimination,[status(thm)],[f417])).
% 6.29/2.17 thf(f417,plain,(
% 6.29/2.17 ! [X0 : nat,X1 : list_a,X2 : nat] : ((ord_less_nat @ X2 @ (divide_divide_nat @ (size_size_list_a @ X1) @ X0)) => ((size_size_list_a @ (nth_list_a @ (listSl97544552lice_a @ X1 @ X0) @ X2)) = X0))),
% 6.29/2.17 inference(rectify,[status(thm)],[f31])).
% 6.29/2.17 thf(f31,axiom,(
% 6.29/2.17 ! [X3 : nat,X0 : list_a,X11 : nat] : ((ord_less_nat @ X11 @ (divide_divide_nat @ (size_size_list_a @ X0) @ X3)) => ((size_size_list_a @ (nth_list_a @ (listSl97544552lice_a @ X0 @ X3) @ X11)) = X3))),
% 6.29/2.17 file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',fact_30_list__slice__nth__length)).
% 6.29/2.17 thf(f1592,plain,(
% 6.29/2.17 (k != (size_size_list_a @ (nth_list_a @ (listSl97544552lice_a @ xs @ k) @ m))) | spl85_1),
% 6.29/2.17 inference(avatar_component_clause,[status(thm)],[f1590])).
% 6.29/2.17 thf(f1598,plain,(
% 6.29/2.17 spl85_2),
% 6.29/2.17 inference(avatar_split_clause,[status(thm)],[f1586,f1594])).
% 6.29/2.17 thf(f1586,plain,(
% 6.29/2.17 ((ord_less_nat @ m @ (size_s1427607542list_a @ (listSl97544552lice_a @ xs @ k))) = $true)),
% 6.29/2.17 inference(forward_demodulation,[status(thm)],[f1360,f1406])).
% 6.29/2.17 thf(f1360,plain,(
% 6.29/2.17 ((ord_less_nat @ m @ (divide_divide_nat @ (size_size_list_a @ xs) @ k)) = $true)),
% 6.29/2.17 inference(cnf_transformation,[status(thm)],[f828])).
% 6.29/2.17 thf(f828,plain,(
% 6.29/2.17 ((ord_less_nat @ m @ (divide_divide_nat @ (size_size_list_a @ xs) @ k)) = $true)),
% 6.29/2.17 inference(fool_elimination,[status(thm)],[f827])).
% 6.29/2.17 thf(f827,plain,(
% 6.29/2.17 (ord_less_nat @ m @ (divide_divide_nat @ (size_size_list_a @ xs) @ k))),
% 6.29/2.17 inference(rectify,[status(thm)],[f349])).
% 6.29/2.17 thf(f349,axiom,(
% 6.29/2.17 (ord_less_nat @ m @ (divide_divide_nat @ (size_size_list_a @ xs) @ k))),
% 6.29/2.17 file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',conj_0)).
% 6.29/2.17 thf(f1597,plain,(
% 6.29/2.17 ~spl85_1 | ~spl85_2),
% 6.29/2.17 inference(avatar_split_clause,[status(thm)],[f1588,f1594,f1590])).
% 6.29/2.17 thf(f1588,plain,(
% 6.29/2.17 ((ord_less_nat @ m @ (size_s1427607542list_a @ (listSl97544552lice_a @ xs @ k))) != $true) | (k != (size_size_list_a @ (nth_list_a @ (listSl97544552lice_a @ xs @ k) @ m)))),
% 6.29/2.17 inference(forward_demodulation,[status(thm)],[f1587,f1406])).
% 6.29/2.17 thf(f1587,plain,(
% 6.29/2.17 (k != (size_size_list_a @ (nth_list_a @ (listSl97544552lice_a @ xs @ k) @ m))) | ((ord_less_nat @ m @ (divide_divide_nat @ (size_size_list_a @ xs) @ k)) != $true)),
% 6.29/2.17 inference(superposition,[status(thm)],[f1475,f1490])).
% 6.29/2.17 thf(f1490,plain,(
% 6.29/2.17 ( ! [X2 : list_a,X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ (divide_divide_nat @ (size_size_list_a @ X2) @ X0)) != $true) | ((nth_list_a @ (listSl97544552lice_a @ X2 @ X0) @ X1) = (nth_list_a @ (listSl1174287072ice2_a @ X2 @ X0) @ X1))) )),
% 6.29/2.17 inference(cnf_transformation,[status(thm)],[f1125])).
