%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWW473^1 : 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 : n019.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 2.97s 1.61s
% Output : Refutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 265 ( 66 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 335 ( 34 ~; 24 |; 18 &; 252 @)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 120 ( 117 usr; 4 con; 0-4 aty)
% Number of variables : 55 ( 0 ^; 49 !; 6 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
x_a: $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
pname: $tType ).
thf(func_def_0,type,
x_a: $tType ).
thf(func_def_1,type,
pname: $tType ).
thf(func_def_2,type,
nat: $tType ).
thf(func_def_3,type,
finite_card_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > nat ).
thf(func_def_4,type,
finite221134632me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > nat ).
thf(func_def_5,type,
finite_card_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > nat ).
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,
finite1302365357_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > $o ).
thf(func_def_13,type,
finite1648353812_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > $o ).
thf(func_def_14,type,
finite1237261006_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > $o ).
thf(func_def_15,type,
finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
thf(func_def_16,type,
finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_17,type,
finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
thf(func_def_18,type,
finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_19,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(func_def_20,type,
finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
thf(func_def_21,type,
finite_finite_a: ( x_a > $o ) > $o ).
thf(func_def_22,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(func_def_23,type,
finite_finite_nat: ( nat > $o ) > $o ).
thf(func_def_24,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_25,type,
suc: nat > nat ).
thf(func_def_26,type,
ord_less_eq_a_o_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
thf(func_def_27,type,
ord_le1828183645_o_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_28,type,
ord_le124054423_o_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $o ).
thf(func_def_29,type,
ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_30,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_31,type,
ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_32,type,
ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(func_def_33,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_34,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_35,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_36,type,
collect_a_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
thf(func_def_37,type,
collect_pname_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_38,type,
collect_nat_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $o ).
thf(func_def_39,type,
collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_40,type,
collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_41,type,
collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_42,type,
collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(func_def_43,type,
collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_44,type,
collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(func_def_45,type,
collect_a: ( x_a > $o ) > x_a > $o ).
thf(func_def_46,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(func_def_47,type,
collect_nat: ( nat > $o ) > nat > $o ).
thf(func_def_48,type,
image_a_o_o_a: ( ( ( x_a > $o ) > $o ) > x_a ) > ( ( ( x_a > $o ) > $o ) > $o ) > x_a > $o ).
thf(func_def_49,type,
image_a_o_o_pname: ( ( ( x_a > $o ) > $o ) > pname ) > ( ( ( x_a > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_50,type,
image_a_o_o_nat: ( ( ( x_a > $o ) > $o ) > nat ) > ( ( ( x_a > $o ) > $o ) > $o ) > nat > $o ).
thf(func_def_51,type,
image_pname_o_o_a: ( ( ( pname > $o ) > $o ) > x_a ) > ( ( ( pname > $o ) > $o ) > $o ) > x_a > $o ).
thf(func_def_52,type,
image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_53,type,
image_pname_o_o_nat: ( ( ( pname > $o ) > $o ) > nat ) > ( ( ( pname > $o ) > $o ) > $o ) > nat > $o ).
thf(func_def_54,type,
image_nat_o_o_a: ( ( ( nat > $o ) > $o ) > x_a ) > ( ( ( nat > $o ) > $o ) > $o ) > x_a > $o ).
thf(func_def_55,type,
image_nat_o_o_pname: ( ( ( nat > $o ) > $o ) > pname ) > ( ( ( nat > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_56,type,
image_nat_o_o_nat: ( ( ( nat > $o ) > $o ) > nat ) > ( ( ( nat > $o ) > $o ) > $o ) > nat > $o ).
thf(func_def_57,type,
image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
thf(func_def_58,type,
image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
thf(func_def_59,type,
image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
thf(func_def_60,type,
image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
thf(func_def_61,type,
image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_62,type,
image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
thf(func_def_63,type,
image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
thf(func_def_64,type,
image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
thf(func_def_65,type,
image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $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_o: ( pname > ( x_a > $o ) > $o ) > ( pname > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_70,type,
image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_71,type,
image_pname_nat_o_o: ( pname > ( nat > $o ) > $o ) > ( pname > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_72,type,
image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
thf(func_def_73,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_74,type,
image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
thf(func_def_75,type,
image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
thf(func_def_76,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(func_def_77,type,
image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
thf(func_def_78,type,
image_nat_a_o_o: ( nat > ( x_a > $o ) > $o ) > ( nat > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_79,type,
image_nat_pname_o_o: ( nat > ( pname > $o ) > $o ) > ( nat > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_80,type,
image_nat_nat_o_o: ( nat > ( nat > $o ) > $o ) > ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_81,type,
image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
thf(func_def_82,type,
image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
thf(func_def_83,type,
image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_84,type,
image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
thf(func_def_85,type,
image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
thf(func_def_86,type,
insert_a_o_o: ( ( x_a > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_87,type,
insert_pname_o_o: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_88,type,
insert_nat_o_o: ( ( nat > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_89,type,
insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(func_def_90,type,
insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_91,type,
insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(func_def_92,type,
insert_a: x_a > ( x_a > $o ) > x_a > $o ).
thf(func_def_93,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(func_def_94,type,
insert_nat: nat > ( nat > $o ) > nat > $o ).
thf(func_def_95,type,
member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_96,type,
member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_97,type,
member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_98,type,
member_a: x_a > ( x_a > $o ) > $o ).
thf(func_def_99,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(func_def_100,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(func_def_101,type,
g: x_a > $o ).
thf(func_def_102,type,
p: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(func_def_103,type,
u: pname > $o ).
thf(func_def_104,type,
mgt_call: pname > x_a ).
thf(func_def_105,type,
na: nat ).
thf(func_def_106,type,
pn: pname ).
thf(func_def_117,type,
sK0: ( x_a > $o ) > ( x_a > $o ) > x_a ).
thf(func_def_118,type,
sK1: ( x_a > $o ) > ( pname > $o ) > ( pname > x_a ) > pname > $o ).
thf(func_def_119,type,
sK2: ( pname > $o ) > ( pname > x_a ) > x_a > pname ).
thf(func_def_120,type,
sK3: nat > nat ).
thf(func_def_121,type,
sK4: ( pname > $o ) > ( x_a > $o ) > ( pname > x_a ) > pname ).
thf(func_def_122,type,
sK5: ( nat > pname > $o ) > nat ).
thf(func_def_123,type,
sK6: ( pname > x_a ) > x_a > ( pname > $o ) > pname ).
thf(func_def_124,type,
sK7: ( nat > $o ) > nat ).
thf(func_def_125,type,
sK8: ( pname > x_a ) > ( x_a > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_126,type,
sK9: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_127,type,
sK10: ( nat > x_a > $o ) > nat ).
thf(func_def_128,type,
sK11: ( nat > nat ) > nat ).
thf(func_def_130,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f1384,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1383,f1082]) ).
thf(f1082,plain,
( ( member_pname @ pn @ u )
= $true ),
inference(cnf_transformation,[status(thm)],[f579]) ).
thf(f579,plain,
( ( member_pname @ pn @ u )
= $true ),
inference(fool_elimination,[status(thm)],[f578]) ).
thf(f578,plain,
member_pname @ pn @ u,
inference(rectify,[status(thm)],[f305]) ).
thf(f305,axiom,
member_pname @ pn @ u,
file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',conj_4) ).
thf(f1383,plain,
( ( member_pname @ pn @ u )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1377]) ).
thf(f1377,plain,
( ( ( member_pname @ pn @ u )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1372,f1252]) ).
thf(f1252,plain,
! [X2: pname > x_a,X3: pname,X0: pname > $o] :
( ( ( member_a @ ( X2 @ X3 ) @ ( image_pname_a @ X2 @ X0 ) )
= $true )
| ( ( member_pname @ X3 @ X0 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f1163]) ).
thf(f1163,plain,
! [X2: pname > x_a,X3: pname,X0: pname > $o,X1: x_a] :
( ( ( member_a @ X1 @ ( image_pname_a @ X2 @ X0 ) )
= $true )
| ( ( X2 @ X3 )
!= X1 )
| ( ( member_pname @ X3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1050]) ).
thf(f1050,plain,
! [X0: pname > $o,X1: x_a,X2: pname > x_a] :
( ( ( ( member_a @ X1 @ ( image_pname_a @ X2 @ X0 ) )
= $true )
| ! [X3: pname] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( member_pname @ X3 @ X0 )
!= $true ) ) )
& ( ( ( ( X2 @ ( sK6 @ X2 @ X1 @ X0 ) )
= X1 )
& ( $true
= ( member_pname @ ( sK6 @ X2 @ X1 @ X0 ) @ X0 ) ) )
| ( ( member_a @ X1 @ ( image_pname_a @ X2 @ X0 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f1048,f1049]) ).
thf(f1049,plain,
! [X0: pname > $o,X1: x_a,X2: pname > x_a] :
( ? [X4: pname] :
( ( ( X2 @ X4 )
= X1 )
& ( ( member_pname @ X4 @ X0 )
= $true ) )
=> ( ( ( X2 @ ( sK6 @ X2 @ X1 @ X0 ) )
= X1 )
& ( $true
= ( member_pname @ ( sK6 @ X2 @ X1 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1048,plain,
! [X0: pname > $o,X1: x_a,X2: pname > x_a] :
( ( ( ( member_a @ X1 @ ( image_pname_a @ X2 @ X0 ) )
= $true )
| ! [X3: pname] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( member_pname @ X3 @ X0 )
!= $true ) ) )
& ( ? [X4: pname] :
( ( ( X2 @ X4 )
= X1 )
& ( ( member_pname @ X4 @ X0 )
= $true ) )
| ( ( member_a @ X1 @ ( image_pname_a @ X2 @ X0 ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f1047]) ).
thf(f1047,plain,
! [X0: pname > $o,X1: x_a,X2: pname > x_a] :
( ( ( ( member_a @ X1 @ ( image_pname_a @ X2 @ X0 ) )
= $true )
| ! [X3: pname] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( member_pname @ X3 @ X0 )
!= $true ) ) )
& ( ? [X3: pname] :
( ( ( X2 @ X3 )
= X1 )
& ( ( member_pname @ X3 @ X0 )
= $true ) )
| ( ( member_a @ X1 @ ( image_pname_a @ X2 @ X0 ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f747]) ).
thf(f747,plain,
! [X0: pname > $o,X1: x_a,X2: pname > x_a] :
( ( ( member_a @ X1 @ ( image_pname_a @ X2 @ X0 ) )
= $true )
<=> ? [X3: pname] :
( ( ( X2 @ X3 )
= X1 )
& ( ( member_pname @ X3 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f746]) ).
thf(f746,plain,
! [X0: pname > $o,X1: x_a,X2: pname > x_a] :
( ( member_a @ X1 @ ( image_pname_a @ X2 @ X0 ) )
<=> ? [X3: pname] :
( ( ( X2 @ X3 )
= X1 )
& ( member_pname @ X3 @ X0 ) ) ),
inference(rectify,[status(thm)],[f261]) ).
thf(f261,axiom,
! [X123: pname > $o,X121: x_a,X122: pname > x_a] :
( ( member_a @ X121 @ ( image_pname_a @ X122 @ X123 ) )
<=> ? [X22: pname] :
( ( ( X122 @ X22 )
= X121 )
& ( member_pname @ X22 @ X123 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',fact_260_image__iff) ).
thf(f1372,plain,
( $true
!= ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) ),
inference(subsumption_resolution,[status(thm)],[f1371,f1109]) ).
thf(f1109,plain,
( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f317]) ).
thf(f317,plain,
( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
= $true ),
inference(fool_elimination,[status(thm)],[f316]) ).
thf(f316,plain,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
inference(rectify,[status(thm)],[f302]) ).
thf(f302,axiom,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',conj_1) ).
thf(f1371,plain,
( ( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
!= $true )
| ( $true
!= ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1368]) ).
thf(f1368,plain,
( ( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
!= $true )
| ( $true
!= ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1165,f1224]) ).
thf(f1224,plain,
! [X2: x_a,X0: x_a > $o,X1: x_a > $o] :
( ( $true
= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X1 ) @ X0 ) )
| ( ( ord_less_eq_a_o @ X1 @ X0 )
!= $true )
| ( ( member_a @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1066]) ).
thf(f1066,plain,
! [X0: x_a > $o,X1: x_a > $o,X2: x_a] :
( ( ( $true
= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X1 ) @ X0 ) )
| ( ( ord_less_eq_a_o @ X1 @ X0 )
!= $true )
| ( ( member_a @ X2 @ X0 )
!= $true ) )
& ( ( ( ( ord_less_eq_a_o @ X1 @ X0 )
= $true )
& ( ( member_a @ X2 @ X0 )
= $true ) )
| ( $true
!= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X1 ) @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f1065]) ).
thf(f1065,plain,
! [X0: x_a > $o,X1: x_a > $o,X2: x_a] :
( ( ( $true
= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X1 ) @ X0 ) )
| ( ( ord_less_eq_a_o @ X1 @ X0 )
!= $true )
| ( ( member_a @ X2 @ X0 )
!= $true ) )
& ( ( ( ( ord_less_eq_a_o @ X1 @ X0 )
= $true )
& ( ( member_a @ X2 @ X0 )
= $true ) )
| ( $true
!= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X1 ) @ X0 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f581]) ).
thf(f581,plain,
! [X0: x_a > $o,X1: x_a > $o,X2: x_a] :
( ( $true
= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X1 ) @ X0 ) )
<=> ( ( ( ord_less_eq_a_o @ X1 @ X0 )
= $true )
& ( ( member_a @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f580]) ).
thf(f580,plain,
! [X0: x_a > $o,X1: x_a > $o,X2: x_a] :
( ( ( ord_less_eq_a_o @ X1 @ X0 )
& ( member_a @ X2 @ X0 ) )
<=> ( ord_less_eq_a_o @ ( insert_a @ X2 @ X1 ) @ X0 ) ),
inference(rectify,[status(thm)],[f275]) ).
thf(f275,axiom,
! [X137: x_a > $o,X136: x_a > $o,X135: x_a] :
( ( ( ord_less_eq_a_o @ X136 @ X137 )
& ( member_a @ X135 @ X137 ) )
<=> ( ord_less_eq_a_o @ ( insert_a @ X135 @ X136 ) @ X137 ) ),
file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',fact_274_insert__subset) ).
thf(f1165,plain,
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f885]) ).
thf(f885,plain,
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(flattening,[status(thm)],[f809]) ).
thf(f809,plain,
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f808]) ).
thf(f808,plain,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(rectify,[status(thm)],[f308]) ).
thf(f308,negated_conjecture,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(negated_conjecture,[status(cth)],[f307]) ).
thf(f307,conjecture,
ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',conj_6) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473^1 : TPTP v9.2.1. Released v5.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 13:40:09 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SWW473^1 : TPTP v9.2.1. Released v5.3.0.
% 0.29/0.46 % Domain : Software Verification
% 0.29/0.46 % Problem : Hoare's Logic with Procedures line 383, 100 axioms selected
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.29/0.46 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bla11]
% 0.29/0.46 % Names : hoare_100_thf_l383 [Bla11]
% 0.29/0.46
% 0.29/0.46 % Status : ContradictoryAxioms
% 0.29/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.43 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v6.0.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.80 v5.3.0
% 0.29/0.46 % Syntax : Number of formulae : 414 ( 50 unt; 107 typ; 0 def)
% 0.29/0.46 % Number of atoms : 1063 ( 137 equ; 37 cnn)
% 0.29/0.46 % Maximal formula atoms : 9 ( 3 avg)
% 0.29/0.46 % Number of connectives : 2278 ( 49 ~; 32 |; 30 &;1806 @)
% 0.29/0.46 % ( 42 <=>; 319 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 15 ( 7 avg)
% 0.29/0.46 % Number of types : 4 ( 3 usr)
% 0.29/0.46 % Number of type conns : 1252 (1252 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 109 ( 104 usr; 6 con; 0-3 aty)
% 0.29/0.46 % Number of variables : 706 ( 42 ^; 658 !; 6 ?; 706 :)
% 0.29/0.46 % SPC : TH0_CAX_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.46 % 2011-08-09 19:22:04
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 %----Should-be-implicit typings (3)
% 0.29/0.46 thf(ty_ty_t__a,type,
% 0.29/0.46 x_a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_ty_tc__Com__Opname,type,
% 0.29/0.46 pname: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_ty_tc__Nat__Onat,type,
% 0.29/0.46 nat: $tType ).
% 0.29/0.46
% 0.29/0.46 %----Explicit typings (104)
% 0.29/0.46 thf(sy_c_Finite__Set_Ocard_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 finite_card_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ocard_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 finite221134632me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ocard_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 finite_card_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > nat ).
% 0.29/0.46
% 0.29/0.46 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_I_062_It__a_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 finite1302365357_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo,type,
% 0.29/0.46 finite1648353812_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 finite1237261006_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > $o ).
