%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWW473^2 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 09:48:10 AM UTC 2026
% Result : Theorem 5.96s 2.19s
% Output : Refutation 5.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 225 ( 50 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 270 ( 29 ~; 19 |; 7 &; 206 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 241 ( 238 usr; 7 con; 0-4 aty)
% Number of variables : 45 ( 0 ^; 45 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
pname: $tType ).
thf(type_def_6,type,
option_com: $tType ).
thf(type_def_8,type,
x_a: $tType ).
thf(type_def_9,type,
nat: $tType ).
thf(type_def_10,type,
com: $tType ).
thf(func_def_0,type,
x_a: $tType ).
thf(func_def_1,type,
com: $tType ).
thf(func_def_2,type,
pname: $tType ).
thf(func_def_3,type,
nat: $tType ).
thf(func_def_4,type,
option_com: $tType ).
thf(func_def_5,type,
body: pname > option_com ).
thf(func_def_6,type,
finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
thf(func_def_7,type,
finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
thf(func_def_8,type,
finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
thf(func_def_9,type,
finite_card_a: ( x_a > $o ) > nat ).
thf(func_def_10,type,
finite_card_pname: ( pname > $o ) > nat ).
thf(func_def_11,type,
finite_card_nat: ( nat > $o ) > nat ).
thf(func_def_12,type,
finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
thf(func_def_13,type,
finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_14,type,
finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
thf(func_def_15,type,
finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_16,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(func_def_17,type,
finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
thf(func_def_18,type,
finite_finite_a: ( x_a > $o ) > $o ).
thf(func_def_19,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(func_def_20,type,
finite_finite_nat: ( nat > $o ) > $o ).
thf(func_def_21,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_22,type,
one_one_nat: nat ).
thf(func_def_23,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_24,type,
zero_zero_nat: nat ).
thf(func_def_25,type,
suc: nat > nat ).
thf(func_def_26,type,
nat_case_o: $o > ( nat > $o ) > nat > $o ).
thf(func_def_27,type,
the_com: option_com > com ).
thf(func_def_28,type,
bot_bot_a_o_o: ( x_a > $o ) > $o ).
thf(func_def_29,type,
bot_bot_pname_o_o: ( pname > $o ) > $o ).
thf(func_def_30,type,
bot_bot_nat_o_o: ( nat > $o ) > $o ).
thf(func_def_31,type,
bot_bot_a_o: x_a > $o ).
thf(func_def_32,type,
bot_bot_pname_o: pname > $o ).
thf(func_def_33,type,
bot_bot_nat_o: nat > $o ).
thf(func_def_35,type,
bot_bot_nat: nat ).
thf(func_def_36,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_37,type,
ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_38,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_39,type,
ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_40,type,
ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(func_def_41,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_42,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_43,type,
ord_less_eq_o: $o > $o > $o ).
thf(func_def_44,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_45,type,
collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_46,type,
collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_47,type,
collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_48,type,
collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(func_def_49,type,
collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_50,type,
collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(func_def_51,type,
collect_a: ( x_a > $o ) > x_a > $o ).
thf(func_def_52,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(func_def_53,type,
collect_nat: ( nat > $o ) > nat > $o ).
thf(func_def_54,type,
image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
thf(func_def_55,type,
image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
thf(func_def_56,type,
image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
thf(func_def_57,type,
image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
thf(func_def_58,type,
image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_59,type,
image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
thf(func_def_60,type,
image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
thf(func_def_61,type,
image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
thf(func_def_62,type,
image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_63,type,
image_a_a_o: ( x_a > x_a > $o ) > ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(func_def_64,type,
image_a_pname_o: ( x_a > pname > $o ) > ( x_a > $o ) > ( pname > $o ) > $o ).
thf(func_def_65,type,
image_a_nat_o: ( x_a > nat > $o ) > ( x_a > $o ) > ( nat > $o ) > $o ).
thf(func_def_66,type,
image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
thf(func_def_67,type,
image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
thf(func_def_68,type,
image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
thf(func_def_69,type,
image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
thf(func_def_70,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_71,type,
image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
thf(func_def_72,type,
image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
thf(func_def_73,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(func_def_74,type,
image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
thf(func_def_75,type,
image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
thf(func_def_76,type,
image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
thf(func_def_77,type,
image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_78,type,
image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
thf(func_def_79,type,
image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
thf(func_def_80,type,
image_nat_nat: ( nat > nat ) > ( nat > $o ) > nat > $o ).
thf(func_def_81,type,
insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(func_def_82,type,
insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_83,type,
insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(func_def_84,type,
insert_a: x_a > ( x_a > $o ) > x_a > $o ).
thf(func_def_85,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(func_def_86,type,
insert_nat: nat > ( nat > $o ) > nat > $o ).
thf(func_def_87,type,
fequal_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(func_def_88,type,
fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_89,type,
fequal_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_90,type,
fequal_a: x_a > x_a > $o ).
thf(func_def_91,type,
fequal_pname: pname > pname > $o ).
thf(func_def_92,type,
fequal_nat: nat > nat > $o ).
thf(func_def_93,type,
member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_94,type,
member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_95,type,
member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_96,type,
member_a: x_a > ( x_a > $o ) > $o ).
thf(func_def_97,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(func_def_98,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(func_def_99,type,
g: x_a > $o ).
thf(func_def_100,type,
p: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(func_def_101,type,
u: pname > $o ).
thf(func_def_102,type,
mgt: com > x_a ).
thf(func_def_103,type,
mgt_call: pname > x_a ).
thf(func_def_104,type,
na: nat ).
thf(func_def_105,type,
pn: pname ).
thf(func_def_106,type,
wt: com > $o ).
thf(func_def_117,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_118,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_121,type,
sK2: ( ( x_a > $o ) > $o ) > ( x_a > x_a > $o ) > ( x_a > $o ) > x_a > $o ).
thf(func_def_122,type,
sK3: ( x_a > $o ) > ( x_a > nat ) > ( nat > $o ) > x_a > $o ).
thf(func_def_123,type,
sK4: ( pname > $o ) > ( pname > nat ) > pname ).
thf(func_def_124,type,
sK5: ( pname > $o ) > pname ).
thf(func_def_125,type,
sK6: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( ( pname > $o ) > pname ) > ( pname > $o ) > $o ).
thf(func_def_126,type,
sK7: ( pname > $o ) > ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(func_def_127,type,
sK8: ( pname > $o ) > ( x_a > $o ) > ( x_a > pname ) > x_a > $o ).
thf(func_def_128,type,
sK9: ( nat > $o ) > nat > nat ).
thf(func_def_129,type,
sK10: ( x_a > $o ) > ( nat > $o ) > ( nat > x_a ) > nat > $o ).
thf(func_def_130,type,
sK11: ( nat > nat ) > nat ).
thf(func_def_131,type,
sK12: ( nat > nat ) > nat ).
thf(func_def_132,type,
sK13: ( pname > pname ) > ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_133,type,
sK14: pname > ( nat > pname ) > ( nat > $o ) > nat ).
thf(func_def_134,type,
sK15: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_135,type,
sK16: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(func_def_136,type,
sK17: ( nat > nat ) > nat ).
thf(func_def_137,type,
sK18: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > x_a ).
thf(func_def_138,type,
sK19: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > x_a > $o ).
thf(func_def_139,type,
sK20: ( x_a > $o ) > ( ( nat > $o ) > $o ) > ( x_a > nat > $o ) > x_a > $o ).
thf(func_def_140,type,
sK21: ( ( nat > $o ) > $o ) > ( pname > nat > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_141,type,
sK22: ( pname > $o ) > ( ( nat > $o ) > $o ) > ( ( nat > $o ) > pname ) > ( nat > $o ) > $o ).
thf(func_def_142,type,
sK23: ( nat > $o ) > ( nat > pname > $o ) > nat ).
thf(func_def_143,type,
sK24: ( pname > x_a ) > ( x_a > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_144,type,
sK25: ( x_a > $o ) > ( x_a > nat > $o ) > x_a ).
thf(func_def_145,type,
sK26: ( nat > pname ) > ( pname > $o ) > ( nat > $o ) > nat ).
thf(func_def_146,type,
sK27: ( x_a > $o ) > ( x_a > $o ) > x_a ).
thf(func_def_147,type,
sK28: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_148,type,
sK29: ( nat > $o ) > nat ).
thf(func_def_149,type,
sK30: nat > ( nat > $o ) > nat ).
thf(func_def_150,type,
sK31: ( pname > $o ) > pname ).
thf(func_def_151,type,
sK32: ( nat > $o ) > ( nat > x_a ) > ( x_a > $o ) > nat > $o ).
thf(func_def_152,type,
sK33: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > nat ) > nat > $o ).
thf(func_def_153,type,
sK34: ( x_a > $o ) > x_a ).
thf(func_def_154,type,
sK35: ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_155,type,
sK36: ( nat > nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_156,type,
sK37: ( pname > nat ) > ( pname > $o ) > nat > pname ).
thf(func_def_157,type,
sK38: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_158,type,
sK39: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_159,type,
sK40: ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_160,type,
sK41: ( nat > $o ) > ( nat > nat ) > ( nat > $o ) > nat > $o ).
thf(func_def_161,type,
sK42: ( pname > nat ) > ( nat > $o ) > ( pname > $o ) > pname ).
thf(func_def_162,type,
sK43: ( x_a > $o ) > ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(func_def_163,type,
sK44: ( ( pname > $o ) > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_164,type,
sK45: ( ( pname > $o ) > $o ) > ( pname > $o ) > pname ).
thf(func_def_165,type,
sK46: ( ( x_a > $o ) > $o ) > ( pname > $o ) > ( ( x_a > $o ) > pname ) > ( x_a > $o ) > $o ).
thf(func_def_166,type,
sK47: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > pname ) > x_a > $o ).
thf(func_def_167,type,
sK48: ( pname > $o ) > ( x_a > pname ) > ( x_a > $o ) > x_a ).
thf(func_def_168,type,
sK49: ( pname > $o ) > ( pname > pname > $o ) > pname ).
thf(func_def_169,type,
sK50: ( nat > $o ) > nat ).
thf(func_def_170,type,
sK51: nat > ( nat > $o ) > nat ).
thf(func_def_171,type,
sK52: ( nat > x_a > $o ) > nat ).
thf(func_def_172,type,
sK53: ( x_a > $o ) > ( ( pname > $o ) > $o ) > ( x_a > pname > $o ) > x_a > $o ).
thf(func_def_173,type,
sK54: ( nat > $o ) > ( x_a > $o ) > ( nat > x_a ) > nat ).
thf(func_def_174,type,
sK55: ( nat > $o ) > nat ).
thf(func_def_175,type,
sK56: ( ( x_a > $o ) > $o ) > x_a > $o ).
thf(func_def_176,type,
sK57: ( nat > $o ) > x_a > ( nat > x_a ) > nat ).
thf(func_def_177,type,
sK58: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > nat ) > ( nat > $o ) > ( x_a > $o ) > $o ).
thf(func_def_178,type,
sK59: ( pname > x_a ) > ( x_a > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_179,type,
sK60: ( nat > $o ) > nat ).
thf(func_def_180,type,
sK61: ( ( pname > $o ) > x_a ) > ( x_a > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_181,type,
sK62: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_182,type,
sK63: ( nat > $o ) > ( nat > nat ) > nat ).
thf(func_def_183,type,
sK64: ( ( ( nat > $o ) > $o ) > $o ) > ( nat > $o ) > $o ).
thf(func_def_184,type,
sK65: ( ( ( nat > $o ) > $o ) > $o ) > nat > $o ).
thf(func_def_185,type,
sK66: ( pname > x_a > $o ) > ( pname > $o ) > pname ).
thf(func_def_186,type,
sK67: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > pname ) > nat > $o ).
thf(func_def_187,type,
sK68: ( ( x_a > $o ) > $o ) > x_a > $o ).
thf(func_def_188,type,
sK69: ( pname > x_a ) > ( pname > $o ) > x_a > pname ).
thf(func_def_189,type,
sK70: ( nat > $o ) > nat > nat ).
thf(func_def_190,type,
sK71: ( nat > pname > $o ) > nat ).
thf(func_def_191,type,
sK72: ( pname > $o ) > ( pname > pname ) > pname ).
thf(func_def_192,type,
sK73: ( x_a > nat ) > ( x_a > $o ) > ( nat > $o ) > x_a > $o ).
thf(func_def_193,type,
sK74: ( x_a > $o ) > ( x_a > $o ) > ( x_a > x_a ) > x_a > $o ).
thf(func_def_194,type,
sK75: ( ( pname > $o ) > $o ) > ( nat > $o ) > ( nat > pname > $o ) > nat > $o ).
thf(func_def_195,type,
sK76: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_196,type,
sK77: nat > nat > nat ).
thf(func_def_197,type,
sK78: ( pname > $o ) > ( pname > x_a ) > pname ).
thf(func_def_198,type,
sK79: ( ( nat > $o ) > $o ) > ( nat > $o ) > nat ).
thf(func_def_199,type,
sK80: ( ( nat > $o ) > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_200,type,
sK81: ( pname > $o ) > pname ).
thf(func_def_201,type,
sK82: ( nat > $o ) > ( pname > $o ) > ( pname > nat ) > pname > $o ).
thf(func_def_202,type,
sK83: ( ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_203,type,
sK84: ( ( pname > $o ) > nat ) > ( nat > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_204,type,
sK85: ( x_a > $o ) > x_a ).
thf(func_def_205,type,
sK86: ( pname > x_a ) > ( pname > $o ) > x_a > pname ).
thf(func_def_206,type,
sK87: ( pname > $o ) > ( nat > $o ) > ( nat > pname ) > nat > $o ).
thf(func_def_207,type,
sK88: ( nat > $o ) > ( x_a > $o ) > ( x_a > nat ) > x_a ).
thf(func_def_208,type,
sK89: nat > nat > nat ).
thf(func_def_209,type,
sK90: ( x_a > $o ) > x_a ).
thf(func_def_210,type,
sK91: ( x_a > $o ) > ( x_a > pname ) > x_a ).
thf(func_def_211,type,
sK92: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_212,type,
sK93: ( x_a > $o ) > ( x_a > pname > $o ) > x_a ).
thf(func_def_213,type,
sK94: nat > nat > nat ).
thf(func_def_214,type,
sK95: ( nat > nat ) > nat ).
thf(func_def_215,type,
sK96: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > nat ) > x_a > $o ).
thf(func_def_216,type,
sK97: ( x_a > x_a ) > ( x_a > $o ) > x_a ).
thf(func_def_217,type,
sK98: ( x_a > $o ) > pname ).
thf(func_def_218,type,
sK99: ( nat > x_a ) > ( nat > $o ) > nat ).
thf(func_def_219,type,
sK100: ( nat > $o ) > ( nat > pname ) > nat ).
thf(func_def_220,type,
sK101: ( ( ( pname > $o ) > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_221,type,
sK102: ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_222,type,
sK103: ( x_a > $o ) > ( x_a > nat ) > x_a ).
thf(func_def_223,type,
sK104: nat > nat ).
thf(func_def_224,type,
sK105: ( nat > $o ) > nat ).
thf(func_def_225,type,
sK106: ( pname > x_a ) > ( x_a > $o ) > ( pname > $o ) > pname ).
thf(func_def_226,type,
sK107: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_227,type,
sK108: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_228,type,
sK109: ( pname > nat > $o ) > ( pname > $o ) > pname ).
thf(func_def_229,type,
sK110: nat > nat > nat ).
thf(func_def_230,type,
sK111: ( nat > nat > $o ) > nat ).
thf(func_def_231,type,
sK112: nat > ( x_a > nat ) > ( x_a > $o ) > x_a ).
thf(func_def_232,type,
sK113: ( ( x_a > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(func_def_233,type,
sK114: ( ( x_a > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > x_a > $o ).
thf(func_def_234,type,
sK115: ( x_a > $o ) > ( x_a > $o ) > x_a ).
thf(func_def_235,type,
sK116: nat > nat > nat ).
thf(func_def_236,type,
sK117: ( ( x_a > $o ) > $o ) > ( nat > $o ) > ( nat > x_a > $o ) > nat > $o ).
thf(func_def_237,type,
sK118: ( ( x_a > $o ) > $o ) > ( pname > x_a > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_238,type,
sK119: ( nat > $o ) > nat ).
thf(func_def_239,type,
sK120: ( x_a > pname ) > ( x_a > $o ) > ( pname > $o ) > x_a > $o ).
thf(func_def_240,type,
sK121: ( nat > nat ) > nat ).
thf(func_def_241,type,
sK122: ( nat > nat ) > nat ).
thf(func_def_242,type,
sK123: ( nat > $o ) > nat ).
thf(func_def_243,type,
sK124: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_244,type,
sK125: ( pname > pname > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_245,type,
sK126: ( pname > $o ) > pname ).
thf(func_def_246,type,
sK127: ( x_a > $o ) > ( x_a > x_a > $o ) > x_a ).
thf(func_def_247,type,
sK128: ( ( ( x_a > $o ) > $o ) > $o ) > x_a > $o ).
thf(func_def_248,type,
sK129: ( ( ( x_a > $o ) > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(func_def_249,type,
sK130: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_250,type,
sK131: ( nat > $o ) > ( nat > x_a > $o ) > nat ).
thf(func_def_251,type,
sK132: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > ( ( x_a > $o ) > x_a ) > ( x_a > $o ) > $o ).
thf(func_def_252,type,
sK133: ( x_a > $o ) > x_a ).
thf(func_def_253,type,
sK134: ( nat > $o ) > nat ).
thf(func_def_254,type,
sK135: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_256,type,
ph137:
!>[X0: $tType] : X0 ).
thf(f5186,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f5185,f3820]) ).
thf(f3820,plain,
( ( member_pname @ pn @ u )
= $true ),
inference(cnf_transformation,[status(thm)],[f805]) ).
thf(f805,plain,
( ( member_pname @ pn @ u )
= $true ),
inference(fool_elimination,[status(thm)],[f804]) ).
thf(f804,plain,
member_pname @ pn @ u,
inference(rectify,[status(thm)],[f717]) ).
thf(f717,axiom,
member_pname @ pn @ u,
file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',conj_4) ).
thf(f5185,plain,
( ( member_pname @ pn @ u )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f5180]) ).
thf(f5180,plain,
( ( ( member_pname @ pn @ u )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f5042,f4725]) ).
thf(f4725,plain,
! [X2: pname > $o,X3: pname,X0: pname > x_a] :
( ( ( member_a @ ( X0 @ X3 ) @ ( image_pname_a @ X0 @ X2 ) )
= $true )
| ( ( member_pname @ X3 @ X2 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f4140]) ).
thf(f4140,plain,
! [X2: pname > $o,X3: pname,X0: pname > x_a,X1: x_a] :
( ( ( member_pname @ X3 @ X2 )
!= $true )
| ( ( X0 @ X3 )
!= X1 )
| ( ( member_a @ X1 @ ( image_pname_a @ X0 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f2476]) ).
thf(f2476,plain,
! [X0: pname > x_a,X1: x_a,X2: pname > $o,X3: pname] :
( ( ( member_pname @ X3 @ X2 )
!= $true )
| ( ( X0 @ X3 )
!= X1 )
| ( ( member_a @ X1 @ ( image_pname_a @ X0 @ X2 ) )
= $true ) ),
inference(flattening,[status(thm)],[f2475]) ).
thf(f2475,plain,
! [X0: pname > x_a,X1: x_a,X2: pname > $o,X3: pname] :
( ( ( member_a @ X1 @ ( image_pname_a @ X0 @ X2 ) )
= $true )
| ( ( X0 @ X3 )
!= X1 )
| ( ( member_pname @ X3 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f1411]) ).
thf(f1411,plain,
! [X0: pname > x_a,X1: x_a,X2: pname > $o,X3: pname] :
( ( ( member_pname @ X3 @ X2 )
= $true )
=> ( ( ( X0 @ X3 )
= X1 )
=> ( ( member_a @ X1 @ ( image_pname_a @ X0 @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f1410]) ).
thf(f1410,plain,
! [X0: pname > x_a,X1: x_a,X2: pname > $o,X3: pname] :
( ( member_pname @ X3 @ X2 )
=> ( ( ( X0 @ X3 )
= X1 )
=> ( member_a @ X1 @ ( image_pname_a @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f313]) ).
thf(f313,axiom,
! [X131: pname > x_a,X130: x_a,X133: pname > $o,X132: pname] :
( ( member_pname @ X132 @ X133 )
=> ( ( ( X131 @ X132 )
= X130 )
=> ( member_a @ X130 @ ( image_pname_a @ X131 @ X133 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',fact_312_rev__image__eqI) ).
thf(f5042,plain,
( ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f5039,f3868]) ).
thf(f3868,plain,
( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1035]) ).
thf(f1035,plain,
( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
= $true ),
inference(fool_elimination,[status(thm)],[f1034]) ).
thf(f1034,plain,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
inference(rectify,[status(thm)],[f714]) ).
thf(f714,axiom,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',conj_1) ).
thf(f5039,plain,
( ( ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true )
| ( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5034]) ).
thf(f5034,plain,
( ( ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true )
| ( $true != $true )
| ( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
!= $true ) ),
inference(superposition,[status(thm)],[f3599,f3517]) ).
thf(f3517,plain,
! [X2: x_a > $o,X0: x_a,X1: x_a > $o] :
( ( ( ord_less_eq_a_o @ ( insert_a @ X0 @ X2 ) @ X1 )
= $true )
| ( $true
!= ( ord_less_eq_a_o @ X2 @ X1 ) )
| ( $true
!= ( member_a @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f3016]) ).
thf(f3016,plain,
! [X0: x_a,X1: x_a > $o,X2: x_a > $o] :
( ( ( ( ord_less_eq_a_o @ ( insert_a @ X0 @ X2 ) @ X1 )
= $true )
| ( $true
!= ( ord_less_eq_a_o @ X2 @ X1 ) )
| ( $true
!= ( member_a @ X0 @ X1 ) ) )
& ( ( ( $true
= ( ord_less_eq_a_o @ X2 @ X1 ) )
& ( $true
= ( member_a @ X0 @ X1 ) ) )
| ( ( ord_less_eq_a_o @ ( insert_a @ X0 @ X2 ) @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f3015]) ).
thf(f3015,plain,
! [X0: x_a,X1: x_a > $o,X2: x_a > $o] :
( ( ( ( ord_less_eq_a_o @ ( insert_a @ X0 @ X2 ) @ X1 )
= $true )
| ( $true
!= ( ord_less_eq_a_o @ X2 @ X1 ) )
| ( $true
!= ( member_a @ X0 @ X1 ) ) )
& ( ( ( $true
= ( ord_less_eq_a_o @ X2 @ X1 ) )
& ( $true
= ( member_a @ X0 @ X1 ) ) )
| ( ( ord_less_eq_a_o @ ( insert_a @ X0 @ X2 ) @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1157]) ).
thf(f1157,plain,
! [X0: x_a,X1: x_a > $o,X2: x_a > $o] :
( ( ( ord_less_eq_a_o @ ( insert_a @ X0 @ X2 ) @ X1 )
= $true )
<=> ( ( $true
= ( ord_less_eq_a_o @ X2 @ X1 ) )
& ( $true
= ( member_a @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f1156]) ).
thf(f1156,plain,
! [X0: x_a,X1: x_a > $o,X2: x_a > $o] :
( ( ( ord_less_eq_a_o @ X2 @ X1 )
& ( member_a @ X0 @ X1 ) )
<=> ( ord_less_eq_a_o @ ( insert_a @ X0 @ X2 ) @ X1 ) ),
inference(rectify,[status(thm)],[f325]) ).
thf(f325,axiom,
! [X138: x_a,X140: x_a > $o,X139: x_a > $o] :
( ( ( ord_less_eq_a_o @ X139 @ X140 )
& ( member_a @ X138 @ X140 ) )
<=> ( ord_less_eq_a_o @ ( insert_a @ X138 @ X139 ) @ X140 ) ),
file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',fact_324_insert__subset) ).
thf(f3599,plain,
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f2261]) ).
thf(f2261,plain,
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(flattening,[status(thm)],[f1677]) ).
thf(f1677,plain,
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f1676]) ).
thf(f1676,plain,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(rectify,[status(thm)],[f720]) ).
thf(f720,negated_conjecture,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(negated_conjecture,[status(cth)],[f719]) ).
thf(f719,conjecture,
ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',conj_6) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473^2 : TPTP v9.2.1. Released v5.3.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 13:40:36 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SWW473^2 : TPTP v9.2.1. Released v5.3.0.
% 0.29/0.45 % Domain : Software Verification
% 0.29/0.45 % Problem : Hoare's Logic with Procedures line 383, 500 axioms selected
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.29/0.45 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bla11]
% 0.29/0.45 % Names : hoare_500_thf_l383 [Bla11]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.57 v7.4.0, 0.56 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.57 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v5.3.0
% 0.29/0.45 % Syntax : Number of formulae : 826 ( 137 unt; 107 typ; 0 def)
% 0.29/0.45 % Number of atoms : 2653 ( 494 equ; 85 cnn)
% 0.29/0.45 % Maximal formula atoms : 9 ( 3 avg)
% 0.29/0.45 % Number of connectives : 5606 ( 202 ~; 57 |; 185 &;4242 @)
% 0.29/0.45 % ( 137 <=>; 783 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 17 ( 7 avg)
% 0.29/0.45 % Number of types : 6 ( 5 usr)
% 0.29/0.45 % Number of type conns : 1635 (1635 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 108 ( 102 usr; 11 con; 0-3 aty)
% 0.29/0.45 % Number of variables : 1787 ( 105 ^;1617 !; 65 ?;1787 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.45 % 2011-08-09 19:38:20
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 %----Should-be-implicit typings (5)
% 0.29/0.45 thf(ty_ty_t__a,type,
% 0.29/0.45 x_a: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_ty_tc__Com__Ocom,type,
% 0.29/0.45 com: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_ty_tc__Com__Opname,type,
% 0.29/0.45 pname: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_ty_tc__Nat__Onat,type,
% 0.29/0.45 nat: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.29/0.45 option_com: $tType ).
% 0.29/0.45
% 0.29/0.45 %----Explicit typings (102)
% 0.29/0.45 thf(sy_c_Com_Obody,type,
% 0.29/0.45 body: pname > option_com ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Finite__Set_Ocard_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ocard_000t__a,type,
% 0.29/0.46 finite_card_a: ( x_a > $o ) > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ocard_000tc__Com__Opname,type,
% 0.29/0.46 finite_card_pname: ( pname > $o ) > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
% 0.29/0.46 finite_card_nat: ( nat > $o ) > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000t__a,type,
% 0.29/0.46 finite_finite_a: ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.29/0.46 finite_finite_pname: ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
% 0.29/0.46 finite_finite_nat: ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.29/0.46 minus_minus_nat: nat > nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.29/0.46 one_one_nat: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.29/0.46 plus_plus_nat: nat > nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.29/0.46 zero_zero_nat: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Nat_OSuc,type,
% 0.29/0.46 suc: nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Nat_Onat_Onat__case_000_Eo,type,
% 0.29/0.46 nat_case_o: $o > ( nat > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 0.29/0.46 the_com: option_com > com ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 bot_bot_a_o_o: ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 bot_bot_nat_o_o: ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 bot_bot_a_o: x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 bot_bot_pname_o: pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 bot_bot_nat_o: nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.29/0.46 bot_bot_o: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_000tc__Nat__Onat,type,
% 0.29/0.46 bot_bot_nat: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.29/0.46 ord_less_nat: nat > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 0.29/0.46 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,
% 0.29/0.46 ord_less_eq_o: $o > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 0.29/0.46 ord_less_eq_nat: nat > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000t__a,type,
% 0.29/0.46 collect_a: ( x_a > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.29/0.46 collect_pname: ( pname > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000tc__Nat__Onat,type,
% 0.29/0.46 collect_nat: ( nat > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000t__a,type,
% 0.29/0.46 image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Com__Opname,type,
% 0.29/0.46 image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Nat__Onat,type,
% 0.29/0.46 image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000t__a,type,
% 0.29/0.46 image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 0.29/0.46 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat,type,
% 0.29/0.46 image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000t__a,type,
% 0.29/0.46 image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Com__Opname,type,
% 0.29/0.46 image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat,type,
% 0.29/0.46 image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000t__a_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 image_a_a_o: ( x_a > x_a > $o ) > ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000t__a_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 image_a_pname_o: ( x_a > pname > $o ) > ( x_a > $o ) > ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000t__a_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 image_a_nat_o: ( x_a > nat > $o ) > ( x_a > $o ) > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000t__a_000t__a,type,
% 0.29/0.46 image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000t__a_000tc__Com__Opname,type,
% 0.29/0.46 image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000t__a_000tc__Nat__Onat,type,
% 0.29/0.46 image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000t__a,type,
% 0.29/0.46 image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.29/0.46 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat,type,
% 0.29/0.46 image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000t__a,type,
% 0.29/0.46 image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,type,
% 0.29/0.46 image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Nat__Onat,type,
% 0.29/0.46 image_nat_nat: ( nat > nat ) > ( nat > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_000t__a,type,
% 0.29/0.46 insert_a: x_a > ( x_a > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.29/0.46 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_000tc__Nat__Onat,type,
% 0.29/0.46 insert_nat: nat > ( nat > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_fequal_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 fequal_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_fequal_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 fequal_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_fequal_000t__a,type,
% 0.29/0.46 fequal_a: x_a > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_fequal_000tc__Com__Opname,type,
% 0.29/0.46 fequal_pname: pname > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_fequal_000tc__Nat__Onat,type,
% 0.29/0.46 fequal_nat: nat > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_000_062_It__a_M_Eo_J,type,
% 0.29/0.46 member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.29/0.46 member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_000t__a,type,
% 0.29/0.46 member_a: x_a > ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_000tc__Com__Opname,type,
% 0.29/0.46 member_pname: pname > ( pname > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_000tc__Nat__Onat,type,
% 0.29/0.46 member_nat: nat > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_G,type,
% 0.29/0.46 g: x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_P,type,
% 0.29/0.46 p: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_U,type,
% 0.29/0.46 u: pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_mgt,type,
% 0.29/0.46 mgt: com > x_a ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_mgt__call,type,
% 0.29/0.46 mgt_call: pname > x_a ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_na,type,
% 0.29/0.46 na: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_pn,type,
% 0.29/0.46 pn: pname ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_wt,type,
% 0.29/0.46 wt: com > $o ).
% 0.29/0.46
% 0.29/0.46 %----Relevant facts (700)
% 0.29/0.46 thf(fact_0_assms_I1_J,axiom,
% 0.29/0.46 ! [Ts: x_a > $o,G: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ Ts @ G )
% 0.29/0.46 => ( p @ G @ Ts ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_1_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_92: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_92 )
% 0.29/0.46 => ( finite1676163439at_o_o
% 0.29/0.46 @ ( collect_nat_o_o
% 0.29/0.46 @ ^ [B_47: ( nat > $o ) > $o] : ( ord_less_eq_nat_o_o @ B_47 @ A_92 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_2_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_92: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_92 )
% 0.29/0.46 => ( finite1066544169me_o_o
% 0.29/0.46 @ ( collect_pname_o_o
% 0.29/0.46 @ ^ [B_47: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_47 @ A_92 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_3_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_92: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_92 )
% 0.29/0.46 => ( finite_finite_a_o_o
% 0.29/0.46 @ ( collect_a_o_o
% 0.29/0.46 @ ^ [B_47: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B_47 @ A_92 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_4_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_92: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_92 )
% 0.29/0.46 => ( finite_finite_a_o
% 0.29/0.46 @ ( collect_a_o
% 0.29/0.46 @ ^ [B_47: x_a > $o] : ( ord_less_eq_a_o @ B_47 @ A_92 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_5_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_92: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_92 )
% 0.29/0.46 => ( finite297249702name_o
% 0.29/0.46 @ ( collect_pname_o
% 0.29/0.46 @ ^ [B_47: pname > $o] : ( ord_less_eq_pname_o @ B_47 @ A_92 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_6_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_92: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_92 )
% 0.29/0.46 => ( finite_finite_nat_o
% 0.29/0.46 @ ( collect_nat_o
% 0.29/0.46 @ ^ [B_47: nat > $o] : ( ord_less_eq_nat_o @ B_47 @ A_92 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_7_finite__imageI,axiom,
% 0.29/0.46 ! [H: pname > nat > $o,F_25: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ F_25 )
% 0.29/0.46 => ( finite_finite_nat_o @ ( image_pname_nat_o @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_8_finite__imageI,axiom,
% 0.29/0.46 ! [H: pname > pname > $o,F_25: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ F_25 )
% 0.29/0.46 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_9_finite__imageI,axiom,
% 0.29/0.46 ! [H: pname > x_a > $o,F_25: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ F_25 )
% 0.29/0.46 => ( finite_finite_a_o @ ( image_pname_a_o @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_10_finite__imageI,axiom,
% 0.29/0.46 ! [H: nat > x_a,F_25: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ F_25 )
% 0.29/0.46 => ( finite_finite_a @ ( image_nat_a @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_11_finite__imageI,axiom,
% 0.29/0.46 ! [H: nat > nat > $o,F_25: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ F_25 )
% 0.29/0.46 => ( finite_finite_nat_o @ ( image_nat_nat_o @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_12_finite__imageI,axiom,
% 0.29/0.46 ! [H: nat > pname > $o,F_25: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ F_25 )
% 0.29/0.46 => ( finite297249702name_o @ ( image_nat_pname_o @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_13_finite__imageI,axiom,
% 0.29/0.46 ! [H: nat > x_a > $o,F_25: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ F_25 )
% 0.29/0.46 => ( finite_finite_a_o @ ( image_nat_a_o @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_14_finite__imageI,axiom,
% 0.29/0.46 ! [H: x_a > pname,F_25: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ F_25 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_a_pname @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_15_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( nat > $o ) > pname,F_25: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ F_25 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_nat_o_pname @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_16_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( pname > $o ) > pname,F_25: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ F_25 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_17_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( x_a > $o ) > pname,F_25: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ F_25 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_a_o_pname @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_18_finite__imageI,axiom,
% 0.29/0.46 ! [H: x_a > nat,F_25: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ F_25 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_a_nat @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_19_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( nat > $o ) > nat,F_25: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ F_25 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_nat_o_nat @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_20_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( pname > $o ) > nat,F_25: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ F_25 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_pname_o_nat @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_21_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( x_a > $o ) > nat,F_25: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ F_25 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_a_o_nat @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_22_finite__imageI,axiom,
% 0.29/0.46 ! [H: pname > x_a,F_25: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ F_25 )
% 0.29/0.46 => ( finite_finite_a @ ( image_pname_a @ H @ F_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_23_finite_OinsertI,axiom,
% 0.29/0.46 ! [A_91: nat > $o,A_90: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_90 )
% 0.29/0.46 => ( finite_finite_nat_o @ ( insert_nat_o @ A_91 @ A_90 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_24_finite_OinsertI,axiom,
% 0.29/0.46 ! [A_91: pname > $o,A_90: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_90 )
% 0.29/0.46 => ( finite297249702name_o @ ( insert_pname_o @ A_91 @ A_90 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_25_finite_OinsertI,axiom,
% 0.29/0.46 ! [A_91: x_a > $o,A_90: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_90 )
% 0.29/0.46 => ( finite_finite_a_o @ ( insert_a_o @ A_91 @ A_90 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_26_finite_OinsertI,axiom,
% 0.29/0.46 ! [A_91: pname,A_90: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_90 )
% 0.29/0.46 => ( finite_finite_pname @ ( insert_pname @ A_91 @ A_90 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_27_finite_OinsertI,axiom,
% 0.29/0.46 ! [A_91: nat,A_90: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_90 )
% 0.29/0.46 => ( finite_finite_nat @ ( insert_nat @ A_91 @ A_90 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_28_finite_OinsertI,axiom,
% 0.29/0.46 ! [A_91: x_a,A_90: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_90 )
% 0.29/0.46 => ( finite_finite_a @ ( insert_a @ A_91 @ A_90 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_29_card__image__le,axiom,
% 0.29/0.46 ! [F_24: pname > pname,A_89: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ F_24 @ A_89 ) ) @ ( finite_card_pname @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_30_card__image__le,axiom,
% 0.29/0.46 ! [F_24: x_a > x_a,A_89: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ F_24 @ A_89 ) ) @ ( finite_card_a @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_31_card__image__le,axiom,
% 0.29/0.46 ! [F_24: ( nat > $o ) > x_a,A_89: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_a @ F_24 @ A_89 ) ) @ ( finite_card_nat_o @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_32_card__image__le,axiom,
% 0.29/0.46 ! [F_24: ( pname > $o ) > x_a,A_89: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_a @ F_24 @ A_89 ) ) @ ( finite_card_pname_o @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_33_card__image__le,axiom,
% 0.29/0.46 ! [F_24: ( x_a > $o ) > x_a,A_89: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ F_24 @ A_89 ) ) @ ( finite_card_a_o @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_34_card__image__le,axiom,
% 0.29/0.46 ! [F_24: pname > nat,A_89: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ F_24 @ A_89 ) ) @ ( finite_card_pname @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_35_card__image__le,axiom,
% 0.29/0.46 ! [F_24: x_a > nat,A_89: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ F_24 @ A_89 ) ) @ ( finite_card_a @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_36_card__image__le,axiom,
% 0.29/0.46 ! [F_24: ( nat > $o ) > nat,A_89: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_o_nat @ F_24 @ A_89 ) ) @ ( finite_card_nat_o @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_37_card__image__le,axiom,
% 0.29/0.46 ! [F_24: ( pname > $o ) > nat,A_89: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_o_nat @ F_24 @ A_89 ) ) @ ( finite_card_pname_o @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_38_card__image__le,axiom,
% 0.29/0.46 ! [F_24: ( x_a > $o ) > nat,A_89: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ F_24 @ A_89 ) ) @ ( finite_card_a_o @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_39_card__image__le,axiom,
% 0.29/0.46 ! [F_24: x_a > pname,A_89: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ F_24 @ A_89 ) ) @ ( finite_card_a @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_40_card__image__le,axiom,
% 0.29/0.46 ! [F_24: nat > pname,A_89: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_pname @ F_24 @ A_89 ) ) @ ( finite_card_nat @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_41_card__image__le,axiom,
% 0.29/0.46 ! [F_24: pname > x_a,A_89: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_89 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ F_24 @ A_89 ) ) @ ( finite_card_pname @ A_89 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_42_card__mono,axiom,
% 0.29/0.46 ! [A_88: ( nat > $o ) > $o,B_46: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ B_46 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o_o @ A_88 @ B_46 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_88 ) @ ( finite_card_nat_o @ B_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_43_card__mono,axiom,
% 0.29/0.46 ! [A_88: ( pname > $o ) > $o,B_46: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ B_46 )
% 0.29/0.46 => ( ( ord_le1205211808me_o_o @ A_88 @ B_46 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_88 ) @ ( finite_card_pname_o @ B_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_44_card__mono,axiom,
% 0.29/0.46 ! [A_88: ( x_a > $o ) > $o,B_46: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ B_46 )
% 0.29/0.46 => ( ( ord_less_eq_a_o_o @ A_88 @ B_46 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_88 ) @ ( finite_card_a_o @ B_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_45_card__mono,axiom,
% 0.29/0.46 ! [A_88: pname > $o,B_46: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ B_46 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ A_88 @ B_46 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_pname @ A_88 ) @ ( finite_card_pname @ B_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_46_card__mono,axiom,
% 0.29/0.46 ! [A_88: x_a > $o,B_46: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ B_46 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ A_88 @ B_46 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_a @ A_88 ) @ ( finite_card_a @ B_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_47_card__mono,axiom,
% 0.29/0.46 ! [A_88: nat > $o,B_46: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ B_46 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ A_88 @ B_46 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_nat @ A_88 ) @ ( finite_card_nat @ B_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_48_card__seteq,axiom,
% 0.29/0.46 ! [A_87: ( nat > $o ) > $o,B_45: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o_o @ A_87 @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_nat @ ( finite_card_nat_o @ B_45 ) @ ( finite_card_nat_o @ A_87 ) )
% 0.29/0.46 => ( A_87 = B_45 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_49_card__seteq,axiom,
% 0.29/0.46 ! [A_87: ( pname > $o ) > $o,B_45: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ B_45 )
% 0.29/0.46 => ( ( ord_le1205211808me_o_o @ A_87 @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_nat @ ( finite_card_pname_o @ B_45 ) @ ( finite_card_pname_o @ A_87 ) )
% 0.29/0.46 => ( A_87 = B_45 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_50_card__seteq,axiom,
% 0.29/0.46 ! [A_87: ( x_a > $o ) > $o,B_45: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_a_o_o @ A_87 @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_nat @ ( finite_card_a_o @ B_45 ) @ ( finite_card_a_o @ A_87 ) )
% 0.29/0.46 => ( A_87 = B_45 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_51_card__seteq,axiom,
% 0.29/0.46 ! [A_87: pname > $o,B_45: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ A_87 @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_nat @ ( finite_card_pname @ B_45 ) @ ( finite_card_pname @ A_87 ) )
% 0.29/0.46 => ( A_87 = B_45 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_52_card__seteq,axiom,
% 0.29/0.46 ! [A_87: x_a > $o,B_45: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ A_87 @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_nat @ ( finite_card_a @ B_45 ) @ ( finite_card_a @ A_87 ) )
% 0.29/0.46 => ( A_87 = B_45 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_53_card__seteq,axiom,
% 0.29/0.46 ! [A_87: nat > $o,B_45: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ A_87 @ B_45 )
% 0.29/0.46 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B_45 ) @ ( finite_card_nat @ A_87 ) )
% 0.29/0.46 => ( A_87 = B_45 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_54_card__insert__le,axiom,
% 0.29/0.46 ! [X_33: nat > $o,A_86: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_86 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_86 ) @ ( finite_card_nat_o @ ( insert_nat_o @ X_33 @ A_86 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_55_card__insert__le,axiom,
% 0.29/0.46 ! [X_33: pname > $o,A_86: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_86 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_86 ) @ ( finite_card_pname_o @ ( insert_pname_o @ X_33 @ A_86 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_56_card__insert__le,axiom,
% 0.29/0.46 ! [X_33: x_a > $o,A_86: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_86 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_86 ) @ ( finite_card_a_o @ ( insert_a_o @ X_33 @ A_86 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_57_card__insert__le,axiom,
% 0.29/0.46 ! [X_33: pname,A_86: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_86 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_pname @ A_86 ) @ ( finite_card_pname @ ( insert_pname @ X_33 @ A_86 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_58_card__insert__le,axiom,
% 0.29/0.46 ! [X_33: nat,A_86: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_86 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_nat @ A_86 ) @ ( finite_card_nat @ ( insert_nat @ X_33 @ A_86 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_59_card__insert__le,axiom,
% 0.29/0.46 ! [X_33: x_a,A_86: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_86 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( finite_card_a @ A_86 ) @ ( finite_card_a @ ( insert_a @ X_33 @ A_86 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_60_card__insert__if,axiom,
% 0.29/0.46 ! [X_32: nat > $o,A_85: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_85 )
% 0.29/0.46 => ( ( ( member_nat_o @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_32 @ A_85 ) )
% 0.29/0.46 = ( finite_card_nat_o @ A_85 ) ) )
% 0.29/0.46 & ( ~ ( member_nat_o @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_32 @ A_85 ) )
% 0.29/0.46 = ( suc @ ( finite_card_nat_o @ A_85 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_61_card__insert__if,axiom,
% 0.29/0.46 ! [X_32: pname > $o,A_85: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_85 )
% 0.29/0.46 => ( ( ( member_pname_o @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_32 @ A_85 ) )
% 0.29/0.46 = ( finite_card_pname_o @ A_85 ) ) )
% 0.29/0.46 & ( ~ ( member_pname_o @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_32 @ A_85 ) )
% 0.29/0.46 = ( suc @ ( finite_card_pname_o @ A_85 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_62_card__insert__if,axiom,
% 0.29/0.46 ! [X_32: x_a > $o,A_85: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_85 )
% 0.29/0.46 => ( ( ( member_a_o @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_a_o @ ( insert_a_o @ X_32 @ A_85 ) )
% 0.29/0.46 = ( finite_card_a_o @ A_85 ) ) )
% 0.29/0.46 & ( ~ ( member_a_o @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_a_o @ ( insert_a_o @ X_32 @ A_85 ) )
% 0.29/0.46 = ( suc @ ( finite_card_a_o @ A_85 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_63_card__insert__if,axiom,
% 0.29/0.46 ! [X_32: nat,A_85: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_85 )
% 0.29/0.46 => ( ( ( member_nat @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_nat @ ( insert_nat @ X_32 @ A_85 ) )
% 0.29/0.46 = ( finite_card_nat @ A_85 ) ) )
% 0.29/0.46 & ( ~ ( member_nat @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_nat @ ( insert_nat @ X_32 @ A_85 ) )
% 0.29/0.46 = ( suc @ ( finite_card_nat @ A_85 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_64_card__insert__if,axiom,
% 0.29/0.46 ! [X_32: pname,A_85: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_85 )
% 0.29/0.46 => ( ( ( member_pname @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_pname @ ( insert_pname @ X_32 @ A_85 ) )
% 0.29/0.46 = ( finite_card_pname @ A_85 ) ) )
% 0.29/0.46 & ( ~ ( member_pname @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_pname @ ( insert_pname @ X_32 @ A_85 ) )
% 0.29/0.46 = ( suc @ ( finite_card_pname @ A_85 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_65_card__insert__if,axiom,
% 0.29/0.46 ! [X_32: x_a,A_85: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_85 )
% 0.29/0.46 => ( ( ( member_a @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_a @ ( insert_a @ X_32 @ A_85 ) )
% 0.29/0.46 = ( finite_card_a @ A_85 ) ) )
% 0.29/0.46 & ( ~ ( member_a @ X_32 @ A_85 )
% 0.29/0.46 => ( ( finite_card_a @ ( insert_a @ X_32 @ A_85 ) )
% 0.29/0.46 = ( suc @ ( finite_card_a @ A_85 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_66_card__insert__disjoint,axiom,
% 0.29/0.46 ! [X_31: nat > $o,A_84: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_84 )
% 0.29/0.46 => ( ~ ( member_nat_o @ X_31 @ A_84 )
% 0.29/0.46 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_31 @ A_84 ) )
% 0.29/0.46 = ( suc @ ( finite_card_nat_o @ A_84 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_67_card__insert__disjoint,axiom,
% 0.29/0.46 ! [X_31: pname > $o,A_84: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_84 )
% 0.29/0.46 => ( ~ ( member_pname_o @ X_31 @ A_84 )
% 0.29/0.46 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_31 @ A_84 ) )
% 0.29/0.46 = ( suc @ ( finite_card_pname_o @ A_84 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_68_card__insert__disjoint,axiom,
% 0.29/0.46 ! [X_31: x_a > $o,A_84: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_84 )
% 0.29/0.46 => ( ~ ( member_a_o @ X_31 @ A_84 )
% 0.29/0.46 => ( ( finite_card_a_o @ ( insert_a_o @ X_31 @ A_84 ) )
% 0.29/0.46 = ( suc @ ( finite_card_a_o @ A_84 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_69_card__insert__disjoint,axiom,
% 0.29/0.46 ! [X_31: nat,A_84: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_84 )
% 0.29/0.46 => ( ~ ( member_nat @ X_31 @ A_84 )
% 0.29/0.46 => ( ( finite_card_nat @ ( insert_nat @ X_31 @ A_84 ) )
% 0.29/0.46 = ( suc @ ( finite_card_nat @ A_84 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_70_card__insert__disjoint,axiom,
% 0.29/0.46 ! [X_31: pname,A_84: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_84 )
% 0.29/0.46 => ( ~ ( member_pname @ X_31 @ A_84 )
% 0.29/0.46 => ( ( finite_card_pname @ ( insert_pname @ X_31 @ A_84 ) )
% 0.29/0.46 = ( suc @ ( finite_card_pname @ A_84 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_71_card__insert__disjoint,axiom,
% 0.29/0.46 ! [X_31: x_a,A_84: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_84 )
% 0.29/0.46 => ( ~ ( member_a @ X_31 @ A_84 )
% 0.29/0.46 => ( ( finite_card_a @ ( insert_a @ X_31 @ A_84 ) )
% 0.29/0.46 = ( suc @ ( finite_card_a @ A_84 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_72_finite__Collect__conjI,axiom,
% 0.29/0.46 ! [Q_1: x_a > $o,P_10: x_a > $o] :
% 0.29/0.46 ( ( ( finite_finite_a @ ( collect_a @ P_10 ) )
% 0.29/0.46 | ( finite_finite_a @ ( collect_a @ Q_1 ) ) )
% 0.29/0.46 => ( finite_finite_a
% 0.29/0.46 @ ( collect_a
% 0.29/0.46 @ ^ [X_1: x_a] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_73_finite__Collect__conjI,axiom,
% 0.29/0.46 ! [Q_1: ( nat > $o ) > $o,P_10: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( ( finite_finite_nat_o @ ( collect_nat_o @ P_10 ) )
% 0.29/0.46 | ( finite_finite_nat_o @ ( collect_nat_o @ Q_1 ) ) )
% 0.29/0.46 => ( finite_finite_nat_o
% 0.29/0.46 @ ( collect_nat_o
% 0.29/0.46 @ ^ [X_1: nat > $o] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_74_finite__Collect__conjI,axiom,
% 0.29/0.46 ! [Q_1: ( pname > $o ) > $o,P_10: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_10 ) )
% 0.29/0.46 | ( finite297249702name_o @ ( collect_pname_o @ Q_1 ) ) )
% 0.29/0.46 => ( finite297249702name_o
% 0.29/0.46 @ ( collect_pname_o
% 0.29/0.46 @ ^ [X_1: pname > $o] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_75_finite__Collect__conjI,axiom,
% 0.29/0.46 ! [Q_1: ( x_a > $o ) > $o,P_10: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( ( finite_finite_a_o @ ( collect_a_o @ P_10 ) )
% 0.29/0.46 | ( finite_finite_a_o @ ( collect_a_o @ Q_1 ) ) )
% 0.29/0.46 => ( finite_finite_a_o
% 0.29/0.46 @ ( collect_a_o
% 0.29/0.46 @ ^ [X_1: x_a > $o] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_76_finite__Collect__conjI,axiom,
% 0.29/0.46 ! [Q_1: pname > $o,P_10: pname > $o] :
% 0.29/0.46 ( ( ( finite_finite_pname @ ( collect_pname @ P_10 ) )
% 0.29/0.46 | ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
% 0.29/0.46 => ( finite_finite_pname
% 0.29/0.46 @ ( collect_pname
% 0.29/0.46 @ ^ [X_1: pname] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_77_finite__Collect__conjI,axiom,
% 0.29/0.46 ! [Q_1: nat > $o,P_10: nat > $o] :
% 0.29/0.46 ( ( ( finite_finite_nat @ ( collect_nat @ P_10 ) )
% 0.29/0.46 | ( finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
% 0.29/0.46 => ( finite_finite_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [X_1: nat] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_78_Suc__diff__le,axiom,
% 0.29/0.46 ! [N: nat,M: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.46 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.29/0.46 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_79_finite__Collect__le__nat,axiom,
% 0.29/0.46 ! [K: nat] :
% 0.29/0.46 ( finite_finite_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [N_2: nat] : ( ord_less_eq_nat @ N_2 @ K ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_80_card__Collect__le__nat,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( finite_card_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [I_1: nat] : ( ord_less_eq_nat @ I_1 @ N ) ) )
% 0.29/0.46 = ( suc @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_81_Suc__inject,axiom,
% 0.29/0.46 ! [X: nat,Y: nat] :
% 0.29/0.46 ( ( ( suc @ X )
% 0.29/0.46 = ( suc @ Y ) )
% 0.29/0.46 => ( X = Y ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_82_nat_Oinject,axiom,
% 0.29/0.46 ! [Nat_2: nat,Nat: nat] :
% 0.29/0.46 ( ( ( suc @ Nat_2 )
% 0.29/0.46 = ( suc @ Nat ) )