% 6.29/2.17 thf(f1125,plain,(
% 6.29/2.17 ! [X0 : nat,X1 : nat,X2 : list_a] : (((ord_less_nat @ X1 @ (divide_divide_nat @ (size_size_list_a @ X2) @ X0)) != $true) | ((nth_list_a @ (listSl97544552lice_a @ X2 @ X0) @ X1) = (nth_list_a @ (listSl1174287072ice2_a @ X2 @ X0) @ X1)))),
% 6.29/2.17 inference(ennf_transformation,[status(thm)],[f870])).
% 6.29/2.17 thf(f870,plain,(
% 6.29/2.17 ! [X0 : nat,X1 : nat,X2 : list_a] : (((ord_less_nat @ X1 @ (divide_divide_nat @ (size_size_list_a @ X2) @ X0)) = $true) => ((nth_list_a @ (listSl97544552lice_a @ X2 @ X0) @ X1) = (nth_list_a @ (listSl1174287072ice2_a @ X2 @ X0) @ X1)))),
% 6.29/2.17 inference(fool_elimination,[status(thm)],[f869])).
% 6.29/2.17 thf(f869,plain,(
% 6.29/2.17 ! [X0 : nat,X1 : nat,X2 : list_a] : ((ord_less_nat @ X1 @ (divide_divide_nat @ (size_size_list_a @ X2) @ X0)) => ((nth_list_a @ (listSl97544552lice_a @ X2 @ X0) @ X1) = (nth_list_a @ (listSl1174287072ice2_a @ X2 @ X0) @ X1)))),
% 6.29/2.17 inference(rectify,[status(thm)],[f20])).
% 6.29/2.17 thf(f20,axiom,(
% 6.29/2.17 ! [X3 : nat,X11 : nat,X0 : list_a] : ((ord_less_nat @ X11 @ (divide_divide_nat @ (size_size_list_a @ X0) @ X3)) => ((nth_list_a @ (listSl1174287072ice2_a @ X0 @ X3) @ X11) = (nth_list_a @ (listSl97544552lice_a @ X0 @ X3) @ X11)))),
% 6.29/2.17 file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',fact_19_list__slice2__list__slice__nth)).
% 6.29/2.17 thf(f1475,plain,(
% 6.29/2.17 (k != (size_size_list_a @ (nth_list_a @ (listSl1174287072ice2_a @ xs @ k) @ m)))),
% 6.29/2.17 inference(cnf_transformation,[status(thm)],[f957])).
% 6.29/2.17 thf(f957,plain,(
% 6.29/2.17 (k != (size_size_list_a @ (nth_list_a @ (listSl1174287072ice2_a @ xs @ k) @ m)))),
% 6.29/2.17 inference(flattening,[status(thm)],[f351])).
% 6.29/2.17 thf(f351,negated_conjecture,(
% 6.29/2.17 ~(k = (size_size_list_a @ (nth_list_a @ (listSl1174287072ice2_a @ xs @ k) @ m)))),
% 6.29/2.17 inference(negated_conjecture,[status(cth)],[f350])).
% 6.29/2.17 thf(f350,conjecture,(
% 6.29/2.17 (k = (size_size_list_a @ (nth_list_a @ (listSl1174287072ice2_a @ xs @ k) @ m)))),
% 6.29/2.17 file('/export/starexec/sandbox2/tmp/tmp.8atHQWA2XJ/DTF2THF_26969.p',conj_1)).
% 6.29/2.17 % SZS output end Proof for DTF2THF_26969
% 6.29/2.17 % (27300)------------------------------
% 6.29/2.17 % (27300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.17 % (27300)Termination reason: Refutation
% 6.29/2.17
% 6.29/2.17 % (27300)Memory used [KB]: 7291
% 6.29/2.17 % (27300)Time elapsed: 0.040 s
% 6.29/2.17 % (27300)Instructions burned: 117 (million)
% 6.29/2.17 % (27300)------------------------------
% 6.29/2.17 % (27300)------------------------------
% 6.29/2.17 % (27236)Success in time 0.578 s
%------------------------------------------------------------------------------