% 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_Nat_OSuc,type,
% 0.29/0.46 suc: nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_E,type,
% 0.29/0.46 ord_less_eq_a_o_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J,type,
% 0.29/0.46 ord_le1828183645_o_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M,type,
% 0.29/0.46 ord_le124054423_o_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $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_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_I_062_It__a_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 collect_a_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 collect_pname_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 collect_nat_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $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_I_062_It__a_M_Eo_J_M_Eo_J_000t__a,type,
% 0.29/0.46 image_a_o_o_a: ( ( ( x_a > $o ) > $o ) > x_a ) > ( ( ( x_a > $o ) > $o ) > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 0.29/0.46 image_a_o_o_pname: ( ( ( x_a > $o ) > $o ) > pname ) > ( ( ( x_a > $o ) > $o ) > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000tc__Nat__Onat,type,
% 0.29/0.46 image_a_o_o_nat: ( ( ( x_a > $o ) > $o ) > nat ) > ( ( ( x_a > $o ) > $o ) > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000t__a,type,
% 0.29/0.46 image_pname_o_o_a: ( ( ( pname > $o ) > $o ) > x_a ) > ( ( ( pname > $o ) > $o ) > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 0.29/0.46 image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Nat__Onat,type,
% 0.29/0.46 image_pname_o_o_nat: ( ( ( pname > $o ) > $o ) > nat ) > ( ( ( pname > $o ) > $o ) > $o ) > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000t__a,type,
% 0.29/0.46 image_nat_o_o_a: ( ( ( nat > $o ) > $o ) > x_a ) > ( ( ( nat > $o ) > $o ) > $o ) > x_a > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 0.29/0.46 image_nat_o_o_pname: ( ( ( nat > $o ) > $o ) > pname ) > ( ( ( nat > $o ) > $o ) > $o ) > pname > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000tc__Nat__Onat,type,
% 0.29/0.46 image_nat_o_o_nat: ( ( ( nat > $o ) > $o ) > nat ) > ( ( ( nat > $o ) > $o ) > $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_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_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 image_pname_a_o_o: ( pname > ( x_a > $o ) > $o ) > ( pname > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 image_pname_nat_o_o: ( pname > ( nat > $o ) > $o ) > ( pname > $o ) > ( ( nat > $o ) > $o ) > $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_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 image_nat_a_o_o: ( nat > ( x_a > $o ) > $o ) > ( nat > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 image_nat_pname_o_o: ( nat > ( pname > $o ) > $o ) > ( nat > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 image_nat_nat_o_o: ( nat > ( nat > $o ) > $o ) > ( nat > $o ) > ( ( nat > $o ) > $o ) > $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_Oinsert_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 insert_a_o_o: ( ( x_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_Oinsert_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 insert_pname_o_o: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.29/0.46 insert_nat_o_o: ( ( nat > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $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_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__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 %----Relevant facts (300)
% 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_59: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ A_59 )
% 0.29/0.46 => ( finite_finite_nat_o
% 0.29/0.46 @ ( collect_nat_o
% 0.29/0.46 @ ^ [B_38: nat > $o] : ( ord_less_eq_nat_o @ B_38 @ A_59 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_2_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_59: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ A_59 )
% 0.29/0.46 => ( finite297249702name_o
% 0.29/0.46 @ ( collect_pname_o
% 0.29/0.46 @ ^ [B_38: pname > $o] : ( ord_less_eq_pname_o @ B_38 @ A_59 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_3_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_59: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ A_59 )
% 0.29/0.46 => ( finite_finite_a_o
% 0.29/0.46 @ ( collect_a_o
% 0.29/0.46 @ ^ [B_38: x_a > $o] : ( ord_less_eq_a_o @ B_38 @ A_59 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_4_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_59: ( ( nat > $o ) > $o ) > $o] :
% 0.29/0.46 ( ( finite1676163439at_o_o @ A_59 )
% 0.29/0.46 => ( finite1237261006_o_o_o
% 0.29/0.46 @ ( collect_nat_o_o_o
% 0.29/0.46 @ ^ [B_38: ( ( nat > $o ) > $o ) > $o] : ( ord_le124054423_o_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_5_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_59: ( ( pname > $o ) > $o ) > $o] :
% 0.29/0.46 ( ( finite1066544169me_o_o @ A_59 )
% 0.29/0.46 => ( finite1648353812_o_o_o
% 0.29/0.46 @ ( collect_pname_o_o_o
% 0.29/0.46 @ ^ [B_38: ( ( pname > $o ) > $o ) > $o] : ( ord_le1828183645_o_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_6_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_59: ( ( x_a > $o ) > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o_o @ A_59 )
% 0.29/0.46 => ( finite1302365357_o_o_o
% 0.29/0.46 @ ( collect_a_o_o_o
% 0.29/0.46 @ ^ [B_38: ( ( x_a > $o ) > $o ) > $o] : ( ord_less_eq_a_o_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_7_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_59: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ A_59 )
% 0.29/0.46 => ( finite_finite_a_o_o
% 0.29/0.46 @ ( collect_a_o_o
% 0.29/0.46 @ ^ [B_38: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_8_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_59: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ A_59 )
% 0.29/0.46 => ( finite1066544169me_o_o
% 0.29/0.46 @ ( collect_pname_o_o
% 0.29/0.46 @ ^ [B_38: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_9_finite__Collect__subsets,axiom,
% 0.29/0.46 ! [A_59: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ A_59 )
% 0.29/0.46 => ( finite1676163439at_o_o
% 0.29/0.46 @ ( collect_nat_o_o
% 0.29/0.46 @ ^ [B_38: ( nat > $o ) > $o] : ( ord_less_eq_nat_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_10_finite__imageI,axiom,
% 0.29/0.46 ! [H: pname > x_a,F_15: pname > $o] :
% 0.29/0.46 ( ( finite_finite_pname @ F_15 )
% 0.29/0.46 => ( finite_finite_a @ ( image_pname_a @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_11_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( ( nat > $o ) > $o ) > nat,F_15: ( ( nat > $o ) > $o ) > $o] :
% 0.29/0.46 ( ( finite1676163439at_o_o @ F_15 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_nat_o_o_nat @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_12_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( ( pname > $o ) > $o ) > nat,F_15: ( ( pname > $o ) > $o ) > $o] :
% 0.29/0.46 ( ( finite1066544169me_o_o @ F_15 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_pname_o_o_nat @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_13_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( ( x_a > $o ) > $o ) > nat,F_15: ( ( x_a > $o ) > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o_o @ F_15 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_a_o_o_nat @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_14_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( x_a > $o ) > nat,F_15: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ F_15 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_a_o_nat @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_15_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( pname > $o ) > nat,F_15: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ F_15 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_pname_o_nat @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_16_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( nat > $o ) > nat,F_15: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ F_15 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_nat_o_nat @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_17_finite__imageI,axiom,
% 0.29/0.46 ! [H: x_a > nat,F_15: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ F_15 )
% 0.29/0.46 => ( finite_finite_nat @ ( image_a_nat @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_18_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( ( nat > $o ) > $o ) > pname,F_15: ( ( nat > $o ) > $o ) > $o] :
% 0.29/0.46 ( ( finite1676163439at_o_o @ F_15 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_nat_o_o_pname @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_19_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( ( pname > $o ) > $o ) > pname,F_15: ( ( pname > $o ) > $o ) > $o] :
% 0.29/0.46 ( ( finite1066544169me_o_o @ F_15 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_471733107_pname @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_20_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( ( x_a > $o ) > $o ) > pname,F_15: ( ( x_a > $o ) > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o_o @ F_15 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_a_o_o_pname @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_21_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( x_a > $o ) > pname,F_15: ( x_a > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_a_o @ F_15 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_a_o_pname @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_22_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( pname > $o ) > pname,F_15: ( pname > $o ) > $o] :
% 0.29/0.46 ( ( finite297249702name_o @ F_15 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_23_finite__imageI,axiom,
% 0.29/0.46 ! [H: ( nat > $o ) > pname,F_15: ( nat > $o ) > $o] :
% 0.29/0.46 ( ( finite_finite_nat_o @ F_15 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_nat_o_pname @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_24_finite__imageI,axiom,
% 0.29/0.46 ! [H: x_a > pname,F_15: x_a > $o] :
% 0.29/0.46 ( ( finite_finite_a @ F_15 )
% 0.29/0.46 => ( finite_finite_pname @ ( image_a_pname @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_25_finite__imageI,axiom,
% 0.29/0.46 ! [H: nat > ( nat > $o ) > $o,F_15: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ F_15 )
% 0.29/0.46 => ( finite1676163439at_o_o @ ( image_nat_nat_o_o @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_26_finite__imageI,axiom,
% 0.29/0.46 ! [H: nat > ( pname > $o ) > $o,F_15: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ F_15 )
% 0.29/0.46 => ( finite1066544169me_o_o @ ( image_nat_pname_o_o @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_27_finite__imageI,axiom,
% 0.29/0.46 ! [H: nat > ( x_a > $o ) > $o,F_15: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ F_15 )
% 0.29/0.46 => ( finite_finite_a_o_o @ ( image_nat_a_o_o @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_28_finite__imageI,axiom,
% 0.29/0.46 ! [H: nat > x_a > $o,F_15: nat > $o] :
% 0.29/0.46 ( ( finite_finite_nat @ F_15 )
% 0.29/0.46 => ( finite_finite_a_o @ ( image_nat_a_o @ H @ F_15 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(fact_29_finite__imageI,axiom,
% 0.29/0.47 ! [H: nat > pname > $o,F_15: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ F_15 )
% 0.29/0.47 => ( finite297249702name_o @ ( image_nat_pname_o @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_30_finite__imageI,axiom,
% 0.29/0.47 ! [H: nat > nat > $o,F_15: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ F_15 )
% 0.29/0.47 => ( finite_finite_nat_o @ ( image_nat_nat_o @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_31_finite__imageI,axiom,
% 0.29/0.47 ! [H: nat > x_a,F_15: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ F_15 )
% 0.29/0.47 => ( finite_finite_a @ ( image_nat_a @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_32_finite__imageI,axiom,
% 0.29/0.47 ! [H: pname > ( nat > $o ) > $o,F_15: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_15 )
% 0.29/0.47 => ( finite1676163439at_o_o @ ( image_pname_nat_o_o @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_33_finite__imageI,axiom,
% 0.29/0.47 ! [H: pname > ( pname > $o ) > $o,F_15: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_15 )
% 0.29/0.47 => ( finite1066544169me_o_o @ ( image_504089495me_o_o @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_34_finite__imageI,axiom,
% 0.29/0.47 ! [H: pname > ( x_a > $o ) > $o,F_15: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_15 )
% 0.29/0.47 => ( finite_finite_a_o_o @ ( image_pname_a_o_o @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_35_finite__imageI,axiom,
% 0.29/0.47 ! [H: pname > x_a > $o,F_15: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_15 )
% 0.29/0.47 => ( finite_finite_a_o @ ( image_pname_a_o @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_36_finite__imageI,axiom,
% 0.29/0.47 ! [H: pname > pname > $o,F_15: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_15 )
% 0.29/0.47 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_37_finite__imageI,axiom,
% 0.29/0.47 ! [H: pname > nat > $o,F_15: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_15 )
% 0.29/0.47 => ( finite_finite_nat_o @ ( image_pname_nat_o @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_38_finite__imageI,axiom,
% 0.29/0.47 ! [H: pname > pname,F_15: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_15 )
% 0.29/0.47 => ( finite_finite_pname @ ( image_pname_pname @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_39_finite__imageI,axiom,
% 0.29/0.47 ! [H: x_a > x_a,F_15: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ F_15 )
% 0.29/0.47 => ( finite_finite_a @ ( image_a_a @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_40_finite__imageI,axiom,
% 0.29/0.47 ! [H: ( nat > $o ) > x_a,F_15: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ F_15 )
% 0.29/0.47 => ( finite_finite_a @ ( image_nat_o_a @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_41_finite__imageI,axiom,
% 0.29/0.47 ! [H: ( pname > $o ) > x_a,F_15: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ F_15 )
% 0.29/0.47 => ( finite_finite_a @ ( image_pname_o_a @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_42_finite__imageI,axiom,
% 0.29/0.47 ! [H: ( x_a > $o ) > x_a,F_15: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ F_15 )
% 0.29/0.47 => ( finite_finite_a @ ( image_a_o_a @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_43_finite__imageI,axiom,
% 0.29/0.47 ! [H: pname > nat,F_15: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ F_15 )
% 0.29/0.47 => ( finite_finite_nat @ ( image_pname_nat @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_44_finite__imageI,axiom,
% 0.29/0.47 ! [H: nat > pname,F_15: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ F_15 )
% 0.29/0.47 => ( finite_finite_pname @ ( image_nat_pname @ H @ F_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_45_finite_OinsertI,axiom,
% 0.29/0.47 ! [A_58: x_a,A_57: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ A_57 )
% 0.29/0.47 => ( finite_finite_a @ ( insert_a @ A_58 @ A_57 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_46_finite_OinsertI,axiom,
% 0.29/0.47 ! [A_58: nat,A_57: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ A_57 )
% 0.29/0.47 => ( finite_finite_nat @ ( insert_nat @ A_58 @ A_57 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_47_finite_OinsertI,axiom,
% 0.29/0.47 ! [A_58: pname,A_57: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_57 )
% 0.29/0.47 => ( finite_finite_pname @ ( insert_pname @ A_58 @ A_57 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_48_finite_OinsertI,axiom,
% 0.29/0.47 ! [A_58: ( nat > $o ) > $o,A_57: ( ( nat > $o ) > $o ) > $o] :
% 0.29/0.47 ( ( finite1676163439at_o_o @ A_57 )
% 0.29/0.47 => ( finite1676163439at_o_o @ ( insert_nat_o_o @ A_58 @ A_57 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_49_finite_OinsertI,axiom,
% 0.29/0.47 ! [A_58: ( pname > $o ) > $o,A_57: ( ( pname > $o ) > $o ) > $o] :
% 0.29/0.47 ( ( finite1066544169me_o_o @ A_57 )
% 0.29/0.47 => ( finite1066544169me_o_o @ ( insert_pname_o_o @ A_58 @ A_57 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_50_finite_OinsertI,axiom,
% 0.29/0.47 ! [A_58: ( x_a > $o ) > $o,A_57: ( ( x_a > $o ) > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o_o @ A_57 )
% 0.29/0.47 => ( finite_finite_a_o_o @ ( insert_a_o_o @ A_58 @ A_57 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_51_finite_OinsertI,axiom,
% 0.29/0.47 ! [A_58: x_a > $o,A_57: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ A_57 )
% 0.29/0.47 => ( finite_finite_a_o @ ( insert_a_o @ A_58 @ A_57 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_52_finite_OinsertI,axiom,