% 0.29/0.46 <=> ( Nat_2 = Nat ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_83_Suc__n__not__n,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( suc @ N )
% 0.29/0.46 != N ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_84_n__not__Suc__n,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( N
% 0.29/0.46 != ( suc @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_85_le__antisym,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.46 => ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.46 => ( M = N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_86_le__trans,axiom,
% 0.29/0.46 ! [K: nat,I: nat,J_1: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.29/0.46 => ( ( ord_less_eq_nat @ J_1 @ K )
% 0.29/0.46 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_87_eq__imp__le,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( M = N )
% 0.29/0.46 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_88_nat__le__linear,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.46 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_89_le__refl,axiom,
% 0.29/0.46 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_90_diff__commute,axiom,
% 0.29/0.46 ! [I: nat,J_1: nat,K: nat] :
% 0.29/0.46 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J_1 ) @ K )
% 0.29/0.46 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_91_finite__Collect__disjI,axiom,
% 0.29/0.46 ! [P_9: x_a > $o,Q: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a
% 0.29/0.46 @ ( collect_a
% 0.29/0.46 @ ^ [X_1: x_a] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.29/0.46 <=> ( ( finite_finite_a @ ( collect_a @ P_9 ) )
% 0.29/0.46 & ( finite_finite_a @ ( collect_a @ Q ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_92_finite__Collect__disjI,axiom,
% 0.29/0.46 ! [P_9: ( nat > $o ) > $o,Q: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o
% 0.29/0.46 @ ( collect_nat_o
% 0.29/0.46 @ ^ [X_1: nat > $o] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.29/0.46 <=> ( ( finite_finite_nat_o @ ( collect_nat_o @ P_9 ) )
% 0.29/0.46 & ( finite_finite_nat_o @ ( collect_nat_o @ Q ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_93_finite__Collect__disjI,axiom,
% 0.29/0.46 ! [P_9: ( pname > $o ) > $o,Q: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o
% 0.29/0.46 @ ( collect_pname_o
% 0.29/0.46 @ ^ [X_1: pname > $o] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.29/0.46 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_9 ) )
% 0.29/0.46 & ( finite297249702name_o @ ( collect_pname_o @ Q ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_94_finite__Collect__disjI,axiom,
% 0.29/0.46 ! [P_9: ( x_a > $o ) > $o,Q: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o
% 0.29/0.46 @ ( collect_a_o
% 0.29/0.46 @ ^ [X_1: x_a > $o] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.29/0.46 <=> ( ( finite_finite_a_o @ ( collect_a_o @ P_9 ) )
% 0.29/0.46 & ( finite_finite_a_o @ ( collect_a_o @ Q ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_95_finite__Collect__disjI,axiom,
% 0.29/0.46 ! [P_9: pname > $o,Q: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname
% 0.29/0.46 @ ( collect_pname
% 0.29/0.46 @ ^ [X_1: pname] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.29/0.46 <=> ( ( finite_finite_pname @ ( collect_pname @ P_9 ) )
% 0.29/0.46 & ( finite_finite_pname @ ( collect_pname @ Q ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_96_finite__Collect__disjI,axiom,
% 0.29/0.46 ! [P_9: nat > $o,Q: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [X_1: nat] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.29/0.46 <=> ( ( finite_finite_nat @ ( collect_nat @ P_9 ) )
% 0.29/0.46 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_97_finite__insert,axiom,
% 0.29/0.46 ! [A_83: nat > $o,A_82: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ ( insert_nat_o @ A_83 @ A_82 ) )
% 0.29/0.46 <=> ( finite_finite_nat_o @ A_82 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_98_finite__insert,axiom,
% 0.29/0.46 ! [A_83: pname > $o,A_82: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ ( insert_pname_o @ A_83 @ A_82 ) )
% 0.29/0.46 <=> ( finite297249702name_o @ A_82 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_99_finite__insert,axiom,
% 0.29/0.46 ! [A_83: x_a > $o,A_82: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ ( insert_a_o @ A_83 @ A_82 ) )
% 0.29/0.46 <=> ( finite_finite_a_o @ A_82 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_100_finite__insert,axiom,
% 0.29/0.46 ! [A_83: pname,A_82: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ ( insert_pname @ A_83 @ A_82 ) )
% 0.29/0.46 <=> ( finite_finite_pname @ A_82 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_101_finite__insert,axiom,
% 0.29/0.46 ! [A_83: nat,A_82: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ ( insert_nat @ A_83 @ A_82 ) )
% 0.29/0.46 <=> ( finite_finite_nat @ A_82 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_102_finite__insert,axiom,
% 0.29/0.46 ! [A_83: x_a,A_82: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ ( insert_a @ A_83 @ A_82 ) )
% 0.29/0.46 <=> ( finite_finite_a @ A_82 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_103_finite__subset,axiom,
% 0.29/0.46 ! [A_81: ( nat > $o ) > $o,B_44: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o_o @ A_81 @ B_44 )
% 0.29/0.46 => ( ( finite_finite_nat_o @ B_44 )
% 0.29/0.46 => ( finite_finite_nat_o @ A_81 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_104_finite__subset,axiom,
% 0.29/0.46 ! [A_81: ( pname > $o ) > $o,B_44: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( ord_le1205211808me_o_o @ A_81 @ B_44 )
% 0.29/0.46 => ( ( finite297249702name_o @ B_44 )
% 0.29/0.46 => ( finite297249702name_o @ A_81 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_105_finite__subset,axiom,
% 0.29/0.46 ! [A_81: ( x_a > $o ) > $o,B_44: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o_o @ A_81 @ B_44 )
% 0.29/0.46 => ( ( finite_finite_a_o @ B_44 )
% 0.29/0.46 => ( finite_finite_a_o @ A_81 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_106_finite__subset,axiom,
% 0.29/0.46 ! [A_81: x_a > $o,B_44: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_81 @ B_44 )
% 0.29/0.46 => ( ( finite_finite_a @ B_44 )
% 0.29/0.46 => ( finite_finite_a @ A_81 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_107_finite__subset,axiom,
% 0.29/0.46 ! [A_81: pname > $o,B_44: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ A_81 @ B_44 )
% 0.29/0.46 => ( ( finite_finite_pname @ B_44 )
% 0.29/0.46 => ( finite_finite_pname @ A_81 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_108_finite__subset,axiom,
% 0.29/0.46 ! [A_81: nat > $o,B_44: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ A_81 @ B_44 )
% 0.29/0.46 => ( ( finite_finite_nat @ B_44 )
% 0.29/0.46 => ( finite_finite_nat @ A_81 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_109_rev__finite__subset,axiom,
% 0.29/0.46 ! [A_80: ( nat > $o ) > $o,B_43: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ B_43 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o_o @ A_80 @ B_43 )
% 0.29/0.46 => ( finite_finite_nat_o @ A_80 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_110_rev__finite__subset,axiom,
% 0.29/0.46 ! [A_80: ( pname > $o ) > $o,B_43: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ B_43 )
% 0.29/0.46 => ( ( ord_le1205211808me_o_o @ A_80 @ B_43 )
% 0.29/0.46 => ( finite297249702name_o @ A_80 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_111_rev__finite__subset,axiom,
% 0.29/0.46 ! [A_80: ( x_a > $o ) > $o,B_43: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ B_43 )
% 0.29/0.46 => ( ( ord_less_eq_a_o_o @ A_80 @ B_43 )
% 0.29/0.46 => ( finite_finite_a_o @ A_80 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_112_rev__finite__subset,axiom,
% 0.29/0.46 ! [A_80: x_a > $o,B_43: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ B_43 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ A_80 @ B_43 )
% 0.29/0.46 => ( finite_finite_a @ A_80 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_113_rev__finite__subset,axiom,
% 0.29/0.46 ! [A_80: pname > $o,B_43: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ B_43 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ A_80 @ B_43 )
% 0.29/0.46 => ( finite_finite_pname @ A_80 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_114_rev__finite__subset,axiom,
% 0.29/0.46 ! [A_80: nat > $o,B_43: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ B_43 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ A_80 @ B_43 )
% 0.29/0.46 => ( finite_finite_nat @ A_80 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_115_Suc__leD,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.46 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_116_le__SucE,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.29/0.46 => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.29/0.46 => ( M
% 0.29/0.46 = ( suc @ N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_117_le__SucI,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.46 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_118_Suc__le__mono,axiom,
% 0.29/0.46 ! [N: nat,M: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.29/0.46 <=> ( ord_less_eq_nat @ N @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_119_le__Suc__eq,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.29/0.46 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.46 | ( M
% 0.29/0.46 = ( suc @ N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_120_not__less__eq__eq,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ~ ( ord_less_eq_nat @ M @ N )
% 0.29/0.46 <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_121_Suc__n__not__le__n,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_122_Suc__diff__diff,axiom,
% 0.29/0.46 ! [M: nat,N: nat,K: nat] :
% 0.29/0.46 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.29/0.46 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_123_diff__Suc__Suc,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.46 = ( minus_minus_nat @ M @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_124_le__diff__iff,axiom,
% 0.29/0.46 ! [N: nat,K: nat,M: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.46 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.46 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.46 <=> ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_125_Nat_Odiff__diff__eq,axiom,
% 0.29/0.46 ! [N: nat,K: nat,M: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.46 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.46 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.46 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_126_eq__diff__iff,axiom,
% 0.29/0.46 ! [N: nat,K: nat,M: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.46 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.46 => ( ( ( minus_minus_nat @ M @ K )
% 0.29/0.46 = ( minus_minus_nat @ N @ K ) )
% 0.29/0.46 <=> ( M = N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_127_diff__diff__cancel,axiom,
% 0.29/0.46 ! [I: nat,N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ I @ N )
% 0.29/0.46 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.29/0.46 = I ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_128_diff__le__mono,axiom,
% 0.29/0.46 ! [L: nat,M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.46 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_129_diff__le__mono2,axiom,
% 0.29/0.46 ! [L: nat,M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.46 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_130_diff__le__self,axiom,
% 0.29/0.46 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_131_finite__surj,axiom,
% 0.29/0.46 ! [B_42: x_a > $o,F_23: x_a > x_a,A_79: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_42 @ ( image_a_a @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_132_finite__surj,axiom,
% 0.29/0.46 ! [B_42: x_a > $o,F_23: ( nat > $o ) > x_a,A_79: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_42 @ ( image_nat_o_a @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_133_finite__surj,axiom,
% 0.29/0.46 ! [B_42: x_a > $o,F_23: ( pname > $o ) > x_a,A_79: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_42 @ ( image_pname_o_a @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_134_finite__surj,axiom,
% 0.29/0.46 ! [B_42: x_a > $o,F_23: ( x_a > $o ) > x_a,A_79: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_42 @ ( image_a_o_a @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_135_finite__surj,axiom,
% 0.29/0.46 ! [B_42: ( nat > $o ) > $o,F_23: pname > nat > $o,A_79: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o_o @ B_42 @ ( image_pname_nat_o @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_nat_o @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_136_finite__surj,axiom,
% 0.29/0.46 ! [B_42: ( pname > $o ) > $o,F_23: pname > pname > $o,A_79: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_79 )
% 0.29/0.46 => ( ( ord_le1205211808me_o_o @ B_42 @ ( image_pname_pname_o @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite297249702name_o @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_137_finite__surj,axiom,
% 0.29/0.46 ! [B_42: ( x_a > $o ) > $o,F_23: pname > x_a > $o,A_79: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_a_o_o @ B_42 @ ( image_pname_a_o @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_a_o @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_138_finite__surj,axiom,
% 0.29/0.46 ! [B_42: pname > $o,F_23: pname > pname,A_79: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_pname_pname @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_139_finite__surj,axiom,
% 0.29/0.46 ! [B_42: nat > $o,F_23: pname > nat,A_79: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_pname_nat @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_140_finite__surj,axiom,
% 0.29/0.46 ! [B_42: x_a > $o,F_23: nat > x_a,A_79: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_42 @ ( image_nat_a @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_141_finite__surj,axiom,
% 0.29/0.46 ! [B_42: ( nat > $o ) > $o,F_23: nat > nat > $o,A_79: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o_o @ B_42 @ ( image_nat_nat_o @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_nat_o @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_142_finite__surj,axiom,
% 0.29/0.46 ! [B_42: ( pname > $o ) > $o,F_23: nat > pname > $o,A_79: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_79 )
% 0.29/0.46 => ( ( ord_le1205211808me_o_o @ B_42 @ ( image_nat_pname_o @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite297249702name_o @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_143_finite__surj,axiom,
% 0.29/0.46 ! [B_42: ( x_a > $o ) > $o,F_23: nat > x_a > $o,A_79: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_a_o_o @ B_42 @ ( image_nat_a_o @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_a_o @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_144_finite__surj,axiom,
% 0.29/0.46 ! [B_42: pname > $o,F_23: nat > pname,A_79: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_nat_pname @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_145_finite__surj,axiom,
% 0.29/0.46 ! [B_42: nat > $o,F_23: nat > nat,A_79: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_nat_nat @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_146_finite__surj,axiom,
% 0.29/0.46 ! [B_42: pname > $o,F_23: x_a > pname,A_79: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_a_pname @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_147_finite__surj,axiom,
% 0.29/0.46 ! [B_42: pname > $o,F_23: ( nat > $o ) > pname,A_79: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_nat_o_pname @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_148_finite__surj,axiom,
% 0.29/0.46 ! [B_42: pname > $o,F_23: ( pname > $o ) > pname,A_79: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_pname_o_pname @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_149_finite__surj,axiom,
% 0.29/0.46 ! [B_42: pname > $o,F_23: ( x_a > $o ) > pname,A_79: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_a_o_pname @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_150_finite__surj,axiom,
% 0.29/0.46 ! [B_42: nat > $o,F_23: x_a > nat,A_79: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_a_nat @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_151_finite__surj,axiom,
% 0.29/0.46 ! [B_42: nat > $o,F_23: ( nat > $o ) > nat,A_79: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_nat_o_nat @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_152_finite__surj,axiom,
% 0.29/0.46 ! [B_42: nat > $o,F_23: ( pname > $o ) > nat,A_79: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_pname_o_nat @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_153_finite__surj,axiom,
% 0.29/0.46 ! [B_42: nat > $o,F_23: ( x_a > $o ) > nat,A_79: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_a_o_nat @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_154_finite__surj,axiom,
% 0.29/0.46 ! [B_42: x_a > $o,F_23: pname > x_a,A_79: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_79 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_42 @ ( image_pname_a @ F_23 @ A_79 ) )
% 0.29/0.46 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_155_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: ( nat > $o ) > x_a,A_78: ( nat > $o ) > $o,B_41: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_41 @ ( image_nat_o_a @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_nat_o @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_nat_o_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_156_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: ( pname > $o ) > x_a,A_78: ( pname > $o ) > $o,B_41: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_41 @ ( image_pname_o_a @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( ord_le1205211808me_o_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite297249702name_o @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_pname_o_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_157_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: ( x_a > $o ) > x_a,A_78: ( x_a > $o ) > $o,B_41: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_41 @ ( image_a_o_a @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_a_o @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_a_o_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_158_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: x_a > x_a,A_78: x_a > $o,B_41: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_41 @ ( image_a_a @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_a @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_a_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_159_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: x_a > nat > $o,A_78: x_a > $o,B_41: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o_o @ B_41 @ ( image_a_nat_o @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_a @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_a_nat_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_160_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: x_a > pname > $o,A_78: x_a > $o,B_41: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ B_41 )
% 0.29/0.46 => ( ( ord_le1205211808me_o_o @ B_41 @ ( image_a_pname_o @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_a @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_a_pname_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_161_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: x_a > x_a > $o,A_78: x_a > $o,B_41: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_a_o_o @ B_41 @ ( image_a_a_o @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_a @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_a_a_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_162_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: x_a > pname,A_78: x_a > $o,B_41: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_a_pname @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_a @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_a_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_163_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: ( nat > $o ) > pname,A_78: ( nat > $o ) > $o,B_41: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_nat_o_pname @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_nat_o @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_nat_o_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_164_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: ( pname > $o ) > pname,A_78: ( pname > $o ) > $o,B_41: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_pname_o_pname @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( ord_le1205211808me_o_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite297249702name_o @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_pname_o_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_165_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: ( x_a > $o ) > pname,A_78: ( x_a > $o ) > $o,B_41: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_a_o_pname @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_a_o @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_a_o_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_166_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: x_a > nat,A_78: x_a > $o,B_41: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_a_nat @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_a @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_a_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_167_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: ( nat > $o ) > nat,A_78: ( nat > $o ) > $o,B_41: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_nat_o_nat @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_nat_o @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_nat_o_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_168_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: ( pname > $o ) > nat,A_78: ( pname > $o ) > $o,B_41: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_pname_o_nat @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( ord_le1205211808me_o_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite297249702name_o @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_pname_o_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_169_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: ( x_a > $o ) > nat,A_78: ( x_a > $o ) > $o,B_41: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_a_o_nat @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_a_o @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_a_o_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_170_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: pname > nat > $o,A_78: pname > $o,B_41: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o_o @ B_41 @ ( image_pname_nat_o @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_pname @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_pname_nat_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_171_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: pname > pname > $o,A_78: pname > $o,B_41: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ B_41 )
% 0.29/0.46 => ( ( ord_le1205211808me_o_o @ B_41 @ ( image_pname_pname_o @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_pname @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_pname_pname_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_172_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: pname > x_a > $o,A_78: pname > $o,B_41: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_a_o_o @ B_41 @ ( image_pname_a_o @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_pname @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_pname_a_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_173_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: pname > pname,A_78: pname > $o,B_41: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_pname_pname @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_pname @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_pname_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_174_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: pname > nat,A_78: pname > $o,B_41: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_pname_nat @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_pname @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_pname_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_175_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: nat > x_a,A_78: nat > $o,B_41: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_41 @ ( image_nat_a @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_nat @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_nat_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_176_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: nat > nat > $o,A_78: nat > $o,B_41: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o_o @ B_41 @ ( image_nat_nat_o @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_nat @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_nat_nat_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_177_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: nat > pname > $o,A_78: nat > $o,B_41: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ B_41 )
% 0.29/0.46 => ( ( ord_le1205211808me_o_o @ B_41 @ ( image_nat_pname_o @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_nat @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_nat_pname_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_178_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: nat > x_a > $o,A_78: nat > $o,B_41: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_a_o_o @ B_41 @ ( image_nat_a_o @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_nat @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_nat_a_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_179_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: nat > pname,A_78: nat > $o,B_41: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_nat_pname @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_nat @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_nat_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_180_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: nat > nat,A_78: nat > $o,B_41: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_nat_nat @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_nat @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_nat_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_181_finite__subset__image,axiom,
% 0.29/0.46 ! [F_22: pname > x_a,A_78: pname > $o,B_41: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ B_41 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_41 @ ( image_pname_a @ F_22 @ A_78 ) )
% 0.29/0.46 => ? [C_12: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.29/0.46 & ( finite_finite_pname @ C_12 )
% 0.29/0.46 & ( B_41
% 0.29/0.46 = ( image_pname_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_182_lift__Suc__mono__le,axiom,
% 0.29/0.46 ! [N_4: nat,N_3: nat,F_21: nat > $o] :
% 0.29/0.46 ( ! [N_2: nat] : ( ord_less_eq_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.29/0.46 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.29/0.46 => ( ord_less_eq_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_183_lift__Suc__mono__le,axiom,
% 0.29/0.46 ! [N_4: nat,N_3: nat,F_21: nat > pname > $o] :
% 0.29/0.46 ( ! [N_2: nat] : ( ord_less_eq_pname_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.29/0.46 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.29/0.46 => ( ord_less_eq_pname_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_184_lift__Suc__mono__le,axiom,
% 0.29/0.46 ! [N_4: nat,N_3: nat,F_21: nat > nat > $o] :
% 0.29/0.46 ( ! [N_2: nat] : ( ord_less_eq_nat_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.29/0.46 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.29/0.46 => ( ord_less_eq_nat_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_185_lift__Suc__mono__le,axiom,
% 0.29/0.46 ! [N_4: nat,N_3: nat,F_21: nat > x_a > $o] :
% 0.29/0.46 ( ! [N_2: nat] : ( ord_less_eq_a_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.29/0.46 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.29/0.46 => ( ord_less_eq_a_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_186_lift__Suc__mono__le,axiom,
% 0.29/0.46 ! [N_4: nat,N_3: nat,F_21: nat > nat] :
% 0.29/0.46 ( ! [N_2: nat] : ( ord_less_eq_nat @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.29/0.46 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.29/0.46 => ( ord_less_eq_nat @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_187_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: nat > pname,A_77: nat > $o] :
% 0.29/0.46 ( ~ ( finite_finite_nat @ A_77 )
% 0.29/0.46 => ( ( finite_finite_pname @ ( image_nat_pname @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [A_2: nat] :
% 0.29/0.46 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_188_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: x_a > pname,A_77: x_a > $o] :
% 0.29/0.46 ( ~ ( finite_finite_a @ A_77 )
% 0.29/0.46 => ( ( finite_finite_pname @ ( image_a_pname @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: x_a] :
% 0.29/0.46 ( ( member_a @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_a
% 0.29/0.46 @ ( collect_a
% 0.29/0.46 @ ^ [A_2: x_a] :
% 0.29/0.46 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_189_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: pname > pname,A_77: pname > $o] :
% 0.29/0.46 ( ~ ( finite_finite_pname @ A_77 )
% 0.29/0.46 => ( ( finite_finite_pname @ ( image_pname_pname @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_pname
% 0.29/0.46 @ ( collect_pname
% 0.29/0.46 @ ^ [A_2: pname] :
% 0.29/0.46 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_190_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: ( nat > $o ) > pname,A_77: ( nat > $o ) > $o] :
% 0.29/0.46 ( ~ ( finite_finite_nat_o @ A_77 )
% 0.29/0.46 => ( ( finite_finite_pname @ ( image_nat_o_pname @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: nat > $o] :
% 0.29/0.46 ( ( member_nat_o @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_nat_o
% 0.29/0.46 @ ( collect_nat_o
% 0.29/0.46 @ ^ [A_2: nat > $o] :
% 0.29/0.46 ( (&) @ ( member_nat_o @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_191_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: ( pname > $o ) > pname,A_77: ( pname > $o ) > $o] :
% 0.29/0.46 ( ~ ( finite297249702name_o @ A_77 )
% 0.29/0.46 => ( ( finite_finite_pname @ ( image_pname_o_pname @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: pname > $o] :
% 0.29/0.46 ( ( member_pname_o @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite297249702name_o
% 0.29/0.46 @ ( collect_pname_o
% 0.29/0.46 @ ^ [A_2: pname > $o] :
% 0.29/0.46 ( (&) @ ( member_pname_o @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_192_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: ( x_a > $o ) > pname,A_77: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ~ ( finite_finite_a_o @ A_77 )
% 0.29/0.46 => ( ( finite_finite_pname @ ( image_a_o_pname @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: x_a > $o] :
% 0.29/0.46 ( ( member_a_o @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_a_o
% 0.29/0.46 @ ( collect_a_o
% 0.29/0.46 @ ^ [A_2: x_a > $o] :
% 0.29/0.46 ( (&) @ ( member_a_o @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_193_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: nat > nat,A_77: nat > $o] :
% 0.29/0.46 ( ~ ( finite_finite_nat @ A_77 )
% 0.29/0.46 => ( ( finite_finite_nat @ ( image_nat_nat @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [A_2: nat] :
% 0.29/0.46 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_194_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: x_a > nat,A_77: x_a > $o] :
% 0.29/0.46 ( ~ ( finite_finite_a @ A_77 )
% 0.29/0.46 => ( ( finite_finite_nat @ ( image_a_nat @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: x_a] :
% 0.29/0.46 ( ( member_a @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_a
% 0.29/0.46 @ ( collect_a
% 0.29/0.46 @ ^ [A_2: x_a] :
% 0.29/0.46 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_195_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: pname > nat,A_77: pname > $o] :
% 0.29/0.46 ( ~ ( finite_finite_pname @ A_77 )
% 0.29/0.46 => ( ( finite_finite_nat @ ( image_pname_nat @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_pname
% 0.29/0.46 @ ( collect_pname
% 0.29/0.46 @ ^ [A_2: pname] :
% 0.29/0.46 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_196_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: ( nat > $o ) > nat,A_77: ( nat > $o ) > $o] :
% 0.29/0.46 ( ~ ( finite_finite_nat_o @ A_77 )
% 0.29/0.46 => ( ( finite_finite_nat @ ( image_nat_o_nat @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: nat > $o] :
% 0.29/0.46 ( ( member_nat_o @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_nat_o
% 0.29/0.46 @ ( collect_nat_o
% 0.29/0.46 @ ^ [A_2: nat > $o] :
% 0.29/0.46 ( (&) @ ( member_nat_o @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_197_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: ( pname > $o ) > nat,A_77: ( pname > $o ) > $o] :
% 0.29/0.46 ( ~ ( finite297249702name_o @ A_77 )
% 0.29/0.46 => ( ( finite_finite_nat @ ( image_pname_o_nat @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: pname > $o] :
% 0.29/0.46 ( ( member_pname_o @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite297249702name_o
% 0.29/0.46 @ ( collect_pname_o
% 0.29/0.46 @ ^ [A_2: pname > $o] :
% 0.29/0.46 ( (&) @ ( member_pname_o @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_198_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: ( x_a > $o ) > nat,A_77: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ~ ( finite_finite_a_o @ A_77 )
% 0.29/0.46 => ( ( finite_finite_nat @ ( image_a_o_nat @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: x_a > $o] :
% 0.29/0.46 ( ( member_a_o @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_a_o
% 0.29/0.46 @ ( collect_a_o
% 0.29/0.46 @ ^ [A_2: x_a > $o] :
% 0.29/0.46 ( (&) @ ( member_a_o @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_199_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: nat > x_a,A_77: nat > $o] :
% 0.29/0.46 ( ~ ( finite_finite_nat @ A_77 )
% 0.29/0.46 => ( ( finite_finite_a @ ( image_nat_a @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [A_2: nat] :
% 0.29/0.46 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_200_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: nat > nat > $o,A_77: nat > $o] :
% 0.29/0.46 ( ~ ( finite_finite_nat @ A_77 )
% 0.29/0.46 => ( ( finite_finite_nat_o @ ( image_nat_nat_o @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [A_2: nat] :
% 0.29/0.46 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_201_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: nat > pname > $o,A_77: nat > $o] :
% 0.29/0.46 ( ~ ( finite_finite_nat @ A_77 )
% 0.29/0.46 => ( ( finite297249702name_o @ ( image_nat_pname_o @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [A_2: nat] :
% 0.29/0.46 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_202_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: nat > x_a > $o,A_77: nat > $o] :
% 0.29/0.46 ( ~ ( finite_finite_nat @ A_77 )
% 0.29/0.46 => ( ( finite_finite_a_o @ ( image_nat_a_o @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_nat
% 0.29/0.46 @ ( collect_nat
% 0.29/0.46 @ ^ [A_2: nat] :
% 0.29/0.46 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_203_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: pname > nat > $o,A_77: pname > $o] :
% 0.29/0.46 ( ~ ( finite_finite_pname @ A_77 )
% 0.29/0.46 => ( ( finite_finite_nat_o @ ( image_pname_nat_o @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_pname
% 0.29/0.46 @ ( collect_pname
% 0.29/0.46 @ ^ [A_2: pname] :
% 0.29/0.46 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_204_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: pname > pname > $o,A_77: pname > $o] :
% 0.29/0.46 ( ~ ( finite_finite_pname @ A_77 )
% 0.29/0.46 => ( ( finite297249702name_o @ ( image_pname_pname_o @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_pname
% 0.29/0.46 @ ( collect_pname
% 0.29/0.46 @ ^ [A_2: pname] :
% 0.29/0.46 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_205_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: pname > x_a > $o,A_77: pname > $o] :
% 0.29/0.46 ( ~ ( finite_finite_pname @ A_77 )
% 0.29/0.46 => ( ( finite_finite_a_o @ ( image_pname_a_o @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_pname
% 0.29/0.46 @ ( collect_pname
% 0.29/0.46 @ ^ [A_2: pname] :
% 0.29/0.46 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_206_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: x_a > x_a,A_77: x_a > $o] :
% 0.29/0.46 ( ~ ( finite_finite_a @ A_77 )
% 0.29/0.46 => ( ( finite_finite_a @ ( image_a_a @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: x_a] :
% 0.29/0.46 ( ( member_a @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_a
% 0.29/0.46 @ ( collect_a
% 0.29/0.46 @ ^ [A_2: x_a] :
% 0.29/0.46 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_207_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: x_a > nat > $o,A_77: x_a > $o] :
% 0.29/0.46 ( ~ ( finite_finite_a @ A_77 )
% 0.29/0.46 => ( ( finite_finite_nat_o @ ( image_a_nat_o @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: x_a] :
% 0.29/0.46 ( ( member_a @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_a
% 0.29/0.46 @ ( collect_a
% 0.29/0.46 @ ^ [A_2: x_a] :
% 0.29/0.46 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_208_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: x_a > pname > $o,A_77: x_a > $o] :
% 0.29/0.46 ( ~ ( finite_finite_a @ A_77 )
% 0.29/0.46 => ( ( finite297249702name_o @ ( image_a_pname_o @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: x_a] :
% 0.29/0.46 ( ( member_a @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_a
% 0.29/0.46 @ ( collect_a
% 0.29/0.46 @ ^ [A_2: x_a] :
% 0.29/0.46 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_209_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: x_a > x_a > $o,A_77: x_a > $o] :
% 0.29/0.46 ( ~ ( finite_finite_a @ A_77 )
% 0.29/0.46 => ( ( finite_finite_a_o @ ( image_a_a_o @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: x_a] :
% 0.29/0.46 ( ( member_a @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_a
% 0.29/0.46 @ ( collect_a
% 0.29/0.46 @ ^ [A_2: x_a] :
% 0.29/0.46 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_210_pigeonhole__infinite,axiom,
% 0.29/0.46 ! [F_20: pname > x_a,A_77: pname > $o] :
% 0.29/0.46 ( ~ ( finite_finite_pname @ A_77 )
% 0.29/0.46 => ( ( finite_finite_a @ ( image_pname_a @ F_20 @ A_77 ) )
% 0.29/0.46 => ? [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_77 )
% 0.29/0.46 & ~ ( finite_finite_pname
% 0.29/0.46 @ ( collect_pname
% 0.29/0.46 @ ^ [A_2: pname] :
% 0.29/0.46 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.29/0.46 @ ( ( F_20 @ A_2 )
% 0.29/0.46 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_211_image__eqI,axiom,
% 0.29/0.46 ! [A_76: pname > $o,B_40: nat,F_19: pname > nat,X_30: pname] :
% 0.29/0.46 ( ( B_40
% 0.29/0.46 = ( F_19 @ X_30 ) )
% 0.29/0.46 => ( ( member_pname @ X_30 @ A_76 )
% 0.29/0.46 => ( member_nat @ B_40 @ ( image_pname_nat @ F_19 @ A_76 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_212_image__eqI,axiom,
% 0.29/0.46 ! [A_76: x_a > $o,B_40: nat,F_19: x_a > nat,X_30: x_a] :
% 0.29/0.46 ( ( B_40
% 0.29/0.46 = ( F_19 @ X_30 ) )
% 0.29/0.46 => ( ( member_a @ X_30 @ A_76 )
% 0.29/0.46 => ( member_nat @ B_40 @ ( image_a_nat @ F_19 @ A_76 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_213_image__eqI,axiom,
% 0.29/0.46 ! [A_76: nat > $o,B_40: pname,F_19: nat > pname,X_30: nat] :
% 0.29/0.46 ( ( B_40
% 0.29/0.46 = ( F_19 @ X_30 ) )
% 0.29/0.46 => ( ( member_nat @ X_30 @ A_76 )
% 0.29/0.46 => ( member_pname @ B_40 @ ( image_nat_pname @ F_19 @ A_76 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_214_image__eqI,axiom,
% 0.29/0.46 ! [A_76: nat > $o,B_40: x_a,F_19: nat > x_a,X_30: nat] :
% 0.29/0.46 ( ( B_40
% 0.29/0.46 = ( F_19 @ X_30 ) )
% 0.29/0.46 => ( ( member_nat @ X_30 @ A_76 )
% 0.29/0.46 => ( member_a @ B_40 @ ( image_nat_a @ F_19 @ A_76 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_215_image__eqI,axiom,
% 0.29/0.46 ! [A_76: pname > $o,B_40: x_a,F_19: pname > x_a,X_30: pname] :
% 0.29/0.46 ( ( B_40
% 0.29/0.46 = ( F_19 @ X_30 ) )
% 0.29/0.46 => ( ( member_pname @ X_30 @ A_76 )
% 0.29/0.46 => ( member_a @ B_40 @ ( image_pname_a @ F_19 @ A_76 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_216_equalityI,axiom,
% 0.29/0.46 ! [A_75: pname > $o,B_39: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ A_75 @ B_39 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_39 @ A_75 )
% 0.29/0.46 => ( A_75 = B_39 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_217_equalityI,axiom,
% 0.29/0.46 ! [A_75: nat > $o,B_39: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ A_75 @ B_39 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_39 @ A_75 )
% 0.29/0.46 => ( A_75 = B_39 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_218_equalityI,axiom,
% 0.29/0.46 ! [A_75: x_a > $o,B_39: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_75 @ B_39 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_39 @ A_75 )
% 0.29/0.46 => ( A_75 = B_39 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_219_subsetD,axiom,
% 0.29/0.46 ! [C_11: nat,A_74: nat > $o,B_38: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ A_74 @ B_38 )
% 0.29/0.46 => ( ( member_nat @ C_11 @ A_74 )
% 0.29/0.46 => ( member_nat @ C_11 @ B_38 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_220_subsetD,axiom,
% 0.29/0.46 ! [C_11: pname,A_74: pname > $o,B_38: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ A_74 @ B_38 )
% 0.29/0.46 => ( ( member_pname @ C_11 @ A_74 )
% 0.29/0.46 => ( member_pname @ C_11 @ B_38 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_221_subsetD,axiom,
% 0.29/0.46 ! [C_11: x_a,A_74: x_a > $o,B_38: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_74 @ B_38 )
% 0.29/0.46 => ( ( member_a @ C_11 @ A_74 )
% 0.29/0.46 => ( member_a @ C_11 @ B_38 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_222_insertCI,axiom,
% 0.29/0.46 ! [B_37: nat,A_73: nat,B_36: nat > $o] :
% 0.29/0.46 ( ( ~ ( member_nat @ A_73 @ B_36 )
% 0.29/0.46 => ( A_73 = B_37 ) )
% 0.29/0.46 => ( member_nat @ A_73 @ ( insert_nat @ B_37 @ B_36 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_223_insertCI,axiom,
% 0.29/0.46 ! [B_37: pname,A_73: pname,B_36: pname > $o] :
% 0.29/0.46 ( ( ~ ( member_pname @ A_73 @ B_36 )
% 0.29/0.46 => ( A_73 = B_37 ) )
% 0.29/0.46 => ( member_pname @ A_73 @ ( insert_pname @ B_37 @ B_36 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_224_insertCI,axiom,
% 0.29/0.46 ! [B_37: x_a,A_73: x_a,B_36: x_a > $o] :
% 0.29/0.46 ( ( ~ ( member_a @ A_73 @ B_36 )
% 0.29/0.46 => ( A_73 = B_37 ) )
% 0.29/0.46 => ( member_a @ A_73 @ ( insert_a @ B_37 @ B_36 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_225_insertE,axiom,
% 0.29/0.46 ! [A_72: nat,B_35: nat,A_71: nat > $o] :
% 0.29/0.46 ( ( member_nat @ A_72 @ ( insert_nat @ B_35 @ A_71 ) )
% 0.29/0.46 => ( ( A_72 != B_35 )
% 0.29/0.46 => ( member_nat @ A_72 @ A_71 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_226_insertE,axiom,
% 0.29/0.46 ! [A_72: pname,B_35: pname,A_71: pname > $o] :
% 0.29/0.46 ( ( member_pname @ A_72 @ ( insert_pname @ B_35 @ A_71 ) )
% 0.29/0.46 => ( ( A_72 != B_35 )
% 0.29/0.46 => ( member_pname @ A_72 @ A_71 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_227_insertE,axiom,
% 0.29/0.46 ! [A_72: x_a,B_35: x_a,A_71: x_a > $o] :
% 0.29/0.46 ( ( member_a @ A_72 @ ( insert_a @ B_35 @ A_71 ) )
% 0.29/0.46 => ( ( A_72 != B_35 )
% 0.29/0.46 => ( member_a @ A_72 @ A_71 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_228_zero__induct__lemma,axiom,
% 0.29/0.46 ! [I: nat,P: nat > $o,K: nat] :
% 0.29/0.46 ( ( P @ K )
% 0.29/0.46 => ( ! [N_2: nat] :
% 0.29/0.46 ( ( P @ ( suc @ N_2 ) )
% 0.29/0.46 => ( P @ N_2 ) )
% 0.29/0.46 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_229_Suc__le__D,axiom,
% 0.29/0.46 ! [N: nat,M_2: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ ( suc @ N ) @ M_2 )
% 0.29/0.46 => ? [M_1: nat] :
% 0.29/0.46 ( M_2
% 0.29/0.46 = ( suc @ M_1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_230_insertI1,axiom,
% 0.29/0.46 ! [A_70: nat,B_34: nat > $o] : ( member_nat @ A_70 @ ( insert_nat @ A_70 @ B_34 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_231_insertI1,axiom,
% 0.29/0.46 ! [A_70: pname,B_34: pname > $o] : ( member_pname @ A_70 @ ( insert_pname @ A_70 @ B_34 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_232_insertI1,axiom,
% 0.29/0.46 ! [A_70: x_a,B_34: x_a > $o] : ( member_a @ A_70 @ ( insert_a @ A_70 @ B_34 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_233_insert__compr,axiom,
% 0.29/0.46 ! [A_69: nat > $o,B_33: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( insert_nat_o @ A_69 @ B_33 )
% 0.29/0.46 = ( collect_nat_o
% 0.29/0.46 @ ^ [X_1: nat > $o] : ( (|) @ ( X_1 = A_69 ) @ ( member_nat_o @ X_1 @ B_33 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_234_insert__compr,axiom,
% 0.29/0.46 ! [A_69: pname > $o,B_33: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( insert_pname_o @ A_69 @ B_33 )
% 0.29/0.46 = ( collect_pname_o
% 0.29/0.46 @ ^ [X_1: pname > $o] : ( (|) @ ( X_1 = A_69 ) @ ( member_pname_o @ X_1 @ B_33 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_235_insert__compr,axiom,
% 0.29/0.46 ! [A_69: x_a > $o,B_33: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( insert_a_o @ A_69 @ B_33 )
% 0.29/0.46 = ( collect_a_o
% 0.29/0.46 @ ^ [X_1: x_a > $o] : ( (|) @ ( X_1 = A_69 ) @ ( member_a_o @ X_1 @ B_33 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_236_insert__compr,axiom,
% 0.29/0.46 ! [A_69: nat,B_33: nat > $o] :
% 0.29/0.46 ( ( insert_nat @ A_69 @ B_33 )
% 0.29/0.46 = ( collect_nat
% 0.29/0.46 @ ^ [X_1: nat] : ( (|) @ ( X_1 = A_69 ) @ ( member_nat @ X_1 @ B_33 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_237_insert__compr,axiom,
% 0.29/0.46 ! [A_69: pname,B_33: pname > $o] :
% 0.29/0.46 ( ( insert_pname @ A_69 @ B_33 )
% 0.29/0.46 = ( collect_pname
% 0.29/0.46 @ ^ [X_1: pname] : ( (|) @ ( X_1 = A_69 ) @ ( member_pname @ X_1 @ B_33 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_238_insert__compr,axiom,
% 0.29/0.46 ! [A_69: x_a,B_33: x_a > $o] :
% 0.29/0.46 ( ( insert_a @ A_69 @ B_33 )
% 0.29/0.46 = ( collect_a
% 0.29/0.46 @ ^ [X_1: x_a] : ( (|) @ ( X_1 = A_69 ) @ ( member_a @ X_1 @ B_33 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_239_insert__Collect,axiom,
% 0.29/0.46 ! [A_68: pname,P_8: pname > $o] :
% 0.29/0.46 ( ( insert_pname @ A_68 @ ( collect_pname @ P_8 ) )
% 0.29/0.46 = ( collect_pname
% 0.29/0.46 @ ^ [U_1: pname] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_240_insert__Collect,axiom,
% 0.29/0.46 ! [A_68: nat > $o,P_8: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( insert_nat_o @ A_68 @ ( collect_nat_o @ P_8 ) )
% 0.29/0.46 = ( collect_nat_o
% 0.29/0.46 @ ^ [U_1: nat > $o] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_241_insert__Collect,axiom,
% 0.29/0.46 ! [A_68: pname > $o,P_8: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( insert_pname_o @ A_68 @ ( collect_pname_o @ P_8 ) )
% 0.29/0.46 = ( collect_pname_o
% 0.29/0.46 @ ^ [U_1: pname > $o] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_242_insert__Collect,axiom,
% 0.29/0.46 ! [A_68: x_a > $o,P_8: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( insert_a_o @ A_68 @ ( collect_a_o @ P_8 ) )
% 0.29/0.46 = ( collect_a_o
% 0.29/0.46 @ ^ [U_1: x_a > $o] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_243_insert__Collect,axiom,
% 0.29/0.46 ! [A_68: nat,P_8: nat > $o] :
% 0.29/0.46 ( ( insert_nat @ A_68 @ ( collect_nat @ P_8 ) )
% 0.29/0.46 = ( collect_nat
% 0.29/0.46 @ ^ [U_1: nat] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_244_insert__Collect,axiom,
% 0.29/0.46 ! [A_68: x_a,P_8: x_a > $o] :
% 0.29/0.46 ( ( insert_a @ A_68 @ ( collect_a @ P_8 ) )
% 0.29/0.46 = ( collect_a
% 0.29/0.46 @ ^ [U_1: x_a] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_245_insert__absorb2,axiom,
% 0.29/0.46 ! [X_29: pname,A_67: pname > $o] :
% 0.29/0.46 ( ( insert_pname @ X_29 @ ( insert_pname @ X_29 @ A_67 ) )
% 0.29/0.46 = ( insert_pname @ X_29 @ A_67 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_246_insert__absorb2,axiom,
% 0.29/0.46 ! [X_29: nat,A_67: nat > $o] :
% 0.29/0.46 ( ( insert_nat @ X_29 @ ( insert_nat @ X_29 @ A_67 ) )
% 0.29/0.46 = ( insert_nat @ X_29 @ A_67 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_247_insert__absorb2,axiom,
% 0.29/0.46 ! [X_29: x_a,A_67: x_a > $o] :
% 0.29/0.46 ( ( insert_a @ X_29 @ ( insert_a @ X_29 @ A_67 ) )
% 0.29/0.46 = ( insert_a @ X_29 @ A_67 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_248_insert__commute,axiom,
% 0.29/0.46 ! [X_28: pname,Y_12: pname,A_66: pname > $o] :
% 0.29/0.46 ( ( insert_pname @ X_28 @ ( insert_pname @ Y_12 @ A_66 ) )
% 0.29/0.46 = ( insert_pname @ Y_12 @ ( insert_pname @ X_28 @ A_66 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_249_insert__commute,axiom,
% 0.29/0.46 ! [X_28: nat,Y_12: nat,A_66: nat > $o] :
% 0.29/0.46 ( ( insert_nat @ X_28 @ ( insert_nat @ Y_12 @ A_66 ) )
% 0.29/0.46 = ( insert_nat @ Y_12 @ ( insert_nat @ X_28 @ A_66 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_250_insert__commute,axiom,
% 0.29/0.46 ! [X_28: x_a,Y_12: x_a,A_66: x_a > $o] :
% 0.29/0.46 ( ( insert_a @ X_28 @ ( insert_a @ Y_12 @ A_66 ) )
% 0.29/0.46 = ( insert_a @ Y_12 @ ( insert_a @ X_28 @ A_66 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_251_insert__iff,axiom,
% 0.29/0.46 ! [A_65: nat,B_32: nat,A_64: nat > $o] :
% 0.29/0.46 ( ( member_nat @ A_65 @ ( insert_nat @ B_32 @ A_64 ) )
% 0.29/0.46 <=> ( ( A_65 = B_32 )
% 0.29/0.46 | ( member_nat @ A_65 @ A_64 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_252_insert__iff,axiom,
% 0.29/0.46 ! [A_65: pname,B_32: pname,A_64: pname > $o] :
% 0.29/0.46 ( ( member_pname @ A_65 @ ( insert_pname @ B_32 @ A_64 ) )
% 0.29/0.46 <=> ( ( A_65 = B_32 )
% 0.29/0.46 | ( member_pname @ A_65 @ A_64 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_253_insert__iff,axiom,
% 0.29/0.46 ! [A_65: x_a,B_32: x_a,A_64: x_a > $o] :
% 0.29/0.46 ( ( member_a @ A_65 @ ( insert_a @ B_32 @ A_64 ) )
% 0.29/0.46 <=> ( ( A_65 = B_32 )
% 0.29/0.46 | ( member_a @ A_65 @ A_64 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_254_insert__code,axiom,
% 0.29/0.46 ! [Y_11: pname,A_63: pname > $o,X_27: pname] :
% 0.29/0.46 ( ( insert_pname @ Y_11 @ A_63 @ X_27 )
% 0.29/0.46 <=> ( ( Y_11 = X_27 )
% 0.29/0.46 | ( A_63 @ X_27 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_255_insert__code,axiom,
% 0.29/0.46 ! [Y_11: nat,A_63: nat > $o,X_27: nat] :
% 0.29/0.46 ( ( insert_nat @ Y_11 @ A_63 @ X_27 )
% 0.29/0.46 <=> ( ( Y_11 = X_27 )
% 0.29/0.46 | ( A_63 @ X_27 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_256_insert__code,axiom,
% 0.29/0.46 ! [Y_11: x_a,A_63: x_a > $o,X_27: x_a] :
% 0.29/0.46 ( ( insert_a @ Y_11 @ A_63 @ X_27 )
% 0.29/0.46 <=> ( ( Y_11 = X_27 )
% 0.29/0.46 | ( A_63 @ X_27 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_257_insert__ident,axiom,
% 0.29/0.46 ! [B_31: nat > $o,X_26: nat,A_62: nat > $o] :
% 0.29/0.46 ( ~ ( member_nat @ X_26 @ A_62 )
% 0.29/0.46 => ( ~ ( member_nat @ X_26 @ B_31 )
% 0.29/0.46 => ( ( ( insert_nat @ X_26 @ A_62 )
% 0.29/0.46 = ( insert_nat @ X_26 @ B_31 ) )
% 0.29/0.46 <=> ( A_62 = B_31 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_258_insert__ident,axiom,
% 0.29/0.46 ! [B_31: pname > $o,X_26: pname,A_62: pname > $o] :
% 0.29/0.46 ( ~ ( member_pname @ X_26 @ A_62 )
% 0.29/0.46 => ( ~ ( member_pname @ X_26 @ B_31 )
% 0.29/0.46 => ( ( ( insert_pname @ X_26 @ A_62 )
% 0.29/0.46 = ( insert_pname @ X_26 @ B_31 ) )
% 0.29/0.46 <=> ( A_62 = B_31 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_259_insert__ident,axiom,
% 0.29/0.46 ! [B_31: x_a > $o,X_26: x_a,A_62: x_a > $o] :
% 0.29/0.46 ( ~ ( member_a @ X_26 @ A_62 )
% 0.29/0.46 => ( ~ ( member_a @ X_26 @ B_31 )
% 0.29/0.46 => ( ( ( insert_a @ X_26 @ A_62 )
% 0.29/0.46 = ( insert_a @ X_26 @ B_31 ) )
% 0.29/0.46 <=> ( A_62 = B_31 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_260_insertI2,axiom,
% 0.29/0.46 ! [B_30: nat,A_61: nat,B_29: nat > $o] :
% 0.29/0.46 ( ( member_nat @ A_61 @ B_29 )
% 0.29/0.46 => ( member_nat @ A_61 @ ( insert_nat @ B_30 @ B_29 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_261_insertI2,axiom,
% 0.29/0.46 ! [B_30: pname,A_61: pname,B_29: pname > $o] :
% 0.29/0.46 ( ( member_pname @ A_61 @ B_29 )
% 0.29/0.46 => ( member_pname @ A_61 @ ( insert_pname @ B_30 @ B_29 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_262_insertI2,axiom,
% 0.29/0.46 ! [B_30: x_a,A_61: x_a,B_29: x_a > $o] :
% 0.29/0.46 ( ( member_a @ A_61 @ B_29 )
% 0.29/0.46 => ( member_a @ A_61 @ ( insert_a @ B_30 @ B_29 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_263_insert__absorb,axiom,
% 0.29/0.46 ! [A_60: nat,A_59: nat > $o] :
% 0.29/0.46 ( ( member_nat @ A_60 @ A_59 )
% 0.29/0.46 => ( ( insert_nat @ A_60 @ A_59 )
% 0.29/0.46 = A_59 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_264_insert__absorb,axiom,
% 0.29/0.46 ! [A_60: pname,A_59: pname > $o] :
% 0.29/0.46 ( ( member_pname @ A_60 @ A_59 )
% 0.29/0.46 => ( ( insert_pname @ A_60 @ A_59 )
% 0.29/0.46 = A_59 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_265_insert__absorb,axiom,
% 0.29/0.46 ! [A_60: x_a,A_59: x_a > $o] :
% 0.29/0.46 ( ( member_a @ A_60 @ A_59 )
% 0.29/0.46 => ( ( insert_a @ A_60 @ A_59 )
% 0.29/0.46 = A_59 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_266_subset__refl,axiom,
% 0.29/0.46 ! [A_58: pname > $o] : ( ord_less_eq_pname_o @ A_58 @ A_58 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_267_subset__refl,axiom,
% 0.29/0.46 ! [A_58: nat > $o] : ( ord_less_eq_nat_o @ A_58 @ A_58 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_268_subset__refl,axiom,
% 0.29/0.46 ! [A_58: x_a > $o] : ( ord_less_eq_a_o @ A_58 @ A_58 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_269_set__eq__subset,axiom,
% 0.29/0.46 ! [A_57: pname > $o,B_28: pname > $o] :
% 0.29/0.46 ( ( A_57 = B_28 )
% 0.29/0.46 <=> ( ( ord_less_eq_pname_o @ A_57 @ B_28 )
% 0.29/0.46 & ( ord_less_eq_pname_o @ B_28 @ A_57 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_270_set__eq__subset,axiom,
% 0.29/0.46 ! [A_57: nat > $o,B_28: nat > $o] :
% 0.29/0.46 ( ( A_57 = B_28 )
% 0.29/0.46 <=> ( ( ord_less_eq_nat_o @ A_57 @ B_28 )
% 0.29/0.46 & ( ord_less_eq_nat_o @ B_28 @ A_57 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_271_set__eq__subset,axiom,
% 0.29/0.46 ! [A_57: x_a > $o,B_28: x_a > $o] :
% 0.29/0.46 ( ( A_57 = B_28 )
% 0.29/0.46 <=> ( ( ord_less_eq_a_o @ A_57 @ B_28 )
% 0.29/0.46 & ( ord_less_eq_a_o @ B_28 @ A_57 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_272_equalityD1,axiom,
% 0.29/0.46 ! [A_56: pname > $o,B_27: pname > $o] :
% 0.29/0.46 ( ( A_56 = B_27 )
% 0.29/0.46 => ( ord_less_eq_pname_o @ A_56 @ B_27 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_273_equalityD1,axiom,
% 0.29/0.46 ! [A_56: nat > $o,B_27: nat > $o] :
% 0.29/0.46 ( ( A_56 = B_27 )
% 0.29/0.46 => ( ord_less_eq_nat_o @ A_56 @ B_27 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_274_equalityD1,axiom,
% 0.29/0.46 ! [A_56: x_a > $o,B_27: x_a > $o] :
% 0.29/0.46 ( ( A_56 = B_27 )
% 0.29/0.46 => ( ord_less_eq_a_o @ A_56 @ B_27 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_275_equalityD2,axiom,
% 0.29/0.46 ! [A_55: pname > $o,B_26: pname > $o] :
% 0.29/0.46 ( ( A_55 = B_26 )
% 0.29/0.46 => ( ord_less_eq_pname_o @ B_26 @ A_55 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_276_equalityD2,axiom,
% 0.29/0.46 ! [A_55: nat > $o,B_26: nat > $o] :
% 0.29/0.46 ( ( A_55 = B_26 )
% 0.29/0.46 => ( ord_less_eq_nat_o @ B_26 @ A_55 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_277_equalityD2,axiom,
% 0.29/0.46 ! [A_55: x_a > $o,B_26: x_a > $o] :
% 0.29/0.46 ( ( A_55 = B_26 )
% 0.29/0.46 => ( ord_less_eq_a_o @ B_26 @ A_55 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_278_in__mono,axiom,
% 0.29/0.46 ! [X_25: nat,A_54: nat > $o,B_25: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ A_54 @ B_25 )