% 0.29/0.47 ! [A_58: pname > $o,A_57: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ A_57 )
% 0.29/0.47 => ( finite297249702name_o @ ( insert_pname_o @ A_58 @ A_57 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_53_finite_OinsertI,axiom,
% 0.29/0.47 ! [A_58: nat > $o,A_57: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ A_57 )
% 0.29/0.47 => ( finite_finite_nat_o @ ( insert_nat_o @ A_58 @ A_57 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_54_card__image__le,axiom,
% 0.29/0.47 ! [F_14: pname > nat,A_56: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_55_card__image__le,axiom,
% 0.29/0.47 ! [F_14: x_a > nat,A_56: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ F_14 @ A_56 ) ) @ ( finite_card_a @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_56_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( nat > $o ) > nat,A_56: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_o_nat @ F_14 @ A_56 ) ) @ ( finite_card_nat_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_57_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( pname > $o ) > nat,A_56: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_o_nat @ F_14 @ A_56 ) ) @ ( finite_card_pname_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_58_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( x_a > $o ) > nat,A_56: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ F_14 @ A_56 ) ) @ ( finite_card_a_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_59_card__image__le,axiom,
% 0.29/0.47 ! [F_14: x_a > pname,A_56: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ F_14 @ A_56 ) ) @ ( finite_card_a @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_60_card__image__le,axiom,
% 0.29/0.47 ! [F_14: nat > pname,A_56: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_pname @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_61_card__image__le,axiom,
% 0.29/0.47 ! [F_14: pname > x_a,A_56: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_62_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( ( nat > $o ) > $o ) > x_a,A_56: ( ( nat > $o ) > $o ) > $o] :
% 0.29/0.47 ( ( finite1676163439at_o_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_o_a @ F_14 @ A_56 ) ) @ ( finite_card_nat_o_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_63_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( ( pname > $o ) > $o ) > x_a,A_56: ( ( pname > $o ) > $o ) > $o] :
% 0.29/0.47 ( ( finite1066544169me_o_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_o_a @ F_14 @ A_56 ) ) @ ( finite221134632me_o_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_64_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( ( x_a > $o ) > $o ) > x_a,A_56: ( ( x_a > $o ) > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_o_a @ F_14 @ A_56 ) ) @ ( finite_card_a_o_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_65_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( x_a > $o ) > x_a,A_56: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ F_14 @ A_56 ) ) @ ( finite_card_a_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_66_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( pname > $o ) > x_a,A_56: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_a @ F_14 @ A_56 ) ) @ ( finite_card_pname_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_67_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( nat > $o ) > x_a,A_56: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_a @ F_14 @ A_56 ) ) @ ( finite_card_nat_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_68_card__image__le,axiom,
% 0.29/0.47 ! [F_14: x_a > x_a,A_56: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ F_14 @ A_56 ) ) @ ( finite_card_a @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_69_card__image__le,axiom,
% 0.29/0.47 ! [F_14: pname > pname,A_56: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_70_card__image__le,axiom,
% 0.29/0.47 ! [F_14: pname > nat > $o,A_56: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat_o @ ( image_pname_nat_o @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_71_card__image__le,axiom,
% 0.29/0.47 ! [F_14: pname > pname > $o,A_56: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname_o @ ( image_pname_pname_o @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_72_card__image__le,axiom,
% 0.29/0.47 ! [F_14: pname > x_a > $o,A_56: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a_o @ ( image_pname_a_o @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_73_card__image__le,axiom,
% 0.29/0.47 ! [F_14: nat > x_a,A_56: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_a @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_74_card__image__le,axiom,
% 0.29/0.47 ! [F_14: nat > nat > $o,A_56: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat_o @ ( image_nat_nat_o @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_75_card__image__le,axiom,
% 0.29/0.47 ! [F_14: nat > pname > $o,A_56: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname_o @ ( image_nat_pname_o @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_76_card__image__le,axiom,
% 0.29/0.47 ! [F_14: nat > x_a > $o,A_56: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a_o @ ( image_nat_a_o @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_77_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( nat > $o ) > pname,A_56: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_o_pname @ F_14 @ A_56 ) ) @ ( finite_card_nat_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_78_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( pname > $o ) > pname,A_56: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_o_pname @ F_14 @ A_56 ) ) @ ( finite_card_pname_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_79_card__image__le,axiom,
% 0.29/0.47 ! [F_14: ( x_a > $o ) > pname,A_56: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ A_56 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_o_pname @ F_14 @ A_56 ) ) @ ( finite_card_a_o @ A_56 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_80_card__mono,axiom,
% 0.29/0.47 ! [A_55: ( nat > $o ) > $o,B_37: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ B_37 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o_o @ A_55 @ B_37 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_55 ) @ ( finite_card_nat_o @ B_37 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_81_card__mono,axiom,
% 0.29/0.47 ! [A_55: ( pname > $o ) > $o,B_37: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ B_37 )
% 0.29/0.47 => ( ( ord_le1205211808me_o_o @ A_55 @ B_37 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_55 ) @ ( finite_card_pname_o @ B_37 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_82_card__mono,axiom,
% 0.29/0.47 ! [A_55: ( x_a > $o ) > $o,B_37: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ B_37 )
% 0.29/0.47 => ( ( ord_less_eq_a_o_o @ A_55 @ B_37 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_55 ) @ ( finite_card_a_o @ B_37 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_83_card__mono,axiom,
% 0.29/0.47 ! [A_55: pname > $o,B_37: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ B_37 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ A_55 @ B_37 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname @ A_55 ) @ ( finite_card_pname @ B_37 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_84_card__mono,axiom,
% 0.29/0.47 ! [A_55: x_a > $o,B_37: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ B_37 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ A_55 @ B_37 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ A_55 ) @ ( finite_card_a @ B_37 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_85_card__mono,axiom,
% 0.29/0.47 ! [A_55: nat > $o,B_37: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ B_37 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ A_55 @ B_37 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat @ A_55 ) @ ( finite_card_nat @ B_37 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_86_card__seteq,axiom,
% 0.29/0.47 ! [A_54: ( nat > $o ) > $o,B_36: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o_o @ A_54 @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( finite_card_nat_o @ B_36 ) @ ( finite_card_nat_o @ A_54 ) )
% 0.29/0.47 => ( A_54 = B_36 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_87_card__seteq,axiom,
% 0.29/0.47 ! [A_54: ( pname > $o ) > $o,B_36: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ B_36 )
% 0.29/0.47 => ( ( ord_le1205211808me_o_o @ A_54 @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( finite_card_pname_o @ B_36 ) @ ( finite_card_pname_o @ A_54 ) )
% 0.29/0.47 => ( A_54 = B_36 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_88_card__seteq,axiom,
% 0.29/0.47 ! [A_54: ( x_a > $o ) > $o,B_36: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_a_o_o @ A_54 @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( finite_card_a_o @ B_36 ) @ ( finite_card_a_o @ A_54 ) )
% 0.29/0.47 => ( A_54 = B_36 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_89_card__seteq,axiom,
% 0.29/0.47 ! [A_54: pname > $o,B_36: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ A_54 @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( finite_card_pname @ B_36 ) @ ( finite_card_pname @ A_54 ) )
% 0.29/0.47 => ( A_54 = B_36 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_90_card__seteq,axiom,
% 0.29/0.47 ! [A_54: x_a > $o,B_36: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ A_54 @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( finite_card_a @ B_36 ) @ ( finite_card_a @ A_54 ) )
% 0.29/0.47 => ( A_54 = B_36 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_91_card__seteq,axiom,
% 0.29/0.47 ! [A_54: nat > $o,B_36: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ A_54 @ B_36 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B_36 ) @ ( finite_card_nat @ A_54 ) )
% 0.29/0.47 => ( A_54 = B_36 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_92_card__insert__le,axiom,
% 0.29/0.47 ! [X_19: nat > $o,A_53: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ A_53 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_53 ) @ ( finite_card_nat_o @ ( insert_nat_o @ X_19 @ A_53 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_93_card__insert__le,axiom,
% 0.29/0.47 ! [X_19: pname > $o,A_53: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ A_53 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_53 ) @ ( finite_card_pname_o @ ( insert_pname_o @ X_19 @ A_53 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_94_card__insert__le,axiom,
% 0.29/0.47 ! [X_19: x_a > $o,A_53: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ A_53 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_53 ) @ ( finite_card_a_o @ ( insert_a_o @ X_19 @ A_53 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_95_card__insert__le,axiom,
% 0.29/0.47 ! [X_19: pname,A_53: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_53 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_pname @ A_53 ) @ ( finite_card_pname @ ( insert_pname @ X_19 @ A_53 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_96_card__insert__le,axiom,
% 0.29/0.47 ! [X_19: nat,A_53: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ A_53 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_nat @ A_53 ) @ ( finite_card_nat @ ( insert_nat @ X_19 @ A_53 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_97_card__insert__le,axiom,
% 0.29/0.47 ! [X_19: x_a,A_53: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ A_53 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( finite_card_a @ A_53 ) @ ( finite_card_a @ ( insert_a @ X_19 @ A_53 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_98_card__insert__if,axiom,
% 0.29/0.47 ! [X_18: nat > $o,A_52: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ A_52 )
% 0.29/0.47 => ( ( ( member_nat_o @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_18 @ A_52 ) )
% 0.29/0.47 = ( finite_card_nat_o @ A_52 ) ) )
% 0.29/0.47 & ( ~ ( member_nat_o @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_18 @ A_52 ) )
% 0.29/0.47 = ( suc @ ( finite_card_nat_o @ A_52 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_99_card__insert__if,axiom,
% 0.29/0.47 ! [X_18: pname > $o,A_52: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ A_52 )
% 0.29/0.47 => ( ( ( member_pname_o @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_18 @ A_52 ) )
% 0.29/0.47 = ( finite_card_pname_o @ A_52 ) ) )
% 0.29/0.47 & ( ~ ( member_pname_o @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_18 @ A_52 ) )
% 0.29/0.47 = ( suc @ ( finite_card_pname_o @ A_52 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_100_card__insert__if,axiom,
% 0.29/0.47 ! [X_18: x_a > $o,A_52: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ A_52 )
% 0.29/0.47 => ( ( ( member_a_o @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_a_o @ ( insert_a_o @ X_18 @ A_52 ) )
% 0.29/0.47 = ( finite_card_a_o @ A_52 ) ) )
% 0.29/0.47 & ( ~ ( member_a_o @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_a_o @ ( insert_a_o @ X_18 @ A_52 ) )
% 0.29/0.47 = ( suc @ ( finite_card_a_o @ A_52 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_101_card__insert__if,axiom,
% 0.29/0.47 ! [X_18: nat,A_52: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ A_52 )
% 0.29/0.47 => ( ( ( member_nat @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_nat @ ( insert_nat @ X_18 @ A_52 ) )
% 0.29/0.47 = ( finite_card_nat @ A_52 ) ) )
% 0.29/0.47 & ( ~ ( member_nat @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_nat @ ( insert_nat @ X_18 @ A_52 ) )
% 0.29/0.47 = ( suc @ ( finite_card_nat @ A_52 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_102_card__insert__if,axiom,
% 0.29/0.47 ! [X_18: pname,A_52: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_52 )
% 0.29/0.47 => ( ( ( member_pname @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_pname @ ( insert_pname @ X_18 @ A_52 ) )
% 0.29/0.47 = ( finite_card_pname @ A_52 ) ) )
% 0.29/0.47 & ( ~ ( member_pname @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_pname @ ( insert_pname @ X_18 @ A_52 ) )
% 0.29/0.47 = ( suc @ ( finite_card_pname @ A_52 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_103_card__insert__if,axiom,
% 0.29/0.47 ! [X_18: x_a,A_52: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ A_52 )
% 0.29/0.47 => ( ( ( member_a @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_a @ ( insert_a @ X_18 @ A_52 ) )
% 0.29/0.47 = ( finite_card_a @ A_52 ) ) )
% 0.29/0.47 & ( ~ ( member_a @ X_18 @ A_52 )
% 0.29/0.47 => ( ( finite_card_a @ ( insert_a @ X_18 @ A_52 ) )
% 0.29/0.47 = ( suc @ ( finite_card_a @ A_52 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_104_card__insert__disjoint,axiom,
% 0.29/0.47 ! [X_17: nat > $o,A_51: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ A_51 )
% 0.29/0.47 => ( ~ ( member_nat_o @ X_17 @ A_51 )
% 0.29/0.47 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_17 @ A_51 ) )
% 0.29/0.47 = ( suc @ ( finite_card_nat_o @ A_51 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_105_card__insert__disjoint,axiom,
% 0.29/0.47 ! [X_17: pname > $o,A_51: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ A_51 )
% 0.29/0.47 => ( ~ ( member_pname_o @ X_17 @ A_51 )
% 0.29/0.47 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_17 @ A_51 ) )
% 0.29/0.47 = ( suc @ ( finite_card_pname_o @ A_51 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_106_card__insert__disjoint,axiom,
% 0.29/0.47 ! [X_17: x_a > $o,A_51: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ A_51 )
% 0.29/0.47 => ( ~ ( member_a_o @ X_17 @ A_51 )
% 0.29/0.47 => ( ( finite_card_a_o @ ( insert_a_o @ X_17 @ A_51 ) )
% 0.29/0.47 = ( suc @ ( finite_card_a_o @ A_51 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_107_card__insert__disjoint,axiom,
% 0.29/0.47 ! [X_17: nat,A_51: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ A_51 )
% 0.29/0.47 => ( ~ ( member_nat @ X_17 @ A_51 )
% 0.29/0.47 => ( ( finite_card_nat @ ( insert_nat @ X_17 @ A_51 ) )
% 0.29/0.47 = ( suc @ ( finite_card_nat @ A_51 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_108_card__insert__disjoint,axiom,
% 0.29/0.47 ! [X_17: pname,A_51: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_51 )
% 0.29/0.47 => ( ~ ( member_pname @ X_17 @ A_51 )
% 0.29/0.47 => ( ( finite_card_pname @ ( insert_pname @ X_17 @ A_51 ) )
% 0.29/0.47 = ( suc @ ( finite_card_pname @ A_51 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_109_card__insert__disjoint,axiom,
% 0.29/0.47 ! [X_17: x_a,A_51: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ A_51 )
% 0.29/0.47 => ( ~ ( member_a @ X_17 @ A_51 )
% 0.29/0.47 => ( ( finite_card_a @ ( insert_a @ X_17 @ A_51 ) )
% 0.29/0.47 = ( suc @ ( finite_card_a @ A_51 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_110_finite__Collect__conjI,axiom,
% 0.29/0.47 ! [Q_1: ( nat > $o ) > $o,P_4: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( ( finite_finite_nat_o @ ( collect_nat_o @ P_4 ) )
% 0.29/0.47 | ( finite_finite_nat_o @ ( collect_nat_o @ Q_1 ) ) )
% 0.29/0.47 => ( finite_finite_nat_o
% 0.29/0.47 @ ( collect_nat_o
% 0.29/0.47 @ ^ [X: nat > $o] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_111_finite__Collect__conjI,axiom,
% 0.29/0.47 ! [Q_1: ( pname > $o ) > $o,P_4: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_4 ) )
% 0.29/0.47 | ( finite297249702name_o @ ( collect_pname_o @ Q_1 ) ) )
% 0.29/0.47 => ( finite297249702name_o
% 0.29/0.47 @ ( collect_pname_o
% 0.29/0.47 @ ^ [X: pname > $o] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_112_finite__Collect__conjI,axiom,
% 0.29/0.47 ! [Q_1: ( x_a > $o ) > $o,P_4: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( ( finite_finite_a_o @ ( collect_a_o @ P_4 ) )
% 0.29/0.47 | ( finite_finite_a_o @ ( collect_a_o @ Q_1 ) ) )
% 0.29/0.47 => ( finite_finite_a_o
% 0.29/0.47 @ ( collect_a_o
% 0.29/0.47 @ ^ [X: x_a > $o] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_113_finite__Collect__conjI,axiom,
% 0.29/0.47 ! [Q_1: x_a > $o,P_4: x_a > $o] :
% 0.29/0.47 ( ( ( finite_finite_a @ ( collect_a @ P_4 ) )
% 0.29/0.47 | ( finite_finite_a @ ( collect_a @ Q_1 ) ) )
% 0.29/0.47 => ( finite_finite_a
% 0.29/0.47 @ ( collect_a
% 0.29/0.47 @ ^ [X: x_a] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_114_finite__Collect__conjI,axiom,
% 0.29/0.47 ! [Q_1: pname > $o,P_4: pname > $o] :
% 0.29/0.47 ( ( ( finite_finite_pname @ ( collect_pname @ P_4 ) )
% 0.29/0.47 | ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
% 0.29/0.47 => ( finite_finite_pname
% 0.29/0.47 @ ( collect_pname
% 0.29/0.47 @ ^ [X: pname] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_115_finite__Collect__conjI,axiom,
% 0.29/0.47 ! [Q_1: nat > $o,P_4: nat > $o] :
% 0.29/0.47 ( ( ( finite_finite_nat @ ( collect_nat @ P_4 ) )
% 0.29/0.47 | ( finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
% 0.29/0.47 => ( finite_finite_nat
% 0.29/0.47 @ ( collect_nat
% 0.29/0.47 @ ^ [X: nat] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_116_Suc__diff__le,axiom,
% 0.29/0.47 ! [N_1: nat,M_2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ N_1 @ M_2 )
% 0.29/0.47 => ( ( minus_minus_nat @ ( suc @ M_2 ) @ N_1 )
% 0.29/0.47 = ( suc @ ( minus_minus_nat @ M_2 @ N_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_117_finite__Collect__le__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_eq_nat @ N_2 @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_118_card__Collect__le__nat,axiom,
% 0.29/0.47 ! [N_1: nat] :
% 0.29/0.47 ( ( finite_card_nat
% 0.29/0.47 @ ( collect_nat
% 0.29/0.47 @ ^ [I_1: nat] : ( ord_less_eq_nat @ I_1 @ N_1 ) ) )
% 0.29/0.47 = ( suc @ N_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_119_Suc__inject,axiom,
% 0.29/0.47 ! [X_16: nat,Y_3: nat] :
% 0.29/0.47 ( ( ( suc @ X_16 )
% 0.29/0.47 = ( suc @ Y_3 ) )
% 0.29/0.47 => ( X_16 = Y_3 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_120_nat_Oinject,axiom,
% 0.29/0.47 ! [Nat_1: nat,Nat: nat] :
% 0.29/0.47 ( ( ( suc @ Nat_1 )
% 0.29/0.47 = ( suc @ Nat ) )
% 0.29/0.47 <=> ( Nat_1 = Nat ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_121_Suc__n__not__n,axiom,
% 0.29/0.47 ! [N_1: nat] :
% 0.29/0.47 ( ( suc @ N_1 )
% 0.29/0.47 != N_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_122_n__not__Suc__n,axiom,
% 0.29/0.47 ! [N_1: nat] :
% 0.29/0.47 ( N_1
% 0.29/0.47 != ( suc @ N_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_123_le__antisym,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ N_1 @ M_2 )
% 0.29/0.47 => ( M_2 = N_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_124_le__trans,axiom,
% 0.29/0.47 ! [K: nat,I: nat,J: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ( ord_less_eq_nat @ J @ K )
% 0.29/0.47 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_125_eq__imp__le,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( M_2 = N_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ M_2 @ N_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_126_nat__le__linear,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.29/0.47 | ( ord_less_eq_nat @ N_1 @ M_2 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_127_le__refl,axiom,
% 0.29/0.47 ! [N_1: nat] : ( ord_less_eq_nat @ N_1 @ N_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_128_diff__commute,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.29/0.47 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_129_finite__Collect__disjI,axiom,
% 0.29/0.47 ! [P_3: pname > $o,Q: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname
% 0.29/0.47 @ ( collect_pname
% 0.29/0.47 @ ^ [X: pname] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.29/0.47 <=> ( ( finite_finite_pname @ ( collect_pname @ P_3 ) )
% 0.29/0.47 & ( finite_finite_pname @ ( collect_pname @ Q ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_130_finite__Collect__disjI,axiom,
% 0.29/0.47 ! [P_3: ( nat > $o ) > $o,Q: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o
% 0.29/0.47 @ ( collect_nat_o
% 0.29/0.47 @ ^ [X: nat > $o] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.29/0.47 <=> ( ( finite_finite_nat_o @ ( collect_nat_o @ P_3 ) )
% 0.29/0.47 & ( finite_finite_nat_o @ ( collect_nat_o @ Q ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_131_finite__Collect__disjI,axiom,
% 0.29/0.47 ! [P_3: ( pname > $o ) > $o,Q: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o
% 0.29/0.47 @ ( collect_pname_o
% 0.29/0.47 @ ^ [X: pname > $o] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.29/0.47 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_3 ) )
% 0.29/0.47 & ( finite297249702name_o @ ( collect_pname_o @ Q ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_132_finite__Collect__disjI,axiom,
% 0.29/0.47 ! [P_3: ( x_a > $o ) > $o,Q: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o
% 0.29/0.47 @ ( collect_a_o
% 0.29/0.47 @ ^ [X: x_a > $o] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.29/0.47 <=> ( ( finite_finite_a_o @ ( collect_a_o @ P_3 ) )
% 0.29/0.47 & ( finite_finite_a_o @ ( collect_a_o @ Q ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_133_finite__Collect__disjI,axiom,
% 0.29/0.47 ! [P_3: nat > $o,Q: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat
% 0.29/0.47 @ ( collect_nat
% 0.29/0.47 @ ^ [X: nat] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.29/0.47 <=> ( ( finite_finite_nat @ ( collect_nat @ P_3 ) )
% 0.29/0.47 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_134_finite__Collect__disjI,axiom,
% 0.29/0.47 ! [P_3: x_a > $o,Q: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a
% 0.29/0.47 @ ( collect_a
% 0.29/0.47 @ ^ [X: x_a] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.29/0.47 <=> ( ( finite_finite_a @ ( collect_a @ P_3 ) )
% 0.29/0.47 & ( finite_finite_a @ ( collect_a @ Q ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_135_finite__insert,axiom,
% 0.29/0.47 ! [A_50: nat,A_49: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ ( insert_nat @ A_50 @ A_49 ) )
% 0.29/0.47 <=> ( finite_finite_nat @ A_49 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_136_finite__insert,axiom,
% 0.29/0.47 ! [A_50: pname,A_49: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ ( insert_pname @ A_50 @ A_49 ) )
% 0.29/0.47 <=> ( finite_finite_pname @ A_49 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_137_finite__insert,axiom,
% 0.29/0.47 ! [A_50: x_a,A_49: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ ( insert_a @ A_50 @ A_49 ) )
% 0.29/0.47 <=> ( finite_finite_a @ A_49 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_138_finite__insert,axiom,
% 0.29/0.47 ! [A_50: nat > $o,A_49: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ ( insert_nat_o @ A_50 @ A_49 ) )
% 0.29/0.47 <=> ( finite_finite_nat_o @ A_49 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_139_finite__insert,axiom,
% 0.29/0.47 ! [A_50: pname > $o,A_49: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ ( insert_pname_o @ A_50 @ A_49 ) )
% 0.29/0.47 <=> ( finite297249702name_o @ A_49 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_140_finite__insert,axiom,
% 0.29/0.47 ! [A_50: x_a > $o,A_49: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ ( insert_a_o @ A_50 @ A_49 ) )
% 0.29/0.47 <=> ( finite_finite_a_o @ A_49 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_141_finite__subset,axiom,
% 0.29/0.47 ! [A_48: ( nat > $o ) > $o,B_35: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o_o @ A_48 @ B_35 )
% 0.29/0.47 => ( ( finite_finite_nat_o @ B_35 )
% 0.29/0.47 => ( finite_finite_nat_o @ A_48 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_142_finite__subset,axiom,
% 0.29/0.47 ! [A_48: ( pname > $o ) > $o,B_35: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( ord_le1205211808me_o_o @ A_48 @ B_35 )
% 0.29/0.47 => ( ( finite297249702name_o @ B_35 )
% 0.29/0.47 => ( finite297249702name_o @ A_48 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_143_finite__subset,axiom,
% 0.29/0.47 ! [A_48: x_a > $o,B_35: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_48 @ B_35 )
% 0.29/0.47 => ( ( finite_finite_a @ B_35 )
% 0.29/0.47 => ( finite_finite_a @ A_48 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_144_finite__subset,axiom,
% 0.29/0.47 ! [A_48: ( x_a > $o ) > $o,B_35: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o_o @ A_48 @ B_35 )
% 0.29/0.47 => ( ( finite_finite_a_o @ B_35 )
% 0.29/0.47 => ( finite_finite_a_o @ A_48 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_145_finite__subset,axiom,
% 0.29/0.47 ! [A_48: nat > $o,B_35: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_48 @ B_35 )
% 0.29/0.47 => ( ( finite_finite_nat @ B_35 )
% 0.29/0.47 => ( finite_finite_nat @ A_48 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_146_finite__subset,axiom,
% 0.29/0.47 ! [A_48: pname > $o,B_35: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_48 @ B_35 )
% 0.29/0.47 => ( ( finite_finite_pname @ B_35 )
% 0.29/0.47 => ( finite_finite_pname @ A_48 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_147_rev__finite__subset,axiom,
% 0.29/0.47 ! [A_47: ( nat > $o ) > $o,B_34: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_nat_o @ B_34 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o_o @ A_47 @ B_34 )
% 0.29/0.47 => ( finite_finite_nat_o @ A_47 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_148_rev__finite__subset,axiom,
% 0.29/0.47 ! [A_47: ( pname > $o ) > $o,B_34: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( finite297249702name_o @ B_34 )
% 0.29/0.47 => ( ( ord_le1205211808me_o_o @ A_47 @ B_34 )
% 0.29/0.47 => ( finite297249702name_o @ A_47 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_149_rev__finite__subset,axiom,
% 0.29/0.47 ! [A_47: x_a > $o,B_34: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ B_34 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ A_47 @ B_34 )
% 0.29/0.47 => ( finite_finite_a @ A_47 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_150_rev__finite__subset,axiom,
% 0.29/0.47 ! [A_47: ( x_a > $o ) > $o,B_34: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( finite_finite_a_o @ B_34 )
% 0.29/0.47 => ( ( ord_less_eq_a_o_o @ A_47 @ B_34 )
% 0.29/0.47 => ( finite_finite_a_o @ A_47 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_151_rev__finite__subset,axiom,
% 0.29/0.47 ! [A_47: nat > $o,B_34: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ B_34 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ A_47 @ B_34 )
% 0.29/0.47 => ( finite_finite_nat @ A_47 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_152_rev__finite__subset,axiom,
% 0.29/0.47 ! [A_47: pname > $o,B_34: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ B_34 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ A_47 @ B_34 )
% 0.29/0.47 => ( finite_finite_pname @ A_47 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_153_Suc__leD,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( suc @ M_2 ) @ N_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ M_2 @ N_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_154_le__SucE,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M_2 @ ( suc @ N_1 ) )
% 0.29/0.47 => ( ~ ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.29/0.47 => ( M_2
% 0.29/0.47 = ( suc @ N_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_155_le__SucI,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ M_2 @ ( suc @ N_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_156_Suc__le__mono,axiom,
% 0.29/0.47 ! [N_1: nat,M_2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( suc @ N_1 ) @ ( suc @ M_2 ) )
% 0.29/0.47 <=> ( ord_less_eq_nat @ N_1 @ M_2 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_157_le__Suc__eq,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M_2 @ ( suc @ N_1 ) )
% 0.29/0.47 <=> ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.29/0.47 | ( M_2
% 0.29/0.47 = ( suc @ N_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_158_not__less__eq__eq,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] :
% 0.29/0.47 ( ~ ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.29/0.47 <=> ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_2 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_159_Suc__n__not__le__n,axiom,
% 0.29/0.47 ! [N_1: nat] :
% 0.29/0.47 ~ ( ord_less_eq_nat @ ( suc @ N_1 ) @ N_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_160_Suc__diff__diff,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat,K: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M_2 ) @ N_1 ) @ ( suc @ K ) )
% 0.29/0.47 = ( minus_minus_nat @ ( minus_minus_nat @ M_2 @ N_1 ) @ K ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_161_diff__Suc__Suc,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( suc @ M_2 ) @ ( suc @ N_1 ) )
% 0.29/0.47 = ( minus_minus_nat @ M_2 @ N_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_162_le__diff__iff,axiom,
% 0.29/0.47 ! [N_1: nat,K: nat,M_2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ M_2 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ N_1 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M_2 @ K ) @ ( minus_minus_nat @ N_1 @ K ) )
% 0.29/0.47 <=> ( ord_less_eq_nat @ M_2 @ N_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_163_Nat_Odiff__diff__eq,axiom,
% 0.29/0.47 ! [N_1: nat,K: nat,M_2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ M_2 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ N_1 )
% 0.29/0.47 => ( ( minus_minus_nat @ ( minus_minus_nat @ M_2 @ K ) @ ( minus_minus_nat @ N_1 @ K ) )
% 0.29/0.47 = ( minus_minus_nat @ M_2 @ N_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_164_eq__diff__iff,axiom,
% 0.29/0.47 ! [N_1: nat,K: nat,M_2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ M_2 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ N_1 )
% 0.29/0.47 => ( ( ( minus_minus_nat @ M_2 @ K )
% 0.29/0.47 = ( minus_minus_nat @ N_1 @ K ) )
% 0.29/0.47 <=> ( M_2 = N_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_165_diff__diff__cancel,axiom,
% 0.29/0.47 ! [I: nat,N_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ N_1 )
% 0.29/0.47 => ( ( minus_minus_nat @ N_1 @ ( minus_minus_nat @ N_1 @ I ) )
% 0.29/0.47 = I ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_166_diff__le__mono,axiom,
% 0.29/0.47 ! [L: nat,M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( minus_minus_nat @ M_2 @ L ) @ ( minus_minus_nat @ N_1 @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_167_diff__le__mono2,axiom,
% 0.29/0.47 ! [L: nat,M_2: nat,N_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N_1 ) @ ( minus_minus_nat @ L @ M_2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_168_diff__le__self,axiom,
% 0.29/0.47 ! [M_2: nat,N_1: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M_2 @ N_1 ) @ M_2 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_169_finite__surj,axiom,
% 0.29/0.47 ! [B_33: x_a > $o,F_13: pname > x_a,A_46: pname > $o] :
% 0.29/0.47 ( ( finite_finite_pname @ A_46 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ B_33 @ ( image_pname_a @ F_13 @ A_46 ) )
% 0.29/0.47 => ( finite_finite_a @ B_33 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_170_finite__subset__image,axiom,
% 0.29/0.47 ! [F_12: pname > x_a,A_45: pname > $o,B_32: x_a > $o] :
% 0.29/0.47 ( ( finite_finite_a @ B_32 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ B_32 @ ( image_pname_a @ F_12 @ A_45 ) )
% 0.29/0.47 => ? [C_3: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ C_3 @ A_45 )
% 0.29/0.47 & ( finite_finite_pname @ C_3 )
% 0.29/0.47 & ( B_32