% 0.29/0.46 => ( ( member_nat @ X_25 @ A_54 )
% 0.29/0.46 => ( member_nat @ X_25 @ B_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_279_in__mono,axiom,
% 0.29/0.46 ! [X_25: pname,A_54: pname > $o,B_25: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ A_54 @ B_25 )
% 0.29/0.46 => ( ( member_pname @ X_25 @ A_54 )
% 0.29/0.46 => ( member_pname @ X_25 @ B_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_280_in__mono,axiom,
% 0.29/0.46 ! [X_25: x_a,A_54: x_a > $o,B_25: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_54 @ B_25 )
% 0.29/0.46 => ( ( member_a @ X_25 @ A_54 )
% 0.29/0.46 => ( member_a @ X_25 @ B_25 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_281_set__rev__mp,axiom,
% 0.29/0.46 ! [B_24: nat > $o,X_24: nat,A_53: nat > $o] :
% 0.29/0.46 ( ( member_nat @ X_24 @ A_53 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ A_53 @ B_24 )
% 0.29/0.46 => ( member_nat @ X_24 @ B_24 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_282_set__rev__mp,axiom,
% 0.29/0.46 ! [B_24: pname > $o,X_24: pname,A_53: pname > $o] :
% 0.29/0.46 ( ( member_pname @ X_24 @ A_53 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ A_53 @ B_24 )
% 0.29/0.46 => ( member_pname @ X_24 @ B_24 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_283_set__rev__mp,axiom,
% 0.29/0.46 ! [B_24: x_a > $o,X_24: x_a,A_53: x_a > $o] :
% 0.29/0.46 ( ( member_a @ X_24 @ A_53 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ A_53 @ B_24 )
% 0.29/0.46 => ( member_a @ X_24 @ B_24 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_284_set__mp,axiom,
% 0.29/0.46 ! [X_23: nat,A_52: nat > $o,B_23: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ A_52 @ B_23 )
% 0.29/0.46 => ( ( member_nat @ X_23 @ A_52 )
% 0.29/0.46 => ( member_nat @ X_23 @ B_23 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_285_set__mp,axiom,
% 0.29/0.46 ! [X_23: pname,A_52: pname > $o,B_23: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ A_52 @ B_23 )
% 0.29/0.46 => ( ( member_pname @ X_23 @ A_52 )
% 0.29/0.46 => ( member_pname @ X_23 @ B_23 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_286_set__mp,axiom,
% 0.29/0.46 ! [X_23: x_a,A_52: x_a > $o,B_23: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_52 @ B_23 )
% 0.29/0.46 => ( ( member_a @ X_23 @ A_52 )
% 0.29/0.46 => ( member_a @ X_23 @ B_23 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_287_mem__def,axiom,
% 0.29/0.46 ! [X_22: nat,A_51: nat > $o] :
% 0.29/0.46 ( ( member_nat @ X_22 @ A_51 )
% 0.29/0.46 <=> ( A_51 @ X_22 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_288_mem__def,axiom,
% 0.29/0.46 ! [X_22: pname,A_51: pname > $o] :
% 0.29/0.46 ( ( member_pname @ X_22 @ A_51 )
% 0.29/0.46 <=> ( A_51 @ X_22 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_289_mem__def,axiom,
% 0.29/0.46 ! [X_22: x_a,A_51: x_a > $o] :
% 0.29/0.46 ( ( member_a @ X_22 @ A_51 )
% 0.29/0.46 <=> ( A_51 @ X_22 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_290_Collect__def,axiom,
% 0.29/0.46 ! [P_7: x_a > $o] :
% 0.29/0.46 ( ( collect_a @ P_7 )
% 0.29/0.46 = P_7 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_291_Collect__def,axiom,
% 0.29/0.46 ! [P_7: pname > $o] :
% 0.29/0.46 ( ( collect_pname @ P_7 )
% 0.29/0.46 = P_7 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_292_Collect__def,axiom,
% 0.29/0.46 ! [P_7: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( collect_nat_o @ P_7 )
% 0.29/0.46 = P_7 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_293_Collect__def,axiom,
% 0.29/0.46 ! [P_7: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( collect_pname_o @ P_7 )
% 0.29/0.46 = P_7 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_294_Collect__def,axiom,
% 0.29/0.46 ! [P_7: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( collect_a_o @ P_7 )
% 0.29/0.46 = P_7 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_295_Collect__def,axiom,
% 0.29/0.46 ! [P_7: nat > $o] :
% 0.29/0.46 ( ( collect_nat @ P_7 )
% 0.29/0.46 = P_7 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_296_subset__trans,axiom,
% 0.29/0.46 ! [C_10: pname > $o,A_50: pname > $o,B_22: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ A_50 @ B_22 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ B_22 @ C_10 )
% 0.29/0.46 => ( ord_less_eq_pname_o @ A_50 @ C_10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_297_subset__trans,axiom,
% 0.29/0.46 ! [C_10: nat > $o,A_50: nat > $o,B_22: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ A_50 @ B_22 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ B_22 @ C_10 )
% 0.29/0.46 => ( ord_less_eq_nat_o @ A_50 @ C_10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_298_subset__trans,axiom,
% 0.29/0.46 ! [C_10: x_a > $o,A_50: x_a > $o,B_22: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_50 @ B_22 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ B_22 @ C_10 )
% 0.29/0.46 => ( ord_less_eq_a_o @ A_50 @ C_10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_299_equalityE,axiom,
% 0.29/0.46 ! [A_49: pname > $o,B_21: pname > $o] :
% 0.29/0.46 ( ( A_49 = B_21 )
% 0.29/0.46 => ~ ( ( ord_less_eq_pname_o @ A_49 @ B_21 )
% 0.29/0.46 => ~ ( ord_less_eq_pname_o @ B_21 @ A_49 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_300_equalityE,axiom,
% 0.29/0.46 ! [A_49: nat > $o,B_21: nat > $o] :
% 0.29/0.46 ( ( A_49 = B_21 )
% 0.29/0.46 => ~ ( ( ord_less_eq_nat_o @ A_49 @ B_21 )
% 0.29/0.46 => ~ ( ord_less_eq_nat_o @ B_21 @ A_49 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_301_equalityE,axiom,
% 0.29/0.46 ! [A_49: x_a > $o,B_21: x_a > $o] :
% 0.29/0.46 ( ( A_49 = B_21 )
% 0.29/0.46 => ~ ( ( ord_less_eq_a_o @ A_49 @ B_21 )
% 0.29/0.46 => ~ ( ord_less_eq_a_o @ B_21 @ A_49 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_302_image__iff,axiom,
% 0.29/0.46 ! [Z_3: x_a,F_18: pname > x_a,A_48: pname > $o] :
% 0.29/0.46 ( ( member_a @ Z_3 @ ( image_pname_a @ F_18 @ A_48 ) )
% 0.29/0.46 <=> ? [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_48 )
% 0.29/0.46 & ( Z_3
% 0.29/0.46 = ( F_18 @ X_1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_303_imageI,axiom,
% 0.29/0.46 ! [F_17: pname > nat,X_21: pname,A_47: pname > $o] :
% 0.29/0.46 ( ( member_pname @ X_21 @ A_47 )
% 0.29/0.46 => ( member_nat @ ( F_17 @ X_21 ) @ ( image_pname_nat @ F_17 @ A_47 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_304_imageI,axiom,
% 0.29/0.46 ! [F_17: x_a > nat,X_21: x_a,A_47: x_a > $o] :
% 0.29/0.46 ( ( member_a @ X_21 @ A_47 )
% 0.29/0.46 => ( member_nat @ ( F_17 @ X_21 ) @ ( image_a_nat @ F_17 @ A_47 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_305_imageI,axiom,
% 0.29/0.46 ! [F_17: nat > pname,X_21: nat,A_47: nat > $o] :
% 0.29/0.46 ( ( member_nat @ X_21 @ A_47 )
% 0.29/0.46 => ( member_pname @ ( F_17 @ X_21 ) @ ( image_nat_pname @ F_17 @ A_47 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_306_imageI,axiom,
% 0.29/0.46 ! [F_17: nat > x_a,X_21: nat,A_47: nat > $o] :
% 0.29/0.46 ( ( member_nat @ X_21 @ A_47 )
% 0.29/0.46 => ( member_a @ ( F_17 @ X_21 ) @ ( image_nat_a @ F_17 @ A_47 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_307_imageI,axiom,
% 0.29/0.46 ! [F_17: pname > x_a,X_21: pname,A_47: pname > $o] :
% 0.29/0.46 ( ( member_pname @ X_21 @ A_47 )
% 0.29/0.46 => ( member_a @ ( F_17 @ X_21 ) @ ( image_pname_a @ F_17 @ A_47 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_308_rev__image__eqI,axiom,
% 0.29/0.46 ! [B_20: nat,F_16: pname > nat,X_20: pname,A_46: pname > $o] :
% 0.29/0.46 ( ( member_pname @ X_20 @ A_46 )
% 0.29/0.46 => ( ( B_20
% 0.29/0.46 = ( F_16 @ X_20 ) )
% 0.29/0.46 => ( member_nat @ B_20 @ ( image_pname_nat @ F_16 @ A_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_309_rev__image__eqI,axiom,
% 0.29/0.46 ! [B_20: nat,F_16: x_a > nat,X_20: x_a,A_46: x_a > $o] :
% 0.29/0.46 ( ( member_a @ X_20 @ A_46 )
% 0.29/0.46 => ( ( B_20
% 0.29/0.46 = ( F_16 @ X_20 ) )
% 0.29/0.46 => ( member_nat @ B_20 @ ( image_a_nat @ F_16 @ A_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_310_rev__image__eqI,axiom,
% 0.29/0.46 ! [B_20: pname,F_16: nat > pname,X_20: nat,A_46: nat > $o] :
% 0.29/0.46 ( ( member_nat @ X_20 @ A_46 )
% 0.29/0.46 => ( ( B_20
% 0.29/0.46 = ( F_16 @ X_20 ) )
% 0.29/0.46 => ( member_pname @ B_20 @ ( image_nat_pname @ F_16 @ A_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_311_rev__image__eqI,axiom,
% 0.29/0.46 ! [B_20: x_a,F_16: nat > x_a,X_20: nat,A_46: nat > $o] :
% 0.29/0.46 ( ( member_nat @ X_20 @ A_46 )
% 0.29/0.46 => ( ( B_20
% 0.29/0.46 = ( F_16 @ X_20 ) )
% 0.29/0.46 => ( member_a @ B_20 @ ( image_nat_a @ F_16 @ A_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_312_rev__image__eqI,axiom,
% 0.29/0.46 ! [B_20: x_a,F_16: pname > x_a,X_20: pname,A_46: pname > $o] :
% 0.29/0.46 ( ( member_pname @ X_20 @ A_46 )
% 0.29/0.46 => ( ( B_20
% 0.29/0.46 = ( F_16 @ X_20 ) )
% 0.29/0.46 => ( member_a @ B_20 @ ( image_pname_a @ F_16 @ A_46 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_313_insert__compr__raw,axiom,
% 0.29/0.46 ! [X_1: nat > $o,Xa: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( insert_nat_o @ X_1 @ Xa )
% 0.29/0.46 = ( collect_nat_o
% 0.29/0.46 @ ^ [Y_10: nat > $o] : ( (|) @ ( Y_10 = X_1 ) @ ( member_nat_o @ Y_10 @ Xa ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_314_insert__compr__raw,axiom,
% 0.29/0.46 ! [X_1: pname > $o,Xa: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( insert_pname_o @ X_1 @ Xa )
% 0.29/0.46 = ( collect_pname_o
% 0.29/0.46 @ ^ [Y_10: pname > $o] : ( (|) @ ( Y_10 = X_1 ) @ ( member_pname_o @ Y_10 @ Xa ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_315_insert__compr__raw,axiom,
% 0.29/0.46 ! [X_1: x_a > $o,Xa: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( insert_a_o @ X_1 @ Xa )
% 0.29/0.46 = ( collect_a_o
% 0.29/0.46 @ ^ [Y_10: x_a > $o] : ( (|) @ ( Y_10 = X_1 ) @ ( member_a_o @ Y_10 @ Xa ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_316_insert__compr__raw,axiom,
% 0.29/0.46 ! [X_1: nat,Xa: nat > $o] :
% 0.29/0.46 ( ( insert_nat @ X_1 @ Xa )
% 0.29/0.46 = ( collect_nat
% 0.29/0.46 @ ^ [Y_10: nat] : ( (|) @ ( Y_10 = X_1 ) @ ( member_nat @ Y_10 @ Xa ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_317_insert__compr__raw,axiom,
% 0.29/0.46 ! [X_1: pname,Xa: pname > $o] :
% 0.29/0.46 ( ( insert_pname @ X_1 @ Xa )
% 0.29/0.46 = ( collect_pname
% 0.29/0.46 @ ^ [Y_10: pname] : ( (|) @ ( Y_10 = X_1 ) @ ( member_pname @ Y_10 @ Xa ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_318_insert__compr__raw,axiom,
% 0.29/0.46 ! [X_1: x_a,Xa: x_a > $o] :
% 0.29/0.46 ( ( insert_a @ X_1 @ Xa )
% 0.29/0.46 = ( collect_a
% 0.29/0.46 @ ^ [Y_10: x_a] : ( (|) @ ( Y_10 = X_1 ) @ ( member_a @ Y_10 @ Xa ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_319_subset__insertI,axiom,
% 0.29/0.46 ! [B_19: pname > $o,A_45: pname] : ( ord_less_eq_pname_o @ B_19 @ ( insert_pname @ A_45 @ B_19 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_320_subset__insertI,axiom,
% 0.29/0.46 ! [B_19: nat > $o,A_45: nat] : ( ord_less_eq_nat_o @ B_19 @ ( insert_nat @ A_45 @ B_19 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_321_subset__insertI,axiom,
% 0.29/0.46 ! [B_19: x_a > $o,A_45: x_a] : ( ord_less_eq_a_o @ B_19 @ ( insert_a @ A_45 @ B_19 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_322_insert__subset,axiom,
% 0.29/0.46 ! [X_19: nat,A_44: nat > $o,B_18: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ ( insert_nat @ X_19 @ A_44 ) @ B_18 )
% 0.29/0.46 <=> ( ( member_nat @ X_19 @ B_18 )
% 0.29/0.46 & ( ord_less_eq_nat_o @ A_44 @ B_18 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_323_insert__subset,axiom,
% 0.29/0.46 ! [X_19: pname,A_44: pname > $o,B_18: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_19 @ A_44 ) @ B_18 )
% 0.29/0.46 <=> ( ( member_pname @ X_19 @ B_18 )
% 0.29/0.46 & ( ord_less_eq_pname_o @ A_44 @ B_18 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_324_insert__subset,axiom,
% 0.29/0.46 ! [X_19: x_a,A_44: x_a > $o,B_18: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ ( insert_a @ X_19 @ A_44 ) @ B_18 )
% 0.29/0.46 <=> ( ( member_a @ X_19 @ B_18 )
% 0.29/0.46 & ( ord_less_eq_a_o @ A_44 @ B_18 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_325_subset__insert,axiom,
% 0.29/0.46 ! [B_17: nat > $o,X_18: nat,A_43: nat > $o] :
% 0.29/0.46 ( ~ ( member_nat @ X_18 @ A_43 )
% 0.29/0.46 => ( ( ord_less_eq_nat_o @ A_43 @ ( insert_nat @ X_18 @ B_17 ) )
% 0.29/0.46 <=> ( ord_less_eq_nat_o @ A_43 @ B_17 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_326_subset__insert,axiom,
% 0.29/0.46 ! [B_17: pname > $o,X_18: pname,A_43: pname > $o] :
% 0.29/0.46 ( ~ ( member_pname @ X_18 @ A_43 )
% 0.29/0.46 => ( ( ord_less_eq_pname_o @ A_43 @ ( insert_pname @ X_18 @ B_17 ) )
% 0.29/0.46 <=> ( ord_less_eq_pname_o @ A_43 @ B_17 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_327_subset__insert,axiom,
% 0.29/0.46 ! [B_17: x_a > $o,X_18: x_a,A_43: x_a > $o] :
% 0.29/0.46 ( ~ ( member_a @ X_18 @ A_43 )
% 0.29/0.46 => ( ( ord_less_eq_a_o @ A_43 @ ( insert_a @ X_18 @ B_17 ) )
% 0.29/0.46 <=> ( ord_less_eq_a_o @ A_43 @ B_17 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_328_subset__insertI2,axiom,
% 0.29/0.46 ! [B_16: pname,A_42: pname > $o,B_15: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ A_42 @ B_15 )
% 0.29/0.46 => ( ord_less_eq_pname_o @ A_42 @ ( insert_pname @ B_16 @ B_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_329_subset__insertI2,axiom,
% 0.29/0.46 ! [B_16: nat,A_42: nat > $o,B_15: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ A_42 @ B_15 )
% 0.29/0.46 => ( ord_less_eq_nat_o @ A_42 @ ( insert_nat @ B_16 @ B_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_330_subset__insertI2,axiom,
% 0.29/0.46 ! [B_16: x_a,A_42: x_a > $o,B_15: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_42 @ B_15 )
% 0.29/0.46 => ( ord_less_eq_a_o @ A_42 @ ( insert_a @ B_16 @ B_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_331_insert__mono,axiom,
% 0.29/0.46 ! [A_41: pname,C_9: pname > $o,D_1: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ C_9 @ D_1 )
% 0.29/0.46 => ( ord_less_eq_pname_o @ ( insert_pname @ A_41 @ C_9 ) @ ( insert_pname @ A_41 @ D_1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_332_insert__mono,axiom,
% 0.29/0.46 ! [A_41: nat,C_9: nat > $o,D_1: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ C_9 @ D_1 )
% 0.29/0.46 => ( ord_less_eq_nat_o @ ( insert_nat @ A_41 @ C_9 ) @ ( insert_nat @ A_41 @ D_1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_333_insert__mono,axiom,
% 0.29/0.46 ! [A_41: x_a,C_9: x_a > $o,D_1: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ C_9 @ D_1 )
% 0.29/0.46 => ( ord_less_eq_a_o @ ( insert_a @ A_41 @ C_9 ) @ ( insert_a @ A_41 @ D_1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_334_image__insert,axiom,
% 0.29/0.46 ! [F_15: x_a > pname,A_40: x_a,B_14: x_a > $o] :
% 0.29/0.46 ( ( image_a_pname @ F_15 @ ( insert_a @ A_40 @ B_14 ) )
% 0.29/0.46 = ( insert_pname @ ( F_15 @ A_40 ) @ ( image_a_pname @ F_15 @ B_14 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_335_image__insert,axiom,
% 0.29/0.46 ! [F_15: x_a > nat,A_40: x_a,B_14: x_a > $o] :
% 0.29/0.46 ( ( image_a_nat @ F_15 @ ( insert_a @ A_40 @ B_14 ) )
% 0.29/0.46 = ( insert_nat @ ( F_15 @ A_40 ) @ ( image_a_nat @ F_15 @ B_14 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_336_image__insert,axiom,
% 0.29/0.46 ! [F_15: nat > x_a,A_40: nat,B_14: nat > $o] :
% 0.29/0.46 ( ( image_nat_a @ F_15 @ ( insert_nat @ A_40 @ B_14 ) )
% 0.29/0.46 = ( insert_a @ ( F_15 @ A_40 ) @ ( image_nat_a @ F_15 @ B_14 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_337_image__insert,axiom,
% 0.29/0.46 ! [F_15: pname > x_a,A_40: pname,B_14: pname > $o] :
% 0.29/0.46 ( ( image_pname_a @ F_15 @ ( insert_pname @ A_40 @ B_14 ) )
% 0.29/0.46 = ( insert_a @ ( F_15 @ A_40 ) @ ( image_pname_a @ F_15 @ B_14 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_338_insert__image,axiom,
% 0.29/0.46 ! [F_14: pname > pname,X_17: pname,A_39: pname > $o] :
% 0.29/0.46 ( ( member_pname @ X_17 @ A_39 )
% 0.29/0.46 => ( ( insert_pname @ ( F_14 @ X_17 ) @ ( image_pname_pname @ F_14 @ A_39 ) )
% 0.29/0.46 = ( image_pname_pname @ F_14 @ A_39 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_339_insert__image,axiom,
% 0.29/0.46 ! [F_14: pname > nat,X_17: pname,A_39: pname > $o] :
% 0.29/0.46 ( ( member_pname @ X_17 @ A_39 )
% 0.29/0.46 => ( ( insert_nat @ ( F_14 @ X_17 ) @ ( image_pname_nat @ F_14 @ A_39 ) )
% 0.29/0.46 = ( image_pname_nat @ F_14 @ A_39 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_340_insert__image,axiom,
% 0.29/0.46 ! [F_14: x_a > pname,X_17: x_a,A_39: x_a > $o] :
% 0.29/0.46 ( ( member_a @ X_17 @ A_39 )
% 0.29/0.46 => ( ( insert_pname @ ( F_14 @ X_17 ) @ ( image_a_pname @ F_14 @ A_39 ) )
% 0.29/0.46 = ( image_a_pname @ F_14 @ A_39 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_341_insert__image,axiom,
% 0.29/0.46 ! [F_14: x_a > nat,X_17: x_a,A_39: x_a > $o] :
% 0.29/0.46 ( ( member_a @ X_17 @ A_39 )
% 0.29/0.46 => ( ( insert_nat @ ( F_14 @ X_17 ) @ ( image_a_nat @ F_14 @ A_39 ) )
% 0.29/0.46 = ( image_a_nat @ F_14 @ A_39 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_342_insert__image,axiom,
% 0.29/0.46 ! [F_14: nat > x_a,X_17: nat,A_39: nat > $o] :
% 0.29/0.46 ( ( member_nat @ X_17 @ A_39 )
% 0.29/0.46 => ( ( insert_a @ ( F_14 @ X_17 ) @ ( image_nat_a @ F_14 @ A_39 ) )
% 0.29/0.46 = ( image_nat_a @ F_14 @ A_39 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_343_insert__image,axiom,
% 0.29/0.46 ! [F_14: pname > x_a,X_17: pname,A_39: pname > $o] :
% 0.29/0.46 ( ( member_pname @ X_17 @ A_39 )
% 0.29/0.46 => ( ( insert_a @ ( F_14 @ X_17 ) @ ( image_pname_a @ F_14 @ A_39 ) )
% 0.29/0.46 = ( image_pname_a @ F_14 @ A_39 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_344_subset__image__iff,axiom,
% 0.29/0.46 ! [B_13: x_a > $o,F_13: nat > x_a,A_38: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ B_13 @ ( image_nat_a @ F_13 @ A_38 ) )
% 0.29/0.46 <=> ? [AA: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ AA @ A_38 )
% 0.29/0.46 & ( B_13
% 0.29/0.46 = ( image_nat_a @ F_13 @ AA ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_345_subset__image__iff,axiom,
% 0.29/0.46 ! [B_13: pname > $o,F_13: x_a > pname,A_38: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ B_13 @ ( image_a_pname @ F_13 @ A_38 ) )
% 0.29/0.46 <=> ? [AA: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ AA @ A_38 )
% 0.29/0.46 & ( B_13
% 0.29/0.46 = ( image_a_pname @ F_13 @ AA ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_346_subset__image__iff,axiom,
% 0.29/0.46 ! [B_13: nat > $o,F_13: x_a > nat,A_38: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ B_13 @ ( image_a_nat @ F_13 @ A_38 ) )
% 0.29/0.46 <=> ? [AA: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ AA @ A_38 )
% 0.29/0.46 & ( B_13
% 0.29/0.46 = ( image_a_nat @ F_13 @ AA ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_347_subset__image__iff,axiom,
% 0.29/0.46 ! [B_13: x_a > $o,F_13: pname > x_a,A_38: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ B_13 @ ( image_pname_a @ F_13 @ A_38 ) )
% 0.29/0.46 <=> ? [AA: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ AA @ A_38 )
% 0.29/0.46 & ( B_13
% 0.29/0.46 = ( image_pname_a @ F_13 @ AA ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_348_image__mono,axiom,
% 0.29/0.46 ! [F_12: x_a > pname,A_37: x_a > $o,B_12: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_37 @ B_12 )
% 0.29/0.46 => ( ord_less_eq_pname_o @ ( image_a_pname @ F_12 @ A_37 ) @ ( image_a_pname @ F_12 @ B_12 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_349_image__mono,axiom,
% 0.29/0.46 ! [F_12: x_a > nat,A_37: x_a > $o,B_12: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_37 @ B_12 )
% 0.29/0.46 => ( ord_less_eq_nat_o @ ( image_a_nat @ F_12 @ A_37 ) @ ( image_a_nat @ F_12 @ B_12 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_350_image__mono,axiom,
% 0.29/0.46 ! [F_12: nat > x_a,A_37: nat > $o,B_12: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ A_37 @ B_12 )
% 0.29/0.46 => ( ord_less_eq_a_o @ ( image_nat_a @ F_12 @ A_37 ) @ ( image_nat_a @ F_12 @ B_12 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_351_image__mono,axiom,
% 0.29/0.46 ! [F_12: pname > x_a,A_37: pname > $o,B_12: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ A_37 @ B_12 )
% 0.29/0.46 => ( ord_less_eq_a_o @ ( image_pname_a @ F_12 @ A_37 ) @ ( image_pname_a @ F_12 @ B_12 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_352_imageE,axiom,
% 0.29/0.46 ! [B_11: pname,F_11: nat > pname,A_36: nat > $o] :
% 0.29/0.46 ( ( member_pname @ B_11 @ ( image_nat_pname @ F_11 @ A_36 ) )
% 0.29/0.46 => ~ ! [X_1: nat] :
% 0.29/0.46 ( ( B_11
% 0.29/0.46 = ( F_11 @ X_1 ) )
% 0.29/0.46 => ~ ( member_nat @ X_1 @ A_36 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_353_imageE,axiom,
% 0.29/0.46 ! [B_11: x_a,F_11: nat > x_a,A_36: nat > $o] :
% 0.29/0.46 ( ( member_a @ B_11 @ ( image_nat_a @ F_11 @ A_36 ) )
% 0.29/0.46 => ~ ! [X_1: nat] :
% 0.29/0.46 ( ( B_11
% 0.29/0.46 = ( F_11 @ X_1 ) )
% 0.29/0.46 => ~ ( member_nat @ X_1 @ A_36 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_354_imageE,axiom,
% 0.29/0.46 ! [B_11: nat,F_11: pname > nat,A_36: pname > $o] :
% 0.29/0.46 ( ( member_nat @ B_11 @ ( image_pname_nat @ F_11 @ A_36 ) )
% 0.29/0.46 => ~ ! [X_1: pname] :
% 0.29/0.46 ( ( B_11
% 0.29/0.46 = ( F_11 @ X_1 ) )
% 0.29/0.46 => ~ ( member_pname @ X_1 @ A_36 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_355_imageE,axiom,
% 0.29/0.46 ! [B_11: nat,F_11: x_a > nat,A_36: x_a > $o] :
% 0.29/0.46 ( ( member_nat @ B_11 @ ( image_a_nat @ F_11 @ A_36 ) )
% 0.29/0.46 => ~ ! [X_1: x_a] :
% 0.29/0.46 ( ( B_11
% 0.29/0.46 = ( F_11 @ X_1 ) )
% 0.29/0.46 => ~ ( member_a @ X_1 @ A_36 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_356_imageE,axiom,
% 0.29/0.46 ! [B_11: x_a,F_11: pname > x_a,A_36: pname > $o] :
% 0.29/0.46 ( ( member_a @ B_11 @ ( image_pname_a @ F_11 @ A_36 ) )
% 0.29/0.46 => ~ ! [X_1: pname] :
% 0.29/0.46 ( ( B_11
% 0.29/0.46 = ( F_11 @ X_1 ) )
% 0.29/0.46 => ~ ( member_pname @ X_1 @ A_36 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_357_subsetI,axiom,
% 0.29/0.46 ! [B_10: nat > $o,A_35: nat > $o] :
% 0.29/0.46 ( ! [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ A_35 )
% 0.29/0.46 => ( member_nat @ X_1 @ B_10 ) )
% 0.29/0.46 => ( ord_less_eq_nat_o @ A_35 @ B_10 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_358_subsetI,axiom,
% 0.29/0.46 ! [B_10: pname > $o,A_35: pname > $o] :
% 0.29/0.46 ( ! [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_35 )
% 0.29/0.46 => ( member_pname @ X_1 @ B_10 ) )
% 0.29/0.46 => ( ord_less_eq_pname_o @ A_35 @ B_10 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_359_subsetI,axiom,
% 0.29/0.46 ! [B_10: x_a > $o,A_35: x_a > $o] :
% 0.29/0.46 ( ! [X_1: x_a] :
% 0.29/0.46 ( ( member_a @ X_1 @ A_35 )
% 0.29/0.46 => ( member_a @ X_1 @ B_10 ) )
% 0.29/0.46 => ( ord_less_eq_a_o @ A_35 @ B_10 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_360_image__subsetI,axiom,
% 0.29/0.46 ! [F_10: pname > nat,B_9: nat > $o,A_34: pname > $o] :
% 0.29/0.46 ( ! [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_34 )
% 0.29/0.46 => ( member_nat @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.29/0.46 => ( ord_less_eq_nat_o @ ( image_pname_nat @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_361_image__subsetI,axiom,
% 0.29/0.46 ! [F_10: pname > pname,B_9: pname > $o,A_34: pname > $o] :
% 0.29/0.46 ( ! [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_34 )
% 0.29/0.46 => ( member_pname @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.29/0.46 => ( ord_less_eq_pname_o @ ( image_pname_pname @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_362_image__subsetI,axiom,
% 0.29/0.46 ! [F_10: x_a > nat,B_9: nat > $o,A_34: x_a > $o] :
% 0.29/0.46 ( ! [X_1: x_a] :
% 0.29/0.46 ( ( member_a @ X_1 @ A_34 )
% 0.29/0.46 => ( member_nat @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.29/0.46 => ( ord_less_eq_nat_o @ ( image_a_nat @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_363_image__subsetI,axiom,
% 0.29/0.46 ! [F_10: x_a > pname,B_9: pname > $o,A_34: x_a > $o] :
% 0.29/0.46 ( ! [X_1: x_a] :
% 0.29/0.46 ( ( member_a @ X_1 @ A_34 )
% 0.29/0.46 => ( member_pname @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.29/0.46 => ( ord_less_eq_pname_o @ ( image_a_pname @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_364_image__subsetI,axiom,
% 0.29/0.46 ! [F_10: nat > pname,B_9: pname > $o,A_34: nat > $o] :
% 0.29/0.46 ( ! [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ A_34 )
% 0.29/0.46 => ( member_pname @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.29/0.46 => ( ord_less_eq_pname_o @ ( image_nat_pname @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_365_image__subsetI,axiom,
% 0.29/0.46 ! [F_10: nat > x_a,B_9: x_a > $o,A_34: nat > $o] :
% 0.29/0.46 ( ! [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ A_34 )
% 0.29/0.46 => ( member_a @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.29/0.46 => ( ord_less_eq_a_o @ ( image_nat_a @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_366_image__subsetI,axiom,
% 0.29/0.46 ! [F_10: pname > x_a,B_9: x_a > $o,A_34: pname > $o] :
% 0.29/0.46 ( ! [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ A_34 )
% 0.29/0.46 => ( member_a @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.29/0.46 => ( ord_less_eq_a_o @ ( image_pname_a @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_367_order__refl,axiom,
% 0.29/0.46 ! [X_16: $o] : ( ord_less_eq_o @ X_16 @ X_16 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_368_order__refl,axiom,
% 0.29/0.46 ! [X_16: pname > $o] : ( ord_less_eq_pname_o @ X_16 @ X_16 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_369_order__refl,axiom,
% 0.29/0.46 ! [X_16: nat > $o] : ( ord_less_eq_nat_o @ X_16 @ X_16 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_370_order__refl,axiom,
% 0.29/0.46 ! [X_16: x_a > $o] : ( ord_less_eq_a_o @ X_16 @ X_16 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_371_order__refl,axiom,
% 0.29/0.46 ! [X_16: nat] : ( ord_less_eq_nat @ X_16 @ X_16 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_372_finite__nat__set__iff__bounded__le,axiom,
% 0.29/0.46 ! [N_1: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ N_1 )
% 0.29/0.46 <=> ? [M_1: nat] :
% 0.29/0.46 ! [X_1: nat] :
% 0.29/0.46 ( ( member_nat @ X_1 @ N_1 )
% 0.29/0.46 => ( ord_less_eq_nat @ X_1 @ M_1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_373_assms_I3_J,axiom,
% 0.29/0.46 ! [G: x_a > $o,C: com] :
% 0.29/0.46 ( ( wt @ C )
% 0.29/0.46 => ( ! [X_1: pname] :
% 0.29/0.46 ( ( member_pname @ X_1 @ u )
% 0.29/0.46 => ( p @ G @ ( insert_a @ ( mgt_call @ X_1 ) @ bot_bot_a_o ) ) )
% 0.29/0.46 => ( p @ G @ ( insert_a @ ( mgt @ C ) @ bot_bot_a_o ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_374_le__fun__def,axiom,
% 0.29/0.46 ! [F_9: pname > $o,G_3: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ F_9 @ G_3 )
% 0.29/0.46 <=> ! [X_1: pname] : ( ord_less_eq_o @ ( F_9 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_375_le__fun__def,axiom,
% 0.29/0.46 ! [F_9: nat > $o,G_3: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ F_9 @ G_3 )
% 0.29/0.46 <=> ! [X_1: nat] : ( ord_less_eq_o @ ( F_9 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_376_le__fun__def,axiom,
% 0.29/0.46 ! [F_9: x_a > $o,G_3: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ F_9 @ G_3 )
% 0.29/0.46 <=> ! [X_1: x_a] : ( ord_less_eq_o @ ( F_9 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_377_le__funD,axiom,
% 0.29/0.46 ! [X_15: pname,F_8: pname > $o,G_2: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ F_8 @ G_2 )
% 0.29/0.46 => ( ord_less_eq_o @ ( F_8 @ X_15 ) @ ( G_2 @ X_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_378_le__funD,axiom,
% 0.29/0.46 ! [X_15: nat,F_8: nat > $o,G_2: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ F_8 @ G_2 )
% 0.29/0.46 => ( ord_less_eq_o @ ( F_8 @ X_15 ) @ ( G_2 @ X_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_379_le__funD,axiom,
% 0.29/0.46 ! [X_15: x_a,F_8: x_a > $o,G_2: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ F_8 @ G_2 )
% 0.29/0.46 => ( ord_less_eq_o @ ( F_8 @ X_15 ) @ ( G_2 @ X_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_380_le__funE,axiom,
% 0.29/0.46 ! [X_14: pname,F_7: pname > $o,G_1: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ F_7 @ G_1 )
% 0.29/0.46 => ( ord_less_eq_o @ ( F_7 @ X_14 ) @ ( G_1 @ X_14 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_381_le__funE,axiom,
% 0.29/0.46 ! [X_14: nat,F_7: nat > $o,G_1: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ F_7 @ G_1 )
% 0.29/0.46 => ( ord_less_eq_o @ ( F_7 @ X_14 ) @ ( G_1 @ X_14 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_382_le__funE,axiom,
% 0.29/0.46 ! [X_14: x_a,F_7: x_a > $o,G_1: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ F_7 @ G_1 )
% 0.29/0.46 => ( ord_less_eq_o @ ( F_7 @ X_14 ) @ ( G_1 @ X_14 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_383_emptyE,axiom,
% 0.29/0.46 ! [A_33: nat] :
% 0.29/0.46 ~ ( member_nat @ A_33 @ bot_bot_nat_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_384_emptyE,axiom,
% 0.29/0.46 ! [A_33: pname] :
% 0.29/0.46 ~ ( member_pname @ A_33 @ bot_bot_pname_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_385_emptyE,axiom,
% 0.29/0.46 ! [A_33: x_a] :
% 0.29/0.46 ~ ( member_a @ A_33 @ bot_bot_a_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_386_finite_OemptyI,axiom,
% 0.29/0.46 finite_finite_nat_o @ bot_bot_nat_o_o ).
% 0.29/0.46
% 0.29/0.46 thf(fact_387_finite_OemptyI,axiom,
% 0.29/0.46 finite297249702name_o @ bot_bot_pname_o_o ).
% 0.29/0.46
% 0.29/0.46 thf(fact_388_finite_OemptyI,axiom,
% 0.29/0.46 finite_finite_a_o @ bot_bot_a_o_o ).
% 0.29/0.46
% 0.29/0.46 thf(fact_389_finite_OemptyI,axiom,
% 0.29/0.46 finite_finite_a @ bot_bot_a_o ).
% 0.29/0.46
% 0.29/0.46 thf(fact_390_finite_OemptyI,axiom,
% 0.29/0.46 finite_finite_pname @ bot_bot_pname_o ).
% 0.29/0.46
% 0.29/0.46 thf(fact_391_finite_OemptyI,axiom,
% 0.29/0.46 finite_finite_nat @ bot_bot_nat_o ).
% 0.29/0.46
% 0.29/0.46 thf(fact_392_empty__subsetI,axiom,
% 0.29/0.46 ! [A_32: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_32 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_393_empty__subsetI,axiom,
% 0.29/0.46 ! [A_32: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A_32 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_394_empty__subsetI,axiom,
% 0.29/0.46 ! [A_32: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A_32 ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_395_equals0D,axiom,
% 0.29/0.46 ! [A_31: nat,A_30: nat > $o] :
% 0.29/0.46 ( ( A_30 = bot_bot_nat_o )
% 0.29/0.46 => ~ ( member_nat @ A_31 @ A_30 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_396_equals0D,axiom,
% 0.29/0.46 ! [A_31: pname,A_30: pname > $o] :
% 0.29/0.46 ( ( A_30 = bot_bot_pname_o )
% 0.29/0.46 => ~ ( member_pname @ A_31 @ A_30 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_397_equals0D,axiom,
% 0.29/0.46 ! [A_31: x_a,A_30: x_a > $o] :
% 0.29/0.46 ( ( A_30 = bot_bot_a_o )
% 0.29/0.46 => ~ ( member_a @ A_31 @ A_30 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_398_Collect__empty__eq,axiom,
% 0.29/0.46 ! [P_6: pname > $o] :
% 0.29/0.46 ( ( ( collect_pname @ P_6 )
% 0.29/0.46 = bot_bot_pname_o )
% 0.29/0.46 <=> ! [X_1: pname] :
% 0.29/0.46 ~ ( P_6 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_399_Collect__empty__eq,axiom,
% 0.29/0.46 ! [P_6: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( ( collect_nat_o @ P_6 )
% 0.29/0.46 = bot_bot_nat_o_o )
% 0.29/0.46 <=> ! [X_1: nat > $o] :
% 0.29/0.46 ~ ( P_6 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_400_Collect__empty__eq,axiom,
% 0.29/0.46 ! [P_6: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( ( collect_pname_o @ P_6 )
% 0.29/0.46 = bot_bot_pname_o_o )
% 0.29/0.46 <=> ! [X_1: pname > $o] :
% 0.29/0.46 ~ ( P_6 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_401_Collect__empty__eq,axiom,
% 0.29/0.46 ! [P_6: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( ( collect_a_o @ P_6 )
% 0.29/0.46 = bot_bot_a_o_o )
% 0.29/0.46 <=> ! [X_1: x_a > $o] :
% 0.29/0.46 ~ ( P_6 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_402_Collect__empty__eq,axiom,
% 0.29/0.46 ! [P_6: x_a > $o] :
% 0.29/0.46 ( ( ( collect_a @ P_6 )
% 0.29/0.46 = bot_bot_a_o )
% 0.29/0.46 <=> ! [X_1: x_a] :
% 0.29/0.46 ~ ( P_6 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_403_Collect__empty__eq,axiom,
% 0.29/0.46 ! [P_6: nat > $o] :
% 0.29/0.46 ( ( ( collect_nat @ P_6 )
% 0.29/0.46 = bot_bot_nat_o )
% 0.29/0.46 <=> ! [X_1: nat] :
% 0.29/0.46 ~ ( P_6 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_404_empty__iff,axiom,
% 0.29/0.46 ! [C_8: nat] :
% 0.29/0.46 ~ ( member_nat @ C_8 @ bot_bot_nat_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_405_empty__iff,axiom,
% 0.29/0.46 ! [C_8: pname] :
% 0.29/0.46 ~ ( member_pname @ C_8 @ bot_bot_pname_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_406_empty__iff,axiom,
% 0.29/0.46 ! [C_8: x_a] :
% 0.29/0.46 ~ ( member_a @ C_8 @ bot_bot_a_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_407_empty__Collect__eq,axiom,
% 0.29/0.46 ! [P_5: pname > $o] :
% 0.29/0.46 ( ( bot_bot_pname_o
% 0.29/0.46 = ( collect_pname @ P_5 ) )
% 0.29/0.46 <=> ! [X_1: pname] :
% 0.29/0.46 ~ ( P_5 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_408_empty__Collect__eq,axiom,
% 0.29/0.46 ! [P_5: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( bot_bot_nat_o_o
% 0.29/0.46 = ( collect_nat_o @ P_5 ) )
% 0.29/0.46 <=> ! [X_1: nat > $o] :
% 0.29/0.46 ~ ( P_5 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_409_empty__Collect__eq,axiom,
% 0.29/0.46 ! [P_5: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( bot_bot_pname_o_o
% 0.29/0.46 = ( collect_pname_o @ P_5 ) )
% 0.29/0.46 <=> ! [X_1: pname > $o] :
% 0.29/0.46 ~ ( P_5 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_410_empty__Collect__eq,axiom,
% 0.29/0.46 ! [P_5: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( bot_bot_a_o_o
% 0.29/0.46 = ( collect_a_o @ P_5 ) )
% 0.29/0.46 <=> ! [X_1: x_a > $o] :
% 0.29/0.46 ~ ( P_5 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_411_empty__Collect__eq,axiom,
% 0.29/0.46 ! [P_5: x_a > $o] :
% 0.29/0.46 ( ( bot_bot_a_o
% 0.29/0.46 = ( collect_a @ P_5 ) )
% 0.29/0.46 <=> ! [X_1: x_a] :
% 0.29/0.46 ~ ( P_5 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_412_empty__Collect__eq,axiom,
% 0.29/0.46 ! [P_5: nat > $o] :
% 0.29/0.46 ( ( bot_bot_nat_o
% 0.29/0.46 = ( collect_nat @ P_5 ) )
% 0.29/0.46 <=> ! [X_1: nat] :
% 0.29/0.46 ~ ( P_5 @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_413_ex__in__conv,axiom,
% 0.29/0.46 ! [A_29: nat > $o] :
% 0.29/0.46 ( ? [X_1: nat] : ( member_nat @ X_1 @ A_29 )
% 0.29/0.46 <=> ( A_29 != bot_bot_nat_o ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_414_ex__in__conv,axiom,
% 0.29/0.46 ! [A_29: pname > $o] :
% 0.29/0.46 ( ? [X_1: pname] : ( member_pname @ X_1 @ A_29 )
% 0.29/0.46 <=> ( A_29 != bot_bot_pname_o ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_415_ex__in__conv,axiom,
% 0.29/0.46 ! [A_29: x_a > $o] :
% 0.29/0.46 ( ? [X_1: x_a] : ( member_a @ X_1 @ A_29 )
% 0.29/0.46 <=> ( A_29 != bot_bot_a_o ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_416_all__not__in__conv,axiom,
% 0.29/0.46 ! [A_28: nat > $o] :
% 0.29/0.46 ( ! [X_1: nat] :
% 0.29/0.46 ~ ( member_nat @ X_1 @ A_28 )
% 0.29/0.46 <=> ( A_28 = bot_bot_nat_o ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_417_all__not__in__conv,axiom,
% 0.29/0.46 ! [A_28: pname > $o] :
% 0.29/0.46 ( ! [X_1: pname] :
% 0.29/0.46 ~ ( member_pname @ X_1 @ A_28 )
% 0.29/0.46 <=> ( A_28 = bot_bot_pname_o ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_418_all__not__in__conv,axiom,
% 0.29/0.46 ! [A_28: x_a > $o] :
% 0.29/0.46 ( ! [X_1: x_a] :
% 0.29/0.46 ~ ( member_a @ X_1 @ A_28 )
% 0.29/0.46 <=> ( A_28 = bot_bot_a_o ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_419_empty__def,axiom,
% 0.29/0.46 ( bot_bot_pname_o
% 0.29/0.46 = ( collect_pname
% 0.29/0.46 @ ^ [X_1: pname] : $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_420_empty__def,axiom,
% 0.29/0.46 ( bot_bot_nat_o_o
% 0.29/0.46 = ( collect_nat_o
% 0.29/0.46 @ ^ [X_1: nat > $o] : $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_421_empty__def,axiom,
% 0.29/0.46 ( bot_bot_pname_o_o
% 0.29/0.46 = ( collect_pname_o
% 0.29/0.46 @ ^ [X_1: pname > $o] : $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_422_empty__def,axiom,
% 0.29/0.46 ( bot_bot_a_o_o
% 0.29/0.46 = ( collect_a_o
% 0.29/0.46 @ ^ [X_1: x_a > $o] : $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_423_empty__def,axiom,
% 0.29/0.46 ( bot_bot_a_o
% 0.29/0.46 = ( collect_a
% 0.29/0.46 @ ^ [X_1: x_a] : $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_424_empty__def,axiom,
% 0.29/0.46 ( bot_bot_nat_o
% 0.29/0.46 = ( collect_nat
% 0.29/0.46 @ ^ [X_1: nat] : $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_425_bot__fun__def,axiom,
% 0.29/0.46 ! [X_1: pname] :
% 0.29/0.46 ( ( bot_bot_pname_o @ X_1 )
% 0.29/0.46 <=> bot_bot_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_426_bot__fun__def,axiom,
% 0.29/0.46 ! [X_1: nat] :
% 0.29/0.46 ( ( bot_bot_nat_o @ X_1 )
% 0.29/0.46 <=> bot_bot_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_427_bot__fun__def,axiom,
% 0.29/0.46 ! [X_1: x_a] :
% 0.29/0.46 ( ( bot_bot_a_o @ X_1 )
% 0.29/0.46 <=> bot_bot_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_428_bot__apply,axiom,
% 0.29/0.46 ! [X_13: pname] :
% 0.29/0.46 ( ( bot_bot_pname_o @ X_13 )
% 0.29/0.46 <=> bot_bot_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_429_bot__apply,axiom,
% 0.29/0.46 ! [X_13: nat] :
% 0.29/0.46 ( ( bot_bot_nat_o @ X_13 )
% 0.29/0.46 <=> bot_bot_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_430_bot__apply,axiom,
% 0.29/0.46 ! [X_13: x_a] :
% 0.29/0.46 ( ( bot_bot_a_o @ X_13 )
% 0.29/0.46 <=> bot_bot_o ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_431_le__bot,axiom,
% 0.29/0.46 ! [A_27: pname > $o] :
% 0.29/0.46 ( ( ord_less_eq_pname_o @ A_27 @ bot_bot_pname_o )
% 0.29/0.46 => ( A_27 = bot_bot_pname_o ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_432_le__bot,axiom,
% 0.29/0.46 ! [A_27: $o] :
% 0.29/0.46 ( ( ord_less_eq_o @ A_27 @ bot_bot_o )
% 0.29/0.46 => ( A_27
% 0.29/0.46 <=> bot_bot_o ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_433_le__bot,axiom,
% 0.29/0.46 ! [A_27: nat > $o] :
% 0.29/0.46 ( ( ord_less_eq_nat_o @ A_27 @ bot_bot_nat_o )
% 0.29/0.46 => ( A_27 = bot_bot_nat_o ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_434_le__bot,axiom,
% 0.29/0.46 ! [A_27: x_a > $o] :
% 0.29/0.46 ( ( ord_less_eq_a_o @ A_27 @ bot_bot_a_o )
% 0.29/0.46 => ( A_27 = bot_bot_a_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_435_le__bot,axiom,
% 0.29/0.47 ! [A_27: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A_27 @ bot_bot_nat )
% 0.29/0.47 => ( A_27 = bot_bot_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_436_bot__unique,axiom,
% 0.29/0.47 ! [A_26: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_26 @ bot_bot_pname_o )
% 0.29/0.47 <=> ( A_26 = bot_bot_pname_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_437_bot__unique,axiom,
% 0.29/0.47 ! [A_26: $o] :
% 0.29/0.47 ( ( ord_less_eq_o @ A_26 @ bot_bot_o )
% 0.29/0.47 <=> ( A_26
% 0.29/0.47 <=> bot_bot_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_438_bot__unique,axiom,
% 0.29/0.47 ! [A_26: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_26 @ bot_bot_nat_o )
% 0.29/0.47 <=> ( A_26 = bot_bot_nat_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_439_bot__unique,axiom,
% 0.29/0.47 ! [A_26: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_26 @ bot_bot_a_o )
% 0.29/0.47 <=> ( A_26 = bot_bot_a_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_440_bot__unique,axiom,
% 0.29/0.47 ! [A_26: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A_26 @ bot_bot_nat )
% 0.29/0.47 <=> ( A_26 = bot_bot_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_441_bot__least,axiom,
% 0.29/0.47 ! [A_25: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_25 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_442_bot__least,axiom,
% 0.29/0.47 ! [A_25: $o] : ( ord_less_eq_o @ bot_bot_o @ A_25 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_443_bot__least,axiom,
% 0.29/0.47 ! [A_25: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A_25 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_444_bot__least,axiom,
% 0.29/0.47 ! [A_25: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A_25 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_445_bot__least,axiom,
% 0.29/0.47 ! [A_25: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A_25 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_446_singleton__inject,axiom,
% 0.29/0.47 ! [A_24: pname,B_8: pname] :
% 0.29/0.47 ( ( ( insert_pname @ A_24 @ bot_bot_pname_o )
% 0.29/0.47 = ( insert_pname @ B_8 @ bot_bot_pname_o ) )
% 0.29/0.47 => ( A_24 = B_8 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_447_singleton__inject,axiom,
% 0.29/0.47 ! [A_24: nat,B_8: nat] :
% 0.29/0.47 ( ( ( insert_nat @ A_24 @ bot_bot_nat_o )
% 0.29/0.47 = ( insert_nat @ B_8 @ bot_bot_nat_o ) )
% 0.29/0.47 => ( A_24 = B_8 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_448_singleton__inject,axiom,
% 0.29/0.47 ! [A_24: x_a,B_8: x_a] :
% 0.29/0.47 ( ( ( insert_a @ A_24 @ bot_bot_a_o )
% 0.29/0.47 = ( insert_a @ B_8 @ bot_bot_a_o ) )
% 0.29/0.47 => ( A_24 = B_8 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_449_singletonE,axiom,
% 0.29/0.47 ! [B_7: nat,A_23: nat] :
% 0.29/0.47 ( ( member_nat @ B_7 @ ( insert_nat @ A_23 @ bot_bot_nat_o ) )
% 0.29/0.47 => ( B_7 = A_23 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_450_singletonE,axiom,
% 0.29/0.47 ! [B_7: pname,A_23: pname] :
% 0.29/0.47 ( ( member_pname @ B_7 @ ( insert_pname @ A_23 @ bot_bot_pname_o ) )
% 0.29/0.47 => ( B_7 = A_23 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_451_singletonE,axiom,
% 0.29/0.47 ! [B_7: x_a,A_23: x_a] :
% 0.29/0.47 ( ( member_a @ B_7 @ ( insert_a @ A_23 @ bot_bot_a_o ) )
% 0.29/0.47 => ( B_7 = A_23 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_452_doubleton__eq__iff,axiom,
% 0.29/0.47 ! [A_22: pname,B_6: pname,C_7: pname,D: pname] :
% 0.29/0.47 ( ( ( insert_pname @ A_22 @ ( insert_pname @ B_6 @ bot_bot_pname_o ) )
% 0.29/0.47 = ( insert_pname @ C_7 @ ( insert_pname @ D @ bot_bot_pname_o ) ) )
% 0.29/0.47 <=> ( ( ( A_22 = C_7 )
% 0.29/0.47 & ( B_6 = D ) )
% 0.29/0.47 | ( ( A_22 = D )
% 0.29/0.47 & ( B_6 = C_7 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_453_doubleton__eq__iff,axiom,
% 0.29/0.47 ! [A_22: nat,B_6: nat,C_7: nat,D: nat] :
% 0.29/0.47 ( ( ( insert_nat @ A_22 @ ( insert_nat @ B_6 @ bot_bot_nat_o ) )
% 0.29/0.47 = ( insert_nat @ C_7 @ ( insert_nat @ D @ bot_bot_nat_o ) ) )
% 0.29/0.47 <=> ( ( ( A_22 = C_7 )
% 0.29/0.47 & ( B_6 = D ) )
% 0.29/0.47 | ( ( A_22 = D )
% 0.29/0.47 & ( B_6 = C_7 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_454_doubleton__eq__iff,axiom,
% 0.29/0.47 ! [A_22: x_a,B_6: x_a,C_7: x_a,D: x_a] :
% 0.29/0.47 ( ( ( insert_a @ A_22 @ ( insert_a @ B_6 @ bot_bot_a_o ) )
% 0.29/0.47 = ( insert_a @ C_7 @ ( insert_a @ D @ bot_bot_a_o ) ) )
% 0.29/0.47 <=> ( ( ( A_22 = C_7 )
% 0.29/0.47 & ( B_6 = D ) )
% 0.29/0.47 | ( ( A_22 = D )
% 0.29/0.47 & ( B_6 = C_7 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_455_singleton__iff,axiom,
% 0.29/0.47 ! [B_5: nat,A_21: nat] :
% 0.29/0.47 ( ( member_nat @ B_5 @ ( insert_nat @ A_21 @ bot_bot_nat_o ) )
% 0.29/0.47 <=> ( B_5 = A_21 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_456_singleton__iff,axiom,
% 0.29/0.47 ! [B_5: pname,A_21: pname] :
% 0.29/0.47 ( ( member_pname @ B_5 @ ( insert_pname @ A_21 @ bot_bot_pname_o ) )
% 0.29/0.47 <=> ( B_5 = A_21 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_457_singleton__iff,axiom,
% 0.29/0.47 ! [B_5: x_a,A_21: x_a] :
% 0.29/0.47 ( ( member_a @ B_5 @ ( insert_a @ A_21 @ bot_bot_a_o ) )
% 0.29/0.47 <=> ( B_5 = A_21 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_458_insert__not__empty,axiom,
% 0.29/0.47 ! [A_20: pname,A_19: pname > $o] :
% 0.29/0.47 ( ( insert_pname @ A_20 @ A_19 )
% 0.29/0.47 != bot_bot_pname_o ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_459_insert__not__empty,axiom,
% 0.29/0.47 ! [A_20: nat,A_19: nat > $o] :
% 0.29/0.47 ( ( insert_nat @ A_20 @ A_19 )
% 0.29/0.47 != bot_bot_nat_o ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_460_insert__not__empty,axiom,
% 0.29/0.47 ! [A_20: x_a,A_19: x_a > $o] :
% 0.29/0.47 ( ( insert_a @ A_20 @ A_19 )
% 0.29/0.47 != bot_bot_a_o ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_461_empty__not__insert,axiom,
% 0.29/0.47 ! [A_18: pname,A_17: pname > $o] :
% 0.29/0.47 ( bot_bot_pname_o
% 0.29/0.47 != ( insert_pname @ A_18 @ A_17 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_462_empty__not__insert,axiom,
% 0.29/0.47 ! [A_18: nat,A_17: nat > $o] :
% 0.29/0.47 ( bot_bot_nat_o
% 0.29/0.47 != ( insert_nat @ A_18 @ A_17 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_463_empty__not__insert,axiom,
% 0.29/0.47 ! [A_18: x_a,A_17: x_a > $o] :
% 0.29/0.47 ( bot_bot_a_o
% 0.29/0.47 != ( insert_a @ A_18 @ A_17 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_464_subset__empty,axiom,
% 0.29/0.47 ! [A_16: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_16 @ bot_bot_nat_o )
% 0.29/0.47 <=> ( A_16 = bot_bot_nat_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_465_subset__empty,axiom,
% 0.29/0.47 ! [A_16: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_16 @ bot_bot_pname_o )
% 0.29/0.47 <=> ( A_16 = bot_bot_pname_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_466_subset__empty,axiom,
% 0.29/0.47 ! [A_16: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_16 @ bot_bot_a_o )
% 0.29/0.47 <=> ( A_16 = bot_bot_a_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_467_image__is__empty,axiom,
% 0.29/0.47 ! [F_6: pname > x_a,A_15: pname > $o] :
% 0.29/0.47 ( ( ( image_pname_a @ F_6 @ A_15 )
% 0.29/0.47 = bot_bot_a_o )
% 0.29/0.47 <=> ( A_15 = bot_bot_pname_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_468_image__empty,axiom,
% 0.29/0.47 ! [F_5: pname > x_a] :
% 0.29/0.47 ( ( image_pname_a @ F_5 @ bot_bot_pname_o )
% 0.29/0.47 = bot_bot_a_o ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_469_empty__is__image,axiom,
% 0.29/0.47 ! [F_4: pname > x_a,A_14: pname > $o] :
% 0.29/0.47 ( ( bot_bot_a_o
% 0.29/0.47 = ( image_pname_a @ F_4 @ A_14 ) )
% 0.29/0.47 <=> ( A_14 = bot_bot_pname_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_470_Collect__conv__if,axiom,
% 0.29/0.47 ! [P_4: nat > $o,A_13: nat] :
% 0.29/0.47 ( ( ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_nat
% 0.29/0.47 @ ^ [X_1: nat] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = ( insert_nat @ A_13 @ bot_bot_nat_o ) ) )
% 0.29/0.47 & ( ~ ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_nat
% 0.29/0.47 @ ^ [X_1: nat] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_nat_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_471_Collect__conv__if,axiom,
% 0.29/0.47 ! [P_4: pname > $o,A_13: pname] :
% 0.29/0.47 ( ( ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_pname
% 0.29/0.47 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = ( insert_pname @ A_13 @ bot_bot_pname_o ) ) )
% 0.29/0.47 & ( ~ ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_pname
% 0.29/0.47 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_pname_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_472_Collect__conv__if,axiom,
% 0.29/0.47 ! [P_4: x_a > $o,A_13: x_a] :
% 0.29/0.47 ( ( ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_a
% 0.29/0.47 @ ^ [X_1: x_a] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = ( insert_a @ A_13 @ bot_bot_a_o ) ) )
% 0.29/0.47 & ( ~ ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_a
% 0.29/0.47 @ ^ [X_1: x_a] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_a_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_473_Collect__conv__if,axiom,
% 0.29/0.47 ! [P_4: ( nat > $o ) > $o,A_13: nat > $o] :
% 0.29/0.47 ( ( ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_nat_o
% 0.29/0.47 @ ^ [X_1: nat > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = ( insert_nat_o @ A_13 @ bot_bot_nat_o_o ) ) )
% 0.29/0.47 & ( ~ ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_nat_o
% 0.29/0.47 @ ^ [X_1: nat > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_nat_o_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_474_Collect__conv__if,axiom,
% 0.29/0.47 ! [P_4: ( pname > $o ) > $o,A_13: pname > $o] :
% 0.29/0.47 ( ( ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_pname_o
% 0.29/0.47 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = ( insert_pname_o @ A_13 @ bot_bot_pname_o_o ) ) )
% 0.29/0.47 & ( ~ ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_pname_o
% 0.29/0.47 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_pname_o_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_475_Collect__conv__if,axiom,
% 0.29/0.47 ! [P_4: ( x_a > $o ) > $o,A_13: x_a > $o] :
% 0.29/0.47 ( ( ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_a_o
% 0.29/0.47 @ ^ [X_1: x_a > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = ( insert_a_o @ A_13 @ bot_bot_a_o_o ) ) )
% 0.29/0.47 & ( ~ ( P_4 @ A_13 )
% 0.29/0.47 => ( ( collect_a_o
% 0.29/0.47 @ ^ [X_1: x_a > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_a_o_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_476_Collect__conv__if2,axiom,
% 0.29/0.47 ! [P_3: nat > $o,A_12: nat] :
% 0.29/0.47 ( ( ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_nat
% 0.29/0.47 @ ^ [X_1: nat] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = ( insert_nat @ A_12 @ bot_bot_nat_o ) ) )
% 0.29/0.47 & ( ~ ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_nat
% 0.29/0.47 @ ^ [X_1: nat] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_nat_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_477_Collect__conv__if2,axiom,
% 0.29/0.47 ! [P_3: pname > $o,A_12: pname] :
% 0.29/0.47 ( ( ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_pname
% 0.29/0.47 @ ^ [X_1: pname] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = ( insert_pname @ A_12 @ bot_bot_pname_o ) ) )
% 0.29/0.47 & ( ~ ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_pname
% 0.29/0.47 @ ^ [X_1: pname] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_pname_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_478_Collect__conv__if2,axiom,
% 0.29/0.47 ! [P_3: x_a > $o,A_12: x_a] :
% 0.29/0.47 ( ( ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_a
% 0.29/0.47 @ ^ [X_1: x_a] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = ( insert_a @ A_12 @ bot_bot_a_o ) ) )
% 0.29/0.47 & ( ~ ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_a
% 0.29/0.47 @ ^ [X_1: x_a] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_a_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_479_Collect__conv__if2,axiom,
% 0.29/0.47 ! [P_3: ( nat > $o ) > $o,A_12: nat > $o] :
% 0.29/0.47 ( ( ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_nat_o
% 0.29/0.47 @ ^ [X_1: nat > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = ( insert_nat_o @ A_12 @ bot_bot_nat_o_o ) ) )
% 0.29/0.47 & ( ~ ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_nat_o
% 0.29/0.47 @ ^ [X_1: nat > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_nat_o_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_480_Collect__conv__if2,axiom,
% 0.29/0.47 ! [P_3: ( pname > $o ) > $o,A_12: pname > $o] :
% 0.29/0.47 ( ( ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_pname_o
% 0.29/0.47 @ ^ [X_1: pname > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = ( insert_pname_o @ A_12 @ bot_bot_pname_o_o ) ) )
% 0.29/0.47 & ( ~ ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_pname_o
% 0.29/0.47 @ ^ [X_1: pname > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_pname_o_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_481_Collect__conv__if2,axiom,
% 0.29/0.47 ! [P_3: ( x_a > $o ) > $o,A_12: x_a > $o] :
% 0.29/0.47 ( ( ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_a_o
% 0.29/0.47 @ ^ [X_1: x_a > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = ( insert_a_o @ A_12 @ bot_bot_a_o_o ) ) )
% 0.29/0.47 & ( ~ ( P_3 @ A_12 )
% 0.29/0.47 => ( ( collect_a_o
% 0.29/0.47 @ ^ [X_1: x_a > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.29/0.47 = bot_bot_a_o_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_482_singleton__conv,axiom,
% 0.29/0.47 ! [A_11: nat] :
% 0.29/0.47 ( ( collect_nat
% 0.29/0.47 @ ^ [X_1: nat] : ( X_1 = A_11 ) )
% 0.29/0.47 = ( insert_nat @ A_11 @ bot_bot_nat_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_483_singleton__conv,axiom,
% 0.29/0.47 ! [A_11: pname] :
% 0.29/0.47 ( ( collect_pname
% 0.29/0.47 @ ^ [X_1: pname] : ( X_1 = A_11 ) )
% 0.29/0.47 = ( insert_pname @ A_11 @ bot_bot_pname_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_484_singleton__conv,axiom,
% 0.29/0.47 ! [A_11: x_a] :
% 0.29/0.47 ( ( collect_a
% 0.29/0.47 @ ^ [X_1: x_a] : ( X_1 = A_11 ) )
% 0.29/0.47 = ( insert_a @ A_11 @ bot_bot_a_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_485_singleton__conv,axiom,
% 0.29/0.47 ! [A_11: nat > $o] :
% 0.29/0.47 ( ( collect_nat_o
% 0.29/0.47 @ ^ [X_1: nat > $o] : ( X_1 = A_11 ) )
% 0.29/0.47 = ( insert_nat_o @ A_11 @ bot_bot_nat_o_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_486_singleton__conv,axiom,
% 0.29/0.47 ! [A_11: pname > $o] :
% 0.29/0.47 ( ( collect_pname_o
% 0.29/0.47 @ ^ [X_1: pname > $o] : ( X_1 = A_11 ) )
% 0.29/0.47 = ( insert_pname_o @ A_11 @ bot_bot_pname_o_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_487_singleton__conv,axiom,
% 0.29/0.47 ! [A_11: x_a > $o] :
% 0.29/0.47 ( ( collect_a_o
% 0.29/0.47 @ ^ [X_1: x_a > $o] : ( X_1 = A_11 ) )
% 0.29/0.47 = ( insert_a_o @ A_11 @ bot_bot_a_o_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_488_singleton__conv2,axiom,
% 0.29/0.47 ! [A_10: nat] :
% 0.29/0.47 ( ( collect_nat @ ( fequal_nat @ A_10 ) )
% 0.29/0.47 = ( insert_nat @ A_10 @ bot_bot_nat_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_489_singleton__conv2,axiom,
% 0.29/0.47 ! [A_10: pname] :
% 0.29/0.47 ( ( collect_pname @ ( fequal_pname @ A_10 ) )
% 0.29/0.47 = ( insert_pname @ A_10 @ bot_bot_pname_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_490_singleton__conv2,axiom,
% 0.29/0.47 ! [A_10: x_a] :
% 0.29/0.47 ( ( collect_a @ ( fequal_a @ A_10 ) )
% 0.29/0.47 = ( insert_a @ A_10 @ bot_bot_a_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_491_singleton__conv2,axiom,
% 0.29/0.47 ! [A_10: nat > $o] :
% 0.29/0.47 ( ( collect_nat_o @ ( fequal_nat_o @ A_10 ) )
% 0.29/0.47 = ( insert_nat_o @ A_10 @ bot_bot_nat_o_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_492_singleton__conv2,axiom,
% 0.29/0.47 ! [A_10: pname > $o] :
% 0.29/0.47 ( ( collect_pname_o @ ( fequal_pname_o @ A_10 ) )
% 0.29/0.47 = ( insert_pname_o @ A_10 @ bot_bot_pname_o_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_493_singleton__conv2,axiom,
% 0.29/0.47 ! [A_10: x_a > $o] :
% 0.29/0.47 ( ( collect_a_o @ ( fequal_a_o @ A_10 ) )
% 0.29/0.47 = ( insert_a_o @ A_10 @ bot_bot_a_o_o ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_494_subset__singletonD,axiom,
% 0.29/0.47 ! [A_9: nat > $o,X_12: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_9 @ ( insert_nat @ X_12 @ bot_bot_nat_o ) )
% 0.29/0.47 => ( ( A_9 = bot_bot_nat_o )
% 0.29/0.47 | ( A_9
% 0.29/0.47 = ( insert_nat @ X_12 @ bot_bot_nat_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_495_subset__singletonD,axiom,
% 0.29/0.47 ! [A_9: pname > $o,X_12: pname] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_9 @ ( insert_pname @ X_12 @ bot_bot_pname_o ) )
% 0.29/0.47 => ( ( A_9 = bot_bot_pname_o )
% 0.29/0.47 | ( A_9
% 0.29/0.47 = ( insert_pname @ X_12 @ bot_bot_pname_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_496_subset__singletonD,axiom,
% 0.29/0.47 ! [A_9: x_a > $o,X_12: x_a] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_9 @ ( insert_a @ X_12 @ bot_bot_a_o ) )
% 0.29/0.47 => ( ( A_9 = bot_bot_a_o )
% 0.29/0.47 | ( A_9
% 0.29/0.47 = ( insert_a @ X_12 @ bot_bot_a_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_497_image__constant,axiom,
% 0.29/0.47 ! [C_6: x_a,X_11: pname,A_8: pname > $o] :
% 0.29/0.47 ( ( member_pname @ X_11 @ A_8 )
% 0.29/0.47 => ( ( image_pname_a
% 0.29/0.47 @ ^ [X_1: pname] : C_6
% 0.29/0.47 @ A_8 )
% 0.29/0.47 = ( insert_a @ C_6 @ bot_bot_a_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_498_image__constant__conv,axiom,
% 0.29/0.47 ! [C_5: x_a,A_7: pname > $o] :
% 0.29/0.47 ( ( ( A_7 = bot_bot_pname_o )
% 0.29/0.47 => ( ( image_pname_a
% 0.29/0.47 @ ^ [X_1: pname] : C_5
% 0.29/0.47 @ A_7 )
% 0.29/0.47 = bot_bot_a_o ) )
% 0.29/0.47 & ( ( A_7 != bot_bot_pname_o )
% 0.29/0.47 => ( ( image_pname_a
% 0.29/0.47 @ ^ [X_1: pname] : C_5
% 0.29/0.47 @ A_7 )
% 0.29/0.47 = ( insert_a @ C_5 @ bot_bot_a_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_499_linorder__le__cases,axiom,
% 0.29/0.47 ! [X_10: nat,Y_9: nat] :
% 0.29/0.47 ( ~ ( ord_less_eq_nat @ X_10 @ Y_9 )
% 0.29/0.47 => ( ord_less_eq_nat @ Y_9 @ X_10 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_500_xt1_I6_J,axiom,
% 0.29/0.47 ! [Z_2: $o,Y_8: $o,X_9: $o] :
% 0.29/0.47 ( ( ord_less_eq_o @ Y_8 @ X_9 )
% 0.29/0.47 => ( ( ord_less_eq_o @ Z_2 @ Y_8 )
% 0.29/0.47 => ( ord_less_eq_o @ Z_2 @ X_9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_501_xt1_I6_J,axiom,
% 0.29/0.47 ! [Z_2: nat > $o,Y_8: nat > $o,X_9: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ Y_8 @ X_9 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ Z_2 @ Y_8 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ Z_2 @ X_9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_502_xt1_I6_J,axiom,
% 0.29/0.47 ! [Z_2: pname > $o,Y_8: pname > $o,X_9: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ Y_8 @ X_9 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ Z_2 @ Y_8 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ Z_2 @ X_9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_503_xt1_I6_J,axiom,
% 0.29/0.47 ! [Z_2: nat,Y_8: nat,X_9: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ Y_8 @ X_9 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ Z_2 @ Y_8 )
% 0.29/0.47 => ( ord_less_eq_nat @ Z_2 @ X_9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_504_xt1_I6_J,axiom,
% 0.29/0.47 ! [Z_2: x_a > $o,Y_8: x_a > $o,X_9: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ Y_8 @ X_9 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ Z_2 @ Y_8 )
% 0.29/0.47 => ( ord_less_eq_a_o @ Z_2 @ X_9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_505_xt1_I5_J,axiom,
% 0.29/0.47 ! [Y_7: $o,X_8: $o] :
% 0.29/0.47 ( ( ord_less_eq_o @ Y_7 @ X_8 )
% 0.29/0.47 => ( ( ord_less_eq_o @ X_8 @ Y_7 )
% 0.29/0.47 => ( X_8
% 0.29/0.47 <=> Y_7 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_506_xt1_I5_J,axiom,
% 0.29/0.47 ! [Y_7: nat > $o,X_8: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ Y_7 @ X_8 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ X_8 @ Y_7 )
% 0.29/0.47 => ( X_8 = Y_7 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_507_xt1_I5_J,axiom,
% 0.29/0.47 ! [Y_7: pname > $o,X_8: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ Y_7 @ X_8 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ X_8 @ Y_7 )
% 0.29/0.47 => ( X_8 = Y_7 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_508_xt1_I5_J,axiom,
% 0.29/0.47 ! [Y_7: nat,X_8: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ Y_7 @ X_8 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ X_8 @ Y_7 )
% 0.29/0.47 => ( X_8 = Y_7 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_509_xt1_I5_J,axiom,
% 0.29/0.47 ! [Y_7: x_a > $o,X_8: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ Y_7 @ X_8 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ X_8 @ Y_7 )
% 0.29/0.47 => ( X_8 = Y_7 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_510_order__trans,axiom,
% 0.29/0.47 ! [Z_1: $o,X_7: $o,Y_6: $o] :
% 0.29/0.47 ( ( ord_less_eq_o @ X_7 @ Y_6 )
% 0.29/0.47 => ( ( ord_less_eq_o @ Y_6 @ Z_1 )
% 0.29/0.47 => ( ord_less_eq_o @ X_7 @ Z_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_511_order__trans,axiom,
% 0.29/0.47 ! [Z_1: nat > $o,X_7: nat > $o,Y_6: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ X_7 @ Y_6 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ Y_6 @ Z_1 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ X_7 @ Z_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_512_order__trans,axiom,
% 0.29/0.47 ! [Z_1: pname > $o,X_7: pname > $o,Y_6: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ X_7 @ Y_6 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ Y_6 @ Z_1 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ X_7 @ Z_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_513_order__trans,axiom,
% 0.29/0.47 ! [Z_1: nat,X_7: nat,Y_6: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X_7 @ Y_6 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ Y_6 @ Z_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ X_7 @ Z_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_514_order__trans,axiom,
% 0.29/0.47 ! [Z_1: x_a > $o,X_7: x_a > $o,Y_6: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ X_7 @ Y_6 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ Y_6 @ Z_1 )
% 0.29/0.47 => ( ord_less_eq_a_o @ X_7 @ Z_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_515_order__antisym,axiom,
% 0.29/0.47 ! [X_6: $o,Y_5: $o] :
% 0.29/0.47 ( ( ord_less_eq_o @ X_6 @ Y_5 )
% 0.29/0.47 => ( ( ord_less_eq_o @ Y_5 @ X_6 )
% 0.29/0.47 => ( X_6
% 0.29/0.47 <=> Y_5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_516_order__antisym,axiom,
% 0.29/0.47 ! [X_6: nat > $o,Y_5: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ X_6 @ Y_5 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ Y_5 @ X_6 )
% 0.29/0.47 => ( X_6 = Y_5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_517_order__antisym,axiom,
% 0.29/0.47 ! [X_6: pname > $o,Y_5: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ X_6 @ Y_5 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ Y_5 @ X_6 )
% 0.29/0.47 => ( X_6 = Y_5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_518_order__antisym,axiom,
% 0.29/0.47 ! [X_6: nat,Y_5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X_6 @ Y_5 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ Y_5 @ X_6 )
% 0.29/0.47 => ( X_6 = Y_5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_519_order__antisym,axiom,
% 0.29/0.47 ! [X_6: x_a > $o,Y_5: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ X_6 @ Y_5 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ Y_5 @ X_6 )
% 0.29/0.47 => ( X_6 = Y_5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_520_xt1_I4_J,axiom,
% 0.29/0.47 ! [C_4: $o,B_4: $o,A_6: $o] :
% 0.29/0.47 ( ( ord_less_eq_o @ B_4 @ A_6 )
% 0.29/0.47 => ( ( B_4
% 0.29/0.47 <=> C_4 )
% 0.29/0.47 => ( ord_less_eq_o @ C_4 @ A_6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_521_xt1_I4_J,axiom,
% 0.29/0.47 ! [C_4: nat > $o,B_4: nat > $o,A_6: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ B_4 @ A_6 )
% 0.29/0.47 => ( ( B_4 = C_4 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ C_4 @ A_6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_522_xt1_I4_J,axiom,
% 0.29/0.47 ! [C_4: pname > $o,B_4: pname > $o,A_6: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ B_4 @ A_6 )
% 0.29/0.47 => ( ( B_4 = C_4 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ C_4 @ A_6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_523_xt1_I4_J,axiom,
% 0.29/0.47 ! [C_4: nat,B_4: nat,A_6: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ B_4 @ A_6 )
% 0.29/0.47 => ( ( B_4 = C_4 )
% 0.29/0.47 => ( ord_less_eq_nat @ C_4 @ A_6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_524_xt1_I4_J,axiom,
% 0.29/0.47 ! [C_4: x_a > $o,B_4: x_a > $o,A_6: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ B_4 @ A_6 )
% 0.29/0.47 => ( ( B_4 = C_4 )
% 0.29/0.47 => ( ord_less_eq_a_o @ C_4 @ A_6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_525_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [C_3: $o,A_5: $o,B_3: $o] :
% 0.29/0.47 ( ( ord_less_eq_o @ A_5 @ B_3 )
% 0.29/0.47 => ( ( B_3
% 0.29/0.47 <=> C_3 )
% 0.29/0.47 => ( ord_less_eq_o @ A_5 @ C_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_526_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [C_3: nat > $o,A_5: nat > $o,B_3: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_5 @ B_3 )
% 0.29/0.47 => ( ( B_3 = C_3 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ A_5 @ C_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_527_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [C_3: pname > $o,A_5: pname > $o,B_3: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_5 @ B_3 )
% 0.29/0.47 => ( ( B_3 = C_3 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ A_5 @ C_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_528_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [C_3: nat,A_5: nat,B_3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A_5 @ B_3 )
% 0.29/0.47 => ( ( B_3 = C_3 )
% 0.29/0.47 => ( ord_less_eq_nat @ A_5 @ C_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_529_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [C_3: x_a > $o,A_5: x_a > $o,B_3: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_5 @ B_3 )
% 0.29/0.47 => ( ( B_3 = C_3 )
% 0.29/0.47 => ( ord_less_eq_a_o @ A_5 @ C_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_530_xt1_I3_J,axiom,
% 0.29/0.47 ! [C_2: $o,B_2: $o,A_4: $o] :
% 0.29/0.47 ( ( A_4
% 0.29/0.47 <=> B_2 )
% 0.29/0.47 => ( ( ord_less_eq_o @ C_2 @ B_2 )
% 0.29/0.47 => ( ord_less_eq_o @ C_2 @ A_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_531_xt1_I3_J,axiom,
% 0.29/0.47 ! [C_2: nat > $o,A_4: nat > $o,B_2: nat > $o] :
% 0.29/0.47 ( ( A_4 = B_2 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ C_2 @ B_2 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ C_2 @ A_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_532_xt1_I3_J,axiom,
% 0.29/0.47 ! [C_2: pname > $o,A_4: pname > $o,B_2: pname > $o] :
% 0.29/0.47 ( ( A_4 = B_2 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ C_2 @ B_2 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ C_2 @ A_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_533_xt1_I3_J,axiom,
% 0.29/0.47 ! [C_2: nat,A_4: nat,B_2: nat] :
% 0.29/0.47 ( ( A_4 = B_2 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ C_2 @ B_2 )
% 0.29/0.47 => ( ord_less_eq_nat @ C_2 @ A_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_534_xt1_I3_J,axiom,
% 0.29/0.47 ! [C_2: x_a > $o,A_4: x_a > $o,B_2: x_a > $o] :
% 0.29/0.47 ( ( A_4 = B_2 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ C_2 @ B_2 )
% 0.29/0.47 => ( ord_less_eq_a_o @ C_2 @ A_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_535_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [C_1: $o,B_1: $o,A_3: $o] :
% 0.29/0.47 ( ( A_3
% 0.29/0.47 <=> B_1 )
% 0.29/0.47 => ( ( ord_less_eq_o @ B_1 @ C_1 )
% 0.29/0.47 => ( ord_less_eq_o @ A_3 @ C_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_536_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [C_1: nat > $o,A_3: nat > $o,B_1: nat > $o] :
% 0.29/0.47 ( ( A_3 = B_1 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ B_1 @ C_1 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ A_3 @ C_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_537_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [C_1: pname > $o,A_3: pname > $o,B_1: pname > $o] :
% 0.29/0.47 ( ( A_3 = B_1 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ B_1 @ C_1 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ A_3 @ C_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_538_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [C_1: nat,A_3: nat,B_1: nat] :
% 0.29/0.47 ( ( A_3 = B_1 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B_1 @ C_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ A_3 @ C_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_539_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [C_1: x_a > $o,A_3: x_a > $o,B_1: x_a > $o] :
% 0.29/0.47 ( ( A_3 = B_1 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ B_1 @ C_1 )
% 0.29/0.47 => ( ord_less_eq_a_o @ A_3 @ C_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_540_order__antisym__conv,axiom,
% 0.29/0.47 ! [Y_4: $o,X_5: $o] :
% 0.29/0.47 ( ( ord_less_eq_o @ Y_4 @ X_5 )
% 0.29/0.47 => ( ( ord_less_eq_o @ X_5 @ Y_4 )
% 0.29/0.47 <=> ( X_5
% 0.29/0.47 <=> Y_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_541_order__antisym__conv,axiom,
% 0.29/0.47 ! [Y_4: nat > $o,X_5: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ Y_4 @ X_5 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ X_5 @ Y_4 )
% 0.29/0.47 <=> ( X_5 = Y_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_542_order__antisym__conv,axiom,
% 0.29/0.47 ! [Y_4: pname > $o,X_5: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ Y_4 @ X_5 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ X_5 @ Y_4 )
% 0.29/0.47 <=> ( X_5 = Y_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_543_order__antisym__conv,axiom,
% 0.29/0.47 ! [Y_4: nat,X_5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ Y_4 @ X_5 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ X_5 @ Y_4 )
% 0.29/0.47 <=> ( X_5 = Y_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_544_order__antisym__conv,axiom,
% 0.29/0.47 ! [Y_4: x_a > $o,X_5: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ Y_4 @ X_5 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ X_5 @ Y_4 )
% 0.29/0.47 <=> ( X_5 = Y_4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_545_order__eq__refl,axiom,
% 0.29/0.47 ! [Y_3: $o,X_4: $o] :
% 0.29/0.47 ( ( X_4
% 0.29/0.47 <=> Y_3 )
% 0.29/0.47 => ( ord_less_eq_o @ X_4 @ Y_3 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_546_order__eq__refl,axiom,
% 0.29/0.47 ! [X_4: nat > $o,Y_3: nat > $o] :
% 0.29/0.47 ( ( X_4 = Y_3 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ X_4 @ Y_3 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_547_order__eq__refl,axiom,
% 0.29/0.47 ! [X_4: pname > $o,Y_3: pname > $o] :
% 0.29/0.47 ( ( X_4 = Y_3 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ X_4 @ Y_3 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_548_order__eq__refl,axiom,
% 0.29/0.47 ! [X_4: nat,Y_3: nat] :
% 0.29/0.47 ( ( X_4 = Y_3 )
% 0.29/0.47 => ( ord_less_eq_nat @ X_4 @ Y_3 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_549_order__eq__refl,axiom,
% 0.29/0.47 ! [X_4: x_a > $o,Y_3: x_a > $o] :
% 0.29/0.47 ( ( X_4 = Y_3 )
% 0.29/0.47 => ( ord_less_eq_a_o @ X_4 @ Y_3 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_550_order__eq__iff,axiom,
% 0.29/0.47 ! [Y_2: $o,X_3: $o] :
% 0.29/0.47 ( ( X_3
% 0.29/0.47 <=> Y_2 )
% 0.29/0.47 <=> ( ( ord_less_eq_o @ X_3 @ Y_2 )
% 0.29/0.47 & ( ord_less_eq_o @ Y_2 @ X_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_551_order__eq__iff,axiom,
% 0.29/0.47 ! [X_3: nat > $o,Y_2: nat > $o] :
% 0.29/0.47 ( ( X_3 = Y_2 )
% 0.29/0.47 <=> ( ( ord_less_eq_nat_o @ X_3 @ Y_2 )
% 0.29/0.47 & ( ord_less_eq_nat_o @ Y_2 @ X_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_552_order__eq__iff,axiom,
% 0.29/0.47 ! [X_3: pname > $o,Y_2: pname > $o] :
% 0.29/0.47 ( ( X_3 = Y_2 )
% 0.29/0.47 <=> ( ( ord_less_eq_pname_o @ X_3 @ Y_2 )
% 0.29/0.47 & ( ord_less_eq_pname_o @ Y_2 @ X_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_553_order__eq__iff,axiom,
% 0.29/0.47 ! [X_3: nat,Y_2: nat] :
% 0.29/0.47 ( ( X_3 = Y_2 )
% 0.29/0.47 <=> ( ( ord_less_eq_nat @ X_3 @ Y_2 )
% 0.29/0.47 & ( ord_less_eq_nat @ Y_2 @ X_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_554_order__eq__iff,axiom,
% 0.29/0.47 ! [X_3: x_a > $o,Y_2: x_a > $o] :
% 0.29/0.47 ( ( X_3 = Y_2 )
% 0.29/0.47 <=> ( ( ord_less_eq_a_o @ X_3 @ Y_2 )
% 0.29/0.47 & ( ord_less_eq_a_o @ Y_2 @ X_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_555_linorder__linear,axiom,
% 0.29/0.47 ! [X_2: nat,Y_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X_2 @ Y_1 )
% 0.29/0.47 | ( ord_less_eq_nat @ Y_1 @ X_2 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_556_finite__subset__induct,axiom,
% 0.29/0.47 ! [P_2: ( nat > $o ) > $o,A_1: nat > $o,F_3: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ F_3 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ F_3 @ A_1 )
% 0.29/0.47 => ( ( P_2 @ bot_bot_nat_o )
% 0.29/0.47 => ( ! [A_2: nat,F_2: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ F_2 )
% 0.29/0.47 => ( ( member_nat @ A_2 @ A_1 )
% 0.29/0.47 => ( ~ ( member_nat @ A_2 @ F_2 )
% 0.29/0.47 => ( ( P_2 @ F_2 )
% 0.29/0.47 => ( P_2 @ ( insert_nat @ A_2 @ F_2 ) ) ) ) ) )
% 0.29/0.47 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_557_finite__subset__induct,axiom,
% 0.29/0.47 ! [P_2: ( pname > $o ) > $o,A_1: pname > $o,F_3: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_3 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ F_3 @ A_1 )
% 0.29/0.47 => ( ( P_2 @ bot_bot_pname_o )
% 0.29/0.47 => ( ! [A_2: pname,F_2: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_2 )
% 0.29/0.47 => ( ( member_pname @ A_2 @ A_1 )
% 0.29/0.47 => ( ~ ( member_pname @ A_2 @ F_2 )
% 0.29/0.47 => ( ( P_2 @ F_2 )
% 0.29/0.47 => ( P_2 @ ( insert_pname @ A_2 @ F_2 ) ) ) ) ) )
% 0.29/0.47 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_558_finite__subset__induct,axiom,
% 0.29/0.47 ! [P_2: ( x_a > $o ) > $o,A_1: x_a > $o,F_3: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ F_3 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ F_3 @ A_1 )
% 0.29/0.47 => ( ( P_2 @ bot_bot_a_o )
% 0.29/0.47 => ( ! [A_2: x_a,F_2: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ F_2 )
% 0.29/0.47 => ( ( member_a @ A_2 @ A_1 )
% 0.29/0.47 => ( ~ ( member_a @ A_2 @ F_2 )
% 0.29/0.47 => ( ( P_2 @ F_2 )
% 0.29/0.47 => ( P_2 @ ( insert_a @ A_2 @ F_2 ) ) ) ) ) )
% 0.29/0.47 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_559_finite__subset__induct,axiom,
% 0.29/0.47 ! [P_2: ( ( nat > $o ) > $o ) > $o,A_1: ( nat > $o ) > $o,F_3: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ F_3 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o_o @ F_3 @ A_1 )
% 0.29/0.47 => ( ( P_2 @ bot_bot_nat_o_o )
% 0.29/0.47 => ( ! [A_2: nat > $o,F_2: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ F_2 )
% 0.29/0.47 => ( ( member_nat_o @ A_2 @ A_1 )
% 0.29/0.47 => ( ~ ( member_nat_o @ A_2 @ F_2 )
% 0.29/0.47 => ( ( P_2 @ F_2 )
% 0.29/0.47 => ( P_2 @ ( insert_nat_o @ A_2 @ F_2 ) ) ) ) ) )
% 0.29/0.47 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_560_finite__subset__induct,axiom,
% 0.29/0.47 ! [P_2: ( ( pname > $o ) > $o ) > $o,A_1: ( pname > $o ) > $o,F_3: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ F_3 )
% 0.29/0.47 => ( ( ord_le1205211808me_o_o @ F_3 @ A_1 )
% 0.29/0.47 => ( ( P_2 @ bot_bot_pname_o_o )
% 0.29/0.47 => ( ! [A_2: pname > $o,F_2: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ F_2 )
% 0.29/0.47 => ( ( member_pname_o @ A_2 @ A_1 )
% 0.29/0.47 => ( ~ ( member_pname_o @ A_2 @ F_2 )
% 0.29/0.47 => ( ( P_2 @ F_2 )
% 0.29/0.47 => ( P_2 @ ( insert_pname_o @ A_2 @ F_2 ) ) ) ) ) )
% 0.29/0.47 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_561_finite__subset__induct,axiom,
% 0.29/0.47 ! [P_2: ( ( x_a > $o ) > $o ) > $o,A_1: ( x_a > $o ) > $o,F_3: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ F_3 )
% 0.29/0.47 => ( ( ord_less_eq_a_o_o @ F_3 @ A_1 )
% 0.29/0.47 => ( ( P_2 @ bot_bot_a_o_o )
% 0.29/0.47 => ( ! [A_2: x_a > $o,F_2: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ F_2 )
% 0.29/0.47 => ( ( member_a_o @ A_2 @ A_1 )
% 0.29/0.47 => ( ~ ( member_a_o @ A_2 @ F_2 )
% 0.29/0.47 => ( ( P_2 @ F_2 )
% 0.29/0.47 => ( P_2 @ ( insert_a_o @ A_2 @ F_2 ) ) ) ) ) )
% 0.29/0.47 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_562_assms_I2_J,axiom,
% 0.29/0.47 ! [Pn: pname,G: x_a > $o] :
% 0.29/0.47 ( ( p @ ( insert_a @ ( mgt_call @ Pn ) @ G ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ Pn ) ) ) @ bot_bot_a_o ) )
% 0.29/0.47 => ( p @ G @ ( insert_a @ ( mgt_call @ Pn ) @ bot_bot_a_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_563_finite__induct,axiom,
% 0.29/0.47 ! [P_1: ( ( nat > $o ) > $o ) > $o,F_1: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ F_1 )
% 0.29/0.47 => ( ( P_1 @ bot_bot_nat_o_o )
% 0.29/0.47 => ( ! [X_1: nat > $o,F_2: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ F_2 )
% 0.29/0.47 => ( ~ ( member_nat_o @ X_1 @ F_2 )
% 0.29/0.47 => ( ( P_1 @ F_2 )
% 0.29/0.47 => ( P_1 @ ( insert_nat_o @ X_1 @ F_2 ) ) ) ) )
% 0.29/0.47 => ( P_1 @ F_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_564_finite__induct,axiom,
% 0.29/0.47 ! [P_1: ( ( pname > $o ) > $o ) > $o,F_1: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ F_1 )
% 0.29/0.47 => ( ( P_1 @ bot_bot_pname_o_o )
% 0.29/0.47 => ( ! [X_1: pname > $o,F_2: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ F_2 )
% 0.29/0.47 => ( ~ ( member_pname_o @ X_1 @ F_2 )
% 0.29/0.47 => ( ( P_1 @ F_2 )
% 0.29/0.47 => ( P_1 @ ( insert_pname_o @ X_1 @ F_2 ) ) ) ) )
% 0.29/0.47 => ( P_1 @ F_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_565_finite__induct,axiom,
% 0.29/0.47 ! [P_1: ( ( x_a > $o ) > $o ) > $o,F_1: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ F_1 )
% 0.29/0.47 => ( ( P_1 @ bot_bot_a_o_o )
% 0.29/0.47 => ( ! [X_1: x_a > $o,F_2: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ F_2 )
% 0.29/0.47 => ( ~ ( member_a_o @ X_1 @ F_2 )
% 0.29/0.47 => ( ( P_1 @ F_2 )
% 0.29/0.47 => ( P_1 @ ( insert_a_o @ X_1 @ F_2 ) ) ) ) )
% 0.29/0.47 => ( P_1 @ F_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_566_finite__less__ub,axiom,
% 0.29/0.47 ! [U: nat,F: nat > nat] :
% 0.29/0.47 ( ! [N_2: nat] : ( ord_less_eq_nat @ N_2 @ ( F @ N_2 ) )
% 0.29/0.47 => ( finite_finite_nat
% 0.29/0.47 @ ( collect_nat
% 0.29/0.47 @ ^ [N_2: nat] : ( ord_less_eq_nat @ ( F @ N_2 ) @ U ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_567_assms_I4_J,axiom,
% 0.29/0.47 ! [Pn: pname] :
% 0.29/0.47 ( ( member_pname @ Pn @ u )
% 0.29/0.47 => ( wt @ ( the_com @ ( body @ Pn ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_568_diff__Suc__eq__diff__pred,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.29/0.47 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_569_diff__Suc__1,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.29/0.47 = N ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_570_less__eq__nat_Osimps_I2_J,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.47 <=> ( nat_case_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_571_add__Suc__right,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.29/0.47 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_572_add__Suc,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.29/0.47 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_573_add__Suc__shift,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.29/0.47 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_574_nat__add__right__cancel,axiom,
% 0.29/0.47 ! [M: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( ( plus_plus_nat @ M @ K )
% 0.29/0.47 = ( plus_plus_nat @ N @ K ) )
% 0.29/0.47 <=> ( M = N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_575_nat__add__left__cancel,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ( plus_plus_nat @ K @ M )
% 0.29/0.47 = ( plus_plus_nat @ K @ N ) )
% 0.29/0.47 <=> ( M = N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_576_nat__add__assoc,axiom,
% 0.29/0.47 ! [M: nat,N: nat,K: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.29/0.47 = ( plus_plus_nat @ M @ ( plus_plus_nat @ N @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_577_nat__add__left__commute,axiom,
% 0.29/0.47 ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ X @ ( plus_plus_nat @ Y @ Z ) )
% 0.29/0.47 = ( plus_plus_nat @ Y @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_578_nat__add__commute,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ M @ N )
% 0.29/0.47 = ( plus_plus_nat @ N @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_579_diff__add__inverse2,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.29/0.47 = M ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_580_diff__add__inverse,axiom,
% 0.29/0.47 ! [N: nat,M: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.29/0.47 = M ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_581_diff__diff__left,axiom,
% 0.29/0.47 ! [I: nat,J_1: nat,K: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J_1 ) @ K )
% 0.29/0.47 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_582_diff__cancel,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.29/0.47 = ( minus_minus_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_583_diff__cancel2,axiom,
% 0.29/0.47 ! [M: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.29/0.47 = ( minus_minus_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_584_le__add2,axiom,
% 0.29/0.47 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_585_le__add1,axiom,
% 0.29/0.47 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_586_le__iff__add,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 <=> ? [K_1: nat] :
% 0.29/0.47 ( N
% 0.29/0.47 = ( plus_plus_nat @ M @ K_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_587_nat__add__left__cancel__le,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.29/0.47 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_588_trans__le__add1,axiom,
% 0.29/0.47 ! [M: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_589_trans__le__add2,axiom,
% 0.29/0.47 ! [M: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_590_add__le__mono1,axiom,
% 0.29/0.47 ! [K: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_591_add__le__mono,axiom,
% 0.29/0.47 ! [K: nat,L: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ L )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_592_add__leD2,axiom,
% 0.29/0.47 ! [M: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_593_add__leD1,axiom,
% 0.29/0.47 ! [M: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_594_add__leE,axiom,
% 0.29/0.47 ! [M: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.29/0.47 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_595_diff__add__assoc2,axiom,
% 0.29/0.47 ! [I: nat,K: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.29/0.47 => ( ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I ) @ K )
% 0.29/0.47 = ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K ) @ I ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_596_add__diff__assoc2,axiom,
% 0.29/0.47 ! [I: nat,K: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.29/0.47 => ( ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K ) @ I )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I ) @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_597_diff__add__assoc,axiom,
% 0.29/0.47 ! [I: nat,K: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.29/0.47 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J_1 ) @ K )
% 0.29/0.47 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J_1 @ K ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_598_le__imp__diff__is__add,axiom,
% 0.29/0.47 ! [K: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.29/0.47 => ( ( ( minus_minus_nat @ J_1 @ I )
% 0.29/0.47 = K )
% 0.29/0.47 <=> ( J_1
% 0.29/0.47 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_599_le__add__diff__inverse2,axiom,
% 0.29/0.47 ! [N: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.47 => ( ( plus_plus_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.29/0.47 = M ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_600_le__diff__conv2,axiom,
% 0.29/0.47 ! [I: nat,K: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.29/0.47 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_601_add__diff__assoc,axiom,
% 0.29/0.47 ! [I: nat,K: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.29/0.47 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J_1 ) @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_602_le__add__diff__inverse,axiom,
% 0.29/0.47 ! [N: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.47 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.29/0.47 = M ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_603_le__add__diff,axiom,
% 0.29/0.47 ! [M: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ M @ ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_604_le__diff__conv,axiom,
% 0.29/0.47 ! [J_1: nat,K: nat,I: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J_1 @ K ) @ I )
% 0.29/0.47 <=> ( ord_less_eq_nat @ J_1 @ ( plus_plus_nat @ I @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_605_diff__diff__right,axiom,
% 0.29/0.47 ! [I: nat,K: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.29/0.47 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_606_Suc__eq__plus1,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ( ( suc @ N )
% 0.29/0.47 = ( plus_plus_nat @ N @ one_one_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_607_Suc__eq__plus1__left,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ( ( suc @ N )
% 0.29/0.47 = ( plus_plus_nat @ one_one_nat @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_608_diff__Suc__diff__eq2,axiom,
% 0.29/0.47 ! [M: nat,K: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.29/0.47 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J_1 @ K ) ) @ M )
% 0.29/0.47 = ( minus_minus_nat @ ( suc @ J_1 ) @ ( plus_plus_nat @ K @ M ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_609_diff__Suc__diff__eq1,axiom,
% 0.29/0.47 ! [M: nat,K: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.29/0.47 => ( ( minus_minus_nat @ M @ ( suc @ ( minus_minus_nat @ J_1 @ K ) ) )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( suc @ J_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_610_termination__basic__simps_I3_J,axiom,
% 0.29/0.47 ! [Z: nat,X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 => ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_611_termination__basic__simps_I4_J,axiom,
% 0.29/0.47 ! [Y: nat,X: nat,Z: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Z )
% 0.29/0.47 => ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_612_lessI,axiom,
% 0.29/0.47 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_613_Suc__mono,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_614_finite__Collect__less__nat,axiom,
% 0.29/0.47 ! [K: nat] :
% 0.29/0.47 ( finite_finite_nat
% 0.29/0.47 @ ( collect_nat
% 0.29/0.47 @ ^ [N_2: nat] : ( ord_less_nat @ N_2 @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_615_termination__basic__simps_I1_J,axiom,
% 0.29/0.47 ! [Z: nat,X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_616_termination__basic__simps_I2_J,axiom,
% 0.29/0.47 ! [Y: nat,X: nat,Z: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Z )
% 0.29/0.47 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_617_add__lessD1,axiom,
% 0.29/0.47 ! [I: nat,J_1: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J_1 ) @ K )
% 0.29/0.47 => ( ord_less_nat @ I @ K ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_618_less__add__eq__less,axiom,
% 0.29/0.47 ! [M: nat,N: nat,K: nat,L: nat] :
% 0.29/0.47 ( ( ord_less_nat @ K @ L )
% 0.29/0.47 => ( ( ( plus_plus_nat @ M @ L )
% 0.29/0.47 = ( plus_plus_nat @ K @ N ) )
% 0.29/0.47 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_619_add__less__mono,axiom,
% 0.29/0.47 ! [K: nat,L: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J_1 )
% 0.29/0.47 => ( ( ord_less_nat @ K @ L )
% 0.29/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_620_add__less__mono1,axiom,
% 0.29/0.47 ! [K: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J_1 )
% 0.29/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_621_trans__less__add2,axiom,
% 0.29/0.47 ! [M: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J_1 )
% 0.29/0.47 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_622_trans__less__add1,axiom,
% 0.29/0.47 ! [M: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J_1 )
% 0.29/0.47 => ( ord_less_nat @ I @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_623_nat__add__left__cancel__less,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.29/0.47 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_624_not__add__less2,axiom,
% 0.29/0.47 ! [J_1: nat,I: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ ( plus_plus_nat @ J_1 @ I ) @ I ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_625_not__add__less1,axiom,
% 0.29/0.47 ! [I: nat,J_1: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J_1 ) @ I ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_626_Suc__less__SucD,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.47 => ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_627_Suc__lessD,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.29/0.47 => ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_628_less__SucE,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.47 => ( ~ ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( M = N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_629_less__trans__Suc,axiom,
% 0.29/0.47 ! [K: nat,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J_1 )
% 0.29/0.47 => ( ( ord_less_nat @ J_1 @ K )
% 0.29/0.47 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_630_Suc__lessI,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( ( ( suc @ M )
% 0.29/0.47 != N )
% 0.29/0.47 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_631_less__SucI,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_632_less__antisym,axiom,
% 0.29/0.47 ! [N: nat,M: nat] :
% 0.29/0.47 ( ~ ( ord_less_nat @ N @ M )
% 0.29/0.47 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.29/0.47 => ( M = N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_633_not__less__less__Suc__eq,axiom,
% 0.29/0.47 ! [N: nat,M: nat] :
% 0.29/0.47 ( ~ ( ord_less_nat @ N @ M )
% 0.29/0.47 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.29/0.47 <=> ( N = M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_634_Suc__less__eq,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.47 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_635_less__Suc__eq,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.47 <=> ( ( ord_less_nat @ M @ N )
% 0.29/0.47 | ( M = N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_636_not__less__eq,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ~ ( ord_less_nat @ M @ N )
% 0.29/0.47 <=> ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_637_less__or__eq__imp__le,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ( ord_less_nat @ M @ N )
% 0.29/0.47 | ( M = N ) )
% 0.29/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_638_le__neq__implies__less,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ( ( M != N )
% 0.29/0.47 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_639_less__imp__le__nat,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_640_le__eq__less__or__eq,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 <=> ( ( ord_less_nat @ M @ N )
% 0.29/0.47 | ( M = N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_641_nat__less__le,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 & ( M != N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_642_diff__less__mono2,axiom,
% 0.29/0.47 ! [L: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( ( ord_less_nat @ M @ L )
% 0.29/0.47 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_643_less__imp__diff__less,axiom,
% 0.29/0.47 ! [N: nat,J_1: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_nat @ J_1 @ K )
% 0.29/0.47 => ( ord_less_nat @ ( minus_minus_nat @ J_1 @ N ) @ K ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_644_termination__basic__simps_I5_J,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_645_less__not__refl,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_646_nat__neq__iff,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( M != N )
% 0.29/0.47 <=> ( ( ord_less_nat @ M @ N )
% 0.29/0.47 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_647_linorder__neqE__nat,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 => ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_648_less__irrefl__nat,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_649_less__not__refl2,axiom,
% 0.29/0.47 ! [N: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_nat @ N @ M )
% 0.29/0.47 => ( M != N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_650_less__not__refl3,axiom,
% 0.29/0.47 ! [S: nat,T: nat] :
% 0.29/0.47 ( ( ord_less_nat @ S @ T )
% 0.29/0.47 => ( S != T ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_651_nat__less__cases,axiom,
% 0.29/0.47 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.29/0.47 ( ( ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( P @ N @ M ) )
% 0.29/0.47 => ( ( ( M = N )
% 0.29/0.47 => ( P @ N @ M ) )
% 0.29/0.47 => ( ( ( ord_less_nat @ N @ M )
% 0.29/0.47 => ( P @ N @ M ) )
% 0.29/0.47 => ( P @ N @ M ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_652_finite__nat__set__iff__bounded,axiom,
% 0.29/0.47 ! [N_1: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ N_1 )
% 0.29/0.47 <=> ? [M_1: nat] :
% 0.29/0.47 ! [X_1: nat] :
% 0.29/0.47 ( ( member_nat @ X_1 @ N_1 )
% 0.29/0.47 => ( ord_less_nat @ X_1 @ M_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_653_card__Collect__less__nat,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ( ( finite_card_nat
% 0.29/0.47 @ ( collect_nat
% 0.29/0.47 @ ^ [I_1: nat] : ( ord_less_nat @ I_1 @ N ) ) )
% 0.29/0.47 = N ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_654_finite__M__bounded__by__nat,axiom,
% 0.29/0.47 ! [P: nat > $o,I: nat] :
% 0.29/0.47 ( finite_finite_nat
% 0.29/0.47 @ ( collect_nat
% 0.29/0.47 @ ^ [K_1: nat] : ( (&) @ ( P @ K_1 ) @ ( ord_less_nat @ K_1 @ I ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_655_less__add__Suc1,axiom,
% 0.29/0.47 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_656_less__add__Suc2,axiom,
% 0.29/0.47 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_657_less__iff__Suc__add,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 <=> ? [K_1: nat] :
% 0.29/0.47 ( N
% 0.29/0.47 = ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_658_less__eq__Suc__le,axiom,
% 0.29/0.47 ! [N: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_nat @ N @ M )
% 0.29/0.47 <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_659_less__Suc__eq__le,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.47 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_660_Suc__le__eq,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.47 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_661_le__imp__less__Suc,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_662_Suc__leI,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_663_le__less__Suc__eq,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.29/0.47 <=> ( N = M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_664_Suc__le__lessD,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.47 => ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_665_diff__less__Suc,axiom,
% 0.29/0.47 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_666_add__diff__inverse,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ~ ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.29/0.47 = M ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_667_less__diff__conv,axiom,
% 0.29/0.47 ! [I: nat,J_1: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.29/0.47 <=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_668_diff__less__mono,axiom,
% 0.29/0.47 ! [C: nat,A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.47 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_669_less__diff__iff,axiom,
% 0.29/0.47 ! [N: nat,K: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.47 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.47 <=> ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_670_less__eq__Suc__le__raw,axiom,
% 0.29/0.47 ! [X_1: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X_1 )
% 0.29/0.47 = ( ord_less_eq_nat @ ( suc @ X_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_671_mono__nat__linear__lb,axiom,
% 0.29/0.47 ! [M: nat,K: nat,F: nat > nat] :
% 0.29/0.47 ( ! [M_1: nat,N_2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M_1 @ N_2 )
% 0.29/0.47 => ( ord_less_nat @ ( F @ M_1 ) @ ( F @ N_2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_672_inc__induct,axiom,
% 0.29/0.47 ! [P: nat > $o,I: nat,J_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.29/0.47 => ( ( P @ J_1 )
% 0.29/0.47 => ( ! [I_1: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.29/0.47 => ( ( P @ ( suc @ I_1 ) )
% 0.29/0.47 => ( P @ I_1 ) ) )
% 0.29/0.47 => ( P @ I ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_673_less__imp__Suc__add,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 => ? [K_1: nat] :
% 0.29/0.47 ( N
% 0.29/0.47 = ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_674_bounded__nat__set__is__finite,axiom,
% 0.29/0.47 ! [N: nat,N_1: nat > $o] :
% 0.29/0.47 ( ! [X_1: nat] :
% 0.29/0.47 ( ( member_nat @ X_1 @ N_1 )
% 0.29/0.47 => ( ord_less_nat @ X_1 @ N ) )
% 0.29/0.47 => ( finite_finite_nat @ N_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_675_less__mono__imp__le__mono,axiom,
% 0.29/0.47 ! [I: nat,J_1: nat,F: nat > nat] :
% 0.29/0.47 ( ! [I_1: nat,J: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I_1 @ J )
% 0.29/0.47 => ( ord_less_nat @ ( F @ I_1 ) @ ( F @ J ) ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ I @ J_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_676_Suc__lessE,axiom,
% 0.29/0.47 ! [I: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.29/0.47 => ~ ! [J: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J )
% 0.29/0.47 => ( K
% 0.29/0.47 != ( suc @ J ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_677_lessE,axiom,
% 0.29/0.47 ! [I: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ K )
% 0.29/0.47 => ( ( K
% 0.29/0.47 != ( suc @ I ) )
% 0.29/0.47 => ~ ! [J: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J )
% 0.29/0.47 => ( K
% 0.29/0.47 != ( suc @ J ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_678_less__zeroE,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_679_le0,axiom,
% 0.29/0.47 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_680_zero__less__Suc,axiom,
% 0.29/0.47 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_681_add__is__1,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ( plus_plus_nat @ M @ N )
% 0.29/0.47 = ( suc @ zero_zero_nat ) )
% 0.29/0.47 <=> ( ( ( M
% 0.29/0.47 = ( suc @ zero_zero_nat ) )
% 0.29/0.47 & ( N = zero_zero_nat ) )
% 0.29/0.47 | ( ( M = zero_zero_nat )
% 0.29/0.47 & ( N
% 0.29/0.47 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_682_one__is__add,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ( suc @ zero_zero_nat )
% 0.29/0.47 = ( plus_plus_nat @ M @ N ) )
% 0.29/0.47 <=> ( ( ( M
% 0.29/0.47 = ( suc @ zero_zero_nat ) )
% 0.29/0.47 & ( N = zero_zero_nat ) )
% 0.29/0.47 | ( ( M = zero_zero_nat )
% 0.29/0.47 & ( N
% 0.29/0.47 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_683_diff__add__0,axiom,
% 0.29/0.47 ! [N: nat,M: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.29/0.47 = zero_zero_nat ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_684_diff__is__0__eq_H,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ( ( minus_minus_nat @ M @ N )
% 0.29/0.47 = zero_zero_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_685_diff__is__0__eq,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ( minus_minus_nat @ M @ N )
% 0.29/0.47 = zero_zero_nat )
% 0.29/0.47 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_686_One__nat__def,axiom,
% 0.29/0.47 ( one_one_nat
% 0.29/0.47 = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_687_diffs0__imp__equal,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ( minus_minus_nat @ M @ N )
% 0.29/0.47 = zero_zero_nat )
% 0.29/0.47 => ( ( ( minus_minus_nat @ N @ M )
% 0.29/0.47 = zero_zero_nat )
% 0.29/0.47 => ( M = N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_688_diff__self__eq__0,axiom,
% 0.29/0.47 ! [M: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ M @ M )
% 0.29/0.47 = zero_zero_nat ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_689_minus__nat_Odiff__0,axiom,
% 0.29/0.47 ! [M: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.29/0.47 = M ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_690_diff__0__eq__0,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.29/0.47 = zero_zero_nat ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_691_Suc__neq__Zero,axiom,
% 0.29/0.47 ! [M: nat] :
% 0.29/0.47 ( ( suc @ M )
% 0.29/0.47 != zero_zero_nat ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_692_Zero__neq__Suc,axiom,
% 0.29/0.47 ! [M: nat] :
% 0.29/0.47 ( zero_zero_nat
% 0.29/0.47 != ( suc @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_693_nat_Osimps_I3_J,axiom,
% 0.29/0.47 ! [Nat_1: nat] :
% 0.29/0.47 ( ( suc @ Nat_1 )
% 0.29/0.47 != zero_zero_nat ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_694_Suc__not__Zero,axiom,
% 0.29/0.47 ! [M: nat] :
% 0.29/0.47 ( ( suc @ M )
% 0.29/0.47 != zero_zero_nat ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_695_nat_Osimps_I2_J,axiom,
% 0.29/0.47 ! [Nat: nat] :
% 0.29/0.47 ( zero_zero_nat
% 0.29/0.47 != ( suc @ Nat ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_696_Zero__not__Suc,axiom,
% 0.29/0.47 ! [M: nat] :
% 0.29/0.47 ( zero_zero_nat
% 0.29/0.47 != ( suc @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_697_bot__nat__def,axiom,
% 0.29/0.47 bot_bot_nat = zero_zero_nat ).
% 0.29/0.47
% 0.29/0.47 thf(fact_698_le__0__eq,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.29/0.47 <=> ( N = zero_zero_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_699_less__eq__nat_Osimps_I1_J,axiom,
% 0.29/0.47 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.29/0.47
% 0.29/0.47 %----Helper facts (12)
% 0.29/0.47 thf(help_fequal_1_1_fequal_000t__a_T,axiom,
% 0.29/0.47 ! [X: x_a,Y: x_a] :
% 0.29/0.47 ( ~ ( fequal_a @ X @ Y )
% 0.29/0.47 | ( X = Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_2_1_fequal_000t__a_T,axiom,
% 0.29/0.47 ! [X: x_a,Y: x_a] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 | ( fequal_a @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ~ ( fequal_nat @ X @ Y )
% 0.29/0.47 | ( X = Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 | ( fequal_nat @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 0.29/0.47 ! [X: pname,Y: pname] :
% 0.29/0.47 ( ~ ( fequal_pname @ X @ Y )
% 0.29/0.47 | ( X = Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 0.29/0.47 ! [X: pname,Y: pname] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 | ( fequal_pname @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_1_1_fequal_000_062_It__a_M_Eo_J_T,axiom,
% 0.29/0.47 ! [X: x_a > $o,Y: x_a > $o] :
% 0.29/0.47 ( ~ ( fequal_a_o @ X @ Y )
% 0.29/0.47 | ( X = Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_2_1_fequal_000_062_It__a_M_Eo_J_T,axiom,
% 0.29/0.47 ! [X: x_a > $o,Y: x_a > $o] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 | ( fequal_a_o @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_1_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T,axiom,
% 0.29/0.47 ! [X: nat > $o,Y: nat > $o] :
% 0.29/0.47 ( ~ ( fequal_nat_o @ X @ Y )
% 0.29/0.47 | ( X = Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_2_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T,axiom,
% 0.29/0.47 ! [X: nat > $o,Y: nat > $o] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 | ( fequal_nat_o @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.29/0.47 ! [X: pname > $o,Y: pname > $o] :
% 0.29/0.47 ( ~ ( fequal_pname_o @ X @ Y )
% 0.29/0.47 | ( X = Y ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.29/0.47 ! [X: pname > $o,Y: pname > $o] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 | ( fequal_pname_o @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 %----Conjectures (7)
% 0.29/0.47 thf(conj_0,hypothesis,
% 0.29/0.47 finite_finite_pname @ u ).
% 0.29/0.47
% 0.29/0.47 thf(conj_1,hypothesis,
% 0.29/0.47 ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_2,hypothesis,
% 0.29/0.47 ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_3,hypothesis,
% 0.29/0.47 ( ( finite_card_a @ g )
% 0.29/0.47 = ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_4,hypothesis,
% 0.29/0.47 member_pname @ pn @ u ).
% 0.29/0.47
% 0.29/0.47 thf(conj_5,hypothesis,
% 0.29/0.47 ~ ( member_a @ ( mgt_call @ pn ) @ g ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_6,conjecture,
% 0.29/0.47 ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 0.30/1.60 ---- Embedded in THF ---
% 0.30/1.60 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.60 %%% Generated on Tue Feb 24 13:40:37 EST 2026
% 0.30/1.60 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.60 %%% Logic specification used:
% 0.30/1.60 %%% thf(spec, logic, $$dhol).
% 0.30/1.60
% 0.30/1.60 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2DTF10942.p
% See solution above
% 0.30/1.60 ------------------------
% 0.30/1.66 ---- Cleaned THF ---
% 0.30/1.66 thf(ty_ty_t__a,type,
% 0.30/1.66 x_a: $tType ).
% 0.30/1.66
% 0.30/1.66 thf(ty_ty_tc__Com__Ocom,type,
% 0.30/1.66 com: $tType ).
% 0.30/1.66
% 0.30/1.66 thf(ty_ty_tc__Com__Opname,type,
% 0.30/1.66 pname: $tType ).
% 0.30/1.66
% 0.30/1.66 thf(ty_ty_tc__Nat__Onat,type,
% 0.30/1.66 nat: $tType ).
% 0.30/1.66
% 0.30/1.66 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.30/1.66 option_com: $tType ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Com_Obody,type,
% 0.30/1.66 body: pname > option_com ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ocard_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ocard_000t__a,type,
% 0.30/1.66 finite_card_a: ( x_a > $o ) > nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ocard_000tc__Com__Opname,type,
% 0.30/1.66 finite_card_pname: ( pname > $o ) > nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
% 0.30/1.66 finite_card_nat: ( nat > $o ) > nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ofinite_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ofinite_000t__a,type,
% 0.30/1.66 finite_finite_a: ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.30/1.66 finite_finite_pname: ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
% 0.30/1.66 finite_finite_nat: ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.30/1.66 minus_minus_nat: nat > nat > nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.30/1.66 one_one_nat: nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.30/1.66 plus_plus_nat: nat > nat > nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.30/1.66 zero_zero_nat: nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Nat_OSuc,type,
% 0.30/1.66 suc: nat > nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Nat_Onat_Onat__case_000_Eo,type,
% 0.30/1.66 nat_case_o: $o > ( nat > $o ) > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 0.30/1.66 the_com: option_com > com ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 bot_bot_a_o_o: ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 bot_bot_nat_o_o: ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Obot__class_Obot_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 bot_bot_a_o: x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 bot_bot_pname_o: pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 bot_bot_nat_o: nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.30/1.66 bot_bot_o: $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Obot__class_Obot_000tc__Nat__Onat,type,
% 0.30/1.66 bot_bot_nat: nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.30/1.66 ord_less_nat: nat > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 0.30/1.66 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,
% 0.30/1.66 ord_less_eq_o: $o > $o > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 0.30/1.66 ord_less_eq_nat: nat > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_OCollect_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.30/1.66 collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_OCollect_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_OCollect_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_OCollect_000t__a,type,
% 0.30/1.66 collect_a: ( x_a > $o ) > x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.30/1.66 collect_pname: ( pname > $o ) > pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_OCollect_000tc__Nat__Onat,type,
% 0.30/1.66 collect_nat: ( nat > $o ) > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000t__a,type,
% 0.30/1.66 image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Com__Opname,type,
% 0.30/1.66 image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Nat__Onat,type,
% 0.30/1.66 image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000t__a,type,
% 0.30/1.66 image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 0.30/1.66 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat,type,
% 0.30/1.66 image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000t__a,type,
% 0.30/1.66 image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Com__Opname,type,
% 0.30/1.66 image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat,type,
% 0.30/1.66 image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000t__a_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 image_a_a_o: ( x_a > x_a > $o ) > ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000t__a_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 image_a_pname_o: ( x_a > pname > $o ) > ( x_a > $o ) > ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000t__a_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 image_a_nat_o: ( x_a > nat > $o ) > ( x_a > $o ) > ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000t__a_000t__a,type,
% 0.30/1.66 image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000t__a_000tc__Com__Opname,type,
% 0.30/1.66 image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000t__a_000tc__Nat__Onat,type,
% 0.30/1.66 image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Com__Opname_000t__a,type,
% 0.30/1.66 image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.30/1.66 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat,type,
% 0.30/1.66 image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000t__a,type,
% 0.30/1.66 image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,type,
% 0.30/1.66 image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Nat__Onat,type,
% 0.30/1.66 image_nat_nat: ( nat > nat ) > ( nat > $o ) > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oinsert_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oinsert_000t__a,type,
% 0.30/1.66 insert_a: x_a > ( x_a > $o ) > x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.30/1.66 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_Set_Oinsert_000tc__Nat__Onat,type,
% 0.30/1.66 insert_nat: nat > ( nat > $o ) > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_fequal_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 fequal_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_fequal_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 fequal_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_fequal_000t__a,type,
% 0.30/1.66 fequal_a: x_a > x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_fequal_000tc__Com__Opname,type,
% 0.30/1.66 fequal_pname: pname > pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_fequal_000tc__Nat__Onat,type,
% 0.30/1.66 fequal_nat: nat > nat > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_member_000_062_It__a_M_Eo_J,type,
% 0.30/1.66 member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/1.66 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/1.66 member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_member_000t__a,type,
% 0.30/1.66 member_a: x_a > ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_member_000tc__Com__Opname,type,
% 0.30/1.66 member_pname: pname > ( pname > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_c_member_000tc__Nat__Onat,type,
% 0.30/1.66 member_nat: nat > ( nat > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_v_G,type,
% 0.30/1.66 g: x_a > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_v_P,type,
% 0.30/1.66 p: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_v_U,type,
% 0.30/1.66 u: pname > $o ).
% 0.30/1.66
% 0.30/1.66 thf(sy_v_mgt,type,
% 0.30/1.66 mgt: com > x_a ).
% 0.30/1.66
% 0.30/1.66 thf(sy_v_mgt__call,type,
% 0.30/1.66 mgt_call: pname > x_a ).
% 0.30/1.66
% 0.30/1.66 thf(sy_v_na,type,
% 0.30/1.66 na: nat ).
% 0.30/1.66
% 0.30/1.66 thf(sy_v_pn,type,
% 0.30/1.66 pn: pname ).
% 0.30/1.66
% 0.30/1.66 thf(sy_v_wt,type,
% 0.30/1.66 wt: com > $o ).