% 0.29/0.47 = ( image_pname_a @ F_12 @ C_3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_171_lift__Suc__mono__le,axiom,
% 0.29/0.47 ! [N_4: nat,N_3: nat,F_11: nat > nat > $o] :
% 0.29/0.47 ( ! [N_2: nat] : ( ord_less_eq_nat_o @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_172_lift__Suc__mono__le,axiom,
% 0.29/0.47 ! [N_4: nat,N_3: nat,F_11: nat > pname > $o] :
% 0.29/0.47 ( ! [N_2: nat] : ( ord_less_eq_pname_o @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_173_lift__Suc__mono__le,axiom,
% 0.29/0.47 ! [N_4: nat,N_3: nat,F_11: nat > nat] :
% 0.29/0.47 ( ! [N_2: nat] : ( ord_less_eq_nat @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_174_lift__Suc__mono__le,axiom,
% 0.29/0.47 ! [N_4: nat,N_3: nat,F_11: nat > x_a > $o] :
% 0.29/0.47 ( ! [N_2: nat] : ( ord_less_eq_a_o @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.29/0.47 => ( ord_less_eq_a_o @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_175_pigeonhole__infinite,axiom,
% 0.29/0.47 ! [F_10: pname > x_a,A_43: pname > $o] :
% 0.29/0.47 ( ~ ( finite_finite_pname @ A_43 )
% 0.29/0.47 => ( ( finite_finite_a @ ( image_pname_a @ F_10 @ A_43 ) )
% 0.29/0.47 => ? [X: pname] :
% 0.29/0.47 ( ( member_pname @ X @ A_43 )
% 0.29/0.47 & ~ ( finite_finite_pname
% 0.29/0.47 @ ( collect_pname
% 0.29/0.47 @ ^ [A_44: pname] :
% 0.29/0.47 ( (&) @ ( member_pname @ A_44 @ A_43 )
% 0.29/0.47 @ ( ( F_10 @ A_44 )
% 0.29/0.47 = ( F_10 @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_176_image__eqI,axiom,
% 0.29/0.47 ! [A_42: pname > $o,B_31: x_a,F_9: pname > x_a,X_15: pname] :
% 0.29/0.47 ( ( B_31
% 0.29/0.47 = ( F_9 @ X_15 ) )
% 0.29/0.47 => ( ( member_pname @ X_15 @ A_42 )
% 0.29/0.47 => ( member_a @ B_31 @ ( image_pname_a @ F_9 @ A_42 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_177_equalityI,axiom,
% 0.29/0.47 ! [A_41: nat > $o,B_30: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_41 @ B_30 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ B_30 @ A_41 )
% 0.29/0.47 => ( A_41 = B_30 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_178_equalityI,axiom,
% 0.29/0.47 ! [A_41: pname > $o,B_30: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_41 @ B_30 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ B_30 @ A_41 )
% 0.29/0.47 => ( A_41 = B_30 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_179_equalityI,axiom,
% 0.29/0.47 ! [A_41: x_a > $o,B_30: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_41 @ B_30 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ B_30 @ A_41 )
% 0.29/0.47 => ( A_41 = B_30 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_180_subsetD,axiom,
% 0.29/0.47 ! [C_2: nat,A_40: nat > $o,B_29: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_40 @ B_29 )
% 0.29/0.47 => ( ( member_nat @ C_2 @ A_40 )
% 0.29/0.47 => ( member_nat @ C_2 @ B_29 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_181_subsetD,axiom,
% 0.29/0.47 ! [C_2: x_a,A_40: x_a > $o,B_29: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_40 @ B_29 )
% 0.29/0.47 => ( ( member_a @ C_2 @ A_40 )
% 0.29/0.47 => ( member_a @ C_2 @ B_29 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_182_subsetD,axiom,
% 0.29/0.47 ! [C_2: pname,A_40: pname > $o,B_29: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_40 @ B_29 )
% 0.29/0.47 => ( ( member_pname @ C_2 @ A_40 )
% 0.29/0.47 => ( member_pname @ C_2 @ B_29 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_183_insertCI,axiom,
% 0.29/0.47 ! [B_28: nat,A_39: nat,B_27: nat > $o] :
% 0.29/0.47 ( ( ~ ( member_nat @ A_39 @ B_27 )
% 0.29/0.47 => ( A_39 = B_28 ) )
% 0.29/0.47 => ( member_nat @ A_39 @ ( insert_nat @ B_28 @ B_27 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_184_insertCI,axiom,
% 0.29/0.47 ! [B_28: pname,A_39: pname,B_27: pname > $o] :
% 0.29/0.47 ( ( ~ ( member_pname @ A_39 @ B_27 )
% 0.29/0.47 => ( A_39 = B_28 ) )
% 0.29/0.47 => ( member_pname @ A_39 @ ( insert_pname @ B_28 @ B_27 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_185_insertCI,axiom,
% 0.29/0.47 ! [B_28: x_a,A_39: x_a,B_27: x_a > $o] :
% 0.29/0.47 ( ( ~ ( member_a @ A_39 @ B_27 )
% 0.29/0.47 => ( A_39 = B_28 ) )
% 0.29/0.47 => ( member_a @ A_39 @ ( insert_a @ B_28 @ B_27 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_186_insertE,axiom,
% 0.29/0.47 ! [A_38: nat,B_26: nat,A_37: nat > $o] :
% 0.29/0.47 ( ( member_nat @ A_38 @ ( insert_nat @ B_26 @ A_37 ) )
% 0.29/0.47 => ( ( A_38 != B_26 )
% 0.29/0.47 => ( member_nat @ A_38 @ A_37 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_187_insertE,axiom,
% 0.29/0.47 ! [A_38: pname,B_26: pname,A_37: pname > $o] :
% 0.29/0.47 ( ( member_pname @ A_38 @ ( insert_pname @ B_26 @ A_37 ) )
% 0.29/0.47 => ( ( A_38 != B_26 )
% 0.29/0.47 => ( member_pname @ A_38 @ A_37 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_188_insertE,axiom,
% 0.29/0.47 ! [A_38: x_a,B_26: x_a,A_37: x_a > $o] :
% 0.29/0.47 ( ( member_a @ A_38 @ ( insert_a @ B_26 @ A_37 ) )
% 0.29/0.47 => ( ( A_38 != B_26 )
% 0.29/0.47 => ( member_a @ A_38 @ A_37 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_189_insertI1,axiom,
% 0.29/0.47 ! [A_36: nat,B_25: nat > $o] : ( member_nat @ A_36 @ ( insert_nat @ A_36 @ B_25 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_190_insertI1,axiom,
% 0.29/0.47 ! [A_36: pname,B_25: pname > $o] : ( member_pname @ A_36 @ ( insert_pname @ A_36 @ B_25 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_191_insertI1,axiom,
% 0.29/0.47 ! [A_36: x_a,B_25: x_a > $o] : ( member_a @ A_36 @ ( insert_a @ A_36 @ B_25 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_192_insert__compr,axiom,
% 0.29/0.47 ! [A_35: nat,B_24: nat > $o] :
% 0.29/0.47 ( ( insert_nat @ A_35 @ B_24 )
% 0.29/0.47 = ( collect_nat
% 0.29/0.47 @ ^ [X: nat] : ( (|) @ ( X = A_35 ) @ ( member_nat @ X @ B_24 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_193_insert__compr,axiom,
% 0.29/0.47 ! [A_35: pname,B_24: pname > $o] :
% 0.29/0.47 ( ( insert_pname @ A_35 @ B_24 )
% 0.29/0.47 = ( collect_pname
% 0.29/0.47 @ ^ [X: pname] : ( (|) @ ( X = A_35 ) @ ( member_pname @ X @ B_24 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_194_insert__compr,axiom,
% 0.29/0.47 ! [A_35: x_a,B_24: x_a > $o] :
% 0.29/0.47 ( ( insert_a @ A_35 @ B_24 )
% 0.29/0.47 = ( collect_a
% 0.29/0.47 @ ^ [X: x_a] : ( (|) @ ( X = A_35 ) @ ( member_a @ X @ B_24 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_195_insert__compr,axiom,
% 0.29/0.47 ! [A_35: nat > $o,B_24: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( insert_nat_o @ A_35 @ B_24 )
% 0.29/0.47 = ( collect_nat_o
% 0.29/0.47 @ ^ [X: nat > $o] : ( (|) @ ( X = A_35 ) @ ( member_nat_o @ X @ B_24 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_196_insert__compr,axiom,
% 0.29/0.47 ! [A_35: pname > $o,B_24: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( insert_pname_o @ A_35 @ B_24 )
% 0.29/0.47 = ( collect_pname_o
% 0.29/0.47 @ ^ [X: pname > $o] : ( (|) @ ( X = A_35 ) @ ( member_pname_o @ X @ B_24 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_197_insert__compr,axiom,
% 0.29/0.47 ! [A_35: x_a > $o,B_24: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( insert_a_o @ A_35 @ B_24 )
% 0.29/0.47 = ( collect_a_o
% 0.29/0.47 @ ^ [X: x_a > $o] : ( (|) @ ( X = A_35 ) @ ( member_a_o @ X @ B_24 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_198_insert__Collect,axiom,
% 0.29/0.47 ! [A_34: nat,P_2: nat > $o] :
% 0.29/0.47 ( ( insert_nat @ A_34 @ ( collect_nat @ P_2 ) )
% 0.29/0.47 = ( collect_nat
% 0.29/0.47 @ ^ [U: nat] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_199_insert__Collect,axiom,
% 0.29/0.47 ! [A_34: pname,P_2: pname > $o] :
% 0.29/0.47 ( ( insert_pname @ A_34 @ ( collect_pname @ P_2 ) )
% 0.29/0.47 = ( collect_pname
% 0.29/0.47 @ ^ [U: pname] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_200_insert__Collect,axiom,
% 0.29/0.47 ! [A_34: x_a,P_2: x_a > $o] :
% 0.29/0.47 ( ( insert_a @ A_34 @ ( collect_a @ P_2 ) )
% 0.29/0.47 = ( collect_a
% 0.29/0.47 @ ^ [U: x_a] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_201_insert__Collect,axiom,
% 0.29/0.47 ! [A_34: nat > $o,P_2: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( insert_nat_o @ A_34 @ ( collect_nat_o @ P_2 ) )
% 0.29/0.47 = ( collect_nat_o
% 0.29/0.47 @ ^ [U: nat > $o] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_202_insert__Collect,axiom,
% 0.29/0.47 ! [A_34: pname > $o,P_2: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( insert_pname_o @ A_34 @ ( collect_pname_o @ P_2 ) )
% 0.29/0.47 = ( collect_pname_o
% 0.29/0.47 @ ^ [U: pname > $o] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_203_insert__Collect,axiom,
% 0.29/0.47 ! [A_34: x_a > $o,P_2: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( insert_a_o @ A_34 @ ( collect_a_o @ P_2 ) )
% 0.29/0.47 = ( collect_a_o
% 0.29/0.47 @ ^ [U: x_a > $o] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_204_insert__absorb2,axiom,
% 0.29/0.47 ! [X_14: nat,A_33: nat > $o] :
% 0.29/0.47 ( ( insert_nat @ X_14 @ ( insert_nat @ X_14 @ A_33 ) )
% 0.29/0.47 = ( insert_nat @ X_14 @ A_33 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_205_insert__absorb2,axiom,
% 0.29/0.47 ! [X_14: pname,A_33: pname > $o] :
% 0.29/0.47 ( ( insert_pname @ X_14 @ ( insert_pname @ X_14 @ A_33 ) )
% 0.29/0.47 = ( insert_pname @ X_14 @ A_33 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_206_insert__absorb2,axiom,
% 0.29/0.47 ! [X_14: x_a,A_33: x_a > $o] :
% 0.29/0.47 ( ( insert_a @ X_14 @ ( insert_a @ X_14 @ A_33 ) )
% 0.29/0.47 = ( insert_a @ X_14 @ A_33 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_207_insert__commute,axiom,
% 0.29/0.47 ! [X_13: nat,Y_2: nat,A_32: nat > $o] :
% 0.29/0.47 ( ( insert_nat @ X_13 @ ( insert_nat @ Y_2 @ A_32 ) )
% 0.29/0.47 = ( insert_nat @ Y_2 @ ( insert_nat @ X_13 @ A_32 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_208_insert__commute,axiom,
% 0.29/0.47 ! [X_13: pname,Y_2: pname,A_32: pname > $o] :
% 0.29/0.47 ( ( insert_pname @ X_13 @ ( insert_pname @ Y_2 @ A_32 ) )
% 0.29/0.47 = ( insert_pname @ Y_2 @ ( insert_pname @ X_13 @ A_32 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_209_insert__commute,axiom,
% 0.29/0.47 ! [X_13: x_a,Y_2: x_a,A_32: x_a > $o] :
% 0.29/0.47 ( ( insert_a @ X_13 @ ( insert_a @ Y_2 @ A_32 ) )
% 0.29/0.47 = ( insert_a @ Y_2 @ ( insert_a @ X_13 @ A_32 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_210_insert__iff,axiom,
% 0.29/0.47 ! [A_31: nat,B_23: nat,A_30: nat > $o] :
% 0.29/0.47 ( ( member_nat @ A_31 @ ( insert_nat @ B_23 @ A_30 ) )
% 0.29/0.47 <=> ( ( A_31 = B_23 )
% 0.29/0.47 | ( member_nat @ A_31 @ A_30 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_211_insert__iff,axiom,
% 0.29/0.47 ! [A_31: pname,B_23: pname,A_30: pname > $o] :
% 0.29/0.47 ( ( member_pname @ A_31 @ ( insert_pname @ B_23 @ A_30 ) )
% 0.29/0.47 <=> ( ( A_31 = B_23 )
% 0.29/0.47 | ( member_pname @ A_31 @ A_30 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_212_insert__iff,axiom,
% 0.29/0.47 ! [A_31: x_a,B_23: x_a,A_30: x_a > $o] :
% 0.29/0.47 ( ( member_a @ A_31 @ ( insert_a @ B_23 @ A_30 ) )
% 0.29/0.47 <=> ( ( A_31 = B_23 )
% 0.29/0.47 | ( member_a @ A_31 @ A_30 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_213_insert__code,axiom,
% 0.29/0.47 ! [Y_1: nat,A_29: nat > $o,X_12: nat] :
% 0.29/0.47 ( ( insert_nat @ Y_1 @ A_29 @ X_12 )
% 0.29/0.47 <=> ( ( Y_1 = X_12 )
% 0.29/0.47 | ( A_29 @ X_12 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_214_insert__code,axiom,
% 0.29/0.47 ! [Y_1: pname,A_29: pname > $o,X_12: pname] :
% 0.29/0.47 ( ( insert_pname @ Y_1 @ A_29 @ X_12 )
% 0.29/0.47 <=> ( ( Y_1 = X_12 )
% 0.29/0.47 | ( A_29 @ X_12 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_215_insert__code,axiom,
% 0.29/0.47 ! [Y_1: x_a,A_29: x_a > $o,X_12: x_a] :
% 0.29/0.47 ( ( insert_a @ Y_1 @ A_29 @ X_12 )
% 0.29/0.47 <=> ( ( Y_1 = X_12 )
% 0.29/0.47 | ( A_29 @ X_12 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_216_insert__ident,axiom,
% 0.29/0.47 ! [B_22: nat > $o,X_11: nat,A_28: nat > $o] :
% 0.29/0.47 ( ~ ( member_nat @ X_11 @ A_28 )
% 0.29/0.47 => ( ~ ( member_nat @ X_11 @ B_22 )
% 0.29/0.47 => ( ( ( insert_nat @ X_11 @ A_28 )
% 0.29/0.47 = ( insert_nat @ X_11 @ B_22 ) )
% 0.29/0.47 <=> ( A_28 = B_22 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_217_insert__ident,axiom,
% 0.29/0.47 ! [B_22: pname > $o,X_11: pname,A_28: pname > $o] :
% 0.29/0.47 ( ~ ( member_pname @ X_11 @ A_28 )
% 0.29/0.47 => ( ~ ( member_pname @ X_11 @ B_22 )
% 0.29/0.47 => ( ( ( insert_pname @ X_11 @ A_28 )
% 0.29/0.47 = ( insert_pname @ X_11 @ B_22 ) )
% 0.29/0.47 <=> ( A_28 = B_22 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_218_insert__ident,axiom,
% 0.29/0.47 ! [B_22: x_a > $o,X_11: x_a,A_28: x_a > $o] :
% 0.29/0.47 ( ~ ( member_a @ X_11 @ A_28 )
% 0.29/0.47 => ( ~ ( member_a @ X_11 @ B_22 )
% 0.29/0.47 => ( ( ( insert_a @ X_11 @ A_28 )
% 0.29/0.47 = ( insert_a @ X_11 @ B_22 ) )
% 0.29/0.47 <=> ( A_28 = B_22 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_219_insertI2,axiom,
% 0.29/0.47 ! [B_21: nat,A_27: nat,B_20: nat > $o] :
% 0.29/0.47 ( ( member_nat @ A_27 @ B_20 )
% 0.29/0.47 => ( member_nat @ A_27 @ ( insert_nat @ B_21 @ B_20 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_220_insertI2,axiom,
% 0.29/0.47 ! [B_21: pname,A_27: pname,B_20: pname > $o] :
% 0.29/0.47 ( ( member_pname @ A_27 @ B_20 )
% 0.29/0.47 => ( member_pname @ A_27 @ ( insert_pname @ B_21 @ B_20 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_221_insertI2,axiom,
% 0.29/0.47 ! [B_21: x_a,A_27: x_a,B_20: x_a > $o] :
% 0.29/0.47 ( ( member_a @ A_27 @ B_20 )
% 0.29/0.47 => ( member_a @ A_27 @ ( insert_a @ B_21 @ B_20 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_222_insert__absorb,axiom,
% 0.29/0.47 ! [A_26: nat,A_25: nat > $o] :
% 0.29/0.47 ( ( member_nat @ A_26 @ A_25 )
% 0.29/0.47 => ( ( insert_nat @ A_26 @ A_25 )
% 0.29/0.47 = A_25 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_223_insert__absorb,axiom,
% 0.29/0.47 ! [A_26: pname,A_25: pname > $o] :
% 0.29/0.47 ( ( member_pname @ A_26 @ A_25 )
% 0.29/0.47 => ( ( insert_pname @ A_26 @ A_25 )
% 0.29/0.47 = A_25 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_224_insert__absorb,axiom,
% 0.29/0.47 ! [A_26: x_a,A_25: x_a > $o] :
% 0.29/0.47 ( ( member_a @ A_26 @ A_25 )
% 0.29/0.47 => ( ( insert_a @ A_26 @ A_25 )
% 0.29/0.47 = A_25 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_225_subset__refl,axiom,
% 0.29/0.47 ! [A_24: nat > $o] : ( ord_less_eq_nat_o @ A_24 @ A_24 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_226_subset__refl,axiom,
% 0.29/0.47 ! [A_24: pname > $o] : ( ord_less_eq_pname_o @ A_24 @ A_24 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_227_subset__refl,axiom,
% 0.29/0.47 ! [A_24: x_a > $o] : ( ord_less_eq_a_o @ A_24 @ A_24 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_228_set__eq__subset,axiom,
% 0.29/0.47 ! [A_23: nat > $o,B_19: nat > $o] :
% 0.29/0.47 ( ( A_23 = B_19 )
% 0.29/0.47 <=> ( ( ord_less_eq_nat_o @ A_23 @ B_19 )
% 0.29/0.47 & ( ord_less_eq_nat_o @ B_19 @ A_23 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_229_set__eq__subset,axiom,
% 0.29/0.47 ! [A_23: pname > $o,B_19: pname > $o] :
% 0.29/0.47 ( ( A_23 = B_19 )
% 0.29/0.47 <=> ( ( ord_less_eq_pname_o @ A_23 @ B_19 )
% 0.29/0.47 & ( ord_less_eq_pname_o @ B_19 @ A_23 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_230_set__eq__subset,axiom,
% 0.29/0.47 ! [A_23: x_a > $o,B_19: x_a > $o] :
% 0.29/0.47 ( ( A_23 = B_19 )
% 0.29/0.47 <=> ( ( ord_less_eq_a_o @ A_23 @ B_19 )
% 0.29/0.47 & ( ord_less_eq_a_o @ B_19 @ A_23 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_231_equalityD1,axiom,
% 0.29/0.47 ! [A_22: nat > $o,B_18: nat > $o] :
% 0.29/0.47 ( ( A_22 = B_18 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ A_22 @ B_18 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_232_equalityD1,axiom,
% 0.29/0.47 ! [A_22: pname > $o,B_18: pname > $o] :
% 0.29/0.47 ( ( A_22 = B_18 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ A_22 @ B_18 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_233_equalityD1,axiom,
% 0.29/0.47 ! [A_22: x_a > $o,B_18: x_a > $o] :
% 0.29/0.47 ( ( A_22 = B_18 )
% 0.29/0.47 => ( ord_less_eq_a_o @ A_22 @ B_18 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_234_equalityD2,axiom,
% 0.29/0.47 ! [A_21: nat > $o,B_17: nat > $o] :
% 0.29/0.47 ( ( A_21 = B_17 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ B_17 @ A_21 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_235_equalityD2,axiom,
% 0.29/0.47 ! [A_21: pname > $o,B_17: pname > $o] :
% 0.29/0.47 ( ( A_21 = B_17 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ B_17 @ A_21 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_236_equalityD2,axiom,
% 0.29/0.47 ! [A_21: x_a > $o,B_17: x_a > $o] :
% 0.29/0.47 ( ( A_21 = B_17 )