% 0.30/1.66
% 0.30/1.66 thf(fact_0_assms_I1_J,axiom,
% 0.30/1.66 ! [Ts: x_a > $o,G: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ Ts @ G )
% 0.30/1.66 => ( p @ G @ Ts ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_1_finite__Collect__subsets,axiom,
% 0.30/1.66 ! [A_92: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_92 )
% 0.30/1.66 => ( finite1676163439at_o_o
% 0.30/1.66 @ ( collect_nat_o_o
% 0.30/1.66 @ ^ [B_47: ( nat > $o ) > $o] : ( ord_less_eq_nat_o_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_2_finite__Collect__subsets,axiom,
% 0.30/1.66 ! [A_92: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_92 )
% 0.30/1.66 => ( finite1066544169me_o_o
% 0.30/1.66 @ ( collect_pname_o_o
% 0.30/1.66 @ ^ [B_47: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_3_finite__Collect__subsets,axiom,
% 0.30/1.66 ! [A_92: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_92 )
% 0.30/1.66 => ( finite_finite_a_o_o
% 0.30/1.66 @ ( collect_a_o_o
% 0.30/1.66 @ ^ [B_47: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_4_finite__Collect__subsets,axiom,
% 0.30/1.66 ! [A_92: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_92 )
% 0.30/1.66 => ( finite_finite_a_o
% 0.30/1.66 @ ( collect_a_o
% 0.30/1.66 @ ^ [B_47: x_a > $o] : ( ord_less_eq_a_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_5_finite__Collect__subsets,axiom,
% 0.30/1.66 ! [A_92: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_92 )
% 0.30/1.66 => ( finite297249702name_o
% 0.30/1.66 @ ( collect_pname_o
% 0.30/1.66 @ ^ [B_47: pname > $o] : ( ord_less_eq_pname_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_6_finite__Collect__subsets,axiom,
% 0.30/1.66 ! [A_92: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_92 )
% 0.30/1.66 => ( finite_finite_nat_o
% 0.30/1.66 @ ( collect_nat_o
% 0.30/1.66 @ ^ [B_47: nat > $o] : ( ord_less_eq_nat_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_7_finite__imageI,axiom,
% 0.30/1.66 ! [H: pname > nat > $o,F_25: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ F_25 )
% 0.30/1.66 => ( finite_finite_nat_o @ ( image_pname_nat_o @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_8_finite__imageI,axiom,
% 0.30/1.66 ! [H: pname > pname > $o,F_25: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ F_25 )
% 0.30/1.66 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_9_finite__imageI,axiom,
% 0.30/1.66 ! [H: pname > x_a > $o,F_25: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ F_25 )
% 0.30/1.66 => ( finite_finite_a_o @ ( image_pname_a_o @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_10_finite__imageI,axiom,
% 0.30/1.66 ! [H: nat > x_a,F_25: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ F_25 )
% 0.30/1.66 => ( finite_finite_a @ ( image_nat_a @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_11_finite__imageI,axiom,
% 0.30/1.66 ! [H: nat > nat > $o,F_25: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ F_25 )
% 0.30/1.66 => ( finite_finite_nat_o @ ( image_nat_nat_o @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_12_finite__imageI,axiom,
% 0.30/1.66 ! [H: nat > pname > $o,F_25: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ F_25 )
% 0.30/1.66 => ( finite297249702name_o @ ( image_nat_pname_o @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_13_finite__imageI,axiom,
% 0.30/1.66 ! [H: nat > x_a > $o,F_25: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ F_25 )
% 0.30/1.66 => ( finite_finite_a_o @ ( image_nat_a_o @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_14_finite__imageI,axiom,
% 0.30/1.66 ! [H: x_a > pname,F_25: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ F_25 )
% 0.30/1.66 => ( finite_finite_pname @ ( image_a_pname @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_15_finite__imageI,axiom,
% 0.30/1.66 ! [H: ( nat > $o ) > pname,F_25: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ F_25 )
% 0.30/1.66 => ( finite_finite_pname @ ( image_nat_o_pname @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_16_finite__imageI,axiom,
% 0.30/1.66 ! [H: ( pname > $o ) > pname,F_25: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ F_25 )
% 0.30/1.66 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_17_finite__imageI,axiom,
% 0.30/1.66 ! [H: ( x_a > $o ) > pname,F_25: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ F_25 )
% 0.30/1.66 => ( finite_finite_pname @ ( image_a_o_pname @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_18_finite__imageI,axiom,
% 0.30/1.66 ! [H: x_a > nat,F_25: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ F_25 )
% 0.30/1.66 => ( finite_finite_nat @ ( image_a_nat @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_19_finite__imageI,axiom,
% 0.30/1.66 ! [H: ( nat > $o ) > nat,F_25: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ F_25 )
% 0.30/1.66 => ( finite_finite_nat @ ( image_nat_o_nat @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_20_finite__imageI,axiom,
% 0.30/1.66 ! [H: ( pname > $o ) > nat,F_25: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ F_25 )
% 0.30/1.66 => ( finite_finite_nat @ ( image_pname_o_nat @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_21_finite__imageI,axiom,
% 0.30/1.66 ! [H: ( x_a > $o ) > nat,F_25: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ F_25 )
% 0.30/1.66 => ( finite_finite_nat @ ( image_a_o_nat @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_22_finite__imageI,axiom,
% 0.30/1.66 ! [H: pname > x_a,F_25: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ F_25 )
% 0.30/1.66 => ( finite_finite_a @ ( image_pname_a @ H @ F_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_23_finite_OinsertI,axiom,
% 0.30/1.66 ! [A_91: nat > $o,A_90: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_90 )
% 0.30/1.66 => ( finite_finite_nat_o @ ( insert_nat_o @ A_91 @ A_90 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_24_finite_OinsertI,axiom,
% 0.30/1.66 ! [A_91: pname > $o,A_90: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_90 )
% 0.30/1.66 => ( finite297249702name_o @ ( insert_pname_o @ A_91 @ A_90 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_25_finite_OinsertI,axiom,
% 0.30/1.66 ! [A_91: x_a > $o,A_90: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_90 )
% 0.30/1.66 => ( finite_finite_a_o @ ( insert_a_o @ A_91 @ A_90 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_26_finite_OinsertI,axiom,
% 0.30/1.66 ! [A_91: pname,A_90: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_90 )
% 0.30/1.66 => ( finite_finite_pname @ ( insert_pname @ A_91 @ A_90 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_27_finite_OinsertI,axiom,
% 0.30/1.66 ! [A_91: nat,A_90: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_90 )
% 0.30/1.66 => ( finite_finite_nat @ ( insert_nat @ A_91 @ A_90 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_28_finite_OinsertI,axiom,
% 0.30/1.66 ! [A_91: x_a,A_90: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_90 )
% 0.30/1.66 => ( finite_finite_a @ ( insert_a @ A_91 @ A_90 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_29_card__image__le,axiom,
% 0.30/1.66 ! [F_24: pname > pname,A_89: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ F_24 @ A_89 ) ) @ ( finite_card_pname @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_30_card__image__le,axiom,
% 0.30/1.66 ! [F_24: x_a > x_a,A_89: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ F_24 @ A_89 ) ) @ ( finite_card_a @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_31_card__image__le,axiom,
% 0.30/1.66 ! [F_24: ( nat > $o ) > x_a,A_89: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_a @ F_24 @ A_89 ) ) @ ( finite_card_nat_o @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_32_card__image__le,axiom,
% 0.30/1.66 ! [F_24: ( pname > $o ) > x_a,A_89: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_a @ F_24 @ A_89 ) ) @ ( finite_card_pname_o @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_33_card__image__le,axiom,
% 0.30/1.66 ! [F_24: ( x_a > $o ) > x_a,A_89: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ F_24 @ A_89 ) ) @ ( finite_card_a_o @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_34_card__image__le,axiom,
% 0.30/1.66 ! [F_24: pname > nat,A_89: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ F_24 @ A_89 ) ) @ ( finite_card_pname @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_35_card__image__le,axiom,
% 0.30/1.66 ! [F_24: x_a > nat,A_89: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ F_24 @ A_89 ) ) @ ( finite_card_a @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_36_card__image__le,axiom,
% 0.30/1.66 ! [F_24: ( nat > $o ) > nat,A_89: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_o_nat @ F_24 @ A_89 ) ) @ ( finite_card_nat_o @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_37_card__image__le,axiom,
% 0.30/1.66 ! [F_24: ( pname > $o ) > nat,A_89: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_o_nat @ F_24 @ A_89 ) ) @ ( finite_card_pname_o @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_38_card__image__le,axiom,
% 0.30/1.66 ! [F_24: ( x_a > $o ) > nat,A_89: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ F_24 @ A_89 ) ) @ ( finite_card_a_o @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_39_card__image__le,axiom,
% 0.30/1.66 ! [F_24: x_a > pname,A_89: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ F_24 @ A_89 ) ) @ ( finite_card_a @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_40_card__image__le,axiom,
% 0.30/1.66 ! [F_24: nat > pname,A_89: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_pname @ F_24 @ A_89 ) ) @ ( finite_card_nat @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_41_card__image__le,axiom,
% 0.30/1.66 ! [F_24: pname > x_a,A_89: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_89 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ F_24 @ A_89 ) ) @ ( finite_card_pname @ A_89 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_42_card__mono,axiom,
% 0.30/1.66 ! [A_88: ( nat > $o ) > $o,B_46: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ B_46 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o_o @ A_88 @ B_46 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_88 ) @ ( finite_card_nat_o @ B_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_43_card__mono,axiom,
% 0.30/1.66 ! [A_88: ( pname > $o ) > $o,B_46: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ B_46 )
% 0.30/1.66 => ( ( ord_le1205211808me_o_o @ A_88 @ B_46 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_88 ) @ ( finite_card_pname_o @ B_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_44_card__mono,axiom,
% 0.30/1.66 ! [A_88: ( x_a > $o ) > $o,B_46: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ B_46 )
% 0.30/1.66 => ( ( ord_less_eq_a_o_o @ A_88 @ B_46 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_88 ) @ ( finite_card_a_o @ B_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_45_card__mono,axiom,
% 0.30/1.66 ! [A_88: pname > $o,B_46: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ B_46 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ A_88 @ B_46 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_pname @ A_88 ) @ ( finite_card_pname @ B_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_46_card__mono,axiom,
% 0.30/1.66 ! [A_88: x_a > $o,B_46: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ B_46 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ A_88 @ B_46 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_a @ A_88 ) @ ( finite_card_a @ B_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_47_card__mono,axiom,
% 0.30/1.66 ! [A_88: nat > $o,B_46: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ B_46 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ A_88 @ B_46 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_nat @ A_88 ) @ ( finite_card_nat @ B_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_48_card__seteq,axiom,
% 0.30/1.66 ! [A_87: ( nat > $o ) > $o,B_45: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o_o @ A_87 @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ ( finite_card_nat_o @ B_45 ) @ ( finite_card_nat_o @ A_87 ) )
% 0.30/1.66 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_49_card__seteq,axiom,
% 0.30/1.66 ! [A_87: ( pname > $o ) > $o,B_45: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ B_45 )
% 0.30/1.66 => ( ( ord_le1205211808me_o_o @ A_87 @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ ( finite_card_pname_o @ B_45 ) @ ( finite_card_pname_o @ A_87 ) )
% 0.30/1.66 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_50_card__seteq,axiom,
% 0.30/1.66 ! [A_87: ( x_a > $o ) > $o,B_45: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_a_o_o @ A_87 @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ ( finite_card_a_o @ B_45 ) @ ( finite_card_a_o @ A_87 ) )
% 0.30/1.66 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_51_card__seteq,axiom,
% 0.30/1.66 ! [A_87: pname > $o,B_45: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ A_87 @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ ( finite_card_pname @ B_45 ) @ ( finite_card_pname @ A_87 ) )
% 0.30/1.66 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_52_card__seteq,axiom,
% 0.30/1.66 ! [A_87: x_a > $o,B_45: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ A_87 @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ ( finite_card_a @ B_45 ) @ ( finite_card_a @ A_87 ) )
% 0.30/1.66 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_53_card__seteq,axiom,
% 0.30/1.66 ! [A_87: nat > $o,B_45: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ A_87 @ B_45 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B_45 ) @ ( finite_card_nat @ A_87 ) )
% 0.30/1.66 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_54_card__insert__le,axiom,
% 0.30/1.66 ! [X_33: nat > $o,A_86: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_86 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_86 ) @ ( finite_card_nat_o @ ( insert_nat_o @ X_33 @ A_86 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_55_card__insert__le,axiom,
% 0.30/1.66 ! [X_33: pname > $o,A_86: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_86 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_86 ) @ ( finite_card_pname_o @ ( insert_pname_o @ X_33 @ A_86 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_56_card__insert__le,axiom,
% 0.30/1.66 ! [X_33: x_a > $o,A_86: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_86 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_86 ) @ ( finite_card_a_o @ ( insert_a_o @ X_33 @ A_86 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_57_card__insert__le,axiom,
% 0.30/1.66 ! [X_33: pname,A_86: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_86 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_pname @ A_86 ) @ ( finite_card_pname @ ( insert_pname @ X_33 @ A_86 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_58_card__insert__le,axiom,
% 0.30/1.66 ! [X_33: nat,A_86: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_86 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_nat @ A_86 ) @ ( finite_card_nat @ ( insert_nat @ X_33 @ A_86 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_59_card__insert__le,axiom,
% 0.30/1.66 ! [X_33: x_a,A_86: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_86 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( finite_card_a @ A_86 ) @ ( finite_card_a @ ( insert_a @ X_33 @ A_86 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_60_card__insert__if,axiom,
% 0.30/1.66 ! [X_32: nat > $o,A_85: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_85 )
% 0.30/1.66 => ( ( ( member_nat_o @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_32 @ A_85 ) )
% 0.30/1.66 = ( finite_card_nat_o @ A_85 ) ) )
% 0.30/1.66 & ( ~ ( member_nat_o @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_32 @ A_85 ) )
% 0.30/1.66 = ( suc @ ( finite_card_nat_o @ A_85 ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_61_card__insert__if,axiom,
% 0.30/1.66 ! [X_32: pname > $o,A_85: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_85 )
% 0.30/1.66 => ( ( ( member_pname_o @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_32 @ A_85 ) )
% 0.30/1.66 = ( finite_card_pname_o @ A_85 ) ) )
% 0.30/1.66 & ( ~ ( member_pname_o @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_32 @ A_85 ) )
% 0.30/1.66 = ( suc @ ( finite_card_pname_o @ A_85 ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_62_card__insert__if,axiom,
% 0.30/1.66 ! [X_32: x_a > $o,A_85: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_85 )
% 0.30/1.66 => ( ( ( member_a_o @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_a_o @ ( insert_a_o @ X_32 @ A_85 ) )
% 0.30/1.66 = ( finite_card_a_o @ A_85 ) ) )
% 0.30/1.66 & ( ~ ( member_a_o @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_a_o @ ( insert_a_o @ X_32 @ A_85 ) )
% 0.30/1.66 = ( suc @ ( finite_card_a_o @ A_85 ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_63_card__insert__if,axiom,
% 0.30/1.66 ! [X_32: nat,A_85: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_85 )
% 0.30/1.66 => ( ( ( member_nat @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_nat @ ( insert_nat @ X_32 @ A_85 ) )
% 0.30/1.66 = ( finite_card_nat @ A_85 ) ) )
% 0.30/1.66 & ( ~ ( member_nat @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_nat @ ( insert_nat @ X_32 @ A_85 ) )
% 0.30/1.66 = ( suc @ ( finite_card_nat @ A_85 ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_64_card__insert__if,axiom,
% 0.30/1.66 ! [X_32: pname,A_85: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_85 )
% 0.30/1.66 => ( ( ( member_pname @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_pname @ ( insert_pname @ X_32 @ A_85 ) )
% 0.30/1.66 = ( finite_card_pname @ A_85 ) ) )
% 0.30/1.66 & ( ~ ( member_pname @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_pname @ ( insert_pname @ X_32 @ A_85 ) )
% 0.30/1.66 = ( suc @ ( finite_card_pname @ A_85 ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_65_card__insert__if,axiom,
% 0.30/1.66 ! [X_32: x_a,A_85: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_85 )
% 0.30/1.66 => ( ( ( member_a @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_a @ ( insert_a @ X_32 @ A_85 ) )
% 0.30/1.66 = ( finite_card_a @ A_85 ) ) )
% 0.30/1.66 & ( ~ ( member_a @ X_32 @ A_85 )
% 0.30/1.66 => ( ( finite_card_a @ ( insert_a @ X_32 @ A_85 ) )
% 0.30/1.66 = ( suc @ ( finite_card_a @ A_85 ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_66_card__insert__disjoint,axiom,
% 0.30/1.66 ! [X_31: nat > $o,A_84: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_84 )
% 0.30/1.66 => ( ~ ( member_nat_o @ X_31 @ A_84 )
% 0.30/1.66 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_31 @ A_84 ) )
% 0.30/1.66 = ( suc @ ( finite_card_nat_o @ A_84 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_67_card__insert__disjoint,axiom,
% 0.30/1.66 ! [X_31: pname > $o,A_84: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_84 )
% 0.30/1.66 => ( ~ ( member_pname_o @ X_31 @ A_84 )
% 0.30/1.66 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_31 @ A_84 ) )
% 0.30/1.66 = ( suc @ ( finite_card_pname_o @ A_84 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_68_card__insert__disjoint,axiom,
% 0.30/1.66 ! [X_31: x_a > $o,A_84: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_84 )
% 0.30/1.66 => ( ~ ( member_a_o @ X_31 @ A_84 )
% 0.30/1.66 => ( ( finite_card_a_o @ ( insert_a_o @ X_31 @ A_84 ) )
% 0.30/1.66 = ( suc @ ( finite_card_a_o @ A_84 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_69_card__insert__disjoint,axiom,
% 0.30/1.66 ! [X_31: nat,A_84: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_84 )
% 0.30/1.66 => ( ~ ( member_nat @ X_31 @ A_84 )
% 0.30/1.66 => ( ( finite_card_nat @ ( insert_nat @ X_31 @ A_84 ) )
% 0.30/1.66 = ( suc @ ( finite_card_nat @ A_84 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_70_card__insert__disjoint,axiom,
% 0.30/1.66 ! [X_31: pname,A_84: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_84 )
% 0.30/1.66 => ( ~ ( member_pname @ X_31 @ A_84 )
% 0.30/1.66 => ( ( finite_card_pname @ ( insert_pname @ X_31 @ A_84 ) )
% 0.30/1.66 = ( suc @ ( finite_card_pname @ A_84 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_71_card__insert__disjoint,axiom,
% 0.30/1.66 ! [X_31: x_a,A_84: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_84 )
% 0.30/1.66 => ( ~ ( member_a @ X_31 @ A_84 )
% 0.30/1.66 => ( ( finite_card_a @ ( insert_a @ X_31 @ A_84 ) )
% 0.30/1.66 = ( suc @ ( finite_card_a @ A_84 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_72_finite__Collect__conjI,axiom,
% 0.30/1.66 ! [Q_1: x_a > $o,P_10: x_a > $o] :
% 0.30/1.66 ( ( ( finite_finite_a @ ( collect_a @ P_10 ) )
% 0.30/1.66 | ( finite_finite_a @ ( collect_a @ Q_1 ) ) )
% 0.30/1.66 => ( finite_finite_a
% 0.30/1.66 @ ( collect_a
% 0.30/1.66 @ ^ [X_1: x_a] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_73_finite__Collect__conjI,axiom,
% 0.30/1.66 ! [Q_1: ( nat > $o ) > $o,P_10: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( ( finite_finite_nat_o @ ( collect_nat_o @ P_10 ) )
% 0.30/1.66 | ( finite_finite_nat_o @ ( collect_nat_o @ Q_1 ) ) )
% 0.30/1.66 => ( finite_finite_nat_o
% 0.30/1.66 @ ( collect_nat_o
% 0.30/1.66 @ ^ [X_1: nat > $o] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_74_finite__Collect__conjI,axiom,
% 0.30/1.66 ! [Q_1: ( pname > $o ) > $o,P_10: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_10 ) )
% 0.30/1.66 | ( finite297249702name_o @ ( collect_pname_o @ Q_1 ) ) )
% 0.30/1.66 => ( finite297249702name_o
% 0.30/1.66 @ ( collect_pname_o
% 0.30/1.66 @ ^ [X_1: pname > $o] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_75_finite__Collect__conjI,axiom,
% 0.30/1.66 ! [Q_1: ( x_a > $o ) > $o,P_10: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( ( finite_finite_a_o @ ( collect_a_o @ P_10 ) )
% 0.30/1.66 | ( finite_finite_a_o @ ( collect_a_o @ Q_1 ) ) )
% 0.30/1.66 => ( finite_finite_a_o
% 0.30/1.66 @ ( collect_a_o
% 0.30/1.66 @ ^ [X_1: x_a > $o] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_76_finite__Collect__conjI,axiom,
% 0.30/1.66 ! [Q_1: pname > $o,P_10: pname > $o] :
% 0.30/1.66 ( ( ( finite_finite_pname @ ( collect_pname @ P_10 ) )
% 0.30/1.66 | ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
% 0.30/1.66 => ( finite_finite_pname
% 0.30/1.66 @ ( collect_pname
% 0.30/1.66 @ ^ [X_1: pname] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_77_finite__Collect__conjI,axiom,
% 0.30/1.66 ! [Q_1: nat > $o,P_10: nat > $o] :
% 0.30/1.66 ( ( ( finite_finite_nat @ ( collect_nat @ P_10 ) )
% 0.30/1.66 | ( finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
% 0.30/1.66 => ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [X_1: nat] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_78_Suc__diff__le,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ N @ M )
% 0.30/1.66 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.30/1.66 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_79_finite__Collect__le__nat,axiom,
% 0.30/1.66 ! [K: nat] :
% 0.30/1.66 ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [N_2: nat] : ( ord_less_eq_nat @ N_2 @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_80_card__Collect__le__nat,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ( ( finite_card_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [I_1: nat] : ( ord_less_eq_nat @ I_1 @ N ) ) )
% 0.30/1.66 = ( suc @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_81_Suc__inject,axiom,
% 0.30/1.66 ! [X: nat,Y: nat] :
% 0.30/1.66 ( ( ( suc @ X )
% 0.30/1.66 = ( suc @ Y ) )
% 0.30/1.66 => ( X = Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_82_nat_Oinject,axiom,
% 0.30/1.66 ! [Nat_2: nat,Nat: nat] :
% 0.30/1.66 ( ( ( suc @ Nat_2 )
% 0.30/1.66 = ( suc @ Nat ) )
% 0.30/1.66 <=> ( Nat_2 = Nat ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_83_Suc__n__not__n,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ( ( suc @ N )
% 0.30/1.66 != N ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_84_n__not__Suc__n,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ( N
% 0.30/1.66 != ( suc @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_85_le__antisym,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ( ( ord_less_eq_nat @ N @ M )
% 0.30/1.66 => ( M = N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_86_le__trans,axiom,
% 0.30/1.66 ! [K: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ J_1 @ K )
% 0.30/1.66 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_87_eq__imp__le,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( M = N )
% 0.30/1.66 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_88_nat__le__linear,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_89_le__refl,axiom,
% 0.30/1.66 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_90_diff__commute,axiom,
% 0.30/1.66 ! [I: nat,J_1: nat,K: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J_1 ) @ K )
% 0.30/1.66 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_91_finite__Collect__disjI,axiom,
% 0.30/1.66 ! [P_9: x_a > $o,Q: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a
% 0.30/1.66 @ ( collect_a
% 0.30/1.66 @ ^ [X_1: x_a] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/1.66 <=> ( ( finite_finite_a @ ( collect_a @ P_9 ) )
% 0.30/1.66 & ( finite_finite_a @ ( collect_a @ Q ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_92_finite__Collect__disjI,axiom,
% 0.30/1.66 ! [P_9: ( nat > $o ) > $o,Q: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o
% 0.30/1.66 @ ( collect_nat_o
% 0.30/1.66 @ ^ [X_1: nat > $o] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/1.66 <=> ( ( finite_finite_nat_o @ ( collect_nat_o @ P_9 ) )
% 0.30/1.66 & ( finite_finite_nat_o @ ( collect_nat_o @ Q ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_93_finite__Collect__disjI,axiom,
% 0.30/1.66 ! [P_9: ( pname > $o ) > $o,Q: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o
% 0.30/1.66 @ ( collect_pname_o
% 0.30/1.66 @ ^ [X_1: pname > $o] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/1.66 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_9 ) )
% 0.30/1.66 & ( finite297249702name_o @ ( collect_pname_o @ Q ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_94_finite__Collect__disjI,axiom,
% 0.30/1.66 ! [P_9: ( x_a > $o ) > $o,Q: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o
% 0.30/1.66 @ ( collect_a_o
% 0.30/1.66 @ ^ [X_1: x_a > $o] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/1.66 <=> ( ( finite_finite_a_o @ ( collect_a_o @ P_9 ) )
% 0.30/1.66 & ( finite_finite_a_o @ ( collect_a_o @ Q ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_95_finite__Collect__disjI,axiom,
% 0.30/1.66 ! [P_9: pname > $o,Q: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname
% 0.30/1.66 @ ( collect_pname
% 0.30/1.66 @ ^ [X_1: pname] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/1.66 <=> ( ( finite_finite_pname @ ( collect_pname @ P_9 ) )
% 0.30/1.66 & ( finite_finite_pname @ ( collect_pname @ Q ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_96_finite__Collect__disjI,axiom,
% 0.30/1.66 ! [P_9: nat > $o,Q: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [X_1: nat] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/1.66 <=> ( ( finite_finite_nat @ ( collect_nat @ P_9 ) )
% 0.30/1.66 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_97_finite__insert,axiom,
% 0.30/1.66 ! [A_83: nat > $o,A_82: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ ( insert_nat_o @ A_83 @ A_82 ) )
% 0.30/1.66 <=> ( finite_finite_nat_o @ A_82 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_98_finite__insert,axiom,
% 0.30/1.66 ! [A_83: pname > $o,A_82: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ ( insert_pname_o @ A_83 @ A_82 ) )
% 0.30/1.66 <=> ( finite297249702name_o @ A_82 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_99_finite__insert,axiom,
% 0.30/1.66 ! [A_83: x_a > $o,A_82: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ ( insert_a_o @ A_83 @ A_82 ) )
% 0.30/1.66 <=> ( finite_finite_a_o @ A_82 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_100_finite__insert,axiom,
% 0.30/1.66 ! [A_83: pname,A_82: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ ( insert_pname @ A_83 @ A_82 ) )
% 0.30/1.66 <=> ( finite_finite_pname @ A_82 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_101_finite__insert,axiom,
% 0.30/1.66 ! [A_83: nat,A_82: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ ( insert_nat @ A_83 @ A_82 ) )
% 0.30/1.66 <=> ( finite_finite_nat @ A_82 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_102_finite__insert,axiom,
% 0.30/1.66 ! [A_83: x_a,A_82: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ ( insert_a @ A_83 @ A_82 ) )
% 0.30/1.66 <=> ( finite_finite_a @ A_82 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_103_finite__subset,axiom,
% 0.30/1.66 ! [A_81: ( nat > $o ) > $o,B_44: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o_o @ A_81 @ B_44 )
% 0.30/1.66 => ( ( finite_finite_nat_o @ B_44 )
% 0.30/1.66 => ( finite_finite_nat_o @ A_81 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_104_finite__subset,axiom,
% 0.30/1.66 ! [A_81: ( pname > $o ) > $o,B_44: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( ord_le1205211808me_o_o @ A_81 @ B_44 )
% 0.30/1.66 => ( ( finite297249702name_o @ B_44 )
% 0.30/1.66 => ( finite297249702name_o @ A_81 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_105_finite__subset,axiom,
% 0.30/1.66 ! [A_81: ( x_a > $o ) > $o,B_44: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o_o @ A_81 @ B_44 )
% 0.30/1.66 => ( ( finite_finite_a_o @ B_44 )
% 0.30/1.66 => ( finite_finite_a_o @ A_81 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_106_finite__subset,axiom,
% 0.30/1.66 ! [A_81: x_a > $o,B_44: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_81 @ B_44 )
% 0.30/1.66 => ( ( finite_finite_a @ B_44 )
% 0.30/1.66 => ( finite_finite_a @ A_81 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_107_finite__subset,axiom,
% 0.30/1.66 ! [A_81: pname > $o,B_44: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_81 @ B_44 )
% 0.30/1.66 => ( ( finite_finite_pname @ B_44 )
% 0.30/1.66 => ( finite_finite_pname @ A_81 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_108_finite__subset,axiom,
% 0.30/1.66 ! [A_81: nat > $o,B_44: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_81 @ B_44 )
% 0.30/1.66 => ( ( finite_finite_nat @ B_44 )
% 0.30/1.66 => ( finite_finite_nat @ A_81 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_109_rev__finite__subset,axiom,
% 0.30/1.66 ! [A_80: ( nat > $o ) > $o,B_43: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ B_43 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o_o @ A_80 @ B_43 )
% 0.30/1.66 => ( finite_finite_nat_o @ A_80 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_110_rev__finite__subset,axiom,
% 0.30/1.66 ! [A_80: ( pname > $o ) > $o,B_43: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ B_43 )
% 0.30/1.66 => ( ( ord_le1205211808me_o_o @ A_80 @ B_43 )
% 0.30/1.66 => ( finite297249702name_o @ A_80 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_111_rev__finite__subset,axiom,
% 0.30/1.66 ! [A_80: ( x_a > $o ) > $o,B_43: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ B_43 )
% 0.30/1.66 => ( ( ord_less_eq_a_o_o @ A_80 @ B_43 )
% 0.30/1.66 => ( finite_finite_a_o @ A_80 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_112_rev__finite__subset,axiom,
% 0.30/1.66 ! [A_80: x_a > $o,B_43: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ B_43 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ A_80 @ B_43 )
% 0.30/1.66 => ( finite_finite_a @ A_80 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_113_rev__finite__subset,axiom,
% 0.30/1.66 ! [A_80: pname > $o,B_43: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ B_43 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ A_80 @ B_43 )
% 0.30/1.66 => ( finite_finite_pname @ A_80 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_114_rev__finite__subset,axiom,
% 0.30/1.66 ! [A_80: nat > $o,B_43: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ B_43 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ A_80 @ B_43 )
% 0.30/1.66 => ( finite_finite_nat @ A_80 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_115_Suc__leD,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.30/1.66 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_116_le__SucE,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/1.66 => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ( M
% 0.30/1.66 = ( suc @ N ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_117_le__SucI,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_118_Suc__le__mono,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.30/1.66 <=> ( ord_less_eq_nat @ N @ M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_119_le__Suc__eq,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/1.66 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 | ( M
% 0.30/1.66 = ( suc @ N ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_120_not__less__eq__eq,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ~ ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_121_Suc__n__not__le__n,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_122_Suc__diff__diff,axiom,
% 0.30/1.66 ! [M: nat,N: nat,K: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.30/1.66 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_123_diff__Suc__Suc,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.30/1.66 = ( minus_minus_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_124_le__diff__iff,axiom,
% 0.30/1.66 ! [N: nat,K: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ M )
% 0.30/1.66 => ( ( ord_less_eq_nat @ K @ N )
% 0.30/1.66 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.30/1.66 <=> ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_125_Nat_Odiff__diff__eq,axiom,
% 0.30/1.66 ! [N: nat,K: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ M )
% 0.30/1.66 => ( ( ord_less_eq_nat @ K @ N )
% 0.30/1.66 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.30/1.66 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_126_eq__diff__iff,axiom,
% 0.30/1.66 ! [N: nat,K: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ M )
% 0.30/1.66 => ( ( ord_less_eq_nat @ K @ N )
% 0.30/1.66 => ( ( ( minus_minus_nat @ M @ K )
% 0.30/1.66 = ( minus_minus_nat @ N @ K ) )
% 0.30/1.66 <=> ( M = N ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_127_diff__diff__cancel,axiom,
% 0.30/1.66 ! [I: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ I @ N )
% 0.30/1.66 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.30/1.66 = I ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_128_diff__le__mono,axiom,
% 0.30/1.66 ! [L: nat,M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_129_diff__le__mono2,axiom,
% 0.30/1.66 ! [L: nat,M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_130_diff__le__self,axiom,
% 0.30/1.66 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_131_finite__surj,axiom,
% 0.30/1.66 ! [B_42: x_a > $o,F_23: x_a > x_a,A_79: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_42 @ ( image_a_a @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_132_finite__surj,axiom,
% 0.30/1.66 ! [B_42: x_a > $o,F_23: ( nat > $o ) > x_a,A_79: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_42 @ ( image_nat_o_a @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_133_finite__surj,axiom,
% 0.30/1.66 ! [B_42: x_a > $o,F_23: ( pname > $o ) > x_a,A_79: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_42 @ ( image_pname_o_a @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_134_finite__surj,axiom,
% 0.30/1.66 ! [B_42: x_a > $o,F_23: ( x_a > $o ) > x_a,A_79: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_42 @ ( image_a_o_a @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_135_finite__surj,axiom,
% 0.30/1.66 ! [B_42: ( nat > $o ) > $o,F_23: pname > nat > $o,A_79: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o_o @ B_42 @ ( image_pname_nat_o @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_nat_o @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_136_finite__surj,axiom,
% 0.30/1.66 ! [B_42: ( pname > $o ) > $o,F_23: pname > pname > $o,A_79: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_79 )
% 0.30/1.66 => ( ( ord_le1205211808me_o_o @ B_42 @ ( image_pname_pname_o @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite297249702name_o @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_137_finite__surj,axiom,
% 0.30/1.66 ! [B_42: ( x_a > $o ) > $o,F_23: pname > x_a > $o,A_79: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_a_o_o @ B_42 @ ( image_pname_a_o @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_a_o @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_138_finite__surj,axiom,
% 0.30/1.66 ! [B_42: pname > $o,F_23: pname > pname,A_79: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_pname_pname @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_139_finite__surj,axiom,
% 0.30/1.66 ! [B_42: nat > $o,F_23: pname > nat,A_79: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_pname_nat @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_140_finite__surj,axiom,
% 0.30/1.66 ! [B_42: x_a > $o,F_23: nat > x_a,A_79: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_42 @ ( image_nat_a @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_141_finite__surj,axiom,
% 0.30/1.66 ! [B_42: ( nat > $o ) > $o,F_23: nat > nat > $o,A_79: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o_o @ B_42 @ ( image_nat_nat_o @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_nat_o @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_142_finite__surj,axiom,
% 0.30/1.66 ! [B_42: ( pname > $o ) > $o,F_23: nat > pname > $o,A_79: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_79 )
% 0.30/1.66 => ( ( ord_le1205211808me_o_o @ B_42 @ ( image_nat_pname_o @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite297249702name_o @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_143_finite__surj,axiom,
% 0.30/1.66 ! [B_42: ( x_a > $o ) > $o,F_23: nat > x_a > $o,A_79: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_a_o_o @ B_42 @ ( image_nat_a_o @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_a_o @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_144_finite__surj,axiom,
% 0.30/1.66 ! [B_42: pname > $o,F_23: nat > pname,A_79: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_nat_pname @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_145_finite__surj,axiom,
% 0.30/1.66 ! [B_42: nat > $o,F_23: nat > nat,A_79: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_nat_nat @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_146_finite__surj,axiom,
% 0.30/1.66 ! [B_42: pname > $o,F_23: x_a > pname,A_79: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_a_pname @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_147_finite__surj,axiom,
% 0.30/1.66 ! [B_42: pname > $o,F_23: ( nat > $o ) > pname,A_79: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_nat_o_pname @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_148_finite__surj,axiom,
% 0.30/1.66 ! [B_42: pname > $o,F_23: ( pname > $o ) > pname,A_79: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_pname_o_pname @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_149_finite__surj,axiom,
% 0.30/1.66 ! [B_42: pname > $o,F_23: ( x_a > $o ) > pname,A_79: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_a_o_pname @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_150_finite__surj,axiom,
% 0.30/1.66 ! [B_42: nat > $o,F_23: x_a > nat,A_79: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_a_nat @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_151_finite__surj,axiom,
% 0.30/1.66 ! [B_42: nat > $o,F_23: ( nat > $o ) > nat,A_79: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_nat_o_nat @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_152_finite__surj,axiom,
% 0.30/1.66 ! [B_42: nat > $o,F_23: ( pname > $o ) > nat,A_79: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_pname_o_nat @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_153_finite__surj,axiom,
% 0.30/1.66 ! [B_42: nat > $o,F_23: ( x_a > $o ) > nat,A_79: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_a_o_nat @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_154_finite__surj,axiom,
% 0.30/1.66 ! [B_42: x_a > $o,F_23: pname > x_a,A_79: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ A_79 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_42 @ ( image_pname_a @ F_23 @ A_79 ) )
% 0.30/1.66 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_155_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: ( nat > $o ) > x_a,A_78: ( nat > $o ) > $o,B_41: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_41 @ ( image_nat_o_a @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_nat_o @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_nat_o_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_156_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: ( pname > $o ) > x_a,A_78: ( pname > $o ) > $o,B_41: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_41 @ ( image_pname_o_a @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( ord_le1205211808me_o_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite297249702name_o @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_pname_o_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_157_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: ( x_a > $o ) > x_a,A_78: ( x_a > $o ) > $o,B_41: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_41 @ ( image_a_o_a @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_a_o @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_a_o_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_158_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: x_a > x_a,A_78: x_a > $o,B_41: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_41 @ ( image_a_a @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_a @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_a_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_159_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: x_a > nat > $o,A_78: x_a > $o,B_41: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o_o @ B_41 @ ( image_a_nat_o @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_a @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_a_nat_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_160_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: x_a > pname > $o,A_78: x_a > $o,B_41: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ B_41 )
% 0.30/1.66 => ( ( ord_le1205211808me_o_o @ B_41 @ ( image_a_pname_o @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_a @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_a_pname_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_161_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: x_a > x_a > $o,A_78: x_a > $o,B_41: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_a_o_o @ B_41 @ ( image_a_a_o @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_a @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_a_a_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_162_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: x_a > pname,A_78: x_a > $o,B_41: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_a_pname @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_a @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_a_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_163_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: ( nat > $o ) > pname,A_78: ( nat > $o ) > $o,B_41: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_nat_o_pname @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_nat_o @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_nat_o_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_164_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: ( pname > $o ) > pname,A_78: ( pname > $o ) > $o,B_41: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_pname_o_pname @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( ord_le1205211808me_o_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite297249702name_o @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_pname_o_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_165_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: ( x_a > $o ) > pname,A_78: ( x_a > $o ) > $o,B_41: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_a_o_pname @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_a_o @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_a_o_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_166_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: x_a > nat,A_78: x_a > $o,B_41: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_a_nat @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_a @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_a_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_167_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: ( nat > $o ) > nat,A_78: ( nat > $o ) > $o,B_41: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_nat_o_nat @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_nat_o @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_nat_o_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_168_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: ( pname > $o ) > nat,A_78: ( pname > $o ) > $o,B_41: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_pname_o_nat @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( ord_le1205211808me_o_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite297249702name_o @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_pname_o_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_169_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: ( x_a > $o ) > nat,A_78: ( x_a > $o ) > $o,B_41: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_a_o_nat @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_a_o @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_a_o_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_170_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: pname > nat > $o,A_78: pname > $o,B_41: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o_o @ B_41 @ ( image_pname_nat_o @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_pname @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_pname_nat_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_171_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: pname > pname > $o,A_78: pname > $o,B_41: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ B_41 )
% 0.30/1.66 => ( ( ord_le1205211808me_o_o @ B_41 @ ( image_pname_pname_o @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_pname @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_pname_pname_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_172_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: pname > x_a > $o,A_78: pname > $o,B_41: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_a_o_o @ B_41 @ ( image_pname_a_o @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_pname @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_pname_a_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_173_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: pname > pname,A_78: pname > $o,B_41: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_pname_pname @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_pname @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_pname_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_174_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: pname > nat,A_78: pname > $o,B_41: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_pname_nat @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_pname @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_pname_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_175_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: nat > x_a,A_78: nat > $o,B_41: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_41 @ ( image_nat_a @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_nat @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_nat_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_176_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: nat > nat > $o,A_78: nat > $o,B_41: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o_o @ B_41 @ ( image_nat_nat_o @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_nat @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_nat_nat_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_177_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: nat > pname > $o,A_78: nat > $o,B_41: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ B_41 )
% 0.30/1.66 => ( ( ord_le1205211808me_o_o @ B_41 @ ( image_nat_pname_o @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_nat @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_nat_pname_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_178_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: nat > x_a > $o,A_78: nat > $o,B_41: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_a_o_o @ B_41 @ ( image_nat_a_o @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_nat @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_nat_a_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_179_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: nat > pname,A_78: nat > $o,B_41: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_nat_pname @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_nat @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_nat_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_180_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: nat > nat,A_78: nat > $o,B_41: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_nat_nat @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_nat @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_nat_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_181_finite__subset__image,axiom,
% 0.30/1.66 ! [F_22: pname > x_a,A_78: pname > $o,B_41: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ B_41 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_41 @ ( image_pname_a @ F_22 @ A_78 ) )
% 0.30/1.66 => ? [C_12: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/1.66 & ( finite_finite_pname @ C_12 )
% 0.30/1.66 & ( B_41
% 0.30/1.66 = ( image_pname_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_182_lift__Suc__mono__le,axiom,
% 0.30/1.66 ! [N_4: nat,N_3: nat,F_21: nat > $o] :
% 0.30/1.66 ( ! [N_2: nat] : ( ord_less_eq_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/1.66 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/1.66 => ( ord_less_eq_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_183_lift__Suc__mono__le,axiom,
% 0.30/1.66 ! [N_4: nat,N_3: nat,F_21: nat > pname > $o] :
% 0.30/1.66 ( ! [N_2: nat] : ( ord_less_eq_pname_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/1.66 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_184_lift__Suc__mono__le,axiom,
% 0.30/1.66 ! [N_4: nat,N_3: nat,F_21: nat > nat > $o] :
% 0.30/1.66 ( ! [N_2: nat] : ( ord_less_eq_nat_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/1.66 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_185_lift__Suc__mono__le,axiom,
% 0.30/1.66 ! [N_4: nat,N_3: nat,F_21: nat > x_a > $o] :
% 0.30/1.66 ( ! [N_2: nat] : ( ord_less_eq_a_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/1.66 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/1.66 => ( ord_less_eq_a_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_186_lift__Suc__mono__le,axiom,
% 0.30/1.66 ! [N_4: nat,N_3: nat,F_21: nat > nat] :
% 0.30/1.66 ( ! [N_2: nat] : ( ord_less_eq_nat @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/1.66 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_187_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: nat > pname,A_77: nat > $o] :
% 0.30/1.66 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/1.66 => ( ( finite_finite_pname @ ( image_nat_pname @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [A_2: nat] :
% 0.30/1.66 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_188_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: x_a > pname,A_77: x_a > $o] :
% 0.30/1.66 ( ~ ( finite_finite_a @ A_77 )
% 0.30/1.66 => ( ( finite_finite_pname @ ( image_a_pname @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: x_a] :
% 0.30/1.66 ( ( member_a @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_a
% 0.30/1.66 @ ( collect_a
% 0.30/1.66 @ ^ [A_2: x_a] :
% 0.30/1.66 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_189_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: pname > pname,A_77: pname > $o] :
% 0.30/1.66 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/1.66 => ( ( finite_finite_pname @ ( image_pname_pname @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_pname
% 0.30/1.66 @ ( collect_pname
% 0.30/1.66 @ ^ [A_2: pname] :
% 0.30/1.66 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_190_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: ( nat > $o ) > pname,A_77: ( nat > $o ) > $o] :
% 0.30/1.66 ( ~ ( finite_finite_nat_o @ A_77 )
% 0.30/1.66 => ( ( finite_finite_pname @ ( image_nat_o_pname @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: nat > $o] :
% 0.30/1.66 ( ( member_nat_o @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_nat_o
% 0.30/1.66 @ ( collect_nat_o
% 0.30/1.66 @ ^ [A_2: nat > $o] :
% 0.30/1.66 ( (&) @ ( member_nat_o @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_191_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: ( pname > $o ) > pname,A_77: ( pname > $o ) > $o] :
% 0.30/1.66 ( ~ ( finite297249702name_o @ A_77 )
% 0.30/1.66 => ( ( finite_finite_pname @ ( image_pname_o_pname @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: pname > $o] :
% 0.30/1.66 ( ( member_pname_o @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite297249702name_o
% 0.30/1.66 @ ( collect_pname_o
% 0.30/1.66 @ ^ [A_2: pname > $o] :
% 0.30/1.66 ( (&) @ ( member_pname_o @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_192_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: ( x_a > $o ) > pname,A_77: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ~ ( finite_finite_a_o @ A_77 )
% 0.30/1.66 => ( ( finite_finite_pname @ ( image_a_o_pname @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: x_a > $o] :
% 0.30/1.66 ( ( member_a_o @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_a_o
% 0.30/1.66 @ ( collect_a_o
% 0.30/1.66 @ ^ [A_2: x_a > $o] :
% 0.30/1.66 ( (&) @ ( member_a_o @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_193_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: nat > nat,A_77: nat > $o] :
% 0.30/1.66 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/1.66 => ( ( finite_finite_nat @ ( image_nat_nat @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [A_2: nat] :
% 0.30/1.66 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_194_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: x_a > nat,A_77: x_a > $o] :
% 0.30/1.66 ( ~ ( finite_finite_a @ A_77 )
% 0.30/1.66 => ( ( finite_finite_nat @ ( image_a_nat @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: x_a] :
% 0.30/1.66 ( ( member_a @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_a
% 0.30/1.66 @ ( collect_a
% 0.30/1.66 @ ^ [A_2: x_a] :
% 0.30/1.66 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_195_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: pname > nat,A_77: pname > $o] :
% 0.30/1.66 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/1.66 => ( ( finite_finite_nat @ ( image_pname_nat @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_pname
% 0.30/1.66 @ ( collect_pname
% 0.30/1.66 @ ^ [A_2: pname] :
% 0.30/1.66 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_196_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: ( nat > $o ) > nat,A_77: ( nat > $o ) > $o] :
% 0.30/1.66 ( ~ ( finite_finite_nat_o @ A_77 )
% 0.30/1.66 => ( ( finite_finite_nat @ ( image_nat_o_nat @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: nat > $o] :
% 0.30/1.66 ( ( member_nat_o @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_nat_o
% 0.30/1.66 @ ( collect_nat_o
% 0.30/1.66 @ ^ [A_2: nat > $o] :
% 0.30/1.66 ( (&) @ ( member_nat_o @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_197_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: ( pname > $o ) > nat,A_77: ( pname > $o ) > $o] :
% 0.30/1.66 ( ~ ( finite297249702name_o @ A_77 )
% 0.30/1.66 => ( ( finite_finite_nat @ ( image_pname_o_nat @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: pname > $o] :
% 0.30/1.66 ( ( member_pname_o @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite297249702name_o
% 0.30/1.66 @ ( collect_pname_o
% 0.30/1.66 @ ^ [A_2: pname > $o] :
% 0.30/1.66 ( (&) @ ( member_pname_o @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_198_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: ( x_a > $o ) > nat,A_77: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ~ ( finite_finite_a_o @ A_77 )
% 0.30/1.66 => ( ( finite_finite_nat @ ( image_a_o_nat @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: x_a > $o] :
% 0.30/1.66 ( ( member_a_o @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_a_o
% 0.30/1.66 @ ( collect_a_o
% 0.30/1.66 @ ^ [A_2: x_a > $o] :
% 0.30/1.66 ( (&) @ ( member_a_o @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_199_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: nat > x_a,A_77: nat > $o] :
% 0.30/1.66 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/1.66 => ( ( finite_finite_a @ ( image_nat_a @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [A_2: nat] :
% 0.30/1.66 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_200_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: nat > nat > $o,A_77: nat > $o] :
% 0.30/1.66 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/1.66 => ( ( finite_finite_nat_o @ ( image_nat_nat_o @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [A_2: nat] :
% 0.30/1.66 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_201_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: nat > pname > $o,A_77: nat > $o] :
% 0.30/1.66 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/1.66 => ( ( finite297249702name_o @ ( image_nat_pname_o @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [A_2: nat] :
% 0.30/1.66 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_202_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: nat > x_a > $o,A_77: nat > $o] :
% 0.30/1.66 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/1.66 => ( ( finite_finite_a_o @ ( image_nat_a_o @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [A_2: nat] :
% 0.30/1.66 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_203_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: pname > nat > $o,A_77: pname > $o] :
% 0.30/1.66 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/1.66 => ( ( finite_finite_nat_o @ ( image_pname_nat_o @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_pname
% 0.30/1.66 @ ( collect_pname
% 0.30/1.66 @ ^ [A_2: pname] :
% 0.30/1.66 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_204_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: pname > pname > $o,A_77: pname > $o] :
% 0.30/1.66 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/1.66 => ( ( finite297249702name_o @ ( image_pname_pname_o @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_pname
% 0.30/1.66 @ ( collect_pname
% 0.30/1.66 @ ^ [A_2: pname] :
% 0.30/1.66 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_205_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: pname > x_a > $o,A_77: pname > $o] :
% 0.30/1.66 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/1.66 => ( ( finite_finite_a_o @ ( image_pname_a_o @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_pname
% 0.30/1.66 @ ( collect_pname
% 0.30/1.66 @ ^ [A_2: pname] :
% 0.30/1.66 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_206_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: x_a > x_a,A_77: x_a > $o] :
% 0.30/1.66 ( ~ ( finite_finite_a @ A_77 )
% 0.30/1.66 => ( ( finite_finite_a @ ( image_a_a @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: x_a] :
% 0.30/1.66 ( ( member_a @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_a
% 0.30/1.66 @ ( collect_a
% 0.30/1.66 @ ^ [A_2: x_a] :
% 0.30/1.66 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_207_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: x_a > nat > $o,A_77: x_a > $o] :
% 0.30/1.66 ( ~ ( finite_finite_a @ A_77 )
% 0.30/1.66 => ( ( finite_finite_nat_o @ ( image_a_nat_o @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: x_a] :
% 0.30/1.66 ( ( member_a @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_a
% 0.30/1.66 @ ( collect_a
% 0.30/1.66 @ ^ [A_2: x_a] :
% 0.30/1.66 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_208_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: x_a > pname > $o,A_77: x_a > $o] :
% 0.30/1.66 ( ~ ( finite_finite_a @ A_77 )
% 0.30/1.66 => ( ( finite297249702name_o @ ( image_a_pname_o @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: x_a] :
% 0.30/1.66 ( ( member_a @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_a
% 0.30/1.66 @ ( collect_a
% 0.30/1.66 @ ^ [A_2: x_a] :
% 0.30/1.66 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_209_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: x_a > x_a > $o,A_77: x_a > $o] :
% 0.30/1.66 ( ~ ( finite_finite_a @ A_77 )
% 0.30/1.66 => ( ( finite_finite_a_o @ ( image_a_a_o @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: x_a] :
% 0.30/1.66 ( ( member_a @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_a
% 0.30/1.66 @ ( collect_a
% 0.30/1.66 @ ^ [A_2: x_a] :
% 0.30/1.66 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_210_pigeonhole__infinite,axiom,
% 0.30/1.66 ! [F_20: pname > x_a,A_77: pname > $o] :
% 0.30/1.66 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/1.66 => ( ( finite_finite_a @ ( image_pname_a @ F_20 @ A_77 ) )
% 0.30/1.66 => ? [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_77 )
% 0.30/1.66 & ~ ( finite_finite_pname
% 0.30/1.66 @ ( collect_pname
% 0.30/1.66 @ ^ [A_2: pname] :
% 0.30/1.66 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/1.66 @ ( ( F_20 @ A_2 )
% 0.30/1.66 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_211_image__eqI,axiom,
% 0.30/1.66 ! [A_76: pname > $o,B_40: nat,F_19: pname > nat,X_30: pname] :
% 0.30/1.66 ( ( B_40
% 0.30/1.66 = ( F_19 @ X_30 ) )
% 0.30/1.66 => ( ( member_pname @ X_30 @ A_76 )
% 0.30/1.66 => ( member_nat @ B_40 @ ( image_pname_nat @ F_19 @ A_76 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_212_image__eqI,axiom,
% 0.30/1.66 ! [A_76: x_a > $o,B_40: nat,F_19: x_a > nat,X_30: x_a] :
% 0.30/1.66 ( ( B_40
% 0.30/1.66 = ( F_19 @ X_30 ) )
% 0.30/1.66 => ( ( member_a @ X_30 @ A_76 )
% 0.30/1.66 => ( member_nat @ B_40 @ ( image_a_nat @ F_19 @ A_76 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_213_image__eqI,axiom,
% 0.30/1.66 ! [A_76: nat > $o,B_40: pname,F_19: nat > pname,X_30: nat] :
% 0.30/1.66 ( ( B_40
% 0.30/1.66 = ( F_19 @ X_30 ) )
% 0.30/1.66 => ( ( member_nat @ X_30 @ A_76 )
% 0.30/1.66 => ( member_pname @ B_40 @ ( image_nat_pname @ F_19 @ A_76 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_214_image__eqI,axiom,
% 0.30/1.66 ! [A_76: nat > $o,B_40: x_a,F_19: nat > x_a,X_30: nat] :
% 0.30/1.66 ( ( B_40
% 0.30/1.66 = ( F_19 @ X_30 ) )
% 0.30/1.66 => ( ( member_nat @ X_30 @ A_76 )
% 0.30/1.66 => ( member_a @ B_40 @ ( image_nat_a @ F_19 @ A_76 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_215_image__eqI,axiom,
% 0.30/1.66 ! [A_76: pname > $o,B_40: x_a,F_19: pname > x_a,X_30: pname] :
% 0.30/1.66 ( ( B_40
% 0.30/1.66 = ( F_19 @ X_30 ) )
% 0.30/1.66 => ( ( member_pname @ X_30 @ A_76 )
% 0.30/1.66 => ( member_a @ B_40 @ ( image_pname_a @ F_19 @ A_76 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_216_equalityI,axiom,
% 0.30/1.66 ! [A_75: pname > $o,B_39: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_75 @ B_39 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_39 @ A_75 )
% 0.30/1.66 => ( A_75 = B_39 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_217_equalityI,axiom,
% 0.30/1.66 ! [A_75: nat > $o,B_39: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_75 @ B_39 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_39 @ A_75 )
% 0.30/1.66 => ( A_75 = B_39 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_218_equalityI,axiom,
% 0.30/1.66 ! [A_75: x_a > $o,B_39: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_75 @ B_39 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_39 @ A_75 )
% 0.30/1.66 => ( A_75 = B_39 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_219_subsetD,axiom,
% 0.30/1.66 ! [C_11: nat,A_74: nat > $o,B_38: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_74 @ B_38 )
% 0.30/1.66 => ( ( member_nat @ C_11 @ A_74 )
% 0.30/1.66 => ( member_nat @ C_11 @ B_38 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_220_subsetD,axiom,
% 0.30/1.66 ! [C_11: pname,A_74: pname > $o,B_38: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_74 @ B_38 )
% 0.30/1.66 => ( ( member_pname @ C_11 @ A_74 )
% 0.30/1.66 => ( member_pname @ C_11 @ B_38 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_221_subsetD,axiom,
% 0.30/1.66 ! [C_11: x_a,A_74: x_a > $o,B_38: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_74 @ B_38 )
% 0.30/1.66 => ( ( member_a @ C_11 @ A_74 )
% 0.30/1.66 => ( member_a @ C_11 @ B_38 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_222_insertCI,axiom,
% 0.30/1.66 ! [B_37: nat,A_73: nat,B_36: nat > $o] :
% 0.30/1.66 ( ( ~ ( member_nat @ A_73 @ B_36 )
% 0.30/1.66 => ( A_73 = B_37 ) )
% 0.30/1.66 => ( member_nat @ A_73 @ ( insert_nat @ B_37 @ B_36 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_223_insertCI,axiom,
% 0.30/1.66 ! [B_37: pname,A_73: pname,B_36: pname > $o] :
% 0.30/1.66 ( ( ~ ( member_pname @ A_73 @ B_36 )
% 0.30/1.66 => ( A_73 = B_37 ) )
% 0.30/1.66 => ( member_pname @ A_73 @ ( insert_pname @ B_37 @ B_36 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_224_insertCI,axiom,
% 0.30/1.66 ! [B_37: x_a,A_73: x_a,B_36: x_a > $o] :
% 0.30/1.66 ( ( ~ ( member_a @ A_73 @ B_36 )
% 0.30/1.66 => ( A_73 = B_37 ) )
% 0.30/1.66 => ( member_a @ A_73 @ ( insert_a @ B_37 @ B_36 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_225_insertE,axiom,
% 0.30/1.66 ! [A_72: nat,B_35: nat,A_71: nat > $o] :
% 0.30/1.66 ( ( member_nat @ A_72 @ ( insert_nat @ B_35 @ A_71 ) )
% 0.30/1.66 => ( ( A_72 != B_35 )
% 0.30/1.66 => ( member_nat @ A_72 @ A_71 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_226_insertE,axiom,
% 0.30/1.66 ! [A_72: pname,B_35: pname,A_71: pname > $o] :
% 0.30/1.66 ( ( member_pname @ A_72 @ ( insert_pname @ B_35 @ A_71 ) )
% 0.30/1.66 => ( ( A_72 != B_35 )
% 0.30/1.66 => ( member_pname @ A_72 @ A_71 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_227_insertE,axiom,
% 0.30/1.66 ! [A_72: x_a,B_35: x_a,A_71: x_a > $o] :
% 0.30/1.66 ( ( member_a @ A_72 @ ( insert_a @ B_35 @ A_71 ) )
% 0.30/1.66 => ( ( A_72 != B_35 )
% 0.30/1.66 => ( member_a @ A_72 @ A_71 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_228_zero__induct__lemma,axiom,
% 0.30/1.66 ! [I: nat,P: nat > $o,K: nat] :
% 0.30/1.66 ( ( P @ K )
% 0.30/1.66 => ( ! [N_2: nat] :
% 0.30/1.66 ( ( P @ ( suc @ N_2 ) )
% 0.30/1.66 => ( P @ N_2 ) )
% 0.30/1.66 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_229_Suc__le__D,axiom,
% 0.30/1.66 ! [N: nat,M_2: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( suc @ N ) @ M_2 )
% 0.30/1.66 => ? [M_1: nat] :
% 0.30/1.66 ( M_2
% 0.30/1.66 = ( suc @ M_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_230_insertI1,axiom,
% 0.30/1.66 ! [A_70: nat,B_34: nat > $o] : ( member_nat @ A_70 @ ( insert_nat @ A_70 @ B_34 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_231_insertI1,axiom,
% 0.30/1.66 ! [A_70: pname,B_34: pname > $o] : ( member_pname @ A_70 @ ( insert_pname @ A_70 @ B_34 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_232_insertI1,axiom,
% 0.30/1.66 ! [A_70: x_a,B_34: x_a > $o] : ( member_a @ A_70 @ ( insert_a @ A_70 @ B_34 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_233_insert__compr,axiom,
% 0.30/1.66 ! [A_69: nat > $o,B_33: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( insert_nat_o @ A_69 @ B_33 )
% 0.30/1.66 = ( collect_nat_o
% 0.30/1.66 @ ^ [X_1: nat > $o] : ( (|) @ ( X_1 = A_69 ) @ ( member_nat_o @ X_1 @ B_33 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_234_insert__compr,axiom,
% 0.30/1.66 ! [A_69: pname > $o,B_33: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( insert_pname_o @ A_69 @ B_33 )
% 0.30/1.66 = ( collect_pname_o
% 0.30/1.66 @ ^ [X_1: pname > $o] : ( (|) @ ( X_1 = A_69 ) @ ( member_pname_o @ X_1 @ B_33 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_235_insert__compr,axiom,
% 0.30/1.66 ! [A_69: x_a > $o,B_33: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( insert_a_o @ A_69 @ B_33 )
% 0.30/1.66 = ( collect_a_o
% 0.30/1.66 @ ^ [X_1: x_a > $o] : ( (|) @ ( X_1 = A_69 ) @ ( member_a_o @ X_1 @ B_33 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_236_insert__compr,axiom,
% 0.30/1.66 ! [A_69: nat,B_33: nat > $o] :
% 0.30/1.66 ( ( insert_nat @ A_69 @ B_33 )
% 0.30/1.66 = ( collect_nat
% 0.30/1.66 @ ^ [X_1: nat] : ( (|) @ ( X_1 = A_69 ) @ ( member_nat @ X_1 @ B_33 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_237_insert__compr,axiom,
% 0.30/1.66 ! [A_69: pname,B_33: pname > $o] :
% 0.30/1.66 ( ( insert_pname @ A_69 @ B_33 )
% 0.30/1.66 = ( collect_pname
% 0.30/1.66 @ ^ [X_1: pname] : ( (|) @ ( X_1 = A_69 ) @ ( member_pname @ X_1 @ B_33 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_238_insert__compr,axiom,
% 0.30/1.66 ! [A_69: x_a,B_33: x_a > $o] :
% 0.30/1.66 ( ( insert_a @ A_69 @ B_33 )
% 0.30/1.66 = ( collect_a
% 0.30/1.66 @ ^ [X_1: x_a] : ( (|) @ ( X_1 = A_69 ) @ ( member_a @ X_1 @ B_33 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_239_insert__Collect,axiom,
% 0.30/1.66 ! [A_68: pname,P_8: pname > $o] :
% 0.30/1.66 ( ( insert_pname @ A_68 @ ( collect_pname @ P_8 ) )
% 0.30/1.66 = ( collect_pname
% 0.30/1.66 @ ^ [U_1: pname] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_240_insert__Collect,axiom,
% 0.30/1.66 ! [A_68: nat > $o,P_8: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( insert_nat_o @ A_68 @ ( collect_nat_o @ P_8 ) )
% 0.30/1.66 = ( collect_nat_o
% 0.30/1.66 @ ^ [U_1: nat > $o] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_241_insert__Collect,axiom,
% 0.30/1.66 ! [A_68: pname > $o,P_8: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( insert_pname_o @ A_68 @ ( collect_pname_o @ P_8 ) )
% 0.30/1.66 = ( collect_pname_o
% 0.30/1.66 @ ^ [U_1: pname > $o] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_242_insert__Collect,axiom,
% 0.30/1.66 ! [A_68: x_a > $o,P_8: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( insert_a_o @ A_68 @ ( collect_a_o @ P_8 ) )
% 0.30/1.66 = ( collect_a_o
% 0.30/1.66 @ ^ [U_1: x_a > $o] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_243_insert__Collect,axiom,
% 0.30/1.66 ! [A_68: nat,P_8: nat > $o] :
% 0.30/1.66 ( ( insert_nat @ A_68 @ ( collect_nat @ P_8 ) )
% 0.30/1.66 = ( collect_nat
% 0.30/1.66 @ ^ [U_1: nat] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_244_insert__Collect,axiom,
% 0.30/1.66 ! [A_68: x_a,P_8: x_a > $o] :
% 0.30/1.66 ( ( insert_a @ A_68 @ ( collect_a @ P_8 ) )
% 0.30/1.66 = ( collect_a
% 0.30/1.66 @ ^ [U_1: x_a] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_245_insert__absorb2,axiom,
% 0.30/1.66 ! [X_29: pname,A_67: pname > $o] :
% 0.30/1.66 ( ( insert_pname @ X_29 @ ( insert_pname @ X_29 @ A_67 ) )
% 0.30/1.66 = ( insert_pname @ X_29 @ A_67 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_246_insert__absorb2,axiom,
% 0.30/1.66 ! [X_29: nat,A_67: nat > $o] :
% 0.30/1.66 ( ( insert_nat @ X_29 @ ( insert_nat @ X_29 @ A_67 ) )
% 0.30/1.66 = ( insert_nat @ X_29 @ A_67 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_247_insert__absorb2,axiom,
% 0.30/1.66 ! [X_29: x_a,A_67: x_a > $o] :
% 0.30/1.66 ( ( insert_a @ X_29 @ ( insert_a @ X_29 @ A_67 ) )
% 0.30/1.66 = ( insert_a @ X_29 @ A_67 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_248_insert__commute,axiom,
% 0.30/1.66 ! [X_28: pname,Y_12: pname,A_66: pname > $o] :
% 0.30/1.66 ( ( insert_pname @ X_28 @ ( insert_pname @ Y_12 @ A_66 ) )
% 0.30/1.66 = ( insert_pname @ Y_12 @ ( insert_pname @ X_28 @ A_66 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_249_insert__commute,axiom,
% 0.30/1.66 ! [X_28: nat,Y_12: nat,A_66: nat > $o] :
% 0.30/1.66 ( ( insert_nat @ X_28 @ ( insert_nat @ Y_12 @ A_66 ) )
% 0.30/1.66 = ( insert_nat @ Y_12 @ ( insert_nat @ X_28 @ A_66 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_250_insert__commute,axiom,
% 0.30/1.66 ! [X_28: x_a,Y_12: x_a,A_66: x_a > $o] :
% 0.30/1.66 ( ( insert_a @ X_28 @ ( insert_a @ Y_12 @ A_66 ) )
% 0.30/1.66 = ( insert_a @ Y_12 @ ( insert_a @ X_28 @ A_66 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_251_insert__iff,axiom,
% 0.30/1.66 ! [A_65: nat,B_32: nat,A_64: nat > $o] :
% 0.30/1.66 ( ( member_nat @ A_65 @ ( insert_nat @ B_32 @ A_64 ) )
% 0.30/1.66 <=> ( ( A_65 = B_32 )
% 0.30/1.66 | ( member_nat @ A_65 @ A_64 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_252_insert__iff,axiom,
% 0.30/1.66 ! [A_65: pname,B_32: pname,A_64: pname > $o] :
% 0.30/1.66 ( ( member_pname @ A_65 @ ( insert_pname @ B_32 @ A_64 ) )
% 0.30/1.66 <=> ( ( A_65 = B_32 )
% 0.30/1.66 | ( member_pname @ A_65 @ A_64 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_253_insert__iff,axiom,
% 0.30/1.66 ! [A_65: x_a,B_32: x_a,A_64: x_a > $o] :
% 0.30/1.66 ( ( member_a @ A_65 @ ( insert_a @ B_32 @ A_64 ) )
% 0.30/1.66 <=> ( ( A_65 = B_32 )
% 0.30/1.66 | ( member_a @ A_65 @ A_64 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_254_insert__code,axiom,
% 0.30/1.66 ! [Y_11: pname,A_63: pname > $o,X_27: pname] :
% 0.30/1.66 ( ( insert_pname @ Y_11 @ A_63 @ X_27 )
% 0.30/1.66 <=> ( ( Y_11 = X_27 )
% 0.30/1.66 | ( A_63 @ X_27 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_255_insert__code,axiom,
% 0.30/1.66 ! [Y_11: nat,A_63: nat > $o,X_27: nat] :
% 0.30/1.66 ( ( insert_nat @ Y_11 @ A_63 @ X_27 )
% 0.30/1.66 <=> ( ( Y_11 = X_27 )
% 0.30/1.66 | ( A_63 @ X_27 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_256_insert__code,axiom,
% 0.30/1.66 ! [Y_11: x_a,A_63: x_a > $o,X_27: x_a] :
% 0.30/1.66 ( ( insert_a @ Y_11 @ A_63 @ X_27 )
% 0.30/1.66 <=> ( ( Y_11 = X_27 )
% 0.30/1.66 | ( A_63 @ X_27 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_257_insert__ident,axiom,
% 0.30/1.66 ! [B_31: nat > $o,X_26: nat,A_62: nat > $o] :
% 0.30/1.66 ( ~ ( member_nat @ X_26 @ A_62 )
% 0.30/1.66 => ( ~ ( member_nat @ X_26 @ B_31 )
% 0.30/1.66 => ( ( ( insert_nat @ X_26 @ A_62 )
% 0.30/1.66 = ( insert_nat @ X_26 @ B_31 ) )
% 0.30/1.66 <=> ( A_62 = B_31 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_258_insert__ident,axiom,
% 0.30/1.66 ! [B_31: pname > $o,X_26: pname,A_62: pname > $o] :
% 0.30/1.66 ( ~ ( member_pname @ X_26 @ A_62 )
% 0.30/1.66 => ( ~ ( member_pname @ X_26 @ B_31 )
% 0.30/1.66 => ( ( ( insert_pname @ X_26 @ A_62 )
% 0.30/1.66 = ( insert_pname @ X_26 @ B_31 ) )
% 0.30/1.66 <=> ( A_62 = B_31 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_259_insert__ident,axiom,
% 0.30/1.66 ! [B_31: x_a > $o,X_26: x_a,A_62: x_a > $o] :
% 0.30/1.66 ( ~ ( member_a @ X_26 @ A_62 )
% 0.30/1.66 => ( ~ ( member_a @ X_26 @ B_31 )
% 0.30/1.66 => ( ( ( insert_a @ X_26 @ A_62 )
% 0.30/1.66 = ( insert_a @ X_26 @ B_31 ) )
% 0.30/1.66 <=> ( A_62 = B_31 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_260_insertI2,axiom,
% 0.30/1.66 ! [B_30: nat,A_61: nat,B_29: nat > $o] :
% 0.30/1.66 ( ( member_nat @ A_61 @ B_29 )
% 0.30/1.66 => ( member_nat @ A_61 @ ( insert_nat @ B_30 @ B_29 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_261_insertI2,axiom,
% 0.30/1.66 ! [B_30: pname,A_61: pname,B_29: pname > $o] :
% 0.30/1.66 ( ( member_pname @ A_61 @ B_29 )
% 0.30/1.66 => ( member_pname @ A_61 @ ( insert_pname @ B_30 @ B_29 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_262_insertI2,axiom,
% 0.30/1.66 ! [B_30: x_a,A_61: x_a,B_29: x_a > $o] :
% 0.30/1.66 ( ( member_a @ A_61 @ B_29 )
% 0.30/1.66 => ( member_a @ A_61 @ ( insert_a @ B_30 @ B_29 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_263_insert__absorb,axiom,
% 0.30/1.66 ! [A_60: nat,A_59: nat > $o] :
% 0.30/1.66 ( ( member_nat @ A_60 @ A_59 )
% 0.30/1.66 => ( ( insert_nat @ A_60 @ A_59 )
% 0.30/1.66 = A_59 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_264_insert__absorb,axiom,
% 0.30/1.66 ! [A_60: pname,A_59: pname > $o] :
% 0.30/1.66 ( ( member_pname @ A_60 @ A_59 )
% 0.30/1.66 => ( ( insert_pname @ A_60 @ A_59 )
% 0.30/1.66 = A_59 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_265_insert__absorb,axiom,
% 0.30/1.66 ! [A_60: x_a,A_59: x_a > $o] :
% 0.30/1.66 ( ( member_a @ A_60 @ A_59 )
% 0.30/1.66 => ( ( insert_a @ A_60 @ A_59 )
% 0.30/1.66 = A_59 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_266_subset__refl,axiom,
% 0.30/1.66 ! [A_58: pname > $o] : ( ord_less_eq_pname_o @ A_58 @ A_58 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_267_subset__refl,axiom,
% 0.30/1.66 ! [A_58: nat > $o] : ( ord_less_eq_nat_o @ A_58 @ A_58 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_268_subset__refl,axiom,
% 0.30/1.66 ! [A_58: x_a > $o] : ( ord_less_eq_a_o @ A_58 @ A_58 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_269_set__eq__subset,axiom,
% 0.30/1.66 ! [A_57: pname > $o,B_28: pname > $o] :
% 0.30/1.66 ( ( A_57 = B_28 )
% 0.30/1.66 <=> ( ( ord_less_eq_pname_o @ A_57 @ B_28 )
% 0.30/1.66 & ( ord_less_eq_pname_o @ B_28 @ A_57 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_270_set__eq__subset,axiom,
% 0.30/1.66 ! [A_57: nat > $o,B_28: nat > $o] :
% 0.30/1.66 ( ( A_57 = B_28 )
% 0.30/1.66 <=> ( ( ord_less_eq_nat_o @ A_57 @ B_28 )
% 0.30/1.66 & ( ord_less_eq_nat_o @ B_28 @ A_57 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_271_set__eq__subset,axiom,
% 0.30/1.66 ! [A_57: x_a > $o,B_28: x_a > $o] :
% 0.30/1.66 ( ( A_57 = B_28 )
% 0.30/1.66 <=> ( ( ord_less_eq_a_o @ A_57 @ B_28 )
% 0.30/1.66 & ( ord_less_eq_a_o @ B_28 @ A_57 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_272_equalityD1,axiom,
% 0.30/1.66 ! [A_56: pname > $o,B_27: pname > $o] :
% 0.30/1.66 ( ( A_56 = B_27 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ A_56 @ B_27 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_273_equalityD1,axiom,
% 0.30/1.66 ! [A_56: nat > $o,B_27: nat > $o] :
% 0.30/1.66 ( ( A_56 = B_27 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ A_56 @ B_27 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_274_equalityD1,axiom,
% 0.30/1.66 ! [A_56: x_a > $o,B_27: x_a > $o] :
% 0.30/1.66 ( ( A_56 = B_27 )
% 0.30/1.66 => ( ord_less_eq_a_o @ A_56 @ B_27 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_275_equalityD2,axiom,
% 0.30/1.66 ! [A_55: pname > $o,B_26: pname > $o] :
% 0.30/1.66 ( ( A_55 = B_26 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ B_26 @ A_55 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_276_equalityD2,axiom,
% 0.30/1.66 ! [A_55: nat > $o,B_26: nat > $o] :
% 0.30/1.66 ( ( A_55 = B_26 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ B_26 @ A_55 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_277_equalityD2,axiom,
% 0.30/1.66 ! [A_55: x_a > $o,B_26: x_a > $o] :
% 0.30/1.66 ( ( A_55 = B_26 )
% 0.30/1.66 => ( ord_less_eq_a_o @ B_26 @ A_55 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_278_in__mono,axiom,
% 0.30/1.66 ! [X_25: nat,A_54: nat > $o,B_25: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_54 @ B_25 )
% 0.30/1.66 => ( ( member_nat @ X_25 @ A_54 )
% 0.30/1.66 => ( member_nat @ X_25 @ B_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_279_in__mono,axiom,
% 0.30/1.66 ! [X_25: pname,A_54: pname > $o,B_25: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_54 @ B_25 )
% 0.30/1.66 => ( ( member_pname @ X_25 @ A_54 )
% 0.30/1.66 => ( member_pname @ X_25 @ B_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_280_in__mono,axiom,
% 0.30/1.66 ! [X_25: x_a,A_54: x_a > $o,B_25: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_54 @ B_25 )
% 0.30/1.66 => ( ( member_a @ X_25 @ A_54 )
% 0.30/1.66 => ( member_a @ X_25 @ B_25 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_281_set__rev__mp,axiom,
% 0.30/1.66 ! [B_24: nat > $o,X_24: nat,A_53: nat > $o] :
% 0.30/1.66 ( ( member_nat @ X_24 @ A_53 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ A_53 @ B_24 )
% 0.30/1.66 => ( member_nat @ X_24 @ B_24 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_282_set__rev__mp,axiom,
% 0.30/1.66 ! [B_24: pname > $o,X_24: pname,A_53: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_24 @ A_53 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ A_53 @ B_24 )
% 0.30/1.66 => ( member_pname @ X_24 @ B_24 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_283_set__rev__mp,axiom,
% 0.30/1.66 ! [B_24: x_a > $o,X_24: x_a,A_53: x_a > $o] :
% 0.30/1.66 ( ( member_a @ X_24 @ A_53 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ A_53 @ B_24 )
% 0.30/1.66 => ( member_a @ X_24 @ B_24 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_284_set__mp,axiom,
% 0.30/1.66 ! [X_23: nat,A_52: nat > $o,B_23: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_52 @ B_23 )
% 0.30/1.66 => ( ( member_nat @ X_23 @ A_52 )
% 0.30/1.66 => ( member_nat @ X_23 @ B_23 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_285_set__mp,axiom,
% 0.30/1.66 ! [X_23: pname,A_52: pname > $o,B_23: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_52 @ B_23 )
% 0.30/1.66 => ( ( member_pname @ X_23 @ A_52 )
% 0.30/1.66 => ( member_pname @ X_23 @ B_23 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_286_set__mp,axiom,
% 0.30/1.66 ! [X_23: x_a,A_52: x_a > $o,B_23: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_52 @ B_23 )
% 0.30/1.66 => ( ( member_a @ X_23 @ A_52 )
% 0.30/1.66 => ( member_a @ X_23 @ B_23 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_287_mem__def,axiom,
% 0.30/1.66 ! [X_22: nat,A_51: nat > $o] :
% 0.30/1.66 ( ( member_nat @ X_22 @ A_51 )
% 0.30/1.66 <=> ( A_51 @ X_22 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_288_mem__def,axiom,
% 0.30/1.66 ! [X_22: pname,A_51: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_22 @ A_51 )
% 0.30/1.66 <=> ( A_51 @ X_22 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_289_mem__def,axiom,
% 0.30/1.66 ! [X_22: x_a,A_51: x_a > $o] :
% 0.30/1.66 ( ( member_a @ X_22 @ A_51 )
% 0.30/1.66 <=> ( A_51 @ X_22 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_290_Collect__def,axiom,
% 0.30/1.66 ! [P_7: x_a > $o] :
% 0.30/1.66 ( ( collect_a @ P_7 )
% 0.30/1.66 = P_7 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_291_Collect__def,axiom,
% 0.30/1.66 ! [P_7: pname > $o] :
% 0.30/1.66 ( ( collect_pname @ P_7 )
% 0.30/1.66 = P_7 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_292_Collect__def,axiom,
% 0.30/1.66 ! [P_7: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( collect_nat_o @ P_7 )
% 0.30/1.66 = P_7 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_293_Collect__def,axiom,
% 0.30/1.66 ! [P_7: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( collect_pname_o @ P_7 )
% 0.30/1.66 = P_7 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_294_Collect__def,axiom,
% 0.30/1.66 ! [P_7: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( collect_a_o @ P_7 )
% 0.30/1.66 = P_7 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_295_Collect__def,axiom,
% 0.30/1.66 ! [P_7: nat > $o] :
% 0.30/1.66 ( ( collect_nat @ P_7 )
% 0.30/1.66 = P_7 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_296_subset__trans,axiom,
% 0.30/1.66 ! [C_10: pname > $o,A_50: pname > $o,B_22: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_50 @ B_22 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_22 @ C_10 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ A_50 @ C_10 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_297_subset__trans,axiom,
% 0.30/1.66 ! [C_10: nat > $o,A_50: nat > $o,B_22: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_50 @ B_22 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_22 @ C_10 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ A_50 @ C_10 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_298_subset__trans,axiom,
% 0.30/1.66 ! [C_10: x_a > $o,A_50: x_a > $o,B_22: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_50 @ B_22 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_22 @ C_10 )
% 0.30/1.66 => ( ord_less_eq_a_o @ A_50 @ C_10 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_299_equalityE,axiom,
% 0.30/1.66 ! [A_49: pname > $o,B_21: pname > $o] :
% 0.30/1.66 ( ( A_49 = B_21 )
% 0.30/1.66 => ~ ( ( ord_less_eq_pname_o @ A_49 @ B_21 )
% 0.30/1.66 => ~ ( ord_less_eq_pname_o @ B_21 @ A_49 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_300_equalityE,axiom,
% 0.30/1.66 ! [A_49: nat > $o,B_21: nat > $o] :
% 0.30/1.66 ( ( A_49 = B_21 )
% 0.30/1.66 => ~ ( ( ord_less_eq_nat_o @ A_49 @ B_21 )
% 0.30/1.66 => ~ ( ord_less_eq_nat_o @ B_21 @ A_49 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_301_equalityE,axiom,
% 0.30/1.66 ! [A_49: x_a > $o,B_21: x_a > $o] :
% 0.30/1.66 ( ( A_49 = B_21 )
% 0.30/1.66 => ~ ( ( ord_less_eq_a_o @ A_49 @ B_21 )
% 0.30/1.66 => ~ ( ord_less_eq_a_o @ B_21 @ A_49 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_302_image__iff,axiom,
% 0.30/1.66 ! [Z_3: x_a,F_18: pname > x_a,A_48: pname > $o] :
% 0.30/1.66 ( ( member_a @ Z_3 @ ( image_pname_a @ F_18 @ A_48 ) )
% 0.30/1.66 <=> ? [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_48 )
% 0.30/1.66 & ( Z_3
% 0.30/1.66 = ( F_18 @ X_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_303_imageI,axiom,
% 0.30/1.66 ! [F_17: pname > nat,X_21: pname,A_47: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_21 @ A_47 )
% 0.30/1.66 => ( member_nat @ ( F_17 @ X_21 ) @ ( image_pname_nat @ F_17 @ A_47 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_304_imageI,axiom,
% 0.30/1.66 ! [F_17: x_a > nat,X_21: x_a,A_47: x_a > $o] :
% 0.30/1.66 ( ( member_a @ X_21 @ A_47 )
% 0.30/1.66 => ( member_nat @ ( F_17 @ X_21 ) @ ( image_a_nat @ F_17 @ A_47 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_305_imageI,axiom,
% 0.30/1.66 ! [F_17: nat > pname,X_21: nat,A_47: nat > $o] :
% 0.30/1.66 ( ( member_nat @ X_21 @ A_47 )
% 0.30/1.66 => ( member_pname @ ( F_17 @ X_21 ) @ ( image_nat_pname @ F_17 @ A_47 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_306_imageI,axiom,
% 0.30/1.66 ! [F_17: nat > x_a,X_21: nat,A_47: nat > $o] :
% 0.30/1.66 ( ( member_nat @ X_21 @ A_47 )
% 0.30/1.66 => ( member_a @ ( F_17 @ X_21 ) @ ( image_nat_a @ F_17 @ A_47 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_307_imageI,axiom,
% 0.30/1.66 ! [F_17: pname > x_a,X_21: pname,A_47: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_21 @ A_47 )
% 0.30/1.66 => ( member_a @ ( F_17 @ X_21 ) @ ( image_pname_a @ F_17 @ A_47 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_308_rev__image__eqI,axiom,
% 0.30/1.66 ! [B_20: nat,F_16: pname > nat,X_20: pname,A_46: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_20 @ A_46 )
% 0.30/1.66 => ( ( B_20
% 0.30/1.66 = ( F_16 @ X_20 ) )
% 0.30/1.66 => ( member_nat @ B_20 @ ( image_pname_nat @ F_16 @ A_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_309_rev__image__eqI,axiom,
% 0.30/1.66 ! [B_20: nat,F_16: x_a > nat,X_20: x_a,A_46: x_a > $o] :
% 0.30/1.66 ( ( member_a @ X_20 @ A_46 )
% 0.30/1.66 => ( ( B_20
% 0.30/1.66 = ( F_16 @ X_20 ) )
% 0.30/1.66 => ( member_nat @ B_20 @ ( image_a_nat @ F_16 @ A_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_310_rev__image__eqI,axiom,
% 0.30/1.66 ! [B_20: pname,F_16: nat > pname,X_20: nat,A_46: nat > $o] :
% 0.30/1.66 ( ( member_nat @ X_20 @ A_46 )
% 0.30/1.66 => ( ( B_20
% 0.30/1.66 = ( F_16 @ X_20 ) )
% 0.30/1.66 => ( member_pname @ B_20 @ ( image_nat_pname @ F_16 @ A_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_311_rev__image__eqI,axiom,
% 0.30/1.66 ! [B_20: x_a,F_16: nat > x_a,X_20: nat,A_46: nat > $o] :
% 0.30/1.66 ( ( member_nat @ X_20 @ A_46 )
% 0.30/1.66 => ( ( B_20
% 0.30/1.66 = ( F_16 @ X_20 ) )
% 0.30/1.66 => ( member_a @ B_20 @ ( image_nat_a @ F_16 @ A_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_312_rev__image__eqI,axiom,
% 0.30/1.66 ! [B_20: x_a,F_16: pname > x_a,X_20: pname,A_46: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_20 @ A_46 )
% 0.30/1.66 => ( ( B_20
% 0.30/1.66 = ( F_16 @ X_20 ) )
% 0.30/1.66 => ( member_a @ B_20 @ ( image_pname_a @ F_16 @ A_46 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_313_insert__compr__raw,axiom,
% 0.30/1.66 ! [X_1: nat > $o,Xa: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( insert_nat_o @ X_1 @ Xa )
% 0.30/1.66 = ( collect_nat_o
% 0.30/1.66 @ ^ [Y_10: nat > $o] : ( (|) @ ( Y_10 = X_1 ) @ ( member_nat_o @ Y_10 @ Xa ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_314_insert__compr__raw,axiom,
% 0.30/1.66 ! [X_1: pname > $o,Xa: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( insert_pname_o @ X_1 @ Xa )
% 0.30/1.66 = ( collect_pname_o
% 0.30/1.66 @ ^ [Y_10: pname > $o] : ( (|) @ ( Y_10 = X_1 ) @ ( member_pname_o @ Y_10 @ Xa ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_315_insert__compr__raw,axiom,
% 0.30/1.66 ! [X_1: x_a > $o,Xa: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( insert_a_o @ X_1 @ Xa )
% 0.30/1.66 = ( collect_a_o
% 0.30/1.66 @ ^ [Y_10: x_a > $o] : ( (|) @ ( Y_10 = X_1 ) @ ( member_a_o @ Y_10 @ Xa ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_316_insert__compr__raw,axiom,
% 0.30/1.66 ! [X_1: nat,Xa: nat > $o] :
% 0.30/1.66 ( ( insert_nat @ X_1 @ Xa )
% 0.30/1.66 = ( collect_nat
% 0.30/1.66 @ ^ [Y_10: nat] : ( (|) @ ( Y_10 = X_1 ) @ ( member_nat @ Y_10 @ Xa ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_317_insert__compr__raw,axiom,
% 0.30/1.66 ! [X_1: pname,Xa: pname > $o] :
% 0.30/1.66 ( ( insert_pname @ X_1 @ Xa )
% 0.30/1.66 = ( collect_pname
% 0.30/1.66 @ ^ [Y_10: pname] : ( (|) @ ( Y_10 = X_1 ) @ ( member_pname @ Y_10 @ Xa ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_318_insert__compr__raw,axiom,
% 0.30/1.66 ! [X_1: x_a,Xa: x_a > $o] :
% 0.30/1.66 ( ( insert_a @ X_1 @ Xa )
% 0.30/1.66 = ( collect_a
% 0.30/1.66 @ ^ [Y_10: x_a] : ( (|) @ ( Y_10 = X_1 ) @ ( member_a @ Y_10 @ Xa ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_319_subset__insertI,axiom,
% 0.30/1.66 ! [B_19: pname > $o,A_45: pname] : ( ord_less_eq_pname_o @ B_19 @ ( insert_pname @ A_45 @ B_19 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_320_subset__insertI,axiom,
% 0.30/1.66 ! [B_19: nat > $o,A_45: nat] : ( ord_less_eq_nat_o @ B_19 @ ( insert_nat @ A_45 @ B_19 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_321_subset__insertI,axiom,
% 0.30/1.66 ! [B_19: x_a > $o,A_45: x_a] : ( ord_less_eq_a_o @ B_19 @ ( insert_a @ A_45 @ B_19 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_322_insert__subset,axiom,
% 0.30/1.66 ! [X_19: nat,A_44: nat > $o,B_18: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ ( insert_nat @ X_19 @ A_44 ) @ B_18 )
% 0.30/1.66 <=> ( ( member_nat @ X_19 @ B_18 )
% 0.30/1.66 & ( ord_less_eq_nat_o @ A_44 @ B_18 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_323_insert__subset,axiom,
% 0.30/1.66 ! [X_19: pname,A_44: pname > $o,B_18: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_19 @ A_44 ) @ B_18 )
% 0.30/1.66 <=> ( ( member_pname @ X_19 @ B_18 )
% 0.30/1.66 & ( ord_less_eq_pname_o @ A_44 @ B_18 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_324_insert__subset,axiom,
% 0.30/1.66 ! [X_19: x_a,A_44: x_a > $o,B_18: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ ( insert_a @ X_19 @ A_44 ) @ B_18 )
% 0.30/1.66 <=> ( ( member_a @ X_19 @ B_18 )
% 0.30/1.66 & ( ord_less_eq_a_o @ A_44 @ B_18 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_325_subset__insert,axiom,
% 0.30/1.66 ! [B_17: nat > $o,X_18: nat,A_43: nat > $o] :
% 0.30/1.66 ( ~ ( member_nat @ X_18 @ A_43 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ A_43 @ ( insert_nat @ X_18 @ B_17 ) )
% 0.30/1.66 <=> ( ord_less_eq_nat_o @ A_43 @ B_17 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_326_subset__insert,axiom,
% 0.30/1.66 ! [B_17: pname > $o,X_18: pname,A_43: pname > $o] :
% 0.30/1.66 ( ~ ( member_pname @ X_18 @ A_43 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ A_43 @ ( insert_pname @ X_18 @ B_17 ) )
% 0.30/1.66 <=> ( ord_less_eq_pname_o @ A_43 @ B_17 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_327_subset__insert,axiom,
% 0.30/1.66 ! [B_17: x_a > $o,X_18: x_a,A_43: x_a > $o] :
% 0.30/1.66 ( ~ ( member_a @ X_18 @ A_43 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ A_43 @ ( insert_a @ X_18 @ B_17 ) )
% 0.30/1.66 <=> ( ord_less_eq_a_o @ A_43 @ B_17 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_328_subset__insertI2,axiom,
% 0.30/1.66 ! [B_16: pname,A_42: pname > $o,B_15: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_42 @ B_15 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ A_42 @ ( insert_pname @ B_16 @ B_15 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_329_subset__insertI2,axiom,
% 0.30/1.66 ! [B_16: nat,A_42: nat > $o,B_15: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_42 @ B_15 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ A_42 @ ( insert_nat @ B_16 @ B_15 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_330_subset__insertI2,axiom,
% 0.30/1.66 ! [B_16: x_a,A_42: x_a > $o,B_15: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_42 @ B_15 )
% 0.30/1.66 => ( ord_less_eq_a_o @ A_42 @ ( insert_a @ B_16 @ B_15 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_331_insert__mono,axiom,
% 0.30/1.66 ! [A_41: pname,C_9: pname > $o,D_1: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ C_9 @ D_1 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ ( insert_pname @ A_41 @ C_9 ) @ ( insert_pname @ A_41 @ D_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_332_insert__mono,axiom,
% 0.30/1.66 ! [A_41: nat,C_9: nat > $o,D_1: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ C_9 @ D_1 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ ( insert_nat @ A_41 @ C_9 ) @ ( insert_nat @ A_41 @ D_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_333_insert__mono,axiom,
% 0.30/1.66 ! [A_41: x_a,C_9: x_a > $o,D_1: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ C_9 @ D_1 )
% 0.30/1.66 => ( ord_less_eq_a_o @ ( insert_a @ A_41 @ C_9 ) @ ( insert_a @ A_41 @ D_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_334_image__insert,axiom,
% 0.30/1.66 ! [F_15: x_a > pname,A_40: x_a,B_14: x_a > $o] :
% 0.30/1.66 ( ( image_a_pname @ F_15 @ ( insert_a @ A_40 @ B_14 ) )
% 0.30/1.66 = ( insert_pname @ ( F_15 @ A_40 ) @ ( image_a_pname @ F_15 @ B_14 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_335_image__insert,axiom,
% 0.30/1.66 ! [F_15: x_a > nat,A_40: x_a,B_14: x_a > $o] :
% 0.30/1.66 ( ( image_a_nat @ F_15 @ ( insert_a @ A_40 @ B_14 ) )
% 0.30/1.66 = ( insert_nat @ ( F_15 @ A_40 ) @ ( image_a_nat @ F_15 @ B_14 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_336_image__insert,axiom,
% 0.30/1.66 ! [F_15: nat > x_a,A_40: nat,B_14: nat > $o] :
% 0.30/1.66 ( ( image_nat_a @ F_15 @ ( insert_nat @ A_40 @ B_14 ) )
% 0.30/1.66 = ( insert_a @ ( F_15 @ A_40 ) @ ( image_nat_a @ F_15 @ B_14 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_337_image__insert,axiom,
% 0.30/1.66 ! [F_15: pname > x_a,A_40: pname,B_14: pname > $o] :
% 0.30/1.66 ( ( image_pname_a @ F_15 @ ( insert_pname @ A_40 @ B_14 ) )
% 0.30/1.66 = ( insert_a @ ( F_15 @ A_40 ) @ ( image_pname_a @ F_15 @ B_14 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_338_insert__image,axiom,
% 0.30/1.66 ! [F_14: pname > pname,X_17: pname,A_39: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_17 @ A_39 )
% 0.30/1.66 => ( ( insert_pname @ ( F_14 @ X_17 ) @ ( image_pname_pname @ F_14 @ A_39 ) )
% 0.30/1.66 = ( image_pname_pname @ F_14 @ A_39 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_339_insert__image,axiom,
% 0.30/1.66 ! [F_14: pname > nat,X_17: pname,A_39: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_17 @ A_39 )
% 0.30/1.66 => ( ( insert_nat @ ( F_14 @ X_17 ) @ ( image_pname_nat @ F_14 @ A_39 ) )
% 0.30/1.66 = ( image_pname_nat @ F_14 @ A_39 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_340_insert__image,axiom,
% 0.30/1.66 ! [F_14: x_a > pname,X_17: x_a,A_39: x_a > $o] :
% 0.30/1.66 ( ( member_a @ X_17 @ A_39 )
% 0.30/1.66 => ( ( insert_pname @ ( F_14 @ X_17 ) @ ( image_a_pname @ F_14 @ A_39 ) )
% 0.30/1.66 = ( image_a_pname @ F_14 @ A_39 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_341_insert__image,axiom,
% 0.30/1.66 ! [F_14: x_a > nat,X_17: x_a,A_39: x_a > $o] :
% 0.30/1.66 ( ( member_a @ X_17 @ A_39 )
% 0.30/1.66 => ( ( insert_nat @ ( F_14 @ X_17 ) @ ( image_a_nat @ F_14 @ A_39 ) )
% 0.30/1.66 = ( image_a_nat @ F_14 @ A_39 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_342_insert__image,axiom,
% 0.30/1.66 ! [F_14: nat > x_a,X_17: nat,A_39: nat > $o] :
% 0.30/1.66 ( ( member_nat @ X_17 @ A_39 )
% 0.30/1.66 => ( ( insert_a @ ( F_14 @ X_17 ) @ ( image_nat_a @ F_14 @ A_39 ) )
% 0.30/1.66 = ( image_nat_a @ F_14 @ A_39 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_343_insert__image,axiom,
% 0.30/1.66 ! [F_14: pname > x_a,X_17: pname,A_39: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_17 @ A_39 )
% 0.30/1.66 => ( ( insert_a @ ( F_14 @ X_17 ) @ ( image_pname_a @ F_14 @ A_39 ) )
% 0.30/1.66 = ( image_pname_a @ F_14 @ A_39 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_344_subset__image__iff,axiom,
% 0.30/1.66 ! [B_13: x_a > $o,F_13: nat > x_a,A_38: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ B_13 @ ( image_nat_a @ F_13 @ A_38 ) )
% 0.30/1.66 <=> ? [AA: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ AA @ A_38 )
% 0.30/1.66 & ( B_13
% 0.30/1.66 = ( image_nat_a @ F_13 @ AA ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_345_subset__image__iff,axiom,
% 0.30/1.66 ! [B_13: pname > $o,F_13: x_a > pname,A_38: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ B_13 @ ( image_a_pname @ F_13 @ A_38 ) )
% 0.30/1.66 <=> ? [AA: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ AA @ A_38 )
% 0.30/1.66 & ( B_13
% 0.30/1.66 = ( image_a_pname @ F_13 @ AA ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_346_subset__image__iff,axiom,
% 0.30/1.66 ! [B_13: nat > $o,F_13: x_a > nat,A_38: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ B_13 @ ( image_a_nat @ F_13 @ A_38 ) )
% 0.30/1.66 <=> ? [AA: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ AA @ A_38 )
% 0.30/1.66 & ( B_13
% 0.30/1.66 = ( image_a_nat @ F_13 @ AA ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_347_subset__image__iff,axiom,
% 0.30/1.66 ! [B_13: x_a > $o,F_13: pname > x_a,A_38: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ B_13 @ ( image_pname_a @ F_13 @ A_38 ) )
% 0.30/1.66 <=> ? [AA: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ AA @ A_38 )
% 0.30/1.66 & ( B_13
% 0.30/1.66 = ( image_pname_a @ F_13 @ AA ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_348_image__mono,axiom,
% 0.30/1.66 ! [F_12: x_a > pname,A_37: x_a > $o,B_12: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_37 @ B_12 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ ( image_a_pname @ F_12 @ A_37 ) @ ( image_a_pname @ F_12 @ B_12 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_349_image__mono,axiom,
% 0.30/1.66 ! [F_12: x_a > nat,A_37: x_a > $o,B_12: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_37 @ B_12 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ ( image_a_nat @ F_12 @ A_37 ) @ ( image_a_nat @ F_12 @ B_12 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_350_image__mono,axiom,
% 0.30/1.66 ! [F_12: nat > x_a,A_37: nat > $o,B_12: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_37 @ B_12 )
% 0.30/1.66 => ( ord_less_eq_a_o @ ( image_nat_a @ F_12 @ A_37 ) @ ( image_nat_a @ F_12 @ B_12 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_351_image__mono,axiom,
% 0.30/1.66 ! [F_12: pname > x_a,A_37: pname > $o,B_12: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_37 @ B_12 )
% 0.30/1.66 => ( ord_less_eq_a_o @ ( image_pname_a @ F_12 @ A_37 ) @ ( image_pname_a @ F_12 @ B_12 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_352_imageE,axiom,
% 0.30/1.66 ! [B_11: pname,F_11: nat > pname,A_36: nat > $o] :
% 0.30/1.66 ( ( member_pname @ B_11 @ ( image_nat_pname @ F_11 @ A_36 ) )
% 0.30/1.66 => ~ ! [X_1: nat] :
% 0.30/1.66 ( ( B_11
% 0.30/1.66 = ( F_11 @ X_1 ) )
% 0.30/1.66 => ~ ( member_nat @ X_1 @ A_36 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_353_imageE,axiom,
% 0.30/1.66 ! [B_11: x_a,F_11: nat > x_a,A_36: nat > $o] :
% 0.30/1.66 ( ( member_a @ B_11 @ ( image_nat_a @ F_11 @ A_36 ) )
% 0.30/1.66 => ~ ! [X_1: nat] :
% 0.30/1.66 ( ( B_11
% 0.30/1.66 = ( F_11 @ X_1 ) )
% 0.30/1.66 => ~ ( member_nat @ X_1 @ A_36 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_354_imageE,axiom,
% 0.30/1.66 ! [B_11: nat,F_11: pname > nat,A_36: pname > $o] :
% 0.30/1.66 ( ( member_nat @ B_11 @ ( image_pname_nat @ F_11 @ A_36 ) )
% 0.30/1.66 => ~ ! [X_1: pname] :
% 0.30/1.66 ( ( B_11
% 0.30/1.66 = ( F_11 @ X_1 ) )
% 0.30/1.66 => ~ ( member_pname @ X_1 @ A_36 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_355_imageE,axiom,
% 0.30/1.66 ! [B_11: nat,F_11: x_a > nat,A_36: x_a > $o] :
% 0.30/1.66 ( ( member_nat @ B_11 @ ( image_a_nat @ F_11 @ A_36 ) )
% 0.30/1.66 => ~ ! [X_1: x_a] :
% 0.30/1.66 ( ( B_11
% 0.30/1.66 = ( F_11 @ X_1 ) )
% 0.30/1.66 => ~ ( member_a @ X_1 @ A_36 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_356_imageE,axiom,
% 0.30/1.66 ! [B_11: x_a,F_11: pname > x_a,A_36: pname > $o] :
% 0.30/1.66 ( ( member_a @ B_11 @ ( image_pname_a @ F_11 @ A_36 ) )
% 0.30/1.66 => ~ ! [X_1: pname] :
% 0.30/1.66 ( ( B_11
% 0.30/1.66 = ( F_11 @ X_1 ) )
% 0.30/1.66 => ~ ( member_pname @ X_1 @ A_36 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_357_subsetI,axiom,
% 0.30/1.66 ! [B_10: nat > $o,A_35: nat > $o] :
% 0.30/1.66 ( ! [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ A_35 )
% 0.30/1.66 => ( member_nat @ X_1 @ B_10 ) )
% 0.30/1.66 => ( ord_less_eq_nat_o @ A_35 @ B_10 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_358_subsetI,axiom,
% 0.30/1.66 ! [B_10: pname > $o,A_35: pname > $o] :
% 0.30/1.66 ( ! [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_35 )
% 0.30/1.66 => ( member_pname @ X_1 @ B_10 ) )
% 0.30/1.66 => ( ord_less_eq_pname_o @ A_35 @ B_10 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_359_subsetI,axiom,
% 0.30/1.66 ! [B_10: x_a > $o,A_35: x_a > $o] :
% 0.30/1.66 ( ! [X_1: x_a] :
% 0.30/1.66 ( ( member_a @ X_1 @ A_35 )
% 0.30/1.66 => ( member_a @ X_1 @ B_10 ) )
% 0.30/1.66 => ( ord_less_eq_a_o @ A_35 @ B_10 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_360_image__subsetI,axiom,
% 0.30/1.66 ! [F_10: pname > nat,B_9: nat > $o,A_34: pname > $o] :
% 0.30/1.66 ( ! [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_34 )
% 0.30/1.66 => ( member_nat @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/1.66 => ( ord_less_eq_nat_o @ ( image_pname_nat @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_361_image__subsetI,axiom,
% 0.30/1.66 ! [F_10: pname > pname,B_9: pname > $o,A_34: pname > $o] :
% 0.30/1.66 ( ! [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_34 )
% 0.30/1.66 => ( member_pname @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/1.66 => ( ord_less_eq_pname_o @ ( image_pname_pname @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_362_image__subsetI,axiom,
% 0.30/1.66 ! [F_10: x_a > nat,B_9: nat > $o,A_34: x_a > $o] :
% 0.30/1.66 ( ! [X_1: x_a] :
% 0.30/1.66 ( ( member_a @ X_1 @ A_34 )
% 0.30/1.66 => ( member_nat @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/1.66 => ( ord_less_eq_nat_o @ ( image_a_nat @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_363_image__subsetI,axiom,
% 0.30/1.66 ! [F_10: x_a > pname,B_9: pname > $o,A_34: x_a > $o] :
% 0.30/1.66 ( ! [X_1: x_a] :
% 0.30/1.66 ( ( member_a @ X_1 @ A_34 )
% 0.30/1.66 => ( member_pname @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/1.66 => ( ord_less_eq_pname_o @ ( image_a_pname @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_364_image__subsetI,axiom,
% 0.30/1.66 ! [F_10: nat > pname,B_9: pname > $o,A_34: nat > $o] :
% 0.30/1.66 ( ! [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ A_34 )
% 0.30/1.66 => ( member_pname @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/1.66 => ( ord_less_eq_pname_o @ ( image_nat_pname @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_365_image__subsetI,axiom,
% 0.30/1.66 ! [F_10: nat > x_a,B_9: x_a > $o,A_34: nat > $o] :
% 0.30/1.66 ( ! [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ A_34 )
% 0.30/1.66 => ( member_a @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/1.66 => ( ord_less_eq_a_o @ ( image_nat_a @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_366_image__subsetI,axiom,
% 0.30/1.66 ! [F_10: pname > x_a,B_9: x_a > $o,A_34: pname > $o] :
% 0.30/1.66 ( ! [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ A_34 )
% 0.30/1.66 => ( member_a @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/1.66 => ( ord_less_eq_a_o @ ( image_pname_a @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_367_order__refl,axiom,
% 0.30/1.66 ! [X_16: $o] : ( ord_less_eq_o @ X_16 @ X_16 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_368_order__refl,axiom,
% 0.30/1.66 ! [X_16: pname > $o] : ( ord_less_eq_pname_o @ X_16 @ X_16 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_369_order__refl,axiom,
% 0.30/1.66 ! [X_16: nat > $o] : ( ord_less_eq_nat_o @ X_16 @ X_16 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_370_order__refl,axiom,
% 0.30/1.66 ! [X_16: x_a > $o] : ( ord_less_eq_a_o @ X_16 @ X_16 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_371_order__refl,axiom,
% 0.30/1.66 ! [X_16: nat] : ( ord_less_eq_nat @ X_16 @ X_16 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_372_finite__nat__set__iff__bounded__le,axiom,
% 0.30/1.66 ! [N_1: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ N_1 )
% 0.30/1.66 <=> ? [M_1: nat] :
% 0.30/1.66 ! [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ N_1 )
% 0.30/1.66 => ( ord_less_eq_nat @ X_1 @ M_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_373_assms_I3_J,axiom,
% 0.30/1.66 ! [G: x_a > $o,C: com] :
% 0.30/1.66 ( ( wt @ C )
% 0.30/1.66 => ( ! [X_1: pname] :
% 0.30/1.66 ( ( member_pname @ X_1 @ u )
% 0.30/1.66 => ( p @ G @ ( insert_a @ ( mgt_call @ X_1 ) @ bot_bot_a_o ) ) )
% 0.30/1.66 => ( p @ G @ ( insert_a @ ( mgt @ C ) @ bot_bot_a_o ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_374_le__fun__def,axiom,
% 0.30/1.66 ! [F_9: pname > $o,G_3: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ F_9 @ G_3 )
% 0.30/1.66 <=> ! [X_1: pname] : ( ord_less_eq_o @ ( F_9 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_375_le__fun__def,axiom,
% 0.30/1.66 ! [F_9: nat > $o,G_3: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ F_9 @ G_3 )
% 0.30/1.66 <=> ! [X_1: nat] : ( ord_less_eq_o @ ( F_9 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_376_le__fun__def,axiom,
% 0.30/1.66 ! [F_9: x_a > $o,G_3: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ F_9 @ G_3 )
% 0.30/1.66 <=> ! [X_1: x_a] : ( ord_less_eq_o @ ( F_9 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_377_le__funD,axiom,
% 0.30/1.66 ! [X_15: pname,F_8: pname > $o,G_2: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ F_8 @ G_2 )
% 0.30/1.66 => ( ord_less_eq_o @ ( F_8 @ X_15 ) @ ( G_2 @ X_15 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_378_le__funD,axiom,
% 0.30/1.66 ! [X_15: nat,F_8: nat > $o,G_2: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ F_8 @ G_2 )
% 0.30/1.66 => ( ord_less_eq_o @ ( F_8 @ X_15 ) @ ( G_2 @ X_15 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_379_le__funD,axiom,
% 0.30/1.66 ! [X_15: x_a,F_8: x_a > $o,G_2: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ F_8 @ G_2 )
% 0.30/1.66 => ( ord_less_eq_o @ ( F_8 @ X_15 ) @ ( G_2 @ X_15 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_380_le__funE,axiom,
% 0.30/1.66 ! [X_14: pname,F_7: pname > $o,G_1: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ F_7 @ G_1 )
% 0.30/1.66 => ( ord_less_eq_o @ ( F_7 @ X_14 ) @ ( G_1 @ X_14 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_381_le__funE,axiom,
% 0.30/1.66 ! [X_14: nat,F_7: nat > $o,G_1: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ F_7 @ G_1 )
% 0.30/1.66 => ( ord_less_eq_o @ ( F_7 @ X_14 ) @ ( G_1 @ X_14 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_382_le__funE,axiom,
% 0.30/1.66 ! [X_14: x_a,F_7: x_a > $o,G_1: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ F_7 @ G_1 )
% 0.30/1.66 => ( ord_less_eq_o @ ( F_7 @ X_14 ) @ ( G_1 @ X_14 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_383_emptyE,axiom,
% 0.30/1.66 ! [A_33: nat] :
% 0.30/1.66 ~ ( member_nat @ A_33 @ bot_bot_nat_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_384_emptyE,axiom,
% 0.30/1.66 ! [A_33: pname] :
% 0.30/1.66 ~ ( member_pname @ A_33 @ bot_bot_pname_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_385_emptyE,axiom,
% 0.30/1.66 ! [A_33: x_a] :
% 0.30/1.66 ~ ( member_a @ A_33 @ bot_bot_a_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_386_finite_OemptyI,axiom,
% 0.30/1.66 finite_finite_nat_o @ bot_bot_nat_o_o ).
% 0.30/1.66
% 0.30/1.66 thf(fact_387_finite_OemptyI,axiom,
% 0.30/1.66 finite297249702name_o @ bot_bot_pname_o_o ).
% 0.30/1.66
% 0.30/1.66 thf(fact_388_finite_OemptyI,axiom,
% 0.30/1.66 finite_finite_a_o @ bot_bot_a_o_o ).
% 0.30/1.66
% 0.30/1.66 thf(fact_389_finite_OemptyI,axiom,
% 0.30/1.66 finite_finite_a @ bot_bot_a_o ).
% 0.30/1.66
% 0.30/1.66 thf(fact_390_finite_OemptyI,axiom,
% 0.30/1.66 finite_finite_pname @ bot_bot_pname_o ).
% 0.30/1.66
% 0.30/1.66 thf(fact_391_finite_OemptyI,axiom,
% 0.30/1.66 finite_finite_nat @ bot_bot_nat_o ).
% 0.30/1.66
% 0.30/1.66 thf(fact_392_empty__subsetI,axiom,
% 0.30/1.66 ! [A_32: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_32 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_393_empty__subsetI,axiom,
% 0.30/1.66 ! [A_32: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A_32 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_394_empty__subsetI,axiom,
% 0.30/1.66 ! [A_32: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A_32 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_395_equals0D,axiom,
% 0.30/1.66 ! [A_31: nat,A_30: nat > $o] :
% 0.30/1.66 ( ( A_30 = bot_bot_nat_o )
% 0.30/1.66 => ~ ( member_nat @ A_31 @ A_30 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_396_equals0D,axiom,
% 0.30/1.66 ! [A_31: pname,A_30: pname > $o] :
% 0.30/1.66 ( ( A_30 = bot_bot_pname_o )
% 0.30/1.66 => ~ ( member_pname @ A_31 @ A_30 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_397_equals0D,axiom,
% 0.30/1.66 ! [A_31: x_a,A_30: x_a > $o] :
% 0.30/1.66 ( ( A_30 = bot_bot_a_o )
% 0.30/1.66 => ~ ( member_a @ A_31 @ A_30 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_398_Collect__empty__eq,axiom,
% 0.30/1.66 ! [P_6: pname > $o] :
% 0.30/1.66 ( ( ( collect_pname @ P_6 )
% 0.30/1.66 = bot_bot_pname_o )
% 0.30/1.66 <=> ! [X_1: pname] :
% 0.30/1.66 ~ ( P_6 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_399_Collect__empty__eq,axiom,
% 0.30/1.66 ! [P_6: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( ( collect_nat_o @ P_6 )
% 0.30/1.66 = bot_bot_nat_o_o )
% 0.30/1.66 <=> ! [X_1: nat > $o] :
% 0.30/1.66 ~ ( P_6 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_400_Collect__empty__eq,axiom,
% 0.30/1.66 ! [P_6: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( ( collect_pname_o @ P_6 )
% 0.30/1.66 = bot_bot_pname_o_o )
% 0.30/1.66 <=> ! [X_1: pname > $o] :
% 0.30/1.66 ~ ( P_6 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_401_Collect__empty__eq,axiom,
% 0.30/1.66 ! [P_6: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( ( collect_a_o @ P_6 )
% 0.30/1.66 = bot_bot_a_o_o )
% 0.30/1.66 <=> ! [X_1: x_a > $o] :
% 0.30/1.66 ~ ( P_6 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_402_Collect__empty__eq,axiom,
% 0.30/1.66 ! [P_6: x_a > $o] :
% 0.30/1.66 ( ( ( collect_a @ P_6 )
% 0.30/1.66 = bot_bot_a_o )
% 0.30/1.66 <=> ! [X_1: x_a] :
% 0.30/1.66 ~ ( P_6 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_403_Collect__empty__eq,axiom,
% 0.30/1.66 ! [P_6: nat > $o] :
% 0.30/1.66 ( ( ( collect_nat @ P_6 )
% 0.30/1.66 = bot_bot_nat_o )
% 0.30/1.66 <=> ! [X_1: nat] :
% 0.30/1.66 ~ ( P_6 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_404_empty__iff,axiom,
% 0.30/1.66 ! [C_8: nat] :
% 0.30/1.66 ~ ( member_nat @ C_8 @ bot_bot_nat_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_405_empty__iff,axiom,
% 0.30/1.66 ! [C_8: pname] :
% 0.30/1.66 ~ ( member_pname @ C_8 @ bot_bot_pname_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_406_empty__iff,axiom,
% 0.30/1.66 ! [C_8: x_a] :
% 0.30/1.66 ~ ( member_a @ C_8 @ bot_bot_a_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_407_empty__Collect__eq,axiom,
% 0.30/1.66 ! [P_5: pname > $o] :
% 0.30/1.66 ( ( bot_bot_pname_o
% 0.30/1.66 = ( collect_pname @ P_5 ) )
% 0.30/1.66 <=> ! [X_1: pname] :
% 0.30/1.66 ~ ( P_5 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_408_empty__Collect__eq,axiom,
% 0.30/1.66 ! [P_5: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( bot_bot_nat_o_o
% 0.30/1.66 = ( collect_nat_o @ P_5 ) )
% 0.30/1.66 <=> ! [X_1: nat > $o] :
% 0.30/1.66 ~ ( P_5 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_409_empty__Collect__eq,axiom,
% 0.30/1.66 ! [P_5: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( bot_bot_pname_o_o
% 0.30/1.66 = ( collect_pname_o @ P_5 ) )
% 0.30/1.66 <=> ! [X_1: pname > $o] :
% 0.30/1.66 ~ ( P_5 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_410_empty__Collect__eq,axiom,
% 0.30/1.66 ! [P_5: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( bot_bot_a_o_o
% 0.30/1.66 = ( collect_a_o @ P_5 ) )
% 0.30/1.66 <=> ! [X_1: x_a > $o] :
% 0.30/1.66 ~ ( P_5 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_411_empty__Collect__eq,axiom,
% 0.30/1.66 ! [P_5: x_a > $o] :
% 0.30/1.66 ( ( bot_bot_a_o
% 0.30/1.66 = ( collect_a @ P_5 ) )
% 0.30/1.66 <=> ! [X_1: x_a] :
% 0.30/1.66 ~ ( P_5 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_412_empty__Collect__eq,axiom,
% 0.30/1.66 ! [P_5: nat > $o] :
% 0.30/1.66 ( ( bot_bot_nat_o
% 0.30/1.66 = ( collect_nat @ P_5 ) )
% 0.30/1.66 <=> ! [X_1: nat] :
% 0.30/1.66 ~ ( P_5 @ X_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_413_ex__in__conv,axiom,
% 0.30/1.66 ! [A_29: nat > $o] :
% 0.30/1.66 ( ? [X_1: nat] : ( member_nat @ X_1 @ A_29 )
% 0.30/1.66 <=> ( A_29 != bot_bot_nat_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_414_ex__in__conv,axiom,
% 0.30/1.66 ! [A_29: pname > $o] :
% 0.30/1.66 ( ? [X_1: pname] : ( member_pname @ X_1 @ A_29 )
% 0.30/1.66 <=> ( A_29 != bot_bot_pname_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_415_ex__in__conv,axiom,
% 0.30/1.66 ! [A_29: x_a > $o] :
% 0.30/1.66 ( ? [X_1: x_a] : ( member_a @ X_1 @ A_29 )
% 0.30/1.66 <=> ( A_29 != bot_bot_a_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_416_all__not__in__conv,axiom,
% 0.30/1.66 ! [A_28: nat > $o] :
% 0.30/1.66 ( ! [X_1: nat] :
% 0.30/1.66 ~ ( member_nat @ X_1 @ A_28 )
% 0.30/1.66 <=> ( A_28 = bot_bot_nat_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_417_all__not__in__conv,axiom,
% 0.30/1.66 ! [A_28: pname > $o] :
% 0.30/1.66 ( ! [X_1: pname] :
% 0.30/1.66 ~ ( member_pname @ X_1 @ A_28 )
% 0.30/1.66 <=> ( A_28 = bot_bot_pname_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_418_all__not__in__conv,axiom,
% 0.30/1.66 ! [A_28: x_a > $o] :
% 0.30/1.66 ( ! [X_1: x_a] :
% 0.30/1.66 ~ ( member_a @ X_1 @ A_28 )
% 0.30/1.66 <=> ( A_28 = bot_bot_a_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_419_empty__def,axiom,
% 0.30/1.66 ( bot_bot_pname_o
% 0.30/1.66 = ( collect_pname
% 0.30/1.66 @ ^ [X_1: pname] : $false ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_420_empty__def,axiom,
% 0.30/1.66 ( bot_bot_nat_o_o
% 0.30/1.66 = ( collect_nat_o
% 0.30/1.66 @ ^ [X_1: nat > $o] : $false ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_421_empty__def,axiom,
% 0.30/1.66 ( bot_bot_pname_o_o
% 0.30/1.66 = ( collect_pname_o
% 0.30/1.66 @ ^ [X_1: pname > $o] : $false ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_422_empty__def,axiom,
% 0.30/1.66 ( bot_bot_a_o_o
% 0.30/1.66 = ( collect_a_o
% 0.30/1.66 @ ^ [X_1: x_a > $o] : $false ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_423_empty__def,axiom,
% 0.30/1.66 ( bot_bot_a_o
% 0.30/1.66 = ( collect_a
% 0.30/1.66 @ ^ [X_1: x_a] : $false ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_424_empty__def,axiom,
% 0.30/1.66 ( bot_bot_nat_o
% 0.30/1.66 = ( collect_nat
% 0.30/1.66 @ ^ [X_1: nat] : $false ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_425_bot__fun__def,axiom,
% 0.30/1.66 ! [X_1: pname] :
% 0.30/1.66 ( ( bot_bot_pname_o @ X_1 )
% 0.30/1.66 <=> bot_bot_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_426_bot__fun__def,axiom,
% 0.30/1.66 ! [X_1: nat] :
% 0.30/1.66 ( ( bot_bot_nat_o @ X_1 )
% 0.30/1.66 <=> bot_bot_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_427_bot__fun__def,axiom,
% 0.30/1.66 ! [X_1: x_a] :
% 0.30/1.66 ( ( bot_bot_a_o @ X_1 )
% 0.30/1.66 <=> bot_bot_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_428_bot__apply,axiom,
% 0.30/1.66 ! [X_13: pname] :
% 0.30/1.66 ( ( bot_bot_pname_o @ X_13 )
% 0.30/1.66 <=> bot_bot_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_429_bot__apply,axiom,
% 0.30/1.66 ! [X_13: nat] :
% 0.30/1.66 ( ( bot_bot_nat_o @ X_13 )
% 0.30/1.66 <=> bot_bot_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_430_bot__apply,axiom,
% 0.30/1.66 ! [X_13: x_a] :
% 0.30/1.66 ( ( bot_bot_a_o @ X_13 )
% 0.30/1.66 <=> bot_bot_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_431_le__bot,axiom,
% 0.30/1.66 ! [A_27: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_27 @ bot_bot_pname_o )
% 0.30/1.66 => ( A_27 = bot_bot_pname_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_432_le__bot,axiom,
% 0.30/1.66 ! [A_27: $o] :
% 0.30/1.66 ( ( ord_less_eq_o @ A_27 @ bot_bot_o )
% 0.30/1.66 => ( A_27
% 0.30/1.66 <=> bot_bot_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_433_le__bot,axiom,
% 0.30/1.66 ! [A_27: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_27 @ bot_bot_nat_o )
% 0.30/1.66 => ( A_27 = bot_bot_nat_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_434_le__bot,axiom,
% 0.30/1.66 ! [A_27: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_27 @ bot_bot_a_o )
% 0.30/1.66 => ( A_27 = bot_bot_a_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_435_le__bot,axiom,
% 0.30/1.66 ! [A_27: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ A_27 @ bot_bot_nat )
% 0.30/1.66 => ( A_27 = bot_bot_nat ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_436_bot__unique,axiom,
% 0.30/1.66 ! [A_26: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_26 @ bot_bot_pname_o )
% 0.30/1.66 <=> ( A_26 = bot_bot_pname_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_437_bot__unique,axiom,
% 0.30/1.66 ! [A_26: $o] :
% 0.30/1.66 ( ( ord_less_eq_o @ A_26 @ bot_bot_o )
% 0.30/1.66 <=> ( A_26
% 0.30/1.66 <=> bot_bot_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_438_bot__unique,axiom,
% 0.30/1.66 ! [A_26: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_26 @ bot_bot_nat_o )
% 0.30/1.66 <=> ( A_26 = bot_bot_nat_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_439_bot__unique,axiom,
% 0.30/1.66 ! [A_26: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_26 @ bot_bot_a_o )
% 0.30/1.66 <=> ( A_26 = bot_bot_a_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_440_bot__unique,axiom,
% 0.30/1.66 ! [A_26: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ A_26 @ bot_bot_nat )
% 0.30/1.66 <=> ( A_26 = bot_bot_nat ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_441_bot__least,axiom,
% 0.30/1.66 ! [A_25: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_25 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_442_bot__least,axiom,
% 0.30/1.66 ! [A_25: $o] : ( ord_less_eq_o @ bot_bot_o @ A_25 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_443_bot__least,axiom,
% 0.30/1.66 ! [A_25: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A_25 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_444_bot__least,axiom,
% 0.30/1.66 ! [A_25: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A_25 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_445_bot__least,axiom,
% 0.30/1.66 ! [A_25: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A_25 ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_446_singleton__inject,axiom,
% 0.30/1.66 ! [A_24: pname,B_8: pname] :
% 0.30/1.66 ( ( ( insert_pname @ A_24 @ bot_bot_pname_o )
% 0.30/1.66 = ( insert_pname @ B_8 @ bot_bot_pname_o ) )
% 0.30/1.66 => ( A_24 = B_8 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_447_singleton__inject,axiom,
% 0.30/1.66 ! [A_24: nat,B_8: nat] :
% 0.30/1.66 ( ( ( insert_nat @ A_24 @ bot_bot_nat_o )
% 0.30/1.66 = ( insert_nat @ B_8 @ bot_bot_nat_o ) )
% 0.30/1.66 => ( A_24 = B_8 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_448_singleton__inject,axiom,
% 0.30/1.66 ! [A_24: x_a,B_8: x_a] :
% 0.30/1.66 ( ( ( insert_a @ A_24 @ bot_bot_a_o )
% 0.30/1.66 = ( insert_a @ B_8 @ bot_bot_a_o ) )
% 0.30/1.66 => ( A_24 = B_8 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_449_singletonE,axiom,
% 0.30/1.66 ! [B_7: nat,A_23: nat] :
% 0.30/1.66 ( ( member_nat @ B_7 @ ( insert_nat @ A_23 @ bot_bot_nat_o ) )
% 0.30/1.66 => ( B_7 = A_23 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_450_singletonE,axiom,
% 0.30/1.66 ! [B_7: pname,A_23: pname] :
% 0.30/1.66 ( ( member_pname @ B_7 @ ( insert_pname @ A_23 @ bot_bot_pname_o ) )
% 0.30/1.66 => ( B_7 = A_23 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_451_singletonE,axiom,
% 0.30/1.66 ! [B_7: x_a,A_23: x_a] :
% 0.30/1.66 ( ( member_a @ B_7 @ ( insert_a @ A_23 @ bot_bot_a_o ) )
% 0.30/1.66 => ( B_7 = A_23 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_452_doubleton__eq__iff,axiom,
% 0.30/1.66 ! [A_22: pname,B_6: pname,C_7: pname,D: pname] :
% 0.30/1.66 ( ( ( insert_pname @ A_22 @ ( insert_pname @ B_6 @ bot_bot_pname_o ) )
% 0.30/1.66 = ( insert_pname @ C_7 @ ( insert_pname @ D @ bot_bot_pname_o ) ) )
% 0.30/1.66 <=> ( ( ( A_22 = C_7 )
% 0.30/1.66 & ( B_6 = D ) )
% 0.30/1.66 | ( ( A_22 = D )
% 0.30/1.66 & ( B_6 = C_7 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_453_doubleton__eq__iff,axiom,
% 0.30/1.66 ! [A_22: nat,B_6: nat,C_7: nat,D: nat] :
% 0.30/1.66 ( ( ( insert_nat @ A_22 @ ( insert_nat @ B_6 @ bot_bot_nat_o ) )
% 0.30/1.66 = ( insert_nat @ C_7 @ ( insert_nat @ D @ bot_bot_nat_o ) ) )
% 0.30/1.66 <=> ( ( ( A_22 = C_7 )
% 0.30/1.66 & ( B_6 = D ) )
% 0.30/1.66 | ( ( A_22 = D )
% 0.30/1.66 & ( B_6 = C_7 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_454_doubleton__eq__iff,axiom,
% 0.30/1.66 ! [A_22: x_a,B_6: x_a,C_7: x_a,D: x_a] :
% 0.30/1.66 ( ( ( insert_a @ A_22 @ ( insert_a @ B_6 @ bot_bot_a_o ) )
% 0.30/1.66 = ( insert_a @ C_7 @ ( insert_a @ D @ bot_bot_a_o ) ) )
% 0.30/1.66 <=> ( ( ( A_22 = C_7 )
% 0.30/1.66 & ( B_6 = D ) )
% 0.30/1.66 | ( ( A_22 = D )
% 0.30/1.66 & ( B_6 = C_7 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_455_singleton__iff,axiom,
% 0.30/1.66 ! [B_5: nat,A_21: nat] :
% 0.30/1.66 ( ( member_nat @ B_5 @ ( insert_nat @ A_21 @ bot_bot_nat_o ) )
% 0.30/1.66 <=> ( B_5 = A_21 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_456_singleton__iff,axiom,
% 0.30/1.66 ! [B_5: pname,A_21: pname] :
% 0.30/1.66 ( ( member_pname @ B_5 @ ( insert_pname @ A_21 @ bot_bot_pname_o ) )
% 0.30/1.66 <=> ( B_5 = A_21 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_457_singleton__iff,axiom,
% 0.30/1.66 ! [B_5: x_a,A_21: x_a] :
% 0.30/1.66 ( ( member_a @ B_5 @ ( insert_a @ A_21 @ bot_bot_a_o ) )
% 0.30/1.66 <=> ( B_5 = A_21 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_458_insert__not__empty,axiom,
% 0.30/1.66 ! [A_20: pname,A_19: pname > $o] :
% 0.30/1.66 ( ( insert_pname @ A_20 @ A_19 )
% 0.30/1.66 != bot_bot_pname_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_459_insert__not__empty,axiom,
% 0.30/1.66 ! [A_20: nat,A_19: nat > $o] :
% 0.30/1.66 ( ( insert_nat @ A_20 @ A_19 )
% 0.30/1.66 != bot_bot_nat_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_460_insert__not__empty,axiom,
% 0.30/1.66 ! [A_20: x_a,A_19: x_a > $o] :
% 0.30/1.66 ( ( insert_a @ A_20 @ A_19 )
% 0.30/1.66 != bot_bot_a_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_461_empty__not__insert,axiom,
% 0.30/1.66 ! [A_18: pname,A_17: pname > $o] :
% 0.30/1.66 ( bot_bot_pname_o
% 0.30/1.66 != ( insert_pname @ A_18 @ A_17 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_462_empty__not__insert,axiom,
% 0.30/1.66 ! [A_18: nat,A_17: nat > $o] :
% 0.30/1.66 ( bot_bot_nat_o
% 0.30/1.66 != ( insert_nat @ A_18 @ A_17 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_463_empty__not__insert,axiom,
% 0.30/1.66 ! [A_18: x_a,A_17: x_a > $o] :
% 0.30/1.66 ( bot_bot_a_o
% 0.30/1.66 != ( insert_a @ A_18 @ A_17 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_464_subset__empty,axiom,
% 0.30/1.66 ! [A_16: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_16 @ bot_bot_nat_o )
% 0.30/1.66 <=> ( A_16 = bot_bot_nat_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_465_subset__empty,axiom,
% 0.30/1.66 ! [A_16: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_16 @ bot_bot_pname_o )
% 0.30/1.66 <=> ( A_16 = bot_bot_pname_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_466_subset__empty,axiom,
% 0.30/1.66 ! [A_16: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_16 @ bot_bot_a_o )
% 0.30/1.66 <=> ( A_16 = bot_bot_a_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_467_image__is__empty,axiom,
% 0.30/1.66 ! [F_6: pname > x_a,A_15: pname > $o] :
% 0.30/1.66 ( ( ( image_pname_a @ F_6 @ A_15 )
% 0.30/1.66 = bot_bot_a_o )
% 0.30/1.66 <=> ( A_15 = bot_bot_pname_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_468_image__empty,axiom,
% 0.30/1.66 ! [F_5: pname > x_a] :
% 0.30/1.66 ( ( image_pname_a @ F_5 @ bot_bot_pname_o )
% 0.30/1.66 = bot_bot_a_o ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_469_empty__is__image,axiom,
% 0.30/1.66 ! [F_4: pname > x_a,A_14: pname > $o] :
% 0.30/1.66 ( ( bot_bot_a_o
% 0.30/1.66 = ( image_pname_a @ F_4 @ A_14 ) )
% 0.30/1.66 <=> ( A_14 = bot_bot_pname_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_470_Collect__conv__if,axiom,
% 0.30/1.66 ! [P_4: nat > $o,A_13: nat] :
% 0.30/1.66 ( ( ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_nat
% 0.30/1.66 @ ^ [X_1: nat] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = ( insert_nat @ A_13 @ bot_bot_nat_o ) ) )
% 0.30/1.66 & ( ~ ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_nat
% 0.30/1.66 @ ^ [X_1: nat] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_nat_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_471_Collect__conv__if,axiom,
% 0.30/1.66 ! [P_4: pname > $o,A_13: pname] :
% 0.30/1.66 ( ( ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_pname
% 0.30/1.66 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = ( insert_pname @ A_13 @ bot_bot_pname_o ) ) )
% 0.30/1.66 & ( ~ ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_pname
% 0.30/1.66 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_pname_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_472_Collect__conv__if,axiom,
% 0.30/1.66 ! [P_4: x_a > $o,A_13: x_a] :
% 0.30/1.66 ( ( ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_a
% 0.30/1.66 @ ^ [X_1: x_a] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = ( insert_a @ A_13 @ bot_bot_a_o ) ) )
% 0.30/1.66 & ( ~ ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_a
% 0.30/1.66 @ ^ [X_1: x_a] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_a_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_473_Collect__conv__if,axiom,
% 0.30/1.66 ! [P_4: ( nat > $o ) > $o,A_13: nat > $o] :
% 0.30/1.66 ( ( ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_nat_o
% 0.30/1.66 @ ^ [X_1: nat > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = ( insert_nat_o @ A_13 @ bot_bot_nat_o_o ) ) )
% 0.30/1.66 & ( ~ ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_nat_o
% 0.30/1.66 @ ^ [X_1: nat > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_nat_o_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_474_Collect__conv__if,axiom,
% 0.30/1.66 ! [P_4: ( pname > $o ) > $o,A_13: pname > $o] :
% 0.30/1.66 ( ( ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_pname_o
% 0.30/1.66 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = ( insert_pname_o @ A_13 @ bot_bot_pname_o_o ) ) )
% 0.30/1.66 & ( ~ ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_pname_o
% 0.30/1.66 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_pname_o_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_475_Collect__conv__if,axiom,
% 0.30/1.66 ! [P_4: ( x_a > $o ) > $o,A_13: x_a > $o] :
% 0.30/1.66 ( ( ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_a_o
% 0.30/1.66 @ ^ [X_1: x_a > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = ( insert_a_o @ A_13 @ bot_bot_a_o_o ) ) )
% 0.30/1.66 & ( ~ ( P_4 @ A_13 )
% 0.30/1.66 => ( ( collect_a_o
% 0.30/1.66 @ ^ [X_1: x_a > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_a_o_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_476_Collect__conv__if2,axiom,
% 0.30/1.66 ! [P_3: nat > $o,A_12: nat] :
% 0.30/1.66 ( ( ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_nat