% 0.29/0.47 => ( ord_less_eq_a_o @ B_17 @ A_21 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_237_in__mono,axiom,
% 0.29/0.47 ! [X_10: nat,A_20: nat > $o,B_16: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_20 @ B_16 )
% 0.29/0.47 => ( ( member_nat @ X_10 @ A_20 )
% 0.29/0.47 => ( member_nat @ X_10 @ B_16 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_238_in__mono,axiom,
% 0.29/0.47 ! [X_10: x_a,A_20: x_a > $o,B_16: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_20 @ B_16 )
% 0.29/0.47 => ( ( member_a @ X_10 @ A_20 )
% 0.29/0.47 => ( member_a @ X_10 @ B_16 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_239_in__mono,axiom,
% 0.29/0.47 ! [X_10: pname,A_20: pname > $o,B_16: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_20 @ B_16 )
% 0.29/0.47 => ( ( member_pname @ X_10 @ A_20 )
% 0.29/0.47 => ( member_pname @ X_10 @ B_16 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_240_set__rev__mp,axiom,
% 0.29/0.47 ! [B_15: nat > $o,X_9: nat,A_19: nat > $o] :
% 0.29/0.47 ( ( member_nat @ X_9 @ A_19 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ A_19 @ B_15 )
% 0.29/0.47 => ( member_nat @ X_9 @ B_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_241_set__rev__mp,axiom,
% 0.29/0.47 ! [B_15: x_a > $o,X_9: x_a,A_19: x_a > $o] :
% 0.29/0.47 ( ( member_a @ X_9 @ A_19 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ A_19 @ B_15 )
% 0.29/0.47 => ( member_a @ X_9 @ B_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_242_set__rev__mp,axiom,
% 0.29/0.47 ! [B_15: pname > $o,X_9: pname,A_19: pname > $o] :
% 0.29/0.47 ( ( member_pname @ X_9 @ A_19 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ A_19 @ B_15 )
% 0.29/0.47 => ( member_pname @ X_9 @ B_15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_243_set__mp,axiom,
% 0.29/0.47 ! [X_8: nat,A_18: nat > $o,B_14: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_18 @ B_14 )
% 0.29/0.47 => ( ( member_nat @ X_8 @ A_18 )
% 0.29/0.47 => ( member_nat @ X_8 @ B_14 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_244_set__mp,axiom,
% 0.29/0.47 ! [X_8: x_a,A_18: x_a > $o,B_14: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_18 @ B_14 )
% 0.29/0.47 => ( ( member_a @ X_8 @ A_18 )
% 0.29/0.47 => ( member_a @ X_8 @ B_14 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_245_set__mp,axiom,
% 0.29/0.47 ! [X_8: pname,A_18: pname > $o,B_14: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_18 @ B_14 )
% 0.29/0.47 => ( ( member_pname @ X_8 @ A_18 )
% 0.29/0.47 => ( member_pname @ X_8 @ B_14 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_246_subset__trans,axiom,
% 0.29/0.47 ! [C_1: nat > $o,A_17: nat > $o,B_13: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_17 @ B_13 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ B_13 @ C_1 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ A_17 @ C_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_247_subset__trans,axiom,
% 0.29/0.47 ! [C_1: pname > $o,A_17: pname > $o,B_13: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_17 @ B_13 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ B_13 @ C_1 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ A_17 @ C_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_248_subset__trans,axiom,
% 0.29/0.47 ! [C_1: x_a > $o,A_17: x_a > $o,B_13: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_17 @ B_13 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ B_13 @ C_1 )
% 0.29/0.47 => ( ord_less_eq_a_o @ A_17 @ C_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_249_equalityE,axiom,
% 0.29/0.47 ! [A_16: nat > $o,B_12: nat > $o] :
% 0.29/0.47 ( ( A_16 = B_12 )
% 0.29/0.47 => ~ ( ( ord_less_eq_nat_o @ A_16 @ B_12 )
% 0.29/0.47 => ~ ( ord_less_eq_nat_o @ B_12 @ A_16 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_250_equalityE,axiom,
% 0.29/0.47 ! [A_16: pname > $o,B_12: pname > $o] :
% 0.29/0.47 ( ( A_16 = B_12 )
% 0.29/0.47 => ~ ( ( ord_less_eq_pname_o @ A_16 @ B_12 )
% 0.29/0.47 => ~ ( ord_less_eq_pname_o @ B_12 @ A_16 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_251_equalityE,axiom,
% 0.29/0.47 ! [A_16: x_a > $o,B_12: x_a > $o] :
% 0.29/0.47 ( ( A_16 = B_12 )
% 0.29/0.47 => ~ ( ( ord_less_eq_a_o @ A_16 @ B_12 )
% 0.29/0.47 => ~ ( ord_less_eq_a_o @ B_12 @ A_16 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_252_mem__def,axiom,
% 0.29/0.47 ! [X_7: nat,A_15: nat > $o] :
% 0.29/0.47 ( ( member_nat @ X_7 @ A_15 )
% 0.29/0.47 <=> ( A_15 @ X_7 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_253_mem__def,axiom,
% 0.29/0.47 ! [X_7: x_a,A_15: x_a > $o] :
% 0.29/0.47 ( ( member_a @ X_7 @ A_15 )
% 0.29/0.47 <=> ( A_15 @ X_7 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_254_mem__def,axiom,
% 0.29/0.47 ! [X_7: pname,A_15: pname > $o] :
% 0.29/0.47 ( ( member_pname @ X_7 @ A_15 )
% 0.29/0.47 <=> ( A_15 @ X_7 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_255_Collect__def,axiom,
% 0.29/0.47 ! [P_1: pname > $o] :
% 0.29/0.47 ( ( collect_pname @ P_1 )
% 0.29/0.47 = P_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_256_Collect__def,axiom,
% 0.29/0.47 ! [P_1: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( collect_nat_o @ P_1 )
% 0.29/0.47 = P_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_257_Collect__def,axiom,
% 0.29/0.47 ! [P_1: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( collect_pname_o @ P_1 )
% 0.29/0.47 = P_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_258_Collect__def,axiom,
% 0.29/0.47 ! [P_1: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( collect_a_o @ P_1 )
% 0.29/0.47 = P_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_259_Collect__def,axiom,
% 0.29/0.47 ! [P_1: nat > $o] :
% 0.29/0.47 ( ( collect_nat @ P_1 )
% 0.29/0.47 = P_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_260_image__iff,axiom,
% 0.29/0.47 ! [Z: x_a,F_8: pname > x_a,A_14: pname > $o] :
% 0.29/0.47 ( ( member_a @ Z @ ( image_pname_a @ F_8 @ A_14 ) )
% 0.29/0.47 <=> ? [X: pname] :
% 0.29/0.47 ( ( member_pname @ X @ A_14 )
% 0.29/0.47 & ( Z
% 0.29/0.47 = ( F_8 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_261_imageI,axiom,
% 0.29/0.47 ! [F_7: pname > x_a,X_6: pname,A_13: pname > $o] :
% 0.29/0.47 ( ( member_pname @ X_6 @ A_13 )
% 0.29/0.47 => ( member_a @ ( F_7 @ X_6 ) @ ( image_pname_a @ F_7 @ A_13 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_262_rev__image__eqI,axiom,
% 0.29/0.47 ! [B_11: x_a,F_6: pname > x_a,X_5: pname,A_12: pname > $o] :
% 0.29/0.47 ( ( member_pname @ X_5 @ A_12 )
% 0.29/0.47 => ( ( B_11
% 0.29/0.47 = ( F_6 @ X_5 ) )
% 0.29/0.47 => ( member_a @ B_11 @ ( image_pname_a @ F_6 @ A_12 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_263_insert__compr__raw,axiom,
% 0.29/0.47 ! [X: nat,Xa: nat > $o] :
% 0.29/0.47 ( ( insert_nat @ X @ Xa )
% 0.29/0.47 = ( collect_nat
% 0.29/0.47 @ ^ [Y: nat] : ( (|) @ ( Y = X ) @ ( member_nat @ Y @ Xa ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_264_insert__compr__raw,axiom,
% 0.29/0.47 ! [X: pname,Xa: pname > $o] :
% 0.29/0.47 ( ( insert_pname @ X @ Xa )
% 0.29/0.47 = ( collect_pname
% 0.29/0.47 @ ^ [Y: pname] : ( (|) @ ( Y = X ) @ ( member_pname @ Y @ Xa ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_265_insert__compr__raw,axiom,
% 0.29/0.47 ! [X: x_a,Xa: x_a > $o] :
% 0.29/0.47 ( ( insert_a @ X @ Xa )
% 0.29/0.47 = ( collect_a
% 0.29/0.47 @ ^ [Y: x_a] : ( (|) @ ( Y = X ) @ ( member_a @ Y @ Xa ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_266_insert__compr__raw,axiom,
% 0.29/0.47 ! [X: nat > $o,Xa: ( nat > $o ) > $o] :
% 0.29/0.47 ( ( insert_nat_o @ X @ Xa )
% 0.29/0.47 = ( collect_nat_o
% 0.29/0.47 @ ^ [Y: nat > $o] : ( (|) @ ( Y = X ) @ ( member_nat_o @ Y @ Xa ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_267_insert__compr__raw,axiom,
% 0.29/0.47 ! [X: pname > $o,Xa: ( pname > $o ) > $o] :
% 0.29/0.47 ( ( insert_pname_o @ X @ Xa )
% 0.29/0.47 = ( collect_pname_o
% 0.29/0.47 @ ^ [Y: pname > $o] : ( (|) @ ( Y = X ) @ ( member_pname_o @ Y @ Xa ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_268_insert__compr__raw,axiom,
% 0.29/0.47 ! [X: x_a > $o,Xa: ( x_a > $o ) > $o] :
% 0.29/0.47 ( ( insert_a_o @ X @ Xa )
% 0.29/0.47 = ( collect_a_o
% 0.29/0.47 @ ^ [Y: x_a > $o] : ( (|) @ ( Y = X ) @ ( member_a_o @ Y @ Xa ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_269_subset__insertI,axiom,
% 0.29/0.47 ! [B_10: nat > $o,A_11: nat] : ( ord_less_eq_nat_o @ B_10 @ ( insert_nat @ A_11 @ B_10 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_270_subset__insertI,axiom,
% 0.29/0.47 ! [B_10: pname > $o,A_11: pname] : ( ord_less_eq_pname_o @ B_10 @ ( insert_pname @ A_11 @ B_10 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_271_subset__insertI,axiom,
% 0.29/0.47 ! [B_10: x_a > $o,A_11: x_a] : ( ord_less_eq_a_o @ B_10 @ ( insert_a @ A_11 @ B_10 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_272_insert__subset,axiom,
% 0.29/0.47 ! [X_4: nat,A_10: nat > $o,B_9: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ ( insert_nat @ X_4 @ A_10 ) @ B_9 )
% 0.29/0.47 <=> ( ( member_nat @ X_4 @ B_9 )
% 0.29/0.47 & ( ord_less_eq_nat_o @ A_10 @ B_9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_273_insert__subset,axiom,
% 0.29/0.47 ! [X_4: pname,A_10: pname > $o,B_9: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_4 @ A_10 ) @ B_9 )
% 0.29/0.47 <=> ( ( member_pname @ X_4 @ B_9 )
% 0.29/0.47 & ( ord_less_eq_pname_o @ A_10 @ B_9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_274_insert__subset,axiom,
% 0.29/0.47 ! [X_4: x_a,A_10: x_a > $o,B_9: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ ( insert_a @ X_4 @ A_10 ) @ B_9 )
% 0.29/0.47 <=> ( ( member_a @ X_4 @ B_9 )
% 0.29/0.47 & ( ord_less_eq_a_o @ A_10 @ B_9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_275_subset__insert,axiom,
% 0.29/0.47 ! [B_8: nat > $o,X_3: nat,A_9: nat > $o] :
% 0.29/0.47 ( ~ ( member_nat @ X_3 @ A_9 )
% 0.29/0.47 => ( ( ord_less_eq_nat_o @ A_9 @ ( insert_nat @ X_3 @ B_8 ) )
% 0.29/0.47 <=> ( ord_less_eq_nat_o @ A_9 @ B_8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_276_subset__insert,axiom,
% 0.29/0.47 ! [B_8: pname > $o,X_3: pname,A_9: pname > $o] :
% 0.29/0.47 ( ~ ( member_pname @ X_3 @ A_9 )
% 0.29/0.47 => ( ( ord_less_eq_pname_o @ A_9 @ ( insert_pname @ X_3 @ B_8 ) )
% 0.29/0.47 <=> ( ord_less_eq_pname_o @ A_9 @ B_8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_277_subset__insert,axiom,
% 0.29/0.47 ! [B_8: x_a > $o,X_3: x_a,A_9: x_a > $o] :
% 0.29/0.47 ( ~ ( member_a @ X_3 @ A_9 )
% 0.29/0.47 => ( ( ord_less_eq_a_o @ A_9 @ ( insert_a @ X_3 @ B_8 ) )
% 0.29/0.47 <=> ( ord_less_eq_a_o @ A_9 @ B_8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_278_subset__insertI2,axiom,
% 0.29/0.47 ! [B_7: nat,A_8: nat > $o,B_6: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ A_8 @ B_6 )
% 0.29/0.47 => ( ord_less_eq_nat_o @ A_8 @ ( insert_nat @ B_7 @ B_6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_279_subset__insertI2,axiom,
% 0.29/0.47 ! [B_7: pname,A_8: pname > $o,B_6: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_8 @ B_6 )
% 0.29/0.47 => ( ord_less_eq_pname_o @ A_8 @ ( insert_pname @ B_7 @ B_6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_280_subset__insertI2,axiom,
% 0.29/0.47 ! [B_7: x_a,A_8: x_a > $o,B_6: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ A_8 @ B_6 )
% 0.29/0.47 => ( ord_less_eq_a_o @ A_8 @ ( insert_a @ B_7 @ B_6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_281_insert__mono,axiom,
% 0.29/0.47 ! [A_7: nat,C: nat > $o,D: nat > $o] :
% 0.29/0.47 ( ( ord_less_eq_nat_o @ C @ D )
% 0.29/0.47 => ( ord_less_eq_nat_o @ ( insert_nat @ A_7 @ C ) @ ( insert_nat @ A_7 @ D ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_282_insert__mono,axiom,
% 0.29/0.47 ! [A_7: pname,C: pname > $o,D: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ C @ D )
% 0.29/0.47 => ( ord_less_eq_pname_o @ ( insert_pname @ A_7 @ C ) @ ( insert_pname @ A_7 @ D ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_283_insert__mono,axiom,
% 0.29/0.47 ! [A_7: x_a,C: x_a > $o,D: x_a > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ C @ D )
% 0.29/0.47 => ( ord_less_eq_a_o @ ( insert_a @ A_7 @ C ) @ ( insert_a @ A_7 @ D ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_284_image__insert,axiom,
% 0.29/0.47 ! [F_5: pname > x_a,A_6: pname,B_5: pname > $o] :
% 0.29/0.47 ( ( image_pname_a @ F_5 @ ( insert_pname @ A_6 @ B_5 ) )
% 0.29/0.47 = ( insert_a @ ( F_5 @ A_6 ) @ ( image_pname_a @ F_5 @ B_5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_285_insert__image,axiom,
% 0.29/0.47 ! [F_4: pname > x_a,X_2: pname,A_5: pname > $o] :
% 0.29/0.47 ( ( member_pname @ X_2 @ A_5 )
% 0.29/0.47 => ( ( insert_a @ ( F_4 @ X_2 ) @ ( image_pname_a @ F_4 @ A_5 ) )
% 0.29/0.47 = ( image_pname_a @ F_4 @ A_5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_286_subset__image__iff,axiom,
% 0.29/0.47 ! [B_4: x_a > $o,F_3: pname > x_a,A_4: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_a_o @ B_4 @ ( image_pname_a @ F_3 @ A_4 ) )
% 0.29/0.47 <=> ? [AA: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ AA @ A_4 )
% 0.29/0.47 & ( B_4
% 0.29/0.47 = ( image_pname_a @ F_3 @ AA ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_287_image__mono,axiom,
% 0.29/0.47 ! [F_2: pname > x_a,A_3: pname > $o,B_3: pname > $o] :
% 0.29/0.47 ( ( ord_less_eq_pname_o @ A_3 @ B_3 )
% 0.29/0.47 => ( ord_less_eq_a_o @ ( image_pname_a @ F_2 @ A_3 ) @ ( image_pname_a @ F_2 @ B_3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_288_imageE,axiom,
% 0.29/0.47 ! [B_2: x_a,F_1: pname > x_a,A_2: pname > $o] :
% 0.29/0.47 ( ( member_a @ B_2 @ ( image_pname_a @ F_1 @ A_2 ) )
% 0.29/0.47 => ~ ! [X: pname] :
% 0.29/0.47 ( ( B_2
% 0.29/0.47 = ( F_1 @ X ) )
% 0.29/0.47 => ~ ( member_pname @ X @ A_2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_289_subsetI,axiom,
% 0.29/0.47 ! [B_1: nat > $o,A_1: nat > $o] :
% 0.29/0.47 ( ! [X: nat] :
% 0.29/0.47 ( ( member_nat @ X @ A_1 )
% 0.29/0.47 => ( member_nat @ X @ B_1 ) )
% 0.29/0.47 => ( ord_less_eq_nat_o @ A_1 @ B_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_290_subsetI,axiom,
% 0.29/0.47 ! [B_1: x_a > $o,A_1: x_a > $o] :
% 0.29/0.47 ( ! [X: x_a] :
% 0.29/0.47 ( ( member_a @ X @ A_1 )
% 0.29/0.47 => ( member_a @ X @ B_1 ) )
% 0.29/0.47 => ( ord_less_eq_a_o @ A_1 @ B_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_291_subsetI,axiom,
% 0.29/0.47 ! [B_1: pname > $o,A_1: pname > $o] :
% 0.29/0.47 ( ! [X: pname] :
% 0.29/0.47 ( ( member_pname @ X @ A_1 )
% 0.29/0.47 => ( member_pname @ X @ B_1 ) )
% 0.29/0.47 => ( ord_less_eq_pname_o @ A_1 @ B_1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_292_zero__induct__lemma,axiom,
% 0.29/0.47 ! [I: nat,P: nat > $o,K: nat] :
% 0.29/0.47 ( ( P @ K )
% 0.29/0.47 => ( ! [N_2: nat] :
% 0.29/0.47 ( ( P @ ( suc @ N_2 ) )
% 0.29/0.47 => ( P @ N_2 ) )
% 0.29/0.47 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_293_Suc__le__D,axiom,
% 0.29/0.47 ! [N_1: nat,M_1: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_1 )
% 0.29/0.47 => ? [M: nat] :
% 0.29/0.47 ( M_1
% 0.29/0.47 = ( suc @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_294_image__subsetI,axiom,
% 0.29/0.47 ! [F: pname > x_a,B: x_a > $o,A: pname > $o] :
% 0.29/0.47 ( ! [X: pname] :
% 0.29/0.47 ( ( member_pname @ X @ A )
% 0.29/0.47 => ( member_a @ ( F @ X ) @ B ) )
% 0.29/0.47 => ( ord_less_eq_a_o @ ( image_pname_a @ F @ A ) @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_295_order__refl,axiom,
% 0.29/0.47 ! [X_1: nat > $o] : ( ord_less_eq_nat_o @ X_1 @ X_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_296_order__refl,axiom,
% 0.29/0.47 ! [X_1: pname > $o] : ( ord_less_eq_pname_o @ X_1 @ X_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_297_order__refl,axiom,
% 0.29/0.47 ! [X_1: nat] : ( ord_less_eq_nat @ X_1 @ X_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_298_order__refl,axiom,
% 0.29/0.47 ! [X_1: x_a > $o] : ( ord_less_eq_a_o @ X_1 @ X_1 ) ).
% 0.29/0.47
% 0.29/0.47 thf(fact_299_finite__nat__set__iff__bounded__le,axiom,
% 0.29/0.47 ! [N: nat > $o] :
% 0.29/0.47 ( ( finite_finite_nat @ N )
% 0.29/0.47 <=> ? [M: nat] :
% 0.29/0.47 ! [X: nat] :
% 0.29/0.47 ( ( member_nat @ X @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ X @ M ) ) ) ).
% 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 ------------------------
% 2.69/1.48 ---- Embedded in THF ---
% 2.69/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.69/1.48 %%% Generated on Tue Feb 24 13:40:10 EST 2026
% 2.69/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.69/1.48 %%% Logic specification used:
% 2.69/1.48 %%% thf(spec, logic, $$dhol).
% 2.69/1.48
% 2.69/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2DTF30594.p
% See solution above
% 2.69/1.48 ------------------------
% 2.93/1.51 ---- Cleaned THF ---
% 2.93/1.51 thf(ty_ty_t__a,type,
% 2.93/1.51 x_a: $tType ).