% 0.30/1.66 @ ^ [X_1: nat] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = ( insert_nat @ A_12 @ bot_bot_nat_o ) ) )
% 0.30/1.66 & ( ~ ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_nat
% 0.30/1.66 @ ^ [X_1: nat] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_nat_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_477_Collect__conv__if2,axiom,
% 0.30/1.66 ! [P_3: pname > $o,A_12: pname] :
% 0.30/1.66 ( ( ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_pname
% 0.30/1.66 @ ^ [X_1: pname] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = ( insert_pname @ A_12 @ bot_bot_pname_o ) ) )
% 0.30/1.66 & ( ~ ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_pname
% 0.30/1.66 @ ^ [X_1: pname] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_pname_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_478_Collect__conv__if2,axiom,
% 0.30/1.66 ! [P_3: x_a > $o,A_12: x_a] :
% 0.30/1.66 ( ( ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_a
% 0.30/1.66 @ ^ [X_1: x_a] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = ( insert_a @ A_12 @ bot_bot_a_o ) ) )
% 0.30/1.66 & ( ~ ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_a
% 0.30/1.66 @ ^ [X_1: x_a] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_a_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_479_Collect__conv__if2,axiom,
% 0.30/1.66 ! [P_3: ( nat > $o ) > $o,A_12: nat > $o] :
% 0.30/1.66 ( ( ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_nat_o
% 0.30/1.66 @ ^ [X_1: nat > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = ( insert_nat_o @ A_12 @ bot_bot_nat_o_o ) ) )
% 0.30/1.66 & ( ~ ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_nat_o
% 0.30/1.66 @ ^ [X_1: nat > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_nat_o_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_480_Collect__conv__if2,axiom,
% 0.30/1.66 ! [P_3: ( pname > $o ) > $o,A_12: pname > $o] :
% 0.30/1.66 ( ( ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_pname_o
% 0.30/1.66 @ ^ [X_1: pname > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = ( insert_pname_o @ A_12 @ bot_bot_pname_o_o ) ) )
% 0.30/1.66 & ( ~ ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_pname_o
% 0.30/1.66 @ ^ [X_1: pname > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_pname_o_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_481_Collect__conv__if2,axiom,
% 0.30/1.66 ! [P_3: ( x_a > $o ) > $o,A_12: x_a > $o] :
% 0.30/1.66 ( ( ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_a_o
% 0.30/1.66 @ ^ [X_1: x_a > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = ( insert_a_o @ A_12 @ bot_bot_a_o_o ) ) )
% 0.30/1.66 & ( ~ ( P_3 @ A_12 )
% 0.30/1.66 => ( ( collect_a_o
% 0.30/1.66 @ ^ [X_1: x_a > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/1.66 = bot_bot_a_o_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_482_singleton__conv,axiom,
% 0.30/1.66 ! [A_11: nat] :
% 0.30/1.66 ( ( collect_nat
% 0.30/1.66 @ ^ [X_1: nat] : ( X_1 = A_11 ) )
% 0.30/1.66 = ( insert_nat @ A_11 @ bot_bot_nat_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_483_singleton__conv,axiom,
% 0.30/1.66 ! [A_11: pname] :
% 0.30/1.66 ( ( collect_pname
% 0.30/1.66 @ ^ [X_1: pname] : ( X_1 = A_11 ) )
% 0.30/1.66 = ( insert_pname @ A_11 @ bot_bot_pname_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_484_singleton__conv,axiom,
% 0.30/1.66 ! [A_11: x_a] :
% 0.30/1.66 ( ( collect_a
% 0.30/1.66 @ ^ [X_1: x_a] : ( X_1 = A_11 ) )
% 0.30/1.66 = ( insert_a @ A_11 @ bot_bot_a_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_485_singleton__conv,axiom,
% 0.30/1.66 ! [A_11: nat > $o] :
% 0.30/1.66 ( ( collect_nat_o
% 0.30/1.66 @ ^ [X_1: nat > $o] : ( X_1 = A_11 ) )
% 0.30/1.66 = ( insert_nat_o @ A_11 @ bot_bot_nat_o_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_486_singleton__conv,axiom,
% 0.30/1.66 ! [A_11: pname > $o] :
% 0.30/1.66 ( ( collect_pname_o
% 0.30/1.66 @ ^ [X_1: pname > $o] : ( X_1 = A_11 ) )
% 0.30/1.66 = ( insert_pname_o @ A_11 @ bot_bot_pname_o_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_487_singleton__conv,axiom,
% 0.30/1.66 ! [A_11: x_a > $o] :
% 0.30/1.66 ( ( collect_a_o
% 0.30/1.66 @ ^ [X_1: x_a > $o] : ( X_1 = A_11 ) )
% 0.30/1.66 = ( insert_a_o @ A_11 @ bot_bot_a_o_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_488_singleton__conv2,axiom,
% 0.30/1.66 ! [A_10: nat] :
% 0.30/1.66 ( ( collect_nat @ ( fequal_nat @ A_10 ) )
% 0.30/1.66 = ( insert_nat @ A_10 @ bot_bot_nat_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_489_singleton__conv2,axiom,
% 0.30/1.66 ! [A_10: pname] :
% 0.30/1.66 ( ( collect_pname @ ( fequal_pname @ A_10 ) )
% 0.30/1.66 = ( insert_pname @ A_10 @ bot_bot_pname_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_490_singleton__conv2,axiom,
% 0.30/1.66 ! [A_10: x_a] :
% 0.30/1.66 ( ( collect_a @ ( fequal_a @ A_10 ) )
% 0.30/1.66 = ( insert_a @ A_10 @ bot_bot_a_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_491_singleton__conv2,axiom,
% 0.30/1.66 ! [A_10: nat > $o] :
% 0.30/1.66 ( ( collect_nat_o @ ( fequal_nat_o @ A_10 ) )
% 0.30/1.66 = ( insert_nat_o @ A_10 @ bot_bot_nat_o_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_492_singleton__conv2,axiom,
% 0.30/1.66 ! [A_10: pname > $o] :
% 0.30/1.66 ( ( collect_pname_o @ ( fequal_pname_o @ A_10 ) )
% 0.30/1.66 = ( insert_pname_o @ A_10 @ bot_bot_pname_o_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_493_singleton__conv2,axiom,
% 0.30/1.66 ! [A_10: x_a > $o] :
% 0.30/1.66 ( ( collect_a_o @ ( fequal_a_o @ A_10 ) )
% 0.30/1.66 = ( insert_a_o @ A_10 @ bot_bot_a_o_o ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_494_subset__singletonD,axiom,
% 0.30/1.66 ! [A_9: nat > $o,X_12: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_9 @ ( insert_nat @ X_12 @ bot_bot_nat_o ) )
% 0.30/1.66 => ( ( A_9 = bot_bot_nat_o )
% 0.30/1.66 | ( A_9
% 0.30/1.66 = ( insert_nat @ X_12 @ bot_bot_nat_o ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_495_subset__singletonD,axiom,
% 0.30/1.66 ! [A_9: pname > $o,X_12: pname] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_9 @ ( insert_pname @ X_12 @ bot_bot_pname_o ) )
% 0.30/1.66 => ( ( A_9 = bot_bot_pname_o )
% 0.30/1.66 | ( A_9
% 0.30/1.66 = ( insert_pname @ X_12 @ bot_bot_pname_o ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_496_subset__singletonD,axiom,
% 0.30/1.66 ! [A_9: x_a > $o,X_12: x_a] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_9 @ ( insert_a @ X_12 @ bot_bot_a_o ) )
% 0.30/1.66 => ( ( A_9 = bot_bot_a_o )
% 0.30/1.66 | ( A_9
% 0.30/1.66 = ( insert_a @ X_12 @ bot_bot_a_o ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_497_image__constant,axiom,
% 0.30/1.66 ! [C_6: x_a,X_11: pname,A_8: pname > $o] :
% 0.30/1.66 ( ( member_pname @ X_11 @ A_8 )
% 0.30/1.66 => ( ( image_pname_a
% 0.30/1.66 @ ^ [X_1: pname] : C_6
% 0.30/1.66 @ A_8 )
% 0.30/1.66 = ( insert_a @ C_6 @ bot_bot_a_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_498_image__constant__conv,axiom,
% 0.30/1.66 ! [C_5: x_a,A_7: pname > $o] :
% 0.30/1.66 ( ( ( A_7 = bot_bot_pname_o )
% 0.30/1.66 => ( ( image_pname_a
% 0.30/1.66 @ ^ [X_1: pname] : C_5
% 0.30/1.66 @ A_7 )
% 0.30/1.66 = bot_bot_a_o ) )
% 0.30/1.66 & ( ( A_7 != bot_bot_pname_o )
% 0.30/1.66 => ( ( image_pname_a
% 0.30/1.66 @ ^ [X_1: pname] : C_5
% 0.30/1.66 @ A_7 )
% 0.30/1.66 = ( insert_a @ C_5 @ bot_bot_a_o ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_499_linorder__le__cases,axiom,
% 0.30/1.66 ! [X_10: nat,Y_9: nat] :
% 0.30/1.66 ( ~ ( ord_less_eq_nat @ X_10 @ Y_9 )
% 0.30/1.66 => ( ord_less_eq_nat @ Y_9 @ X_10 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_500_xt1_I6_J,axiom,
% 0.30/1.66 ! [Z_2: $o,Y_8: $o,X_9: $o] :
% 0.30/1.66 ( ( ord_less_eq_o @ Y_8 @ X_9 )
% 0.30/1.66 => ( ( ord_less_eq_o @ Z_2 @ Y_8 )
% 0.30/1.66 => ( ord_less_eq_o @ Z_2 @ X_9 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_501_xt1_I6_J,axiom,
% 0.30/1.66 ! [Z_2: nat > $o,Y_8: nat > $o,X_9: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ Y_8 @ X_9 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ Z_2 @ Y_8 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ Z_2 @ X_9 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_502_xt1_I6_J,axiom,
% 0.30/1.66 ! [Z_2: pname > $o,Y_8: pname > $o,X_9: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ Y_8 @ X_9 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ Z_2 @ Y_8 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ Z_2 @ X_9 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_503_xt1_I6_J,axiom,
% 0.30/1.66 ! [Z_2: nat,Y_8: nat,X_9: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ Y_8 @ X_9 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ Z_2 @ Y_8 )
% 0.30/1.66 => ( ord_less_eq_nat @ Z_2 @ X_9 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_504_xt1_I6_J,axiom,
% 0.30/1.66 ! [Z_2: x_a > $o,Y_8: x_a > $o,X_9: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ Y_8 @ X_9 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ Z_2 @ Y_8 )
% 0.30/1.66 => ( ord_less_eq_a_o @ Z_2 @ X_9 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_505_xt1_I5_J,axiom,
% 0.30/1.66 ! [Y_7: $o,X_8: $o] :
% 0.30/1.66 ( ( ord_less_eq_o @ Y_7 @ X_8 )
% 0.30/1.66 => ( ( ord_less_eq_o @ X_8 @ Y_7 )
% 0.30/1.66 => ( X_8
% 0.30/1.66 <=> Y_7 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_506_xt1_I5_J,axiom,
% 0.30/1.66 ! [Y_7: nat > $o,X_8: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ Y_7 @ X_8 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ X_8 @ Y_7 )
% 0.30/1.66 => ( X_8 = Y_7 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_507_xt1_I5_J,axiom,
% 0.30/1.66 ! [Y_7: pname > $o,X_8: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ Y_7 @ X_8 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ X_8 @ Y_7 )
% 0.30/1.66 => ( X_8 = Y_7 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_508_xt1_I5_J,axiom,
% 0.30/1.66 ! [Y_7: nat,X_8: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ Y_7 @ X_8 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ X_8 @ Y_7 )
% 0.30/1.66 => ( X_8 = Y_7 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_509_xt1_I5_J,axiom,
% 0.30/1.66 ! [Y_7: x_a > $o,X_8: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ Y_7 @ X_8 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ X_8 @ Y_7 )
% 0.30/1.66 => ( X_8 = Y_7 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_510_order__trans,axiom,
% 0.30/1.66 ! [Z_1: $o,X_7: $o,Y_6: $o] :
% 0.30/1.66 ( ( ord_less_eq_o @ X_7 @ Y_6 )
% 0.30/1.66 => ( ( ord_less_eq_o @ Y_6 @ Z_1 )
% 0.30/1.66 => ( ord_less_eq_o @ X_7 @ Z_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_511_order__trans,axiom,
% 0.30/1.66 ! [Z_1: nat > $o,X_7: nat > $o,Y_6: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ X_7 @ Y_6 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ Y_6 @ Z_1 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ X_7 @ Z_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_512_order__trans,axiom,
% 0.30/1.66 ! [Z_1: pname > $o,X_7: pname > $o,Y_6: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ X_7 @ Y_6 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ Y_6 @ Z_1 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ X_7 @ Z_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_513_order__trans,axiom,
% 0.30/1.66 ! [Z_1: nat,X_7: nat,Y_6: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ X_7 @ Y_6 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ Y_6 @ Z_1 )
% 0.30/1.66 => ( ord_less_eq_nat @ X_7 @ Z_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_514_order__trans,axiom,
% 0.30/1.66 ! [Z_1: x_a > $o,X_7: x_a > $o,Y_6: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ X_7 @ Y_6 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ Y_6 @ Z_1 )
% 0.30/1.66 => ( ord_less_eq_a_o @ X_7 @ Z_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_515_order__antisym,axiom,
% 0.30/1.66 ! [X_6: $o,Y_5: $o] :
% 0.30/1.66 ( ( ord_less_eq_o @ X_6 @ Y_5 )
% 0.30/1.66 => ( ( ord_less_eq_o @ Y_5 @ X_6 )
% 0.30/1.66 => ( X_6
% 0.30/1.66 <=> Y_5 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_516_order__antisym,axiom,
% 0.30/1.66 ! [X_6: nat > $o,Y_5: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ X_6 @ Y_5 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ Y_5 @ X_6 )
% 0.30/1.66 => ( X_6 = Y_5 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_517_order__antisym,axiom,
% 0.30/1.66 ! [X_6: pname > $o,Y_5: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ X_6 @ Y_5 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ Y_5 @ X_6 )
% 0.30/1.66 => ( X_6 = Y_5 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_518_order__antisym,axiom,
% 0.30/1.66 ! [X_6: nat,Y_5: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ X_6 @ Y_5 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ Y_5 @ X_6 )
% 0.30/1.66 => ( X_6 = Y_5 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_519_order__antisym,axiom,
% 0.30/1.66 ! [X_6: x_a > $o,Y_5: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ X_6 @ Y_5 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ Y_5 @ X_6 )
% 0.30/1.66 => ( X_6 = Y_5 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_520_xt1_I4_J,axiom,
% 0.30/1.66 ! [C_4: $o,B_4: $o,A_6: $o] :
% 0.30/1.66 ( ( ord_less_eq_o @ B_4 @ A_6 )
% 0.30/1.66 => ( ( B_4
% 0.30/1.66 <=> C_4 )
% 0.30/1.66 => ( ord_less_eq_o @ C_4 @ A_6 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_521_xt1_I4_J,axiom,
% 0.30/1.66 ! [C_4: nat > $o,B_4: nat > $o,A_6: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ B_4 @ A_6 )
% 0.30/1.66 => ( ( B_4 = C_4 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ C_4 @ A_6 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_522_xt1_I4_J,axiom,
% 0.30/1.66 ! [C_4: pname > $o,B_4: pname > $o,A_6: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ B_4 @ A_6 )
% 0.30/1.66 => ( ( B_4 = C_4 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ C_4 @ A_6 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_523_xt1_I4_J,axiom,
% 0.30/1.66 ! [C_4: nat,B_4: nat,A_6: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ B_4 @ A_6 )
% 0.30/1.66 => ( ( B_4 = C_4 )
% 0.30/1.66 => ( ord_less_eq_nat @ C_4 @ A_6 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_524_xt1_I4_J,axiom,
% 0.30/1.66 ! [C_4: x_a > $o,B_4: x_a > $o,A_6: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ B_4 @ A_6 )
% 0.30/1.66 => ( ( B_4 = C_4 )
% 0.30/1.66 => ( ord_less_eq_a_o @ C_4 @ A_6 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_525_ord__le__eq__trans,axiom,
% 0.30/1.66 ! [C_3: $o,A_5: $o,B_3: $o] :
% 0.30/1.66 ( ( ord_less_eq_o @ A_5 @ B_3 )
% 0.30/1.66 => ( ( B_3
% 0.30/1.66 <=> C_3 )
% 0.30/1.66 => ( ord_less_eq_o @ A_5 @ C_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_526_ord__le__eq__trans,axiom,
% 0.30/1.66 ! [C_3: nat > $o,A_5: nat > $o,B_3: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ A_5 @ B_3 )
% 0.30/1.66 => ( ( B_3 = C_3 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ A_5 @ C_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_527_ord__le__eq__trans,axiom,
% 0.30/1.66 ! [C_3: pname > $o,A_5: pname > $o,B_3: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ A_5 @ B_3 )
% 0.30/1.66 => ( ( B_3 = C_3 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ A_5 @ C_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_528_ord__le__eq__trans,axiom,
% 0.30/1.66 ! [C_3: nat,A_5: nat,B_3: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ A_5 @ B_3 )
% 0.30/1.66 => ( ( B_3 = C_3 )
% 0.30/1.66 => ( ord_less_eq_nat @ A_5 @ C_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_529_ord__le__eq__trans,axiom,
% 0.30/1.66 ! [C_3: x_a > $o,A_5: x_a > $o,B_3: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ A_5 @ B_3 )
% 0.30/1.66 => ( ( B_3 = C_3 )
% 0.30/1.66 => ( ord_less_eq_a_o @ A_5 @ C_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_530_xt1_I3_J,axiom,
% 0.30/1.66 ! [C_2: $o,B_2: $o,A_4: $o] :
% 0.30/1.66 ( ( A_4
% 0.30/1.66 <=> B_2 )
% 0.30/1.66 => ( ( ord_less_eq_o @ C_2 @ B_2 )
% 0.30/1.66 => ( ord_less_eq_o @ C_2 @ A_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_531_xt1_I3_J,axiom,
% 0.30/1.66 ! [C_2: nat > $o,A_4: nat > $o,B_2: nat > $o] :
% 0.30/1.66 ( ( A_4 = B_2 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ C_2 @ B_2 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ C_2 @ A_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_532_xt1_I3_J,axiom,
% 0.30/1.66 ! [C_2: pname > $o,A_4: pname > $o,B_2: pname > $o] :
% 0.30/1.66 ( ( A_4 = B_2 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ C_2 @ B_2 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ C_2 @ A_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_533_xt1_I3_J,axiom,
% 0.30/1.66 ! [C_2: nat,A_4: nat,B_2: nat] :
% 0.30/1.66 ( ( A_4 = B_2 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ C_2 @ B_2 )
% 0.30/1.66 => ( ord_less_eq_nat @ C_2 @ A_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_534_xt1_I3_J,axiom,
% 0.30/1.66 ! [C_2: x_a > $o,A_4: x_a > $o,B_2: x_a > $o] :
% 0.30/1.66 ( ( A_4 = B_2 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ C_2 @ B_2 )
% 0.30/1.66 => ( ord_less_eq_a_o @ C_2 @ A_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_535_ord__eq__le__trans,axiom,
% 0.30/1.66 ! [C_1: $o,B_1: $o,A_3: $o] :
% 0.30/1.66 ( ( A_3
% 0.30/1.66 <=> B_1 )
% 0.30/1.66 => ( ( ord_less_eq_o @ B_1 @ C_1 )
% 0.30/1.66 => ( ord_less_eq_o @ A_3 @ C_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_536_ord__eq__le__trans,axiom,
% 0.30/1.66 ! [C_1: nat > $o,A_3: nat > $o,B_1: nat > $o] :
% 0.30/1.66 ( ( A_3 = B_1 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ B_1 @ C_1 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ A_3 @ C_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_537_ord__eq__le__trans,axiom,
% 0.30/1.66 ! [C_1: pname > $o,A_3: pname > $o,B_1: pname > $o] :
% 0.30/1.66 ( ( A_3 = B_1 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ B_1 @ C_1 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ A_3 @ C_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_538_ord__eq__le__trans,axiom,
% 0.30/1.66 ! [C_1: nat,A_3: nat,B_1: nat] :
% 0.30/1.66 ( ( A_3 = B_1 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ B_1 @ C_1 )
% 0.30/1.66 => ( ord_less_eq_nat @ A_3 @ C_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_539_ord__eq__le__trans,axiom,
% 0.30/1.66 ! [C_1: x_a > $o,A_3: x_a > $o,B_1: x_a > $o] :
% 0.30/1.66 ( ( A_3 = B_1 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ B_1 @ C_1 )
% 0.30/1.66 => ( ord_less_eq_a_o @ A_3 @ C_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_540_order__antisym__conv,axiom,
% 0.30/1.66 ! [Y_4: $o,X_5: $o] :
% 0.30/1.66 ( ( ord_less_eq_o @ Y_4 @ X_5 )
% 0.30/1.66 => ( ( ord_less_eq_o @ X_5 @ Y_4 )
% 0.30/1.66 <=> ( X_5
% 0.30/1.66 <=> Y_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_541_order__antisym__conv,axiom,
% 0.30/1.66 ! [Y_4: nat > $o,X_5: nat > $o] :
% 0.30/1.66 ( ( ord_less_eq_nat_o @ Y_4 @ X_5 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ X_5 @ Y_4 )
% 0.30/1.66 <=> ( X_5 = Y_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_542_order__antisym__conv,axiom,
% 0.30/1.66 ! [Y_4: pname > $o,X_5: pname > $o] :
% 0.30/1.66 ( ( ord_less_eq_pname_o @ Y_4 @ X_5 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ X_5 @ Y_4 )
% 0.30/1.66 <=> ( X_5 = Y_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_543_order__antisym__conv,axiom,
% 0.30/1.66 ! [Y_4: nat,X_5: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ Y_4 @ X_5 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ X_5 @ Y_4 )
% 0.30/1.66 <=> ( X_5 = Y_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_544_order__antisym__conv,axiom,
% 0.30/1.66 ! [Y_4: x_a > $o,X_5: x_a > $o] :
% 0.30/1.66 ( ( ord_less_eq_a_o @ Y_4 @ X_5 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ X_5 @ Y_4 )
% 0.30/1.66 <=> ( X_5 = Y_4 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_545_order__eq__refl,axiom,
% 0.30/1.66 ! [Y_3: $o,X_4: $o] :
% 0.30/1.66 ( ( X_4
% 0.30/1.66 <=> Y_3 )
% 0.30/1.66 => ( ord_less_eq_o @ X_4 @ Y_3 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_546_order__eq__refl,axiom,
% 0.30/1.66 ! [X_4: nat > $o,Y_3: nat > $o] :
% 0.30/1.66 ( ( X_4 = Y_3 )
% 0.30/1.66 => ( ord_less_eq_nat_o @ X_4 @ Y_3 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_547_order__eq__refl,axiom,
% 0.30/1.66 ! [X_4: pname > $o,Y_3: pname > $o] :
% 0.30/1.66 ( ( X_4 = Y_3 )
% 0.30/1.66 => ( ord_less_eq_pname_o @ X_4 @ Y_3 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_548_order__eq__refl,axiom,
% 0.30/1.66 ! [X_4: nat,Y_3: nat] :
% 0.30/1.66 ( ( X_4 = Y_3 )
% 0.30/1.66 => ( ord_less_eq_nat @ X_4 @ Y_3 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_549_order__eq__refl,axiom,
% 0.30/1.66 ! [X_4: x_a > $o,Y_3: x_a > $o] :
% 0.30/1.66 ( ( X_4 = Y_3 )
% 0.30/1.66 => ( ord_less_eq_a_o @ X_4 @ Y_3 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_550_order__eq__iff,axiom,
% 0.30/1.66 ! [Y_2: $o,X_3: $o] :
% 0.30/1.66 ( ( X_3
% 0.30/1.66 <=> Y_2 )
% 0.30/1.66 <=> ( ( ord_less_eq_o @ X_3 @ Y_2 )
% 0.30/1.66 & ( ord_less_eq_o @ Y_2 @ X_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_551_order__eq__iff,axiom,
% 0.30/1.66 ! [X_3: nat > $o,Y_2: nat > $o] :
% 0.30/1.66 ( ( X_3 = Y_2 )
% 0.30/1.66 <=> ( ( ord_less_eq_nat_o @ X_3 @ Y_2 )
% 0.30/1.66 & ( ord_less_eq_nat_o @ Y_2 @ X_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_552_order__eq__iff,axiom,
% 0.30/1.66 ! [X_3: pname > $o,Y_2: pname > $o] :
% 0.30/1.66 ( ( X_3 = Y_2 )
% 0.30/1.66 <=> ( ( ord_less_eq_pname_o @ X_3 @ Y_2 )
% 0.30/1.66 & ( ord_less_eq_pname_o @ Y_2 @ X_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_553_order__eq__iff,axiom,
% 0.30/1.66 ! [X_3: nat,Y_2: nat] :
% 0.30/1.66 ( ( X_3 = Y_2 )
% 0.30/1.66 <=> ( ( ord_less_eq_nat @ X_3 @ Y_2 )
% 0.30/1.66 & ( ord_less_eq_nat @ Y_2 @ X_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_554_order__eq__iff,axiom,
% 0.30/1.66 ! [X_3: x_a > $o,Y_2: x_a > $o] :
% 0.30/1.66 ( ( X_3 = Y_2 )
% 0.30/1.66 <=> ( ( ord_less_eq_a_o @ X_3 @ Y_2 )
% 0.30/1.66 & ( ord_less_eq_a_o @ Y_2 @ X_3 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_555_linorder__linear,axiom,
% 0.30/1.66 ! [X_2: nat,Y_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ X_2 @ Y_1 )
% 0.30/1.66 | ( ord_less_eq_nat @ Y_1 @ X_2 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_556_finite__subset__induct,axiom,
% 0.30/1.66 ! [P_2: ( nat > $o ) > $o,A_1: nat > $o,F_3: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ F_3 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o @ F_3 @ A_1 )
% 0.30/1.66 => ( ( P_2 @ bot_bot_nat_o )
% 0.30/1.66 => ( ! [A_2: nat,F_2: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ F_2 )
% 0.30/1.66 => ( ( member_nat @ A_2 @ A_1 )
% 0.30/1.66 => ( ~ ( member_nat @ A_2 @ F_2 )
% 0.30/1.66 => ( ( P_2 @ F_2 )
% 0.30/1.66 => ( P_2 @ ( insert_nat @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/1.66 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_557_finite__subset__induct,axiom,
% 0.30/1.66 ! [P_2: ( pname > $o ) > $o,A_1: pname > $o,F_3: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ F_3 )
% 0.30/1.66 => ( ( ord_less_eq_pname_o @ F_3 @ A_1 )
% 0.30/1.66 => ( ( P_2 @ bot_bot_pname_o )
% 0.30/1.66 => ( ! [A_2: pname,F_2: pname > $o] :
% 0.30/1.66 ( ( finite_finite_pname @ F_2 )
% 0.30/1.66 => ( ( member_pname @ A_2 @ A_1 )
% 0.30/1.66 => ( ~ ( member_pname @ A_2 @ F_2 )
% 0.30/1.66 => ( ( P_2 @ F_2 )
% 0.30/1.66 => ( P_2 @ ( insert_pname @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/1.66 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_558_finite__subset__induct,axiom,
% 0.30/1.66 ! [P_2: ( x_a > $o ) > $o,A_1: x_a > $o,F_3: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ F_3 )
% 0.30/1.66 => ( ( ord_less_eq_a_o @ F_3 @ A_1 )
% 0.30/1.66 => ( ( P_2 @ bot_bot_a_o )
% 0.30/1.66 => ( ! [A_2: x_a,F_2: x_a > $o] :
% 0.30/1.66 ( ( finite_finite_a @ F_2 )
% 0.30/1.66 => ( ( member_a @ A_2 @ A_1 )
% 0.30/1.66 => ( ~ ( member_a @ A_2 @ F_2 )
% 0.30/1.66 => ( ( P_2 @ F_2 )
% 0.30/1.66 => ( P_2 @ ( insert_a @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/1.66 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_559_finite__subset__induct,axiom,
% 0.30/1.66 ! [P_2: ( ( nat > $o ) > $o ) > $o,A_1: ( nat > $o ) > $o,F_3: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ F_3 )
% 0.30/1.66 => ( ( ord_less_eq_nat_o_o @ F_3 @ A_1 )
% 0.30/1.66 => ( ( P_2 @ bot_bot_nat_o_o )
% 0.30/1.66 => ( ! [A_2: nat > $o,F_2: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ F_2 )
% 0.30/1.66 => ( ( member_nat_o @ A_2 @ A_1 )
% 0.30/1.66 => ( ~ ( member_nat_o @ A_2 @ F_2 )
% 0.30/1.66 => ( ( P_2 @ F_2 )
% 0.30/1.66 => ( P_2 @ ( insert_nat_o @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/1.66 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_560_finite__subset__induct,axiom,
% 0.30/1.66 ! [P_2: ( ( pname > $o ) > $o ) > $o,A_1: ( pname > $o ) > $o,F_3: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ F_3 )
% 0.30/1.66 => ( ( ord_le1205211808me_o_o @ F_3 @ A_1 )
% 0.30/1.66 => ( ( P_2 @ bot_bot_pname_o_o )
% 0.30/1.66 => ( ! [A_2: pname > $o,F_2: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ F_2 )
% 0.30/1.66 => ( ( member_pname_o @ A_2 @ A_1 )
% 0.30/1.66 => ( ~ ( member_pname_o @ A_2 @ F_2 )
% 0.30/1.66 => ( ( P_2 @ F_2 )
% 0.30/1.66 => ( P_2 @ ( insert_pname_o @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/1.66 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_561_finite__subset__induct,axiom,
% 0.30/1.66 ! [P_2: ( ( x_a > $o ) > $o ) > $o,A_1: ( x_a > $o ) > $o,F_3: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ F_3 )
% 0.30/1.66 => ( ( ord_less_eq_a_o_o @ F_3 @ A_1 )
% 0.30/1.66 => ( ( P_2 @ bot_bot_a_o_o )
% 0.30/1.66 => ( ! [A_2: x_a > $o,F_2: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ F_2 )
% 0.30/1.66 => ( ( member_a_o @ A_2 @ A_1 )
% 0.30/1.66 => ( ~ ( member_a_o @ A_2 @ F_2 )
% 0.30/1.66 => ( ( P_2 @ F_2 )
% 0.30/1.66 => ( P_2 @ ( insert_a_o @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/1.66 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_562_assms_I2_J,axiom,
% 0.30/1.66 ! [Pn: pname,G: x_a > $o] :
% 0.30/1.66 ( ( p @ ( insert_a @ ( mgt_call @ Pn ) @ G ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ Pn ) ) ) @ bot_bot_a_o ) )
% 0.30/1.66 => ( p @ G @ ( insert_a @ ( mgt_call @ Pn ) @ bot_bot_a_o ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_563_finite__induct,axiom,
% 0.30/1.66 ! [P_1: ( ( nat > $o ) > $o ) > $o,F_1: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ F_1 )
% 0.30/1.66 => ( ( P_1 @ bot_bot_nat_o_o )
% 0.30/1.66 => ( ! [X_1: nat > $o,F_2: ( nat > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_nat_o @ F_2 )
% 0.30/1.66 => ( ~ ( member_nat_o @ X_1 @ F_2 )
% 0.30/1.66 => ( ( P_1 @ F_2 )
% 0.30/1.66 => ( P_1 @ ( insert_nat_o @ X_1 @ F_2 ) ) ) ) )
% 0.30/1.66 => ( P_1 @ F_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_564_finite__induct,axiom,
% 0.30/1.66 ! [P_1: ( ( pname > $o ) > $o ) > $o,F_1: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ F_1 )
% 0.30/1.66 => ( ( P_1 @ bot_bot_pname_o_o )
% 0.30/1.66 => ( ! [X_1: pname > $o,F_2: ( pname > $o ) > $o] :
% 0.30/1.66 ( ( finite297249702name_o @ F_2 )
% 0.30/1.66 => ( ~ ( member_pname_o @ X_1 @ F_2 )
% 0.30/1.66 => ( ( P_1 @ F_2 )
% 0.30/1.66 => ( P_1 @ ( insert_pname_o @ X_1 @ F_2 ) ) ) ) )
% 0.30/1.66 => ( P_1 @ F_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_565_finite__induct,axiom,
% 0.30/1.66 ! [P_1: ( ( x_a > $o ) > $o ) > $o,F_1: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ F_1 )
% 0.30/1.66 => ( ( P_1 @ bot_bot_a_o_o )
% 0.30/1.66 => ( ! [X_1: x_a > $o,F_2: ( x_a > $o ) > $o] :
% 0.30/1.66 ( ( finite_finite_a_o @ F_2 )
% 0.30/1.66 => ( ~ ( member_a_o @ X_1 @ F_2 )
% 0.30/1.66 => ( ( P_1 @ F_2 )
% 0.30/1.66 => ( P_1 @ ( insert_a_o @ X_1 @ F_2 ) ) ) ) )
% 0.30/1.66 => ( P_1 @ F_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_566_finite__less__ub,axiom,
% 0.30/1.66 ! [U: nat,F: nat > nat] :
% 0.30/1.66 ( ! [N_2: nat] : ( ord_less_eq_nat @ N_2 @ ( F @ N_2 ) )
% 0.30/1.66 => ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [N_2: nat] : ( ord_less_eq_nat @ ( F @ N_2 ) @ U ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_567_assms_I4_J,axiom,
% 0.30/1.66 ! [Pn: pname] :
% 0.30/1.66 ( ( member_pname @ Pn @ u )
% 0.30/1.66 => ( wt @ ( the_com @ ( body @ Pn ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_568_diff__Suc__eq__diff__pred,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.30/1.66 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_569_diff__Suc__1,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.30/1.66 = N ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_570_less__eq__nat_Osimps_I2_J,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.30/1.66 <=> ( nat_case_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_571_add__Suc__right,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.30/1.66 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_572_add__Suc,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.30/1.66 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_573_add__Suc__shift,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.30/1.66 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_574_nat__add__right__cancel,axiom,
% 0.30/1.66 ! [M: nat,K: nat,N: nat] :
% 0.30/1.66 ( ( ( plus_plus_nat @ M @ K )
% 0.30/1.66 = ( plus_plus_nat @ N @ K ) )
% 0.30/1.66 <=> ( M = N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_575_nat__add__left__cancel,axiom,
% 0.30/1.66 ! [K: nat,M: nat,N: nat] :
% 0.30/1.66 ( ( ( plus_plus_nat @ K @ M )
% 0.30/1.66 = ( plus_plus_nat @ K @ N ) )
% 0.30/1.66 <=> ( M = N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_576_nat__add__assoc,axiom,
% 0.30/1.66 ! [M: nat,N: nat,K: nat] :
% 0.30/1.66 ( ( plus_plus_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.30/1.66 = ( plus_plus_nat @ M @ ( plus_plus_nat @ N @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_577_nat__add__left__commute,axiom,
% 0.30/1.66 ! [X: nat,Y: nat,Z: nat] :
% 0.30/1.66 ( ( plus_plus_nat @ X @ ( plus_plus_nat @ Y @ Z ) )
% 0.30/1.66 = ( plus_plus_nat @ Y @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_578_nat__add__commute,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( plus_plus_nat @ M @ N )
% 0.30/1.66 = ( plus_plus_nat @ N @ M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_579_diff__add__inverse2,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.30/1.66 = M ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_580_diff__add__inverse,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.30/1.66 = M ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_581_diff__diff__left,axiom,
% 0.30/1.66 ! [I: nat,J_1: nat,K: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J_1 ) @ K )
% 0.30/1.66 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_582_diff__cancel,axiom,
% 0.30/1.66 ! [K: nat,M: nat,N: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.30/1.66 = ( minus_minus_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_583_diff__cancel2,axiom,
% 0.30/1.66 ! [M: nat,K: nat,N: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.30/1.66 = ( minus_minus_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_584_le__add2,axiom,
% 0.30/1.66 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_585_le__add1,axiom,
% 0.30/1.66 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_586_le__iff__add,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 <=> ? [K_1: nat] :
% 0.30/1.66 ( N
% 0.30/1.66 = ( plus_plus_nat @ M @ K_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_587_nat__add__left__cancel__le,axiom,
% 0.30/1.66 ! [K: nat,M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.30/1.66 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_588_trans__le__add1,axiom,
% 0.30/1.66 ! [M: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/1.66 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_589_trans__le__add2,axiom,
% 0.30/1.66 ! [M: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/1.66 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_590_add__le__mono1,axiom,
% 0.30/1.66 ! [K: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_591_add__le__mono,axiom,
% 0.30/1.66 ! [K: nat,L: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ K @ L )
% 0.30/1.66 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_592_add__leD2,axiom,
% 0.30/1.66 ! [M: nat,K: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.30/1.66 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_593_add__leD1,axiom,
% 0.30/1.66 ! [M: nat,K: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.30/1.66 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_594_add__leE,axiom,
% 0.30/1.66 ! [M: nat,K: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.30/1.66 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_595_diff__add__assoc2,axiom,
% 0.30/1.66 ! [I: nat,K: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/1.66 => ( ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I ) @ K )
% 0.30/1.66 = ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K ) @ I ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_596_add__diff__assoc2,axiom,
% 0.30/1.66 ! [I: nat,K: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/1.66 => ( ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K ) @ I )
% 0.30/1.66 = ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I ) @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_597_diff__add__assoc,axiom,
% 0.30/1.66 ! [I: nat,K: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/1.66 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J_1 ) @ K )
% 0.30/1.66 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J_1 @ K ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_598_le__imp__diff__is__add,axiom,
% 0.30/1.66 ! [K: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/1.66 => ( ( ( minus_minus_nat @ J_1 @ I )
% 0.30/1.66 = K )
% 0.30/1.66 <=> ( J_1
% 0.30/1.66 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_599_le__add__diff__inverse2,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ N @ M )
% 0.30/1.66 => ( ( plus_plus_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.30/1.66 = M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_600_le__diff__conv2,axiom,
% 0.30/1.66 ! [I: nat,K: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/1.66 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.30/1.66 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_601_add__diff__assoc,axiom,
% 0.30/1.66 ! [I: nat,K: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/1.66 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.30/1.66 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J_1 ) @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_602_le__add__diff__inverse,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ N @ M )
% 0.30/1.66 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.30/1.66 = M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_603_le__add__diff,axiom,
% 0.30/1.66 ! [M: nat,K: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ N )
% 0.30/1.66 => ( ord_less_eq_nat @ M @ ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_604_le__diff__conv,axiom,
% 0.30/1.66 ! [J_1: nat,K: nat,I: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J_1 @ K ) @ I )
% 0.30/1.66 <=> ( ord_less_eq_nat @ J_1 @ ( plus_plus_nat @ I @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_605_diff__diff__right,axiom,
% 0.30/1.66 ! [I: nat,K: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/1.66 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.30/1.66 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_606_Suc__eq__plus1,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ( ( suc @ N )
% 0.30/1.66 = ( plus_plus_nat @ N @ one_one_nat ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_607_Suc__eq__plus1__left,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ( ( suc @ N )
% 0.30/1.66 = ( plus_plus_nat @ one_one_nat @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_608_diff__Suc__diff__eq2,axiom,
% 0.30/1.66 ! [M: nat,K: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/1.66 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J_1 @ K ) ) @ M )
% 0.30/1.66 = ( minus_minus_nat @ ( suc @ J_1 ) @ ( plus_plus_nat @ K @ M ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_609_diff__Suc__diff__eq1,axiom,
% 0.30/1.66 ! [M: nat,K: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/1.66 => ( ( minus_minus_nat @ M @ ( suc @ ( minus_minus_nat @ J_1 @ K ) ) )
% 0.30/1.66 = ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( suc @ J_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_610_termination__basic__simps_I3_J,axiom,
% 0.30/1.66 ! [Z: nat,X: nat,Y: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ X @ Y )
% 0.30/1.66 => ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_611_termination__basic__simps_I4_J,axiom,
% 0.30/1.66 ! [Y: nat,X: nat,Z: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ X @ Z )
% 0.30/1.66 => ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_612_lessI,axiom,
% 0.30/1.66 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_613_Suc__mono,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ N )
% 0.30/1.66 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_614_finite__Collect__less__nat,axiom,
% 0.30/1.66 ! [K: nat] :
% 0.30/1.66 ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [N_2: nat] : ( ord_less_nat @ N_2 @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_615_termination__basic__simps_I1_J,axiom,
% 0.30/1.66 ! [Z: nat,X: nat,Y: nat] :
% 0.30/1.66 ( ( ord_less_nat @ X @ Y )
% 0.30/1.66 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_616_termination__basic__simps_I2_J,axiom,
% 0.30/1.66 ! [Y: nat,X: nat,Z: nat] :
% 0.30/1.66 ( ( ord_less_nat @ X @ Z )
% 0.30/1.66 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_617_add__lessD1,axiom,
% 0.30/1.66 ! [I: nat,J_1: nat,K: nat] :
% 0.30/1.66 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J_1 ) @ K )
% 0.30/1.66 => ( ord_less_nat @ I @ K ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_618_less__add__eq__less,axiom,
% 0.30/1.66 ! [M: nat,N: nat,K: nat,L: nat] :
% 0.30/1.66 ( ( ord_less_nat @ K @ L )
% 0.30/1.66 => ( ( ( plus_plus_nat @ M @ L )
% 0.30/1.66 = ( plus_plus_nat @ K @ N ) )
% 0.30/1.66 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_619_add__less__mono,axiom,
% 0.30/1.66 ! [K: nat,L: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I @ J_1 )
% 0.30/1.66 => ( ( ord_less_nat @ K @ L )
% 0.30/1.66 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_620_add__less__mono1,axiom,
% 0.30/1.66 ! [K: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I @ J_1 )
% 0.30/1.66 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_621_trans__less__add2,axiom,
% 0.30/1.66 ! [M: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I @ J_1 )
% 0.30/1.66 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_622_trans__less__add1,axiom,
% 0.30/1.66 ! [M: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I @ J_1 )
% 0.30/1.66 => ( ord_less_nat @ I @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_623_nat__add__left__cancel__less,axiom,
% 0.30/1.66 ! [K: nat,M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.30/1.66 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_624_not__add__less2,axiom,
% 0.30/1.66 ! [J_1: nat,I: nat] :
% 0.30/1.66 ~ ( ord_less_nat @ ( plus_plus_nat @ J_1 @ I ) @ I ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_625_not__add__less1,axiom,
% 0.30/1.66 ! [I: nat,J_1: nat] :
% 0.30/1.66 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J_1 ) @ I ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_626_Suc__less__SucD,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.30/1.66 => ( ord_less_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_627_Suc__lessD,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.30/1.66 => ( ord_less_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_628_less__SucE,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.30/1.66 => ( ~ ( ord_less_nat @ M @ N )
% 0.30/1.66 => ( M = N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_629_less__trans__Suc,axiom,
% 0.30/1.66 ! [K: nat,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I @ J_1 )
% 0.30/1.66 => ( ( ord_less_nat @ J_1 @ K )
% 0.30/1.66 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_630_Suc__lessI,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ N )
% 0.30/1.66 => ( ( ( suc @ M )
% 0.30/1.66 != N )
% 0.30/1.66 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_631_less__SucI,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ N )
% 0.30/1.66 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_632_less__antisym,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ~ ( ord_less_nat @ N @ M )
% 0.30/1.66 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.30/1.66 => ( M = N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_633_not__less__less__Suc__eq,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ~ ( ord_less_nat @ N @ M )
% 0.30/1.66 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.30/1.66 <=> ( N = M ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_634_Suc__less__eq,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.30/1.66 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_635_less__Suc__eq,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.30/1.66 <=> ( ( ord_less_nat @ M @ N )
% 0.30/1.66 | ( M = N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_636_not__less__eq,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ~ ( ord_less_nat @ M @ N )
% 0.30/1.66 <=> ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_637_less__or__eq__imp__le,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ( ord_less_nat @ M @ N )
% 0.30/1.66 | ( M = N ) )
% 0.30/1.66 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_638_le__neq__implies__less,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ( ( M != N )
% 0.30/1.66 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_639_less__imp__le__nat,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ N )
% 0.30/1.66 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_640_le__eq__less__or__eq,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 <=> ( ( ord_less_nat @ M @ N )
% 0.30/1.66 | ( M = N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_641_nat__less__le,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ N )
% 0.30/1.66 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 & ( M != N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_642_diff__less__mono2,axiom,
% 0.30/1.66 ! [L: nat,M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ N )
% 0.30/1.66 => ( ( ord_less_nat @ M @ L )
% 0.30/1.66 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_643_less__imp__diff__less,axiom,
% 0.30/1.66 ! [N: nat,J_1: nat,K: nat] :
% 0.30/1.66 ( ( ord_less_nat @ J_1 @ K )
% 0.30/1.66 => ( ord_less_nat @ ( minus_minus_nat @ J_1 @ N ) @ K ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_644_termination__basic__simps_I5_J,axiom,
% 0.30/1.66 ! [X: nat,Y: nat] :
% 0.30/1.66 ( ( ord_less_nat @ X @ Y )
% 0.30/1.66 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_645_less__not__refl,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_646_nat__neq__iff,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( M != N )
% 0.30/1.66 <=> ( ( ord_less_nat @ M @ N )
% 0.30/1.66 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_647_linorder__neqE__nat,axiom,
% 0.30/1.66 ! [X: nat,Y: nat] :
% 0.30/1.66 ( ( X != Y )
% 0.30/1.66 => ( ~ ( ord_less_nat @ X @ Y )
% 0.30/1.66 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_648_less__irrefl__nat,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_649_less__not__refl2,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_nat @ N @ M )
% 0.30/1.66 => ( M != N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_650_less__not__refl3,axiom,
% 0.30/1.66 ! [S: nat,T: nat] :
% 0.30/1.66 ( ( ord_less_nat @ S @ T )
% 0.30/1.66 => ( S != T ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_651_nat__less__cases,axiom,
% 0.30/1.66 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.30/1.66 ( ( ( ord_less_nat @ M @ N )
% 0.30/1.66 => ( P @ N @ M ) )
% 0.30/1.66 => ( ( ( M = N )
% 0.30/1.66 => ( P @ N @ M ) )
% 0.30/1.66 => ( ( ( ord_less_nat @ N @ M )
% 0.30/1.66 => ( P @ N @ M ) )
% 0.30/1.66 => ( P @ N @ M ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_652_finite__nat__set__iff__bounded,axiom,
% 0.30/1.66 ! [N_1: nat > $o] :
% 0.30/1.66 ( ( finite_finite_nat @ N_1 )
% 0.30/1.66 <=> ? [M_1: nat] :
% 0.30/1.66 ! [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ N_1 )
% 0.30/1.66 => ( ord_less_nat @ X_1 @ M_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_653_card__Collect__less__nat,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ( ( finite_card_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [I_1: nat] : ( ord_less_nat @ I_1 @ N ) ) )
% 0.30/1.66 = N ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_654_finite__M__bounded__by__nat,axiom,
% 0.30/1.66 ! [P: nat > $o,I: nat] :
% 0.30/1.66 ( finite_finite_nat
% 0.30/1.66 @ ( collect_nat
% 0.30/1.66 @ ^ [K_1: nat] : ( (&) @ ( P @ K_1 ) @ ( ord_less_nat @ K_1 @ I ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_655_less__add__Suc1,axiom,
% 0.30/1.66 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_656_less__add__Suc2,axiom,
% 0.30/1.66 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_657_less__iff__Suc__add,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ N )
% 0.30/1.66 <=> ? [K_1: nat] :
% 0.30/1.66 ( N
% 0.30/1.66 = ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_658_less__eq__Suc__le,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_nat @ N @ M )
% 0.30/1.66 <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_659_less__Suc__eq__le,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.30/1.66 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_660_Suc__le__eq,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.30/1.66 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_661_le__imp__less__Suc,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_662_Suc__leI,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ N )
% 0.30/1.66 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_663_le__less__Suc__eq,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.30/1.66 <=> ( N = M ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_664_Suc__le__lessD,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.30/1.66 => ( ord_less_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_665_diff__less__Suc,axiom,
% 0.30/1.66 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_666_add__diff__inverse,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ~ ( ord_less_nat @ M @ N )
% 0.30/1.66 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.30/1.66 = M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_667_less__diff__conv,axiom,
% 0.30/1.66 ! [I: nat,J_1: nat,K: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.30/1.66 <=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_668_diff__less__mono,axiom,
% 0.30/1.66 ! [C: nat,A: nat,B: nat] :
% 0.30/1.66 ( ( ord_less_nat @ A @ B )
% 0.30/1.66 => ( ( ord_less_eq_nat @ C @ A )
% 0.30/1.66 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_669_less__diff__iff,axiom,
% 0.30/1.66 ! [N: nat,K: nat,M: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ K @ M )
% 0.30/1.66 => ( ( ord_less_eq_nat @ K @ N )
% 0.30/1.66 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.30/1.66 <=> ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_670_less__eq__Suc__le__raw,axiom,
% 0.30/1.66 ! [X_1: nat] :
% 0.30/1.66 ( ( ord_less_nat @ X_1 )
% 0.30/1.66 = ( ord_less_eq_nat @ ( suc @ X_1 ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_671_mono__nat__linear__lb,axiom,
% 0.30/1.66 ! [M: nat,K: nat,F: nat > nat] :
% 0.30/1.66 ( ! [M_1: nat,N_2: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M_1 @ N_2 )
% 0.30/1.66 => ( ord_less_nat @ ( F @ M_1 ) @ ( F @ N_2 ) ) )
% 0.30/1.66 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_672_inc__induct,axiom,
% 0.30/1.66 ! [P: nat > $o,I: nat,J_1: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/1.66 => ( ( P @ J_1 )
% 0.30/1.66 => ( ! [I_1: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.30/1.66 => ( ( P @ ( suc @ I_1 ) )
% 0.30/1.66 => ( P @ I_1 ) ) )
% 0.30/1.66 => ( P @ I ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_673_less__imp__Suc__add,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_nat @ M @ N )
% 0.30/1.66 => ? [K_1: nat] :
% 0.30/1.66 ( N
% 0.30/1.66 = ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_674_bounded__nat__set__is__finite,axiom,
% 0.30/1.66 ! [N: nat,N_1: nat > $o] :
% 0.30/1.66 ( ! [X_1: nat] :
% 0.30/1.66 ( ( member_nat @ X_1 @ N_1 )
% 0.30/1.66 => ( ord_less_nat @ X_1 @ N ) )
% 0.30/1.66 => ( finite_finite_nat @ N_1 ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_675_less__mono__imp__le__mono,axiom,
% 0.30/1.66 ! [I: nat,J_1: nat,F: nat > nat] :
% 0.30/1.66 ( ! [I_1: nat,J: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I_1 @ J )
% 0.30/1.66 => ( ord_less_nat @ ( F @ I_1 ) @ ( F @ J ) ) )
% 0.30/1.66 => ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/1.66 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J_1 ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_676_Suc__lessE,axiom,
% 0.30/1.66 ! [I: nat,K: nat] :
% 0.30/1.66 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.30/1.66 => ~ ! [J: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I @ J )
% 0.30/1.66 => ( K
% 0.30/1.66 != ( suc @ J ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_677_lessE,axiom,
% 0.30/1.66 ! [I: nat,K: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I @ K )
% 0.30/1.66 => ( ( K
% 0.30/1.66 != ( suc @ I ) )
% 0.30/1.66 => ~ ! [J: nat] :
% 0.30/1.66 ( ( ord_less_nat @ I @ J )
% 0.30/1.66 => ( K
% 0.30/1.66 != ( suc @ J ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_678_less__zeroE,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_679_le0,axiom,
% 0.30/1.66 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_680_zero__less__Suc,axiom,
% 0.30/1.66 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_681_add__is__1,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ( plus_plus_nat @ M @ N )
% 0.30/1.66 = ( suc @ zero_zero_nat ) )
% 0.30/1.66 <=> ( ( ( M
% 0.30/1.66 = ( suc @ zero_zero_nat ) )
% 0.30/1.66 & ( N = zero_zero_nat ) )
% 0.30/1.66 | ( ( M = zero_zero_nat )
% 0.30/1.66 & ( N
% 0.30/1.66 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_682_one__is__add,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ( suc @ zero_zero_nat )
% 0.30/1.66 = ( plus_plus_nat @ M @ N ) )
% 0.30/1.66 <=> ( ( ( M
% 0.30/1.66 = ( suc @ zero_zero_nat ) )
% 0.30/1.66 & ( N = zero_zero_nat ) )
% 0.30/1.66 | ( ( M = zero_zero_nat )
% 0.30/1.66 & ( N
% 0.30/1.66 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_683_diff__add__0,axiom,
% 0.30/1.66 ! [N: nat,M: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.30/1.66 = zero_zero_nat ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_684_diff__is__0__eq_H,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ M @ N )
% 0.30/1.66 => ( ( minus_minus_nat @ M @ N )
% 0.30/1.66 = zero_zero_nat ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_685_diff__is__0__eq,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ( minus_minus_nat @ M @ N )
% 0.30/1.66 = zero_zero_nat )
% 0.30/1.66 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_686_One__nat__def,axiom,
% 0.30/1.66 ( one_one_nat
% 0.30/1.66 = ( suc @ zero_zero_nat ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_687_diffs0__imp__equal,axiom,
% 0.30/1.66 ! [M: nat,N: nat] :
% 0.30/1.66 ( ( ( minus_minus_nat @ M @ N )
% 0.30/1.66 = zero_zero_nat )
% 0.30/1.66 => ( ( ( minus_minus_nat @ N @ M )
% 0.30/1.66 = zero_zero_nat )
% 0.30/1.66 => ( M = N ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_688_diff__self__eq__0,axiom,
% 0.30/1.66 ! [M: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ M @ M )
% 0.30/1.66 = zero_zero_nat ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_689_minus__nat_Odiff__0,axiom,
% 0.30/1.66 ! [M: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.30/1.66 = M ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_690_diff__0__eq__0,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.30/1.66 = zero_zero_nat ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_691_Suc__neq__Zero,axiom,
% 0.30/1.66 ! [M: nat] :
% 0.30/1.66 ( ( suc @ M )
% 0.30/1.66 != zero_zero_nat ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_692_Zero__neq__Suc,axiom,
% 0.30/1.66 ! [M: nat] :
% 0.30/1.66 ( zero_zero_nat
% 0.30/1.66 != ( suc @ M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_693_nat_Osimps_I3_J,axiom,
% 0.30/1.66 ! [Nat_1: nat] :
% 0.30/1.66 ( ( suc @ Nat_1 )
% 0.30/1.66 != zero_zero_nat ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_694_Suc__not__Zero,axiom,
% 0.30/1.66 ! [M: nat] :
% 0.30/1.66 ( ( suc @ M )
% 0.30/1.66 != zero_zero_nat ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_695_nat_Osimps_I2_J,axiom,
% 0.30/1.66 ! [Nat: nat] :
% 0.30/1.66 ( zero_zero_nat
% 0.30/1.66 != ( suc @ Nat ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_696_Zero__not__Suc,axiom,
% 0.30/1.66 ! [M: nat] :
% 0.30/1.66 ( zero_zero_nat
% 0.30/1.66 != ( suc @ M ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_697_bot__nat__def,axiom,
% 0.30/1.66 bot_bot_nat = zero_zero_nat ).
% 0.30/1.66
% 0.30/1.66 thf(fact_698_le__0__eq,axiom,
% 0.30/1.66 ! [N: nat] :
% 0.30/1.66 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.30/1.66 <=> ( N = zero_zero_nat ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(fact_699_less__eq__nat_Osimps_I1_J,axiom,
% 0.30/1.66 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_1_1_fequal_000t__a_T,axiom,
% 0.30/1.66 ! [X: x_a,Y: x_a] :
% 0.30/1.66 ( ~ ( fequal_a @ X @ Y )
% 0.30/1.66 | ( X = Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_2_1_fequal_000t__a_T,axiom,
% 0.30/1.66 ! [X: x_a,Y: x_a] :
% 0.30/1.66 ( ( X != Y )
% 0.30/1.66 | ( fequal_a @ X @ Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.30/1.66 ! [X: nat,Y: nat] :
% 0.30/1.66 ( ~ ( fequal_nat @ X @ Y )
% 0.30/1.66 | ( X = Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.30/1.66 ! [X: nat,Y: nat] :
% 0.30/1.66 ( ( X != Y )
% 0.30/1.66 | ( fequal_nat @ X @ Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 0.30/1.66 ! [X: pname,Y: pname] :
% 0.30/1.66 ( ~ ( fequal_pname @ X @ Y )
% 0.30/1.66 | ( X = Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 0.30/1.66 ! [X: pname,Y: pname] :
% 0.30/1.66 ( ( X != Y )
% 0.30/1.66 | ( fequal_pname @ X @ Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_1_1_fequal_000_062_It__a_M_Eo_J_T,axiom,
% 0.30/1.66 ! [X: x_a > $o,Y: x_a > $o] :
% 0.30/1.66 ( ~ ( fequal_a_o @ X @ Y )
% 0.30/1.66 | ( X = Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_2_1_fequal_000_062_It__a_M_Eo_J_T,axiom,
% 0.30/1.66 ! [X: x_a > $o,Y: x_a > $o] :
% 0.30/1.66 ( ( X != Y )
% 0.30/1.66 | ( fequal_a_o @ X @ Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_1_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T,axiom,
% 0.30/1.66 ! [X: nat > $o,Y: nat > $o] :
% 0.30/1.66 ( ~ ( fequal_nat_o @ X @ Y )
% 0.30/1.66 | ( X = Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_2_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T,axiom,
% 0.30/1.66 ! [X: nat > $o,Y: nat > $o] :
% 0.30/1.66 ( ( X != Y )
% 0.30/1.66 | ( fequal_nat_o @ X @ Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.30/1.66 ! [X: pname > $o,Y: pname > $o] :
% 0.30/1.66 ( ~ ( fequal_pname_o @ X @ Y )
% 0.30/1.66 | ( X = Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.30/1.66 ! [X: pname > $o,Y: pname > $o] :
% 0.30/1.66 ( ( X != Y )
% 0.30/1.66 | ( fequal_pname_o @ X @ Y ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(conj_0,hypothesis,
% 0.30/1.66 finite_finite_pname @ u ).
% 0.30/1.66
% 0.30/1.66 thf(conj_1,hypothesis,
% 0.30/1.66 ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) ).
% 0.30/1.66
% 0.30/1.66 thf(conj_2,hypothesis,
% 0.30/1.66 ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(conj_3,hypothesis,
% 0.30/1.66 ( ( finite_card_a @ g )
% 0.30/1.66 = ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ) ).
% 0.30/1.66
% 0.30/1.66 thf(conj_4,hypothesis,
% 0.30/1.66 member_pname @ pn @ u ).
% 0.30/1.66
% 0.30/1.66 thf(conj_5,hypothesis,
% 0.30/1.66 ~ ( member_a @ ( mgt_call @ pn ) @ g ) ).
% 0.30/1.66
% 0.30/1.66 thf(conj_6,conjecture,
% 0.30/1.66 ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ).
% 0.30/1.66 ------------------------
% 3.34/1.72 % (11191)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/183Mi)
% 3.34/1.72 % (11193)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_10942 for (2999ds/27Mi)
% 3.34/1.72 % (11192)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_10942 for (2999ds/4Mi)
% 3.34/1.72 % (11194)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/2Mi)
% 3.34/1.72 % (11194)Instruction limit reached!
% 3.34/1.72 % (11194)------------------------------
% 3.34/1.72 % (11194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.72 % (11194)Termination reason: Unknown
% 3.34/1.72 % (11194)Termination phase: shuffling
% 3.34/1.72
% 3.34/1.72 % (11194)Memory used [KB]: 2046
% 3.34/1.72 % (11194)Time elapsed: 0.002 s
% 3.34/1.72 % (11194)Instructions burned: 2 (million)
% 3.34/1.72 % (11194)------------------------------
% 3.34/1.72 % (11194)------------------------------
% 3.34/1.72 % (11192)Instruction limit reached!
% 3.34/1.72 % (11192)------------------------------
% 3.34/1.72 % (11192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.72 % (11192)Termination reason: Unknown
% 3.34/1.72 % (11192)Termination phase: shuffling
% 3.34/1.72
% 3.34/1.72 % (11192)Memory used [KB]: 2302
% 3.34/1.72 % (11192)Time elapsed: 0.004 s
% 3.34/1.72 % (11192)Instructions burned: 7 (million)
% 3.34/1.72 % (11192)------------------------------
% 3.34/1.72 % (11192)------------------------------
% 3.34/1.73 % (11195)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_10942 for (2999ds/2Mi)
% 3.34/1.73 % (11196)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_10942 for (2999ds/275Mi)
% 3.34/1.73 % (11197)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/18Mi)
% 3.34/1.73 % (11193)Instruction limit reached!
% 3.34/1.73 % (11193)------------------------------
% 3.34/1.73 % (11193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.73 % (11193)Termination reason: Unknown
% 3.34/1.73 % (11193)Termination phase: shuffling
% 3.34/1.73
% 3.34/1.73 % (11193)Memory used [KB]: 2942
% 3.34/1.73 % (11193)Time elapsed: 0.011 s
% 3.34/1.73 % (11193)Instructions burned: 28 (million)
% 3.34/1.73 % (11193)------------------------------
% 3.34/1.73 % (11193)------------------------------
% 3.34/1.73 % (11195)Instruction limit reached!
% 3.34/1.73 % (11195)------------------------------
% 3.34/1.73 % (11195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.73 % (11195)Termination reason: Unknown
% 3.34/1.73 % (11195)Termination phase: shuffling
% 3.34/1.73
% 3.34/1.73 % (11195)Memory used [KB]: 2174
% 3.34/1.73 % (11195)Time elapsed: 0.004 s
% 3.34/1.73 % (11195)Instructions burned: 2 (million)
% 3.34/1.73 % (11195)------------------------------
% 3.34/1.73 % (11195)------------------------------
% 3.34/1.73 % (11199)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_10942 for (2999ds/37Mi)
% 3.34/1.73 % (11198)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/3Mi)
% 3.34/1.73 % (11198)Instruction limit reached!
% 3.34/1.73 % (11198)------------------------------
% 3.34/1.73 % (11198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.73 % (11198)Termination reason: Unknown
% 3.34/1.73 % (11198)Termination phase: shuffling
% 3.34/1.73
% 3.34/1.73 % (11198)Memory used [KB]: 2174
% 3.34/1.73 % (11198)Time elapsed: 0.003 s
% 3.34/1.73 % (11198)Instructions burned: 3 (million)
% 3.34/1.73 % (11198)------------------------------
% 3.34/1.73 % (11198)------------------------------
% 3.34/1.74 % (11200)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_10942 for (2999ds/15Mi)
% 3.34/1.74 % (11197)Instruction limit reached!
% 3.34/1.74 % (11197)------------------------------
% 3.34/1.74 % (11197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.74 % (11197)Termination reason: Unknown
% 3.34/1.74 % (11197)Termination phase: shuffling
% 3.34/1.74
% 3.34/1.74 % (11197)Memory used [KB]: 2686
% 3.34/1.74 % (11197)Time elapsed: 0.014 s
% 3.34/1.74 % (11197)Instructions burned: 18 (million)
% 3.34/1.74 % (11197)------------------------------
% 3.34/1.74 % (11197)------------------------------
% 3.34/1.74 % (11199)Instruction limit reached!
% 3.34/1.74 % (11199)------------------------------
% 3.34/1.74 % (11199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.74 % (11199)Termination reason: Unknown
% 3.34/1.74 % (11199)Termination phase: shuffling
% 3.34/1.74
% 3.34/1.74 % (11199)Memory used [KB]: 3326
% 3.34/1.74 % (11199)Time elapsed: 0.012 s
% 3.34/1.74 % (11199)Instructions burned: 39 (million)
% 3.34/1.74 % (11199)------------------------------
% 3.34/1.74 % (11199)------------------------------
% 3.34/1.74 % (11202)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_10942 for (2999ds/1041Mi)
% 3.34/1.74 % (11200)Instruction limit reached!
% 3.34/1.74 % (11200)------------------------------
% 3.34/1.74 % (11200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.74 % (11200)Termination reason: Unknown
% 3.34/1.74 % (11200)Termination phase: shuffling
% 3.34/1.74
% 3.34/1.74 % (11200)Memory used [KB]: 2558
% 3.34/1.74 % (11200)Time elapsed: 0.007 s
% 3.34/1.74 % (11200)Instructions burned: 16 (million)
% 3.34/1.74 % (11200)------------------------------
% 3.34/1.74 % (11200)------------------------------
% 3.34/1.75 % (11201)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_10942 for (2999ds/3Mi)
% 3.34/1.75 % (11201)Instruction limit reached!
% 3.34/1.75 % (11201)------------------------------
% 3.34/1.75 % (11201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.75 % (11201)Termination reason: Unknown
% 3.34/1.75 % (11201)Termination phase: shuffling
% 3.34/1.75
% 3.34/1.75 % (11201)Memory used [KB]: 2174
% 3.34/1.75 % (11201)Time elapsed: 0.005 s
% 3.34/1.75 % (11201)Instructions burned: 4 (million)
% 3.34/1.75 % (11201)------------------------------
% 3.34/1.75 % (11201)------------------------------
% 3.34/1.75 % (11204)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/16Mi)
% 3.34/1.75 % (11205)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_10942 for (2999ds/3Mi)
% 3.34/1.75 % (11205)Instruction limit reached!
% 3.34/1.75 % (11205)------------------------------
% 3.34/1.75 % (11205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.75 % (11205)Termination reason: Unknown
% 3.34/1.75 % (11205)Termination phase: shuffling
% 3.34/1.75
% 3.34/1.75 % (11205)Memory used [KB]: 2174
% 3.34/1.75 % (11205)Time elapsed: 0.003 s
% 3.34/1.75 % (11205)Instructions burned: 4 (million)
% 3.34/1.75 % (11205)------------------------------
% 3.34/1.75 % (11205)------------------------------
% 3.34/1.76 % (11203)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/7Mi)
% 3.34/1.76 % (11204)Instruction limit reached!
% 3.34/1.76 % (11204)------------------------------
% 3.34/1.76 % (11204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.76 % (11204)Termination reason: Unknown
% 3.34/1.76 % (11204)Termination phase: shuffling
% 3.34/1.76
% 3.34/1.76 % (11204)Memory used [KB]: 2686
% 3.34/1.76 % (11204)Time elapsed: 0.007 s
% 3.34/1.76 % (11204)Instructions burned: 17 (million)
% 3.34/1.76 % (11204)------------------------------
% 3.34/1.76 % (11204)------------------------------
% 3.34/1.76 % (11203)Instruction limit reached!
% 3.34/1.76 % (11203)------------------------------
% 3.34/1.76 % (11203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.76 % (11203)Termination reason: Unknown
% 3.34/1.76 % (11203)Termination phase: shuffling
% 3.34/1.76
% 3.34/1.76 % (11203)Memory used [KB]: 2430
% 3.34/1.76 % (11203)Time elapsed: 0.007 s
% 3.34/1.76 % (11203)Instructions burned: 7 (million)
% 3.34/1.76 % (11203)------------------------------
% 3.34/1.76 % (11203)------------------------------
% 3.34/1.76 % (11207)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/7Mi)
% 3.34/1.77 % (11208)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/3Mi)
% 3.34/1.77 % (11206)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_10942 for (2999ds/3Mi)
% 3.34/1.77 % (11207)Instruction limit reached!
% 3.34/1.77 % (11207)------------------------------
% 3.34/1.77 % (11207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.77 % (11207)Termination reason: Unknown
% 3.34/1.77 % (11207)Termination phase: shuffling
% 3.34/1.77
% 3.34/1.77 % (11207)Memory used [KB]: 2430
% 3.34/1.77 % (11207)Time elapsed: 0.004 s
% 3.34/1.77 % (11207)Instructions burned: 8 (million)
% 3.34/1.77 % (11207)------------------------------
% 3.34/1.77 % (11207)------------------------------
% 3.34/1.77 % (11208)Instruction limit reached!
% 3.34/1.77 % (11208)------------------------------
% 3.34/1.77 % (11208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.77 % (11208)Termination reason: Unknown
% 3.34/1.77 % (11208)Termination phase: shuffling
% 3.34/1.77
% 3.34/1.77 % (11208)Memory used [KB]: 2302
% 3.34/1.77 % (11208)Time elapsed: 0.003 s
% 3.34/1.77 % (11208)Instructions burned: 5 (million)
% 3.34/1.77 % (11208)------------------------------
% 3.34/1.77 % (11208)------------------------------
% 3.34/1.77 % (11206)Instruction limit reached!
% 3.34/1.77 % (11206)------------------------------
% 3.34/1.77 % (11206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.77 % (11206)Termination reason: Unknown
% 3.34/1.77 % (11206)Termination phase: shuffling
% 3.34/1.77
% 3.34/1.77 % (11206)Memory used [KB]: 2174
% 3.34/1.77 % (11206)Time elapsed: 0.004 s
% 3.34/1.77 % (11206)Instructions burned: 3 (million)
% 3.34/1.77 % (11206)------------------------------
% 3.34/1.77 % (11206)------------------------------
% 3.34/1.77 % (11191)Instruction limit reached!
% 3.34/1.77 % (11191)------------------------------
% 3.34/1.77 % (11191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.77 % (11191)Termination reason: Unknown
% 3.34/1.77 % (11191)Termination phase: Property scanning
% 3.34/1.77
% 3.34/1.77 % (11191)Memory used [KB]: 4349
% 3.34/1.77 % (11191)Time elapsed: 0.054 s
% 3.34/1.77 % (11191)Instructions burned: 183 (million)
% 3.34/1.77 % (11191)------------------------------
% 3.34/1.77 % (11191)------------------------------
% 3.34/1.78 % (11210)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/18Mi)
% 3.34/1.78 % (11211)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/710Mi)
% 3.34/1.78 % (11209)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/4Mi)
% 3.34/1.78 % (11213)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_10942 for (2999ds/902Mi)
% 3.34/1.78 % (11209)Instruction limit reached!
% 3.34/1.78 % (11209)------------------------------
% 3.34/1.78 % (11209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.78 % (11209)Termination reason: Unknown
% 3.34/1.78 % (11209)Termination phase: shuffling
% 3.34/1.78
% 3.34/1.78 % (11209)Memory used [KB]: 2174
% 3.34/1.78 % (11209)Time elapsed: 0.005 s
% 3.34/1.78 % (11209)Instructions burned: 4 (million)
% 3.34/1.78 % (11209)------------------------------
% 3.34/1.78 % (11209)------------------------------
% 3.34/1.78 % (11212)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10942 for (2999ds/6Mi)
% 3.34/1.78 % (11210)Instruction limit reached!
% 3.34/1.78 % (11210)------------------------------
% 3.34/1.78 % (11210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.78 % (11210)Termination reason: Unknown
% 3.34/1.78 % (11210)Termination phase: shuffling
% 3.34/1.78
% 3.34/1.78 % (11210)Memory used [KB]: 2686
% 3.34/1.78 % (11210)Time elapsed: 0.008 s
% 3.34/1.78 % (11210)Instructions burned: 20 (million)
% 3.34/1.78 % (11210)------------------------------
% 3.34/1.78 % (11210)------------------------------
% 3.34/1.79 % (11212)Instruction limit reached!
% 3.34/1.79 % (11212)------------------------------
% 3.34/1.79 % (11212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.79 % (11212)Termination reason: Unknown
% 3.34/1.79 % (11212)Termination phase: shuffling
% 3.34/1.79
% 3.34/1.79 % (11212)Memory used [KB]: 2302
% 3.34/1.79 % (11212)Time elapsed: 0.005 s
% 3.34/1.79 % (11212)Instructions burned: 7 (million)
% 3.34/1.79 % (11212)------------------------------
% 3.34/1.79 % (11212)------------------------------
% 3.34/1.79 % (11215)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10942 for (2998ds/5Mi)
% 3.34/1.79 % (11215)Instruction limit reached!
% 3.34/1.79 % (11215)------------------------------
% 3.34/1.79 % (11215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.79 % (11215)Termination reason: Unknown
% 3.34/1.79 % (11215)Termination phase: shuffling
% 3.34/1.79
% 3.34/1.79 % (11215)Memory used [KB]: 2302
% 3.34/1.79 % (11215)Time elapsed: 0.003 s
% 3.34/1.79 % (11215)Instructions burned: 6 (million)
% 3.34/1.79 % (11215)------------------------------
% 3.34/1.79 % (11215)------------------------------
% 3.34/1.80 % (11216)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_10942 for (2998ds/6Mi)
% 3.34/1.80 % (11216)Instruction limit reached!
% 3.34/1.80 % (11216)------------------------------
% 3.34/1.80 % (11216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.80 % (11216)Termination reason: Unknown
% 3.34/1.80 % (11216)Termination phase: shuffling
% 3.34/1.80
% 3.34/1.80 % (11216)Memory used [KB]: 2302
% 3.34/1.80 % (11216)Time elapsed: 0.004 s
% 3.34/1.80 % (11216)Instructions burned: 6 (million)
% 3.34/1.80 % (11216)------------------------------
% 3.34/1.80 % (11216)------------------------------
% 3.34/1.80 % (11214)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_10942 for (2998ds/21Mi)
% 3.34/1.80 % (11217)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10942 for (2998ds/377Mi)
% 3.34/1.81 % (11218)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_10942 for (2998ds/779Mi)
% 3.34/1.81 % (11214)Instruction limit reached!
% 3.34/1.81 % (11214)------------------------------
% 3.34/1.81 % (11214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.81 % (11214)Termination reason: Unknown
% 3.34/1.81 % (11214)Termination phase: shuffling
% 3.34/1.81
% 3.34/1.81 % (11214)Memory used [KB]: 2686
% 3.34/1.81 % (11214)Time elapsed: 0.015 s
% 3.34/1.81 % (11214)Instructions burned: 21 (million)
% 3.34/1.81 % (11214)------------------------------
% 3.34/1.81 % (11214)------------------------------
% 3.34/1.83 % (11219)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_10942 for (2998ds/19Mi)
% 3.34/1.84 % (11219)Instruction limit reached!
% 3.34/1.84 % (11219)------------------------------
% 3.34/1.84 % (11219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.84 % (11219)Termination reason: Unknown
% 3.34/1.84 % (11219)Termination phase: shuffling
% 3.34/1.84
% 3.34/1.84 % (11219)Memory used [KB]: 2686
% 3.34/1.84 % (11219)Time elapsed: 0.012 s
% 3.34/1.84 % (11219)Instructions burned: 19 (million)
% 3.34/1.84 % (11219)------------------------------
% 3.34/1.84 % (11219)------------------------------
% 3.34/1.85 % (11220)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10942 for (2998ds/879Mi)
% 3.34/1.87 % (11196)Instruction limit reached!
% 3.34/1.87 % (11196)------------------------------
% 3.34/1.87 % (11196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.87 % (11196)Termination reason: Unknown
% 3.34/1.87 % (11196)Termination phase: Saturation
% 3.34/1.87
% 3.34/1.87 % (11196)Memory used [KB]: 8827
% 3.34/1.87 % (11196)Time elapsed: 0.147 s
% 3.34/1.87 % (11196)Instructions burned: 277 (million)
% 3.34/1.87 % (11196)------------------------------
% 3.34/1.87 % (11196)------------------------------
% 3.34/1.88 % (11221)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10942 for (2998ds/17Mi)
% 3.34/1.89 % (11221)Instruction limit reached!
% 3.34/1.89 % (11221)------------------------------
% 3.34/1.89 % (11221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.89 % (11221)Termination reason: Unknown
% 3.34/1.89 % (11221)Termination phase: shuffling
% 3.34/1.89
% 3.34/1.89 % (11221)Memory used [KB]: 2686
% 3.34/1.89 % (11221)Time elapsed: 0.008 s
% 3.34/1.89 % (11221)Instructions burned: 19 (million)
% 3.34/1.89 % (11221)------------------------------
% 3.34/1.89 % (11221)------------------------------
% 3.34/1.90 % (11222)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10942 for (2997ds/3Mi)
% 3.34/1.90 % (11222)Instruction limit reached!
% 3.34/1.90 % (11222)------------------------------
% 3.34/1.90 % (11222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.90 % (11222)Termination reason: Unknown
% 3.34/1.90 % (11222)Termination phase: shuffling
% 3.34/1.90
% 3.34/1.90 % (11222)Memory used [KB]: 2174
% 3.34/1.90 % (11222)Time elapsed: 0.003 s
% 3.34/1.90 % (11222)Instructions burned: 3 (million)
% 3.34/1.90 % (11222)------------------------------
% 3.34/1.90 % (11222)------------------------------
% 3.34/1.91 % (11223)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10942 for (2997ds/30Mi)
% 3.34/1.92 % (11217)Instruction limit reached!
% 3.34/1.92 % (11217)------------------------------
% 3.34/1.92 % (11217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.92 % (11217)Termination reason: Unknown
% 3.34/1.92 % (11217)Termination phase: Saturation
% 3.34/1.92
% 3.34/1.92 % (11217)Memory used [KB]: 10106
% 3.34/1.92 % (11217)Time elapsed: 0.117 s
% 3.34/1.92 % (11217)Instructions burned: 378 (million)
% 3.34/1.92 % (11217)------------------------------
% 3.34/1.92 % (11217)------------------------------
% 3.34/1.92 % (11223)Instruction limit reached!
% 3.34/1.92 % (11223)------------------------------
% 3.34/1.92 % (11223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.92 % (11223)Termination reason: Unknown
% 3.34/1.92 % (11223)Termination phase: shuffling
% 3.34/1.92
% 3.34/1.92 % (11223)Memory used [KB]: 2942
% 3.34/1.92 % (11223)Time elapsed: 0.013 s
% 3.34/1.92 % (11223)Instructions burned: 32 (million)
% 3.34/1.92 % (11223)------------------------------
% 3.34/1.92 % (11223)------------------------------
% 3.34/1.93 % (11224)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10942 for (2997ds/127Mi)
% 3.34/1.93 % (11225)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10942 for (2997ds/100Mi)
% 3.34/1.96 % (11225)Instruction limit reached!
% 3.34/1.96 % (11225)------------------------------
% 3.34/1.96 % (11225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.96 % (11225)Termination reason: Unknown
% 3.34/1.96 % (11225)Termination phase: Property scanning
% 3.34/1.96
% 3.34/1.96 % (11225)Memory used [KB]: 4221
% 3.34/1.96 % (11225)Time elapsed: 0.032 s
% 3.34/1.96 % (11225)Instructions burned: 103 (million)
% 3.34/1.96 % (11225)------------------------------
% 3.34/1.96 % (11225)------------------------------
% 3.34/1.97 % (11224)Instruction limit reached!
% 3.34/1.97 % (11224)------------------------------
% 3.34/1.97 % (11224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.97 % (11224)Termination reason: Unknown
% 3.34/1.97 % (11224)Termination phase: Preprocessing 3
% 3.34/1.97
% 3.34/1.97 % (11224)Memory used [KB]: 4093
% 3.34/1.97 % (11224)Time elapsed: 0.040 s
% 3.34/1.97 % (11224)Instructions burned: 128 (million)
% 3.34/1.97 % (11224)------------------------------
% 3.34/1.97 % (11224)------------------------------
% 3.34/1.97 % (11226)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_10942 for (2996ds/3Mi)
% 3.34/1.98 % (11226)Instruction limit reached!
% 3.34/1.98 % (11226)------------------------------
% 3.34/1.98 % (11226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.98 % (11226)Termination reason: Unknown
% 3.34/1.98 % (11226)Termination phase: shuffling
% 3.34/1.98
% 3.34/1.98 % (11226)Memory used [KB]: 2302
% 3.34/1.98 % (11226)Time elapsed: 0.004 s
% 3.34/1.98 % (11226)Instructions burned: 6 (million)
% 3.34/1.98 % (11226)------------------------------
% 3.34/1.98 % (11226)------------------------------
% 3.34/1.98 % (11227)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_10942 for (2996ds/20Mi)
% 3.34/1.99 % (11227)Instruction limit reached!
% 3.34/1.99 % (11227)------------------------------
% 3.34/1.99 % (11227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.99 % (11227)Termination reason: Unknown
% 3.34/1.99 % (11227)Termination phase: shuffling
% 3.34/1.99
% 3.34/1.99 % (11227)Memory used [KB]: 2686
% 3.34/1.99 % (11227)Time elapsed: 0.008 s
% 3.34/1.99 % (11227)Instructions burned: 20 (million)
% 3.34/1.99 % (11227)------------------------------
% 3.34/1.99 % (11227)------------------------------
% 3.34/1.99 % (11228)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_10942 for (2996ds/86Mi)
% 3.34/1.99 % (11211)Refutation not found, non-redundant clauses discarded% (11211)------------------------------
% 3.34/1.99 % (11211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/1.99 % (11211)Termination reason: Refutation not found, non-redundant clauses discarded
% 3.34/1.99
% 3.34/1.99 % (11211)Memory used [KB]: 9466
% 3.34/1.99 % (11211)Time elapsed: 0.210 s
% 3.34/1.99 % (11211)Instructions burned: 656 (million)
% 3.34/1.99 % (11211)------------------------------
% 3.34/1.99 % (11211)------------------------------
% 3.34/1.99 % (11229)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_10942 for (2996ds/107Mi)
% 3.34/2.00 % (11230)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_10942 for (2996ds/39Mi)
% 3.34/2.01 % (11230)Instruction limit reached!
% 3.34/2.01 % (11230)------------------------------
% 3.34/2.01 % (11230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/2.01 % (11230)Termination reason: Unknown
% 3.34/2.01 % (11230)Termination phase: shuffling
% 3.34/2.01
% 3.34/2.01 % (11230)Memory used [KB]: 3326
% 3.34/2.01 % (11230)Time elapsed: 0.012 s
% 3.34/2.01 % (11230)Instructions burned: 39 (million)
% 3.34/2.01 % (11230)------------------------------
% 3.34/2.01 % (11230)------------------------------
% 5.42/2.01 % (11228)Instruction limit reached!
% 5.42/2.01 % (11228)------------------------------
% 5.42/2.01 % (11228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.01 % (11228)Termination reason: Unknown
% 5.42/2.01 % (11228)Termination phase: Preprocessing 1
% 5.42/2.01
% 5.42/2.01 % (11228)Memory used [KB]: 3454
% 5.42/2.01 % (11228)Time elapsed: 0.031 s
% 5.42/2.01 % (11228)Instructions burned: 89 (million)
% 5.42/2.01 % (11228)------------------------------
% 5.42/2.01 % (11228)------------------------------
% 5.42/2.02 % (11231)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_10942 for (2996ds/448Mi)
% 5.42/2.03 % (11232)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_10942 for (2996ds/46Mi)
% 5.42/2.03 % (11229)Instruction limit reached!
% 5.42/2.03 % (11229)------------------------------
% 5.42/2.03 % (11229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.03 % (11229)Termination reason: Unknown
% 5.42/2.03 % (11229)Termination phase: Preprocessing 1
% 5.42/2.03
% 5.42/2.03 % (11229)Memory used [KB]: 3454
% 5.42/2.03 % (11229)Time elapsed: 0.034 s
% 5.42/2.03 % (11229)Instructions burned: 108 (million)
% 5.42/2.03 % (11229)------------------------------
% 5.42/2.03 % (11229)------------------------------
% 5.42/2.04 % (11233)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_10942 for (2996ds/98Mi)
% 5.42/2.04 % (11232)Instruction limit reached!
% 5.42/2.04 % (11232)------------------------------
% 5.42/2.04 % (11232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.04 % (11232)Termination reason: Unknown
% 5.42/2.04 % (11232)Termination phase: shuffling
% 5.42/2.04
% 5.42/2.04 % (11232)Memory used [KB]: 3198
% 5.42/2.04 % (11232)Time elapsed: 0.018 s
% 5.42/2.04 % (11232)Instructions burned: 47 (million)
% 5.42/2.04 % (11232)------------------------------
% 5.42/2.04 % (11232)------------------------------
% 5.42/2.05 % (11218)Instruction limit reached!
% 5.42/2.05 % (11218)------------------------------
% 5.42/2.05 % (11218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.05 % (11218)Termination reason: Unknown
% 5.42/2.05 % (11218)Termination phase: Saturation
% 5.42/2.05
% 5.42/2.05 % (11218)Memory used [KB]: 11001
% 5.42/2.05 % (11218)Time elapsed: 0.266 s
% 5.42/2.05 % (11218)Instructions burned: 779 (million)
% 5.42/2.05 % (11218)------------------------------
% 5.42/2.05 % (11218)------------------------------
% 5.42/2.05 % (11234)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_10942 for (2996ds/507Mi)
% 5.42/2.05 % (11202)Instruction limit reached!
% 5.42/2.05 % (11202)------------------------------
% 5.42/2.05 % (11202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.05 % (11202)Termination reason: Unknown
% 5.42/2.05 % (11202)Termination phase: Saturation
% 5.42/2.05
% 5.42/2.05 % (11202)Memory used [KB]: 11385
% 5.42/2.05 % (11202)Time elapsed: 0.315 s
% 5.42/2.05 % (11202)Instructions burned: 1044 (million)
% 5.42/2.05 % (11202)------------------------------
% 5.42/2.05 % (11202)------------------------------
% 5.42/2.06 % (11235)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_10942 for (2996ds/149Mi)
% 5.42/2.06 % (11233)Instruction limit reached!
% 5.42/2.06 % (11233)------------------------------
% 5.42/2.06 % (11233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.06 % (11233)Termination reason: Unknown
% 5.42/2.06 % (11233)Termination phase: Property scanning
% 5.42/2.06
% 5.42/2.06 % (11233)Memory used [KB]: 4221
% 5.42/2.06 % (11233)Time elapsed: 0.028 s
% 5.42/2.06 % (11233)Instructions burned: 98 (million)
% 5.42/2.06 % (11233)------------------------------
% 5.42/2.06 % (11233)------------------------------
% 5.42/2.06 % (11236)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_10942 for (2996ds/39Mi)
% 5.42/2.07 % (11237)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_10942 for (2996ds/6Mi)
% 5.42/2.08 % (11237)Instruction limit reached!
% 5.42/2.08 % (11237)------------------------------
% 5.42/2.08 % (11237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.08 % (11237)Termination reason: Unknown
% 5.42/2.08 % (11237)Termination phase: shuffling
% 5.42/2.08
% 5.42/2.08 % (11237)Memory used [KB]: 2302
% 5.42/2.08 % (11237)Time elapsed: 0.003 s
% 5.42/2.08 % (11237)Instructions burned: 6 (million)
% 5.42/2.08 % (11237)------------------------------
% 5.42/2.08 % (11237)------------------------------
% 5.42/2.08 % (11236)Instruction limit reached!
% 5.42/2.08 % (11236)------------------------------
% 5.42/2.08 % (11236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.08 % (11236)Termination reason: Unknown
% 5.42/2.08 % (11236)Termination phase: shuffling
% 5.42/2.08
% 5.42/2.08 % (11236)Memory used [KB]: 3070
% 5.42/2.08 % (11236)Time elapsed: 0.015 s
% 5.42/2.08 % (11236)Instructions burned: 41 (million)
% 5.42/2.08 % (11236)------------------------------
% 5.42/2.08 % (11236)------------------------------
% 5.42/2.09 % (11238)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_10942 for (2996ds/1087Mi)
% 5.42/2.09 % (11239)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_10942 for (2995ds/47Mi)
% 5.42/2.10 % (11213)Instruction limit reached!
% 5.42/2.10 % (11213)------------------------------
% 5.42/2.10 % (11213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.10 % (11213)Termination reason: Unknown
% 5.42/2.10 % (11213)Termination phase: Saturation
% 5.42/2.10
% 5.42/2.10 % (11213)Memory used [KB]: 10746
% 5.42/2.10 % (11213)Time elapsed: 0.319 s
% 5.42/2.10 % (11213)Instructions burned: 902 (million)
% 5.42/2.10 % (11213)------------------------------
% 5.42/2.10 % (11213)------------------------------
% 5.42/2.10 % (11239)Instruction limit reached!
% 5.42/2.10 % (11239)------------------------------
% 5.42/2.10 % (11239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.10 % (11239)Termination reason: Unknown
% 5.42/2.10 % (11239)Termination phase: shuffling
% 5.42/2.10
% 5.42/2.10 % (11239)Memory used [KB]: 3198
% 5.42/2.10 % (11239)Time elapsed: 0.017 s
% 5.42/2.10 % (11239)Instructions burned: 48 (million)
% 5.42/2.10 % (11239)------------------------------
% 5.42/2.10 % (11239)------------------------------
% 5.42/2.11 % (11235)Instruction limit reached!
% 5.42/2.11 % (11235)------------------------------
% 5.42/2.11 % (11235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.11 % (11235)Termination reason: Unknown
% 5.42/2.11 % (11235)Termination phase: Property scanning
% 5.42/2.11
% 5.42/2.11 % (11235)Memory used [KB]: 4221
% 5.42/2.11 % (11235)Time elapsed: 0.049 s
% 5.42/2.11 % (11235)Instructions burned: 152 (million)
% 5.42/2.11 % (11235)------------------------------
% 5.42/2.11 % (11235)------------------------------
% 5.96/2.11 % (11241)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_10942 for (2995ds/432Mi)
% 5.96/2.12 % (11240)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_10942 for (2995ds/44Mi)
% 5.96/2.12 % (11242)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_10942 for (2995ds/62Mi)
% 5.96/2.13 % (11240)Instruction limit reached!
% 5.96/2.13 % (11240)------------------------------
% 5.96/2.13 % (11240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.13 % (11240)Termination reason: Unknown
% 5.96/2.13 % (11240)Termination phase: shuffling
% 5.96/2.13
% 5.96/2.13 % (11240)Memory used [KB]: 3326
% 5.96/2.13 % (11240)Time elapsed: 0.017 s
% 5.96/2.13 % (11240)Instructions burned: 44 (million)
% 5.96/2.13 % (11240)------------------------------
% 5.96/2.13 % (11240)------------------------------
% 5.96/2.14 % (11231)Instruction limit reached!
% 5.96/2.14 % (11231)------------------------------
% 5.96/2.14 % (11231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.14 % (11231)Termination reason: Unknown
% 5.96/2.14 % (11231)Termination phase: Saturation
% 5.96/2.14
% 5.96/2.14 % (11231)Memory used [KB]: 10746
% 5.96/2.14 % (11231)Time elapsed: 0.123 s
% 5.96/2.14 % (11231)Instructions burned: 450 (million)
% 5.96/2.14 % (11231)------------------------------
% 5.96/2.14 % (11231)------------------------------
% 5.96/2.14 % (11242)Instruction limit reached!
% 5.96/2.14 % (11242)------------------------------
% 5.96/2.14 % (11242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.14 % (11242)Termination reason: Unknown
% 5.96/2.14 % (11242)Termination phase: shuffling
% 5.96/2.14
% 5.96/2.14 % (11242)Memory used [KB]: 3582
% 5.96/2.14 % (11242)Time elapsed: 0.021 s
% 5.96/2.14 % (11242)Instructions burned: 64 (million)
% 5.96/2.14 % (11242)------------------------------
% 5.96/2.14 % (11242)------------------------------
% 5.96/2.14 % (11243)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_10942 for (2995ds/31Mi)
% 5.96/2.15 % (11220)Instruction limit reached!
% 5.96/2.15 % (11220)------------------------------
% 5.96/2.15 % (11220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.15 % (11220)Termination reason: Unknown
% 5.96/2.15 % (11220)Termination phase: Saturation
% 5.96/2.15
% 5.96/2.15 % (11220)Memory used [KB]: 9466
% 5.96/2.15 % (11220)Time elapsed: 0.318 s
% 5.96/2.15 % (11220)Instructions burned: 879 (million)
% 5.96/2.15 % (11220)------------------------------
% 5.96/2.15 % (11220)------------------------------
% 5.96/2.15 % (11244)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_10942 for (2995ds/96Mi)
% 5.96/2.15 % (11245)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_10942 for (2995ds/453Mi)
% 5.96/2.15 % (11243)Instruction limit reached!
% 5.96/2.15 % (11243)------------------------------
% 5.96/2.15 % (11243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.15 % (11243)Termination reason: Unknown
% 5.96/2.15 % (11243)Termination phase: shuffling
% 5.96/2.15
% 5.96/2.15 % (11243)Memory used [KB]: 2942
% 5.96/2.15 % (11243)Time elapsed: 0.013 s
% 5.96/2.15 % (11243)Instructions burned: 33 (million)
% 5.96/2.15 % (11243)------------------------------
% 5.96/2.15 % (11243)------------------------------
% 5.96/2.16 % (11246)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_10942 for (2995ds/71Mi)
% 5.96/2.17 % (11247)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_10942 for (2995ds/83Mi)
% 5.96/2.18 % (11244)Instruction limit reached!
% 5.96/2.18 % (11244)------------------------------
% 5.96/2.18 % (11244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.18 % (11244)Termination reason: Unknown
% 5.96/2.18 % (11244)Termination phase: Naming
% 5.96/2.18
% 5.96/2.18 % (11244)Memory used [KB]: 3837
% 5.96/2.18 % (11244)Time elapsed: 0.031 s
% 5.96/2.18 % (11244)Instructions burned: 96 (million)
% 5.96/2.18 % (11244)------------------------------
% 5.96/2.18 % (11244)------------------------------
% 5.96/2.18 % (11246)Instruction limit reached!
% 5.96/2.18 % (11246)------------------------------
% 5.96/2.18 % (11246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.18 % (11246)Termination reason: Unknown
% 5.96/2.18 % (11246)Termination phase: Property scanning
% 5.96/2.18
% 5.96/2.18 % (11246)Memory used [KB]: 3454
% 5.96/2.18 % (11246)Time elapsed: 0.024 s
% 5.96/2.18 % (11246)Instructions burned: 71 (million)
% 5.96/2.18 % (11246)------------------------------
% 5.96/2.18 % (11246)------------------------------
% 5.96/2.19 % (11234)First to succeed.
% 5.96/2.19 % (11248)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_10942 for (2995ds/11Mi)
% 5.96/2.19 % (11234)Refutation found. Thanks to Tanya!
% 5.96/2.19 % SZS status Theorem for DTF2THF_10942
% 5.96/2.19 % SZS output start Proof for DTF2THF_10942
% 5.96/2.19 thf(type_def_5, type, pname: $tType).
% 5.96/2.19 thf(type_def_6, type, option_com: $tType).
% 5.96/2.19 thf(type_def_8, type, x_a: $tType).
% 5.96/2.19 thf(type_def_9, type, nat: $tType).
% 5.96/2.19 thf(type_def_10, type, com: $tType).
% 5.96/2.19 thf(func_def_0, type, x_a: $tType).
% 5.96/2.19 thf(func_def_1, type, com: $tType).
% 5.96/2.19 thf(func_def_2, type, pname: $tType).
% 5.96/2.19 thf(func_def_3, type, nat: $tType).
% 5.96/2.19 thf(func_def_4, type, option_com: $tType).
% 5.96/2.19 thf(func_def_5, type, body: pname > option_com).
% 5.96/2.19 thf(func_def_6, type, finite_card_a_o: ((x_a > $o) > $o) > nat).
% 5.96/2.19 thf(func_def_7, type, finite_card_pname_o: ((pname > $o) > $o) > nat).
% 5.96/2.19 thf(func_def_8, type, finite_card_nat_o: ((nat > $o) > $o) > nat).
% 5.96/2.19 thf(func_def_9, type, finite_card_a: (x_a > $o) > nat).
% 5.96/2.19 thf(func_def_10, type, finite_card_pname: (pname > $o) > nat).
% 5.96/2.19 thf(func_def_11, type, finite_card_nat: (nat > $o) > nat).
% 5.96/2.19 thf(func_def_12, type, finite_finite_a_o_o: (((x_a > $o) > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_13, type, finite1066544169me_o_o: (((pname > $o) > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_14, type, finite1676163439at_o_o: (((nat > $o) > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_15, type, finite_finite_a_o: ((x_a > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_16, type, finite297249702name_o: ((pname > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_17, type, finite_finite_nat_o: ((nat > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_18, type, finite_finite_a: (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_19, type, finite_finite_pname: (pname > $o) > $o).
% 5.96/2.19 thf(func_def_20, type, finite_finite_nat: (nat > $o) > $o).
% 5.96/2.19 thf(func_def_21, type, minus_minus_nat: nat > nat > nat).
% 5.96/2.19 thf(func_def_22, type, one_one_nat: nat).
% 5.96/2.19 thf(func_def_23, type, plus_plus_nat: nat > nat > nat).
% 5.96/2.19 thf(func_def_24, type, zero_zero_nat: nat).
% 5.96/2.19 thf(func_def_25, type, suc: nat > nat).
% 5.96/2.19 thf(func_def_26, type, nat_case_o: $o > (nat > $o) > nat > $o).
% 5.96/2.19 thf(func_def_27, type, the_com: option_com > com).
% 5.96/2.19 thf(func_def_28, type, bot_bot_a_o_o: (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_29, type, bot_bot_pname_o_o: (pname > $o) > $o).
% 5.96/2.19 thf(func_def_30, type, bot_bot_nat_o_o: (nat > $o) > $o).
% 5.96/2.19 thf(func_def_31, type, bot_bot_a_o: x_a > $o).
% 5.96/2.19 thf(func_def_32, type, bot_bot_pname_o: pname > $o).
% 5.96/2.19 thf(func_def_33, type, bot_bot_nat_o: nat > $o).
% 5.96/2.19 thf(func_def_35, type, bot_bot_nat: nat).
% 5.96/2.19 thf(func_def_36, type, ord_less_nat: nat > nat > $o).
% 5.96/2.19 thf(func_def_37, type, ord_less_eq_a_o_o: ((x_a > $o) > $o) > ((x_a > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_38, type, ord_le1205211808me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_39, type, ord_less_eq_nat_o_o: ((nat > $o) > $o) > ((nat > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_40, type, ord_less_eq_a_o: (x_a > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_41, type, ord_less_eq_pname_o: (pname > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_42, type, ord_less_eq_nat_o: (nat > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_43, type, ord_less_eq_o: $o > $o > $o).
% 5.96/2.19 thf(func_def_44, type, ord_less_eq_nat: nat > nat > $o).
% 5.96/2.19 thf(func_def_45, type, collect_a_o_o: (((x_a > $o) > $o) > $o) > ((x_a > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_46, type, collect_pname_o_o: (((pname > $o) > $o) > $o) > ((pname > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_47, type, collect_nat_o_o: (((nat > $o) > $o) > $o) > ((nat > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_48, type, collect_a_o: ((x_a > $o) > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_49, type, collect_pname_o: ((pname > $o) > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_50, type, collect_nat_o: ((nat > $o) > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_51, type, collect_a: (x_a > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_52, type, collect_pname: (pname > $o) > pname > $o).
% 5.96/2.19 thf(func_def_53, type, collect_nat: (nat > $o) > nat > $o).
% 5.96/2.19 thf(func_def_54, type, image_a_o_a: ((x_a > $o) > x_a) > ((x_a > $o) > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_55, type, image_a_o_pname: ((x_a > $o) > pname) > ((x_a > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_56, type, image_a_o_nat: ((x_a > $o) > nat) > ((x_a > $o) > $o) > nat > $o).
% 5.96/2.19 thf(func_def_57, type, image_pname_o_a: ((pname > $o) > x_a) > ((pname > $o) > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_58, type, image_pname_o_pname: ((pname > $o) > pname) > ((pname > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_59, type, image_pname_o_nat: ((pname > $o) > nat) > ((pname > $o) > $o) > nat > $o).
% 5.96/2.19 thf(func_def_60, type, image_nat_o_a: ((nat > $o) > x_a) > ((nat > $o) > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_61, type, image_nat_o_pname: ((nat > $o) > pname) > ((nat > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_62, type, image_nat_o_nat: ((nat > $o) > nat) > ((nat > $o) > $o) > nat > $o).
% 5.96/2.19 thf(func_def_63, type, image_a_a_o: (x_a > x_a > $o) > (x_a > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_64, type, image_a_pname_o: (x_a > pname > $o) > (x_a > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_65, type, image_a_nat_o: (x_a > nat > $o) > (x_a > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_66, type, image_a_a: (x_a > x_a) > (x_a > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_67, type, image_a_pname: (x_a > pname) > (x_a > $o) > pname > $o).
% 5.96/2.19 thf(func_def_68, type, image_a_nat: (x_a > nat) > (x_a > $o) > nat > $o).
% 5.96/2.19 thf(func_def_69, type, image_pname_a_o: (pname > x_a > $o) > (pname > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_70, type, image_pname_pname_o: (pname > pname > $o) > (pname > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_71, type, image_pname_nat_o: (pname > nat > $o) > (pname > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_72, type, image_pname_a: (pname > x_a) > (pname > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_73, type, image_pname_pname: (pname > pname) > (pname > $o) > pname > $o).
% 5.96/2.19 thf(func_def_74, type, image_pname_nat: (pname > nat) > (pname > $o) > nat > $o).
% 5.96/2.19 thf(func_def_75, type, image_nat_a_o: (nat > x_a > $o) > (nat > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_76, type, image_nat_pname_o: (nat > pname > $o) > (nat > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_77, type, image_nat_nat_o: (nat > nat > $o) > (nat > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_78, type, image_nat_a: (nat > x_a) > (nat > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_79, type, image_nat_pname: (nat > pname) > (nat > $o) > pname > $o).
% 5.96/2.19 thf(func_def_80, type, image_nat_nat: (nat > nat) > (nat > $o) > nat > $o).
% 5.96/2.19 thf(func_def_81, type, insert_a_o: (x_a > $o) > ((x_a > $o) > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_82, type, insert_pname_o: (pname > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_83, type, insert_nat_o: (nat > $o) > ((nat > $o) > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_84, type, insert_a: x_a > (x_a > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_85, type, insert_pname: pname > (pname > $o) > pname > $o).
% 5.96/2.19 thf(func_def_86, type, insert_nat: nat > (nat > $o) > nat > $o).
% 5.96/2.19 thf(func_def_87, type, fequal_a_o: (x_a > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_88, type, fequal_pname_o: (pname > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_89, type, fequal_nat_o: (nat > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_90, type, fequal_a: x_a > x_a > $o).
% 5.96/2.19 thf(func_def_91, type, fequal_pname: pname > pname > $o).
% 5.96/2.19 thf(func_def_92, type, fequal_nat: nat > nat > $o).
% 5.96/2.19 thf(func_def_93, type, member_a_o: (x_a > $o) > ((x_a > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_94, type, member_pname_o: (pname > $o) > ((pname > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_95, type, member_nat_o: (nat > $o) > ((nat > $o) > $o) > $o).
% 5.96/2.19 thf(func_def_96, type, member_a: x_a > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_97, type, member_pname: pname > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_98, type, member_nat: nat > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_99, type, g: x_a > $o).
% 5.96/2.19 thf(func_def_100, type, p: (x_a > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_101, type, u: pname > $o).
% 5.96/2.19 thf(func_def_102, type, mgt: com > x_a).
% 5.96/2.19 thf(func_def_103, type, mgt_call: pname > x_a).
% 5.96/2.19 thf(func_def_104, type, na: nat).
% 5.96/2.19 thf(func_def_105, type, pn: pname).
% 5.96/2.19 thf(func_def_106, type, wt: com > $o).
% 5.96/2.19 thf(func_def_117, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 5.96/2.19 thf(func_def_118, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 5.96/2.19 thf(func_def_121, type, sK2: ((x_a > $o) > $o) > (x_a > x_a > $o) > (x_a > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_122, type, sK3: (x_a > $o) > (x_a > nat) > (nat > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_123, type, sK4: (pname > $o) > (pname > nat) > pname).
% 5.96/2.19 thf(func_def_124, type, sK5: (pname > $o) > pname).
% 5.96/2.19 thf(func_def_125, type, sK6: (pname > $o) > ((pname > $o) > $o) > ((pname > $o) > pname) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_126, type, sK7: (pname > $o) > (pname > pname) > (pname > $o) > pname > $o).
% 5.96/2.19 thf(func_def_127, type, sK8: (pname > $o) > (x_a > $o) > (x_a > pname) > x_a > $o).
% 5.96/2.19 thf(func_def_128, type, sK9: (nat > $o) > nat > nat).
% 5.96/2.19 thf(func_def_129, type, sK10: (x_a > $o) > (nat > $o) > (nat > x_a) > nat > $o).
% 5.96/2.19 thf(func_def_130, type, sK11: (nat > nat) > nat).
% 5.96/2.19 thf(func_def_131, type, sK12: (nat > nat) > nat).
% 5.96/2.19 thf(func_def_132, type, sK13: (pname > pname) > (pname > $o) > (pname > $o) > pname).
% 5.96/2.19 thf(func_def_133, type, sK14: pname > (nat > pname) > (nat > $o) > nat).
% 5.96/2.19 thf(func_def_134, type, sK15: (((nat > $o) > $o) > $o) > ((nat > $o) > $o) > nat > $o).
% 5.96/2.19 thf(func_def_135, type, sK16: (((nat > $o) > $o) > $o) > ((nat > $o) > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_136, type, sK17: (nat > nat) > nat).
% 5.96/2.19 thf(func_def_137, type, sK18: ((x_a > $o) > $o) > (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_138, type, sK19: ((x_a > $o) > $o) > (x_a > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_139, type, sK20: (x_a > $o) > ((nat > $o) > $o) > (x_a > nat > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_140, type, sK21: ((nat > $o) > $o) > (pname > nat > $o) > (pname > $o) > pname > $o).
% 5.96/2.19 thf(func_def_141, type, sK22: (pname > $o) > ((nat > $o) > $o) > ((nat > $o) > pname) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_142, type, sK23: (nat > $o) > (nat > pname > $o) > nat).
% 5.96/2.19 thf(func_def_143, type, sK24: (pname > x_a) > (x_a > $o) > (pname > $o) > pname > $o).
% 5.96/2.19 thf(func_def_144, type, sK25: (x_a > $o) > (x_a > nat > $o) > x_a).
% 5.96/2.19 thf(func_def_145, type, sK26: (nat > pname) > (pname > $o) > (nat > $o) > nat).
% 5.96/2.19 thf(func_def_146, type, sK27: (x_a > $o) > (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_147, type, sK28: (pname > $o) > (pname > $o) > pname).
% 5.96/2.19 thf(func_def_148, type, sK29: (nat > $o) > nat).
% 5.96/2.19 thf(func_def_149, type, sK30: nat > (nat > $o) > nat).
% 5.96/2.19 thf(func_def_150, type, sK31: (pname > $o) > pname).
% 5.96/2.19 thf(func_def_151, type, sK32: (nat > $o) > (nat > x_a) > (x_a > $o) > nat > $o).
% 5.96/2.19 thf(func_def_152, type, sK33: ((nat > $o) > $o) > ((nat > $o) > nat) > nat > $o).
% 5.96/2.19 thf(func_def_153, type, sK34: (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_154, type, sK35: ((pname > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_155, type, sK36: (nat > nat > $o) > (nat > $o) > nat).
% 5.96/2.19 thf(func_def_156, type, sK37: (pname > nat) > (pname > $o) > nat > pname).
% 5.96/2.19 thf(func_def_157, type, sK38: ((pname > $o) > $o) > (((pname > $o) > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_158, type, sK39: ((pname > $o) > $o) > (((pname > $o) > $o) > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_159, type, sK40: ((pname > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_160, type, sK41: (nat > $o) > (nat > nat) > (nat > $o) > nat > $o).
% 5.96/2.19 thf(func_def_161, type, sK42: (pname > nat) > (nat > $o) > (pname > $o) > pname).
% 5.96/2.19 thf(func_def_162, type, sK43: (x_a > $o) > ((nat > $o) > x_a) > ((nat > $o) > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_163, type, sK44: ((pname > $o) > $o) > (pname > $o) > pname > $o).
% 5.96/2.19 thf(func_def_164, type, sK45: ((pname > $o) > $o) > (pname > $o) > pname).
% 5.96/2.19 thf(func_def_165, type, sK46: ((x_a > $o) > $o) > (pname > $o) > ((x_a > $o) > pname) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_166, type, sK47: ((x_a > $o) > $o) > ((x_a > $o) > pname) > x_a > $o).
% 5.96/2.19 thf(func_def_167, type, sK48: (pname > $o) > (x_a > pname) > (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_168, type, sK49: (pname > $o) > (pname > pname > $o) > pname).
% 5.96/2.19 thf(func_def_169, type, sK50: (nat > $o) > nat).
% 5.96/2.19 thf(func_def_170, type, sK51: nat > (nat > $o) > nat).
% 5.96/2.19 thf(func_def_171, type, sK52: (nat > x_a > $o) > nat).
% 5.96/2.19 thf(func_def_172, type, sK53: (x_a > $o) > ((pname > $o) > $o) > (x_a > pname > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_173, type, sK54: (nat > $o) > (x_a > $o) > (nat > x_a) > nat).
% 5.96/2.19 thf(func_def_174, type, sK55: (nat > $o) > nat).
% 5.96/2.19 thf(func_def_175, type, sK56: ((x_a > $o) > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_176, type, sK57: (nat > $o) > x_a > (nat > x_a) > nat).
% 5.96/2.19 thf(func_def_177, type, sK58: ((x_a > $o) > $o) > ((x_a > $o) > nat) > (nat > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_178, type, sK59: (pname > x_a) > (x_a > $o) > (pname > $o) > pname > $o).
% 5.96/2.19 thf(func_def_179, type, sK60: (nat > $o) > nat).
% 5.96/2.19 thf(func_def_180, type, sK61: ((pname > $o) > x_a) > (x_a > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_181, type, sK62: ((pname > $o) > pname) > ((pname > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_182, type, sK63: (nat > $o) > (nat > nat) > nat).
% 5.96/2.19 thf(func_def_183, type, sK64: (((nat > $o) > $o) > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_184, type, sK65: (((nat > $o) > $o) > $o) > nat > $o).
% 5.96/2.19 thf(func_def_185, type, sK66: (pname > x_a > $o) > (pname > $o) > pname).
% 5.96/2.19 thf(func_def_186, type, sK67: ((nat > $o) > $o) > ((nat > $o) > pname) > nat > $o).
% 5.96/2.19 thf(func_def_187, type, sK68: ((x_a > $o) > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_188, type, sK69: (pname > x_a) > (pname > $o) > x_a > pname).
% 5.96/2.19 thf(func_def_189, type, sK70: (nat > $o) > nat > nat).
% 5.96/2.19 thf(func_def_190, type, sK71: (nat > pname > $o) > nat).
% 5.96/2.19 thf(func_def_191, type, sK72: (pname > $o) > (pname > pname) > pname).
% 5.96/2.19 thf(func_def_192, type, sK73: (x_a > nat) > (x_a > $o) > (nat > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_193, type, sK74: (x_a > $o) > (x_a > $o) > (x_a > x_a) > x_a > $o).
% 5.96/2.19 thf(func_def_194, type, sK75: ((pname > $o) > $o) > (nat > $o) > (nat > pname > $o) > nat > $o).
% 5.96/2.19 thf(func_def_195, type, sK76: (nat > $o) > (nat > $o) > nat).
% 5.96/2.19 thf(func_def_196, type, sK77: nat > nat > nat).
% 5.96/2.19 thf(func_def_197, type, sK78: (pname > $o) > (pname > x_a) > pname).
% 5.96/2.19 thf(func_def_198, type, sK79: ((nat > $o) > $o) > (nat > $o) > nat).
% 5.96/2.19 thf(func_def_199, type, sK80: ((nat > $o) > $o) > (nat > $o) > nat > $o).
% 5.96/2.19 thf(func_def_200, type, sK81: (pname > $o) > pname).
% 5.96/2.19 thf(func_def_201, type, sK82: (nat > $o) > (pname > $o) > (pname > nat) > pname > $o).
% 5.96/2.19 thf(func_def_202, type, sK83: ((nat > $o) > $o) > (nat > nat > $o) > (nat > $o) > nat > $o).
% 5.96/2.19 thf(func_def_203, type, sK84: ((pname > $o) > nat) > (nat > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_204, type, sK85: (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_205, type, sK86: (pname > x_a) > (pname > $o) > x_a > pname).
% 5.96/2.19 thf(func_def_206, type, sK87: (pname > $o) > (nat > $o) > (nat > pname) > nat > $o).
% 5.96/2.19 thf(func_def_207, type, sK88: (nat > $o) > (x_a > $o) > (x_a > nat) > x_a).
% 5.96/2.19 thf(func_def_208, type, sK89: nat > nat > nat).
% 5.96/2.19 thf(func_def_209, type, sK90: (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_210, type, sK91: (x_a > $o) > (x_a > pname) > x_a).
% 5.96/2.19 thf(func_def_211, type, sK92: ((pname > $o) > nat) > ((pname > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_212, type, sK93: (x_a > $o) > (x_a > pname > $o) > x_a).
% 5.96/2.19 thf(func_def_213, type, sK94: nat > nat > nat).
% 5.96/2.19 thf(func_def_214, type, sK95: (nat > nat) > nat).
% 5.96/2.19 thf(func_def_215, type, sK96: ((x_a > $o) > $o) > ((x_a > $o) > nat) > x_a > $o).
% 5.96/2.19 thf(func_def_216, type, sK97: (x_a > x_a) > (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_217, type, sK98: (x_a > $o) > pname).
% 5.96/2.19 thf(func_def_218, type, sK99: (nat > x_a) > (nat > $o) > nat).
% 5.96/2.19 thf(func_def_219, type, sK100: (nat > $o) > (nat > pname) > nat).
% 5.96/2.19 thf(func_def_220, type, sK101: (((pname > $o) > $o) > $o) > (pname > $o) > $o).
% 5.96/2.19 thf(func_def_221, type, sK102: (((pname > $o) > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_222, type, sK103: (x_a > $o) > (x_a > nat) > x_a).
% 5.96/2.19 thf(func_def_223, type, sK104: nat > nat).
% 5.96/2.19 thf(func_def_224, type, sK105: (nat > $o) > nat).
% 5.96/2.19 thf(func_def_225, type, sK106: (pname > x_a) > (x_a > $o) > (pname > $o) > pname).
% 5.96/2.19 thf(func_def_226, type, sK107: ((nat > $o) > $o) > nat > $o).
% 5.96/2.19 thf(func_def_227, type, sK108: (nat > $o) > (nat > $o) > nat).
% 5.96/2.19 thf(func_def_228, type, sK109: (pname > nat > $o) > (pname > $o) > pname).
% 5.96/2.19 thf(func_def_229, type, sK110: nat > nat > nat).
% 5.96/2.19 thf(func_def_230, type, sK111: (nat > nat > $o) > nat).
% 5.96/2.19 thf(func_def_231, type, sK112: nat > (x_a > nat) > (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_232, type, sK113: ((x_a > $o) > $o) > (((x_a > $o) > $o) > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_233, type, sK114: ((x_a > $o) > $o) > (((x_a > $o) > $o) > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_234, type, sK115: (x_a > $o) > (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_235, type, sK116: nat > nat > nat).
% 5.96/2.19 thf(func_def_236, type, sK117: ((x_a > $o) > $o) > (nat > $o) > (nat > x_a > $o) > nat > $o).
% 5.96/2.19 thf(func_def_237, type, sK118: ((x_a > $o) > $o) > (pname > x_a > $o) > (pname > $o) > pname > $o).
% 5.96/2.19 thf(func_def_238, type, sK119: (nat > $o) > nat).
% 5.96/2.19 thf(func_def_239, type, sK120: (x_a > pname) > (x_a > $o) > (pname > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_240, type, sK121: (nat > nat) > nat).
% 5.96/2.19 thf(func_def_241, type, sK122: (nat > nat) > nat).
% 5.96/2.19 thf(func_def_242, type, sK123: (nat > $o) > nat).
% 5.96/2.19 thf(func_def_243, type, sK124: ((nat > $o) > nat) > ((nat > $o) > $o) > (nat > $o) > (nat > $o) > $o).
% 5.96/2.19 thf(func_def_244, type, sK125: (pname > pname > $o) > (pname > $o) > ((pname > $o) > $o) > pname > $o).
% 5.96/2.19 thf(func_def_245, type, sK126: (pname > $o) > pname).
% 5.96/2.19 thf(func_def_246, type, sK127: (x_a > $o) > (x_a > x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_247, type, sK128: (((x_a > $o) > $o) > $o) > x_a > $o).
% 5.96/2.19 thf(func_def_248, type, sK129: (((x_a > $o) > $o) > $o) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_249, type, sK130: (pname > $o) > (pname > $o) > pname).
% 5.96/2.19 thf(func_def_250, type, sK131: (nat > $o) > (nat > x_a > $o) > nat).
% 5.96/2.19 thf(func_def_251, type, sK132: ((x_a > $o) > $o) > (x_a > $o) > ((x_a > $o) > x_a) > (x_a > $o) > $o).
% 5.96/2.19 thf(func_def_252, type, sK133: (x_a > $o) > x_a).
% 5.96/2.19 thf(func_def_253, type, sK134: (nat > $o) > nat).
% 5.96/2.19 thf(func_def_254, type, sK135: ((nat > $o) > $o) > nat > $o).
% 5.96/2.19 thf(func_def_256, type, ph137: !>[X0: $tType]:(X0)).
% 5.96/2.19 thf(f5186,plain,(
% 5.96/2.19 $false),
% 5.96/2.19 inference(subsumption_resolution,[status(thm)],[f5185,f3820])).
% 5.96/2.19 thf(f3820,plain,(
% 5.96/2.19 ((member_pname @ pn @ u) = $true)),
% 5.96/2.19 inference(cnf_transformation,[status(thm)],[f805])).
% 5.96/2.19 thf(f805,plain,(
% 5.96/2.19 ((member_pname @ pn @ u) = $true)),
% 5.96/2.19 inference(fool_elimination,[status(thm)],[f804])).
% 5.96/2.19 thf(f804,plain,(
% 5.96/2.19 (member_pname @ pn @ u)),
% 5.96/2.19 inference(rectify,[status(thm)],[f717])).
% 5.96/2.19 thf(f717,axiom,(
% 5.96/2.19 (member_pname @ pn @ u)),
% 5.96/2.19 file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',conj_4)).
% 5.96/2.19 thf(f5185,plain,(
% 5.96/2.19 ((member_pname @ pn @ u) != $true)),
% 5.96/2.19 inference(trivial_inequality_removal,[status(thm)],[f5180])).
% 5.96/2.19 thf(f5180,plain,(
% 5.96/2.19 ((member_pname @ pn @ u) != $true) | ($true != $true)),
% 5.96/2.19 inference(superposition,[status(thm)],[f5042,f4725])).
% 5.96/2.19 thf(f4725,plain,(
% 5.96/2.19 ( ! [X2 : pname > $o,X3 : pname,X0 : pname > x_a] : (((member_a @ (X0 @ X3) @ (image_pname_a @ X0 @ X2)) = $true) | ((member_pname @ X3 @ X2) != $true)) )),
% 5.96/2.19 inference(equality_resolution,[status(thm)],[f4140])).
% 5.96/2.19 thf(f4140,plain,(
% 5.96/2.19 ( ! [X2 : pname > $o,X3 : pname,X0 : pname > x_a,X1 : x_a] : (((member_pname @ X3 @ X2) != $true) | ((X0 @ X3) != X1) | ((member_a @ X1 @ (image_pname_a @ X0 @ X2)) = $true)) )),
% 5.96/2.19 inference(cnf_transformation,[status(thm)],[f2476])).
% 5.96/2.19 thf(f2476,plain,(
% 5.96/2.19 ! [X0 : pname > x_a,X1 : x_a,X2 : pname > $o,X3 : pname] : (((member_pname @ X3 @ X2) != $true) | ((X0 @ X3) != X1) | ((member_a @ X1 @ (image_pname_a @ X0 @ X2)) = $true))),
% 5.96/2.19 inference(flattening,[status(thm)],[f2475])).
% 5.96/2.19 thf(f2475,plain,(
% 5.96/2.19 ! [X0 : pname > x_a,X1 : x_a,X2 : pname > $o,X3 : pname] : ((((member_a @ X1 @ (image_pname_a @ X0 @ X2)) = $true) | ((X0 @ X3) != X1)) | ((member_pname @ X3 @ X2) != $true))),
% 5.96/2.19 inference(ennf_transformation,[status(thm)],[f1411])).
% 5.96/2.19 thf(f1411,plain,(
% 5.96/2.19 ! [X0 : pname > x_a,X1 : x_a,X2 : pname > $o,X3 : pname] : (((member_pname @ X3 @ X2) = $true) => (((X0 @ X3) = X1) => ((member_a @ X1 @ (image_pname_a @ X0 @ X2)) = $true)))),
% 5.96/2.19 inference(fool_elimination,[status(thm)],[f1410])).
% 5.96/2.19 thf(f1410,plain,(
% 5.96/2.19 ! [X0 : pname > x_a,X1 : x_a,X2 : pname > $o,X3 : pname] : ((member_pname @ X3 @ X2) => (((X0 @ X3) = X1) => (member_a @ X1 @ (image_pname_a @ X0 @ X2))))),
% 5.96/2.19 inference(rectify,[status(thm)],[f313])).
% 5.96/2.19 thf(f313,axiom,(
% 5.96/2.19 ! [X131 : pname > x_a,X130 : x_a,X133 : pname > $o,X132 : pname] : ((member_pname @ X132 @ X133) => (((X131 @ X132) = X130) => (member_a @ X130 @ (image_pname_a @ X131 @ X133))))),
% 5.96/2.19 file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',fact_312_rev__image__eqI)).
% 5.96/2.19 thf(f5042,plain,(
% 5.96/2.19 ((member_a @ (mgt_call @ pn) @ (image_pname_a @ mgt_call @ u)) != $true)),
% 5.96/2.19 inference(subsumption_resolution,[status(thm)],[f5039,f3868])).
% 5.96/2.19 thf(f3868,plain,(
% 5.96/2.19 ((ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u)) = $true)),
% 5.96/2.19 inference(cnf_transformation,[status(thm)],[f1035])).
% 5.96/2.19 thf(f1035,plain,(
% 5.96/2.19 ((ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u)) = $true)),
% 5.96/2.19 inference(fool_elimination,[status(thm)],[f1034])).
% 5.96/2.19 thf(f1034,plain,(
% 5.96/2.19 (ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u))),
% 5.96/2.19 inference(rectify,[status(thm)],[f714])).
% 5.96/2.19 thf(f714,axiom,(
% 5.96/2.19 (ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u))),
% 5.96/2.19 file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',conj_1)).
% 5.96/2.19 thf(f5039,plain,(
% 5.96/2.19 ((member_a @ (mgt_call @ pn) @ (image_pname_a @ mgt_call @ u)) != $true) | ((ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u)) != $true)),
% 5.96/2.19 inference(trivial_inequality_removal,[status(thm)],[f5034])).
% 5.96/2.19 thf(f5034,plain,(
% 5.96/2.19 ((member_a @ (mgt_call @ pn) @ (image_pname_a @ mgt_call @ u)) != $true) | ($true != $true) | ((ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u)) != $true)),
% 5.96/2.19 inference(superposition,[status(thm)],[f3599,f3517])).
% 5.96/2.19 thf(f3517,plain,(
% 5.96/2.19 ( ! [X2 : x_a > $o,X0 : x_a,X1 : x_a > $o] : (((ord_less_eq_a_o @ (insert_a @ X0 @ X2) @ X1) = $true) | ($true != (ord_less_eq_a_o @ X2 @ X1)) | ($true != (member_a @ X0 @ X1))) )),
% 5.96/2.19 inference(cnf_transformation,[status(thm)],[f3016])).
% 5.96/2.19 thf(f3016,plain,(
% 5.96/2.19 ! [X0 : x_a,X1 : x_a > $o,X2 : x_a > $o] : ((((ord_less_eq_a_o @ (insert_a @ X0 @ X2) @ X1) = $true) | ($true != (ord_less_eq_a_o @ X2 @ X1)) | ($true != (member_a @ X0 @ X1))) & ((($true = (ord_less_eq_a_o @ X2 @ X1)) & ($true = (member_a @ X0 @ X1))) | ((ord_less_eq_a_o @ (insert_a @ X0 @ X2) @ X1) != $true)))),
% 5.96/2.19 inference(flattening,[status(thm)],[f3015])).
% 5.96/2.19 thf(f3015,plain,(
% 5.96/2.19 ! [X0 : x_a,X1 : x_a > $o,X2 : x_a > $o] : ((((ord_less_eq_a_o @ (insert_a @ X0 @ X2) @ X1) = $true) | (($true != (ord_less_eq_a_o @ X2 @ X1)) | ($true != (member_a @ X0 @ X1)))) & ((($true = (ord_less_eq_a_o @ X2 @ X1)) & ($true = (member_a @ X0 @ X1))) | ((ord_less_eq_a_o @ (insert_a @ X0 @ X2) @ X1) != $true)))),
% 5.96/2.19 inference(nnf_transformation,[status(thm)],[f1157])).
% 5.96/2.19 thf(f1157,plain,(
% 5.96/2.19 ! [X0 : x_a,X1 : x_a > $o,X2 : x_a > $o] : (((ord_less_eq_a_o @ (insert_a @ X0 @ X2) @ X1) = $true) <=> (($true = (ord_less_eq_a_o @ X2 @ X1)) & ($true = (member_a @ X0 @ X1))))),
% 5.96/2.19 inference(fool_elimination,[status(thm)],[f1156])).
% 5.96/2.19 thf(f1156,plain,(
% 5.96/2.19 ! [X0 : x_a,X1 : x_a > $o,X2 : x_a > $o] : (((ord_less_eq_a_o @ X2 @ X1) & (member_a @ X0 @ X1)) <=> (ord_less_eq_a_o @ (insert_a @ X0 @ X2) @ X1))),
% 5.96/2.19 inference(rectify,[status(thm)],[f325])).
% 5.96/2.19 thf(f325,axiom,(
% 5.96/2.19 ! [X138 : x_a,X140 : x_a > $o,X139 : x_a > $o] : (((ord_less_eq_a_o @ X139 @ X140) & (member_a @ X138 @ X140)) <=> (ord_less_eq_a_o @ (insert_a @ X138 @ X139) @ X140))),
% 5.96/2.19 file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',fact_324_insert__subset)).
% 5.96/2.19 thf(f3599,plain,(
% 5.96/2.19 ((ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u)) != $true)),
% 5.96/2.19 inference(cnf_transformation,[status(thm)],[f2261])).
% 5.96/2.19 thf(f2261,plain,(
% 5.96/2.19 ((ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u)) != $true)),
% 5.96/2.19 inference(flattening,[status(thm)],[f1677])).
% 5.96/2.19 thf(f1677,plain,(
% 5.96/2.19 ~((ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u)) = $true)),
% 5.96/2.19 inference(fool_elimination,[status(thm)],[f1676])).
% 5.96/2.19 thf(f1676,plain,(
% 5.96/2.19 ~(ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u))),
% 5.96/2.19 inference(rectify,[status(thm)],[f720])).
% 5.96/2.19 thf(f720,negated_conjecture,(
% 5.96/2.19 ~(ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u))),
% 5.96/2.19 inference(negated_conjecture,[status(cth)],[f719])).
% 5.96/2.19 thf(f719,conjecture,(
% 5.96/2.19 (ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u))),
% 5.96/2.19 file('/export/starexec/sandbox2/tmp/tmp.uWQ2IaO3Uc/DTF2THF_10942.p',conj_6)).
% 5.96/2.19 % SZS output end Proof for DTF2THF_10942
% 5.96/2.19 % (11234)------------------------------
% 5.96/2.19 % (11234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.19 % (11234)Termination reason: Refutation
% 5.96/2.19
% 5.96/2.19 % (11234)Memory used [KB]: 10490
% 5.96/2.19 % (11234)Time elapsed: 0.137 s
% 5.96/2.19 % (11234)Instructions burned: 404 (million)
% 5.96/2.19 % (11234)------------------------------
% 5.96/2.19 % (11234)------------------------------
% 5.96/2.19 % (11190)Success in time 0.528 s
%------------------------------------------------------------------------------