% 2.93/1.51
% 2.93/1.51 thf(ty_ty_tc__Com__Opname,type,
% 2.93/1.51 pname: $tType ).
% 2.93/1.51
% 2.93/1.51 thf(ty_ty_tc__Nat__Onat,type,
% 2.93/1.51 nat: $tType ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ocard_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 finite_card_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ocard_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 finite221134632me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ocard_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 finite_card_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ocard_000_062_It__a_M_Eo_J,type,
% 2.93/1.51 finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Com__Opname_M_Eo_J,type,
% 2.93/1.51 finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 2.93/1.51 finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ocard_000t__a,type,
% 2.93/1.51 finite_card_a: ( x_a > $o ) > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ocard_000tc__Com__Opname,type,
% 2.93/1.51 finite_card_pname: ( pname > $o ) > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
% 2.93/1.51 finite_card_nat: ( nat > $o ) > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 finite1302365357_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo,type,
% 2.93/1.51 finite1648353812_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 finite1237261006_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000_062_It__a_M_Eo_J,type,
% 2.93/1.51 finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 2.93/1.51 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 2.93/1.51 finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000t__a,type,
% 2.93/1.51 finite_finite_a: ( x_a > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 2.93/1.51 finite_finite_pname: ( pname > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
% 2.93/1.51 finite_finite_nat: ( nat > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 2.93/1.51 minus_minus_nat: nat > nat > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Nat_OSuc,type,
% 2.93/1.51 suc: nat > nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_E,type,
% 2.93/1.51 ord_less_eq_a_o_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J,type,
% 2.93/1.51 ord_le1828183645_o_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M,type,
% 2.93/1.51 ord_le124054423_o_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 2.93/1.51 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_It__a_M_Eo_J,type,
% 2.93/1.51 ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 2.93/1.51 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 2.93/1.51 ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 2.93/1.51 ord_less_eq_nat: nat > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 collect_a_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 collect_pname_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 collect_nat_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000_062_It__a_M_Eo_J,type,
% 2.93/1.51 collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 2.93/1.51 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 2.93/1.51 collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000t__a,type,
% 2.93/1.51 collect_a: ( x_a > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 2.93/1.51 collect_pname: ( pname > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_OCollect_000tc__Nat__Onat,type,
% 2.93/1.51 collect_nat: ( nat > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000t__a,type,
% 2.93/1.51 image_a_o_o_a: ( ( ( x_a > $o ) > $o ) > x_a ) > ( ( ( x_a > $o ) > $o ) > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 2.93/1.51 image_a_o_o_pname: ( ( ( x_a > $o ) > $o ) > pname ) > ( ( ( x_a > $o ) > $o ) > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000tc__Nat__Onat,type,
% 2.93/1.51 image_a_o_o_nat: ( ( ( x_a > $o ) > $o ) > nat ) > ( ( ( x_a > $o ) > $o ) > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000t__a,type,
% 2.93/1.51 image_pname_o_o_a: ( ( ( pname > $o ) > $o ) > x_a ) > ( ( ( pname > $o ) > $o ) > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 2.93/1.51 image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Nat__Onat,type,
% 2.93/1.51 image_pname_o_o_nat: ( ( ( pname > $o ) > $o ) > nat ) > ( ( ( pname > $o ) > $o ) > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000t__a,type,
% 2.93/1.51 image_nat_o_o_a: ( ( ( nat > $o ) > $o ) > x_a ) > ( ( ( nat > $o ) > $o ) > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 2.93/1.51 image_nat_o_o_pname: ( ( ( nat > $o ) > $o ) > pname ) > ( ( ( nat > $o ) > $o ) > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000tc__Nat__Onat,type,
% 2.93/1.51 image_nat_o_o_nat: ( ( ( nat > $o ) > $o ) > nat ) > ( ( ( nat > $o ) > $o ) > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000t__a,type,
% 2.93/1.51 image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Com__Opname,type,
% 2.93/1.51 image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Nat__Onat,type,
% 2.93/1.51 image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000t__a,type,
% 2.93/1.51 image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 2.93/1.51 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat,type,
% 2.93/1.51 image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000t__a,type,
% 2.93/1.51 image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Com__Opname,type,
% 2.93/1.51 image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat,type,
% 2.93/1.51 image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000t__a_000t__a,type,
% 2.93/1.51 image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000t__a_000tc__Com__Opname,type,
% 2.93/1.51 image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000t__a_000tc__Nat__Onat,type,
% 2.93/1.51 image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 image_pname_a_o_o: ( pname > ( x_a > $o ) > $o ) > ( pname > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 image_pname_nat_o_o: ( pname > ( nat > $o ) > $o ) > ( pname > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_It__a_M_Eo_J,type,
% 2.93/1.51 image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 2.93/1.51 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 2.93/1.51 image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Com__Opname_000t__a,type,
% 2.93/1.51 image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 2.93/1.51 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat,type,
% 2.93/1.51 image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 image_nat_a_o_o: ( nat > ( x_a > $o ) > $o ) > ( nat > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 image_nat_pname_o_o: ( nat > ( pname > $o ) > $o ) > ( nat > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 image_nat_nat_o_o: ( nat > ( nat > $o ) > $o ) > ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_It__a_M_Eo_J,type,
% 2.93/1.51 image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Com__Opname_M_Eo_J,type,
% 2.93/1.51 image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 2.93/1.51 image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000t__a,type,
% 2.93/1.51 image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,type,
% 2.93/1.51 image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oinsert_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 insert_a_o_o: ( ( x_a > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 insert_pname_o_o: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 2.93/1.51 insert_nat_o_o: ( ( nat > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oinsert_000_062_It__a_M_Eo_J,type,
% 2.93/1.51 insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 2.93/1.51 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 2.93/1.51 insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oinsert_000t__a,type,
% 2.93/1.51 insert_a: x_a > ( x_a > $o ) > x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 2.93/1.51 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_Set_Oinsert_000tc__Nat__Onat,type,
% 2.93/1.51 insert_nat: nat > ( nat > $o ) > nat > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_member_000_062_It__a_M_Eo_J,type,
% 2.93/1.51 member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 2.93/1.51 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 2.93/1.51 member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_member_000t__a,type,
% 2.93/1.51 member_a: x_a > ( x_a > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_member_000tc__Com__Opname,type,
% 2.93/1.51 member_pname: pname > ( pname > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_c_member_000tc__Nat__Onat,type,
% 2.93/1.51 member_nat: nat > ( nat > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_v_G,type,
% 2.93/1.51 g: x_a > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_v_P,type,
% 2.93/1.51 p: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_v_U,type,
% 2.93/1.51 u: pname > $o ).
% 2.93/1.51
% 2.93/1.51 thf(sy_v_mgt__call,type,
% 2.93/1.51 mgt_call: pname > x_a ).
% 2.93/1.51
% 2.93/1.51 thf(sy_v_na,type,
% 2.93/1.51 na: nat ).
% 2.93/1.51
% 2.93/1.51 thf(sy_v_pn,type,
% 2.93/1.51 pn: pname ).
% 2.93/1.51
% 2.93/1.51 thf(fact_0_assms_I1_J,axiom,
% 2.93/1.51 ! [Ts: x_a > $o,G: x_a > $o] :
% 2.93/1.51 ( ( ord_less_eq_a_o @ Ts @ G )
% 2.93/1.51 => ( p @ G @ Ts ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_1_finite__Collect__subsets,axiom,
% 2.93/1.51 ! [A_59: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ A_59 )
% 2.93/1.51 => ( finite_finite_nat_o
% 2.93/1.51 @ ( collect_nat_o
% 2.93/1.51 @ ^ [B_38: nat > $o] : ( ord_less_eq_nat_o @ B_38 @ A_59 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_2_finite__Collect__subsets,axiom,
% 2.93/1.51 ! [A_59: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ A_59 )
% 2.93/1.51 => ( finite297249702name_o
% 2.93/1.51 @ ( collect_pname_o
% 2.93/1.51 @ ^ [B_38: pname > $o] : ( ord_less_eq_pname_o @ B_38 @ A_59 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_3_finite__Collect__subsets,axiom,
% 2.93/1.51 ! [A_59: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ A_59 )
% 2.93/1.51 => ( finite_finite_a_o
% 2.93/1.51 @ ( collect_a_o
% 2.93/1.51 @ ^ [B_38: x_a > $o] : ( ord_less_eq_a_o @ B_38 @ A_59 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_4_finite__Collect__subsets,axiom,
% 2.93/1.51 ! [A_59: ( ( nat > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1676163439at_o_o @ A_59 )
% 2.93/1.51 => ( finite1237261006_o_o_o
% 2.93/1.51 @ ( collect_nat_o_o_o
% 2.93/1.51 @ ^ [B_38: ( ( nat > $o ) > $o ) > $o] : ( ord_le124054423_o_o_o @ B_38 @ A_59 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_5_finite__Collect__subsets,axiom,
% 2.93/1.51 ! [A_59: ( ( pname > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1066544169me_o_o @ A_59 )
% 2.93/1.51 => ( finite1648353812_o_o_o
% 2.93/1.51 @ ( collect_pname_o_o_o
% 2.93/1.51 @ ^ [B_38: ( ( pname > $o ) > $o ) > $o] : ( ord_le1828183645_o_o_o @ B_38 @ A_59 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_6_finite__Collect__subsets,axiom,
% 2.93/1.51 ! [A_59: ( ( x_a > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o_o @ A_59 )
% 2.93/1.51 => ( finite1302365357_o_o_o
% 2.93/1.51 @ ( collect_a_o_o_o
% 2.93/1.51 @ ^ [B_38: ( ( x_a > $o ) > $o ) > $o] : ( ord_less_eq_a_o_o_o @ B_38 @ A_59 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_7_finite__Collect__subsets,axiom,
% 2.93/1.51 ! [A_59: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ A_59 )
% 2.93/1.51 => ( finite_finite_a_o_o
% 2.93/1.51 @ ( collect_a_o_o
% 2.93/1.51 @ ^ [B_38: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B_38 @ A_59 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_8_finite__Collect__subsets,axiom,
% 2.93/1.51 ! [A_59: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ A_59 )
% 2.93/1.51 => ( finite1066544169me_o_o
% 2.93/1.51 @ ( collect_pname_o_o
% 2.93/1.51 @ ^ [B_38: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_38 @ A_59 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_9_finite__Collect__subsets,axiom,
% 2.93/1.51 ! [A_59: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ A_59 )
% 2.93/1.51 => ( finite1676163439at_o_o
% 2.93/1.51 @ ( collect_nat_o_o
% 2.93/1.51 @ ^ [B_38: ( nat > $o ) > $o] : ( ord_less_eq_nat_o_o @ B_38 @ A_59 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_10_finite__imageI,axiom,
% 2.93/1.51 ! [H: pname > x_a,F_15: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ F_15 )
% 2.93/1.51 => ( finite_finite_a @ ( image_pname_a @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_11_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( ( nat > $o ) > $o ) > nat,F_15: ( ( nat > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1676163439at_o_o @ F_15 )
% 2.93/1.51 => ( finite_finite_nat @ ( image_nat_o_o_nat @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_12_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( ( pname > $o ) > $o ) > nat,F_15: ( ( pname > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1066544169me_o_o @ F_15 )
% 2.93/1.51 => ( finite_finite_nat @ ( image_pname_o_o_nat @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_13_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( ( x_a > $o ) > $o ) > nat,F_15: ( ( x_a > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o_o @ F_15 )
% 2.93/1.51 => ( finite_finite_nat @ ( image_a_o_o_nat @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_14_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( x_a > $o ) > nat,F_15: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ F_15 )
% 2.93/1.51 => ( finite_finite_nat @ ( image_a_o_nat @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_15_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( pname > $o ) > nat,F_15: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ F_15 )
% 2.93/1.51 => ( finite_finite_nat @ ( image_pname_o_nat @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_16_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( nat > $o ) > nat,F_15: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ F_15 )
% 2.93/1.51 => ( finite_finite_nat @ ( image_nat_o_nat @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_17_finite__imageI,axiom,
% 2.93/1.51 ! [H: x_a > nat,F_15: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ F_15 )
% 2.93/1.51 => ( finite_finite_nat @ ( image_a_nat @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_18_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( ( nat > $o ) > $o ) > pname,F_15: ( ( nat > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1676163439at_o_o @ F_15 )
% 2.93/1.51 => ( finite_finite_pname @ ( image_nat_o_o_pname @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_19_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( ( pname > $o ) > $o ) > pname,F_15: ( ( pname > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1066544169me_o_o @ F_15 )
% 2.93/1.51 => ( finite_finite_pname @ ( image_471733107_pname @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_20_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( ( x_a > $o ) > $o ) > pname,F_15: ( ( x_a > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o_o @ F_15 )
% 2.93/1.51 => ( finite_finite_pname @ ( image_a_o_o_pname @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_21_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( x_a > $o ) > pname,F_15: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ F_15 )
% 2.93/1.51 => ( finite_finite_pname @ ( image_a_o_pname @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_22_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( pname > $o ) > pname,F_15: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ F_15 )
% 2.93/1.51 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_23_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( nat > $o ) > pname,F_15: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ F_15 )
% 2.93/1.51 => ( finite_finite_pname @ ( image_nat_o_pname @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_24_finite__imageI,axiom,
% 2.93/1.51 ! [H: x_a > pname,F_15: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ F_15 )
% 2.93/1.51 => ( finite_finite_pname @ ( image_a_pname @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_25_finite__imageI,axiom,
% 2.93/1.51 ! [H: nat > ( nat > $o ) > $o,F_15: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ F_15 )
% 2.93/1.51 => ( finite1676163439at_o_o @ ( image_nat_nat_o_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_26_finite__imageI,axiom,
% 2.93/1.51 ! [H: nat > ( pname > $o ) > $o,F_15: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ F_15 )
% 2.93/1.51 => ( finite1066544169me_o_o @ ( image_nat_pname_o_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_27_finite__imageI,axiom,
% 2.93/1.51 ! [H: nat > ( x_a > $o ) > $o,F_15: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ F_15 )
% 2.93/1.51 => ( finite_finite_a_o_o @ ( image_nat_a_o_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_28_finite__imageI,axiom,
% 2.93/1.51 ! [H: nat > x_a > $o,F_15: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ F_15 )
% 2.93/1.51 => ( finite_finite_a_o @ ( image_nat_a_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_29_finite__imageI,axiom,
% 2.93/1.51 ! [H: nat > pname > $o,F_15: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ F_15 )
% 2.93/1.51 => ( finite297249702name_o @ ( image_nat_pname_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_30_finite__imageI,axiom,
% 2.93/1.51 ! [H: nat > nat > $o,F_15: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ F_15 )
% 2.93/1.51 => ( finite_finite_nat_o @ ( image_nat_nat_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_31_finite__imageI,axiom,
% 2.93/1.51 ! [H: nat > x_a,F_15: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ F_15 )
% 2.93/1.51 => ( finite_finite_a @ ( image_nat_a @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_32_finite__imageI,axiom,
% 2.93/1.51 ! [H: pname > ( nat > $o ) > $o,F_15: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ F_15 )
% 2.93/1.51 => ( finite1676163439at_o_o @ ( image_pname_nat_o_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_33_finite__imageI,axiom,
% 2.93/1.51 ! [H: pname > ( pname > $o ) > $o,F_15: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ F_15 )
% 2.93/1.51 => ( finite1066544169me_o_o @ ( image_504089495me_o_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_34_finite__imageI,axiom,
% 2.93/1.51 ! [H: pname > ( x_a > $o ) > $o,F_15: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ F_15 )
% 2.93/1.51 => ( finite_finite_a_o_o @ ( image_pname_a_o_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_35_finite__imageI,axiom,
% 2.93/1.51 ! [H: pname > x_a > $o,F_15: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ F_15 )
% 2.93/1.51 => ( finite_finite_a_o @ ( image_pname_a_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_36_finite__imageI,axiom,
% 2.93/1.51 ! [H: pname > pname > $o,F_15: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ F_15 )
% 2.93/1.51 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_37_finite__imageI,axiom,
% 2.93/1.51 ! [H: pname > nat > $o,F_15: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ F_15 )
% 2.93/1.51 => ( finite_finite_nat_o @ ( image_pname_nat_o @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_38_finite__imageI,axiom,
% 2.93/1.51 ! [H: pname > pname,F_15: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ F_15 )
% 2.93/1.51 => ( finite_finite_pname @ ( image_pname_pname @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_39_finite__imageI,axiom,
% 2.93/1.51 ! [H: x_a > x_a,F_15: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ F_15 )
% 2.93/1.51 => ( finite_finite_a @ ( image_a_a @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_40_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( nat > $o ) > x_a,F_15: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ F_15 )
% 2.93/1.51 => ( finite_finite_a @ ( image_nat_o_a @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_41_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( pname > $o ) > x_a,F_15: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ F_15 )
% 2.93/1.51 => ( finite_finite_a @ ( image_pname_o_a @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_42_finite__imageI,axiom,
% 2.93/1.51 ! [H: ( x_a > $o ) > x_a,F_15: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ F_15 )
% 2.93/1.51 => ( finite_finite_a @ ( image_a_o_a @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_43_finite__imageI,axiom,
% 2.93/1.51 ! [H: pname > nat,F_15: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ F_15 )
% 2.93/1.51 => ( finite_finite_nat @ ( image_pname_nat @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_44_finite__imageI,axiom,
% 2.93/1.51 ! [H: nat > pname,F_15: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ F_15 )
% 2.93/1.51 => ( finite_finite_pname @ ( image_nat_pname @ H @ F_15 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_45_finite_OinsertI,axiom,
% 2.93/1.51 ! [A_58: x_a,A_57: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ A_57 )
% 2.93/1.51 => ( finite_finite_a @ ( insert_a @ A_58 @ A_57 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_46_finite_OinsertI,axiom,
% 2.93/1.51 ! [A_58: nat,A_57: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ A_57 )
% 2.93/1.51 => ( finite_finite_nat @ ( insert_nat @ A_58 @ A_57 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_47_finite_OinsertI,axiom,
% 2.93/1.51 ! [A_58: pname,A_57: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ A_57 )
% 2.93/1.51 => ( finite_finite_pname @ ( insert_pname @ A_58 @ A_57 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_48_finite_OinsertI,axiom,
% 2.93/1.51 ! [A_58: ( nat > $o ) > $o,A_57: ( ( nat > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1676163439at_o_o @ A_57 )
% 2.93/1.51 => ( finite1676163439at_o_o @ ( insert_nat_o_o @ A_58 @ A_57 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_49_finite_OinsertI,axiom,
% 2.93/1.51 ! [A_58: ( pname > $o ) > $o,A_57: ( ( pname > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1066544169me_o_o @ A_57 )
% 2.93/1.51 => ( finite1066544169me_o_o @ ( insert_pname_o_o @ A_58 @ A_57 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_50_finite_OinsertI,axiom,
% 2.93/1.51 ! [A_58: ( x_a > $o ) > $o,A_57: ( ( x_a > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o_o @ A_57 )
% 2.93/1.51 => ( finite_finite_a_o_o @ ( insert_a_o_o @ A_58 @ A_57 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_51_finite_OinsertI,axiom,
% 2.93/1.51 ! [A_58: x_a > $o,A_57: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ A_57 )
% 2.93/1.51 => ( finite_finite_a_o @ ( insert_a_o @ A_58 @ A_57 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_52_finite_OinsertI,axiom,
% 2.93/1.51 ! [A_58: pname > $o,A_57: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ A_57 )
% 2.93/1.51 => ( finite297249702name_o @ ( insert_pname_o @ A_58 @ A_57 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_53_finite_OinsertI,axiom,
% 2.93/1.51 ! [A_58: nat > $o,A_57: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ A_57 )
% 2.93/1.51 => ( finite_finite_nat_o @ ( insert_nat_o @ A_58 @ A_57 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_54_card__image__le,axiom,
% 2.93/1.51 ! [F_14: pname > nat,A_56: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_55_card__image__le,axiom,
% 2.93/1.51 ! [F_14: x_a > nat,A_56: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ F_14 @ A_56 ) ) @ ( finite_card_a @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_56_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( nat > $o ) > nat,A_56: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_o_nat @ F_14 @ A_56 ) ) @ ( finite_card_nat_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_57_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( pname > $o ) > nat,A_56: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_o_nat @ F_14 @ A_56 ) ) @ ( finite_card_pname_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_58_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( x_a > $o ) > nat,A_56: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ F_14 @ A_56 ) ) @ ( finite_card_a_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_59_card__image__le,axiom,
% 2.93/1.51 ! [F_14: x_a > pname,A_56: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ F_14 @ A_56 ) ) @ ( finite_card_a @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_60_card__image__le,axiom,
% 2.93/1.51 ! [F_14: nat > pname,A_56: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_pname @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_61_card__image__le,axiom,
% 2.93/1.51 ! [F_14: pname > x_a,A_56: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_62_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( ( nat > $o ) > $o ) > x_a,A_56: ( ( nat > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1676163439at_o_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_o_a @ F_14 @ A_56 ) ) @ ( finite_card_nat_o_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_63_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( ( pname > $o ) > $o ) > x_a,A_56: ( ( pname > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite1066544169me_o_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_o_a @ F_14 @ A_56 ) ) @ ( finite221134632me_o_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_64_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( ( x_a > $o ) > $o ) > x_a,A_56: ( ( x_a > $o ) > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_o_a @ F_14 @ A_56 ) ) @ ( finite_card_a_o_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_65_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( x_a > $o ) > x_a,A_56: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ F_14 @ A_56 ) ) @ ( finite_card_a_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_66_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( pname > $o ) > x_a,A_56: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_a @ F_14 @ A_56 ) ) @ ( finite_card_pname_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_67_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( nat > $o ) > x_a,A_56: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_a @ F_14 @ A_56 ) ) @ ( finite_card_nat_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_68_card__image__le,axiom,
% 2.93/1.51 ! [F_14: x_a > x_a,A_56: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ F_14 @ A_56 ) ) @ ( finite_card_a @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_69_card__image__le,axiom,
% 2.93/1.51 ! [F_14: pname > pname,A_56: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_70_card__image__le,axiom,
% 2.93/1.51 ! [F_14: pname > nat > $o,A_56: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat_o @ ( image_pname_nat_o @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_71_card__image__le,axiom,
% 2.93/1.51 ! [F_14: pname > pname > $o,A_56: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname_o @ ( image_pname_pname_o @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_72_card__image__le,axiom,
% 2.93/1.51 ! [F_14: pname > x_a > $o,A_56: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a_o @ ( image_pname_a_o @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_73_card__image__le,axiom,
% 2.93/1.51 ! [F_14: nat > x_a,A_56: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_a @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_74_card__image__le,axiom,
% 2.93/1.51 ! [F_14: nat > nat > $o,A_56: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat_o @ ( image_nat_nat_o @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_75_card__image__le,axiom,
% 2.93/1.51 ! [F_14: nat > pname > $o,A_56: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname_o @ ( image_nat_pname_o @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_76_card__image__le,axiom,
% 2.93/1.51 ! [F_14: nat > x_a > $o,A_56: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a_o @ ( image_nat_a_o @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_77_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( nat > $o ) > pname,A_56: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_o_pname @ F_14 @ A_56 ) ) @ ( finite_card_nat_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_78_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( pname > $o ) > pname,A_56: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_o_pname @ F_14 @ A_56 ) ) @ ( finite_card_pname_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_79_card__image__le,axiom,
% 2.93/1.51 ! [F_14: ( x_a > $o ) > pname,A_56: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ A_56 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_o_pname @ F_14 @ A_56 ) ) @ ( finite_card_a_o @ A_56 ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_80_card__mono,axiom,
% 2.93/1.51 ! [A_55: ( nat > $o ) > $o,B_37: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ B_37 )
% 2.93/1.51 => ( ( ord_less_eq_nat_o_o @ A_55 @ B_37 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_55 ) @ ( finite_card_nat_o @ B_37 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_81_card__mono,axiom,
% 2.93/1.51 ! [A_55: ( pname > $o ) > $o,B_37: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ B_37 )
% 2.93/1.51 => ( ( ord_le1205211808me_o_o @ A_55 @ B_37 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_55 ) @ ( finite_card_pname_o @ B_37 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_82_card__mono,axiom,
% 2.93/1.51 ! [A_55: ( x_a > $o ) > $o,B_37: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ B_37 )
% 2.93/1.51 => ( ( ord_less_eq_a_o_o @ A_55 @ B_37 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_55 ) @ ( finite_card_a_o @ B_37 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_83_card__mono,axiom,
% 2.93/1.51 ! [A_55: pname > $o,B_37: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ B_37 )
% 2.93/1.51 => ( ( ord_less_eq_pname_o @ A_55 @ B_37 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname @ A_55 ) @ ( finite_card_pname @ B_37 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_84_card__mono,axiom,
% 2.93/1.51 ! [A_55: x_a > $o,B_37: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ B_37 )
% 2.93/1.51 => ( ( ord_less_eq_a_o @ A_55 @ B_37 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ A_55 ) @ ( finite_card_a @ B_37 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_85_card__mono,axiom,
% 2.93/1.51 ! [A_55: nat > $o,B_37: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ B_37 )
% 2.93/1.51 => ( ( ord_less_eq_nat_o @ A_55 @ B_37 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat @ A_55 ) @ ( finite_card_nat @ B_37 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_86_card__seteq,axiom,
% 2.93/1.51 ! [A_54: ( nat > $o ) > $o,B_36: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_nat_o_o @ A_54 @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_nat @ ( finite_card_nat_o @ B_36 ) @ ( finite_card_nat_o @ A_54 ) )
% 2.93/1.51 => ( A_54 = B_36 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_87_card__seteq,axiom,
% 2.93/1.51 ! [A_54: ( pname > $o ) > $o,B_36: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ B_36 )
% 2.93/1.51 => ( ( ord_le1205211808me_o_o @ A_54 @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_nat @ ( finite_card_pname_o @ B_36 ) @ ( finite_card_pname_o @ A_54 ) )
% 2.93/1.51 => ( A_54 = B_36 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_88_card__seteq,axiom,
% 2.93/1.51 ! [A_54: ( x_a > $o ) > $o,B_36: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_a_o_o @ A_54 @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_nat @ ( finite_card_a_o @ B_36 ) @ ( finite_card_a_o @ A_54 ) )
% 2.93/1.51 => ( A_54 = B_36 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_89_card__seteq,axiom,
% 2.93/1.51 ! [A_54: pname > $o,B_36: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_pname_o @ A_54 @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_nat @ ( finite_card_pname @ B_36 ) @ ( finite_card_pname @ A_54 ) )
% 2.93/1.51 => ( A_54 = B_36 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_90_card__seteq,axiom,
% 2.93/1.51 ! [A_54: x_a > $o,B_36: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_a_o @ A_54 @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_nat @ ( finite_card_a @ B_36 ) @ ( finite_card_a @ A_54 ) )
% 2.93/1.51 => ( A_54 = B_36 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_91_card__seteq,axiom,
% 2.93/1.51 ! [A_54: nat > $o,B_36: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_nat_o @ A_54 @ B_36 )
% 2.93/1.51 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B_36 ) @ ( finite_card_nat @ A_54 ) )
% 2.93/1.51 => ( A_54 = B_36 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_92_card__insert__le,axiom,
% 2.93/1.51 ! [X_19: nat > $o,A_53: ( nat > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_nat_o @ A_53 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_53 ) @ ( finite_card_nat_o @ ( insert_nat_o @ X_19 @ A_53 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_93_card__insert__le,axiom,
% 2.93/1.51 ! [X_19: pname > $o,A_53: ( pname > $o ) > $o] :
% 2.93/1.51 ( ( finite297249702name_o @ A_53 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_53 ) @ ( finite_card_pname_o @ ( insert_pname_o @ X_19 @ A_53 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_94_card__insert__le,axiom,
% 2.93/1.51 ! [X_19: x_a > $o,A_53: ( x_a > $o ) > $o] :
% 2.93/1.51 ( ( finite_finite_a_o @ A_53 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_53 ) @ ( finite_card_a_o @ ( insert_a_o @ X_19 @ A_53 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_95_card__insert__le,axiom,
% 2.93/1.51 ! [X_19: pname,A_53: pname > $o] :
% 2.93/1.51 ( ( finite_finite_pname @ A_53 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_pname @ A_53 ) @ ( finite_card_pname @ ( insert_pname @ X_19 @ A_53 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_96_card__insert__le,axiom,
% 2.93/1.51 ! [X_19: nat,A_53: nat > $o] :
% 2.93/1.51 ( ( finite_finite_nat @ A_53 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_nat @ A_53 ) @ ( finite_card_nat @ ( insert_nat @ X_19 @ A_53 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_97_card__insert__le,axiom,
% 2.93/1.51 ! [X_19: x_a,A_53: x_a > $o] :
% 2.93/1.51 ( ( finite_finite_a @ A_53 )
% 2.93/1.51 => ( ord_less_eq_nat @ ( finite_card_a @ A_53 ) @ ( finite_card_a @ ( insert_a @ X_19 @ A_53 ) ) ) ) ).
% 2.93/1.51
% 2.93/1.51 thf(fact_98_card__insert__if,axiom,
% 2.93/1.52 ! [X_18: nat > $o,A_52: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_nat_o @ A_52 )
% 2.93/1.52 => ( ( ( member_nat_o @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_18 @ A_52 ) )
% 2.93/1.52 = ( finite_card_nat_o @ A_52 ) ) )
% 2.93/1.52 & ( ~ ( member_nat_o @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_18 @ A_52 ) )
% 2.93/1.52 = ( suc @ ( finite_card_nat_o @ A_52 ) ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_99_card__insert__if,axiom,
% 2.93/1.52 ! [X_18: pname > $o,A_52: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( finite297249702name_o @ A_52 )
% 2.93/1.52 => ( ( ( member_pname_o @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_18 @ A_52 ) )
% 2.93/1.52 = ( finite_card_pname_o @ A_52 ) ) )
% 2.93/1.52 & ( ~ ( member_pname_o @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_18 @ A_52 ) )
% 2.93/1.52 = ( suc @ ( finite_card_pname_o @ A_52 ) ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_100_card__insert__if,axiom,
% 2.93/1.52 ! [X_18: x_a > $o,A_52: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_a_o @ A_52 )
% 2.93/1.52 => ( ( ( member_a_o @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_a_o @ ( insert_a_o @ X_18 @ A_52 ) )
% 2.93/1.52 = ( finite_card_a_o @ A_52 ) ) )
% 2.93/1.52 & ( ~ ( member_a_o @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_a_o @ ( insert_a_o @ X_18 @ A_52 ) )
% 2.93/1.52 = ( suc @ ( finite_card_a_o @ A_52 ) ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_101_card__insert__if,axiom,
% 2.93/1.52 ! [X_18: nat,A_52: nat > $o] :
% 2.93/1.52 ( ( finite_finite_nat @ A_52 )
% 2.93/1.52 => ( ( ( member_nat @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_nat @ ( insert_nat @ X_18 @ A_52 ) )
% 2.93/1.52 = ( finite_card_nat @ A_52 ) ) )
% 2.93/1.52 & ( ~ ( member_nat @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_nat @ ( insert_nat @ X_18 @ A_52 ) )
% 2.93/1.52 = ( suc @ ( finite_card_nat @ A_52 ) ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_102_card__insert__if,axiom,
% 2.93/1.52 ! [X_18: pname,A_52: pname > $o] :
% 2.93/1.52 ( ( finite_finite_pname @ A_52 )
% 2.93/1.52 => ( ( ( member_pname @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_pname @ ( insert_pname @ X_18 @ A_52 ) )
% 2.93/1.52 = ( finite_card_pname @ A_52 ) ) )
% 2.93/1.52 & ( ~ ( member_pname @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_pname @ ( insert_pname @ X_18 @ A_52 ) )
% 2.93/1.52 = ( suc @ ( finite_card_pname @ A_52 ) ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_103_card__insert__if,axiom,
% 2.93/1.52 ! [X_18: x_a,A_52: x_a > $o] :
% 2.93/1.52 ( ( finite_finite_a @ A_52 )
% 2.93/1.52 => ( ( ( member_a @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_a @ ( insert_a @ X_18 @ A_52 ) )
% 2.93/1.52 = ( finite_card_a @ A_52 ) ) )
% 2.93/1.52 & ( ~ ( member_a @ X_18 @ A_52 )
% 2.93/1.52 => ( ( finite_card_a @ ( insert_a @ X_18 @ A_52 ) )
% 2.93/1.52 = ( suc @ ( finite_card_a @ A_52 ) ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_104_card__insert__disjoint,axiom,
% 2.93/1.52 ! [X_17: nat > $o,A_51: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_nat_o @ A_51 )
% 2.93/1.52 => ( ~ ( member_nat_o @ X_17 @ A_51 )
% 2.93/1.52 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_17 @ A_51 ) )
% 2.93/1.52 = ( suc @ ( finite_card_nat_o @ A_51 ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_105_card__insert__disjoint,axiom,
% 2.93/1.52 ! [X_17: pname > $o,A_51: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( finite297249702name_o @ A_51 )
% 2.93/1.52 => ( ~ ( member_pname_o @ X_17 @ A_51 )
% 2.93/1.52 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_17 @ A_51 ) )
% 2.93/1.52 = ( suc @ ( finite_card_pname_o @ A_51 ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_106_card__insert__disjoint,axiom,
% 2.93/1.52 ! [X_17: x_a > $o,A_51: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_a_o @ A_51 )
% 2.93/1.52 => ( ~ ( member_a_o @ X_17 @ A_51 )
% 2.93/1.52 => ( ( finite_card_a_o @ ( insert_a_o @ X_17 @ A_51 ) )
% 2.93/1.52 = ( suc @ ( finite_card_a_o @ A_51 ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_107_card__insert__disjoint,axiom,
% 2.93/1.52 ! [X_17: nat,A_51: nat > $o] :
% 2.93/1.52 ( ( finite_finite_nat @ A_51 )
% 2.93/1.52 => ( ~ ( member_nat @ X_17 @ A_51 )
% 2.93/1.52 => ( ( finite_card_nat @ ( insert_nat @ X_17 @ A_51 ) )
% 2.93/1.52 = ( suc @ ( finite_card_nat @ A_51 ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_108_card__insert__disjoint,axiom,
% 2.93/1.52 ! [X_17: pname,A_51: pname > $o] :
% 2.93/1.52 ( ( finite_finite_pname @ A_51 )
% 2.93/1.52 => ( ~ ( member_pname @ X_17 @ A_51 )
% 2.93/1.52 => ( ( finite_card_pname @ ( insert_pname @ X_17 @ A_51 ) )
% 2.93/1.52 = ( suc @ ( finite_card_pname @ A_51 ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_109_card__insert__disjoint,axiom,
% 2.93/1.52 ! [X_17: x_a,A_51: x_a > $o] :
% 2.93/1.52 ( ( finite_finite_a @ A_51 )
% 2.93/1.52 => ( ~ ( member_a @ X_17 @ A_51 )
% 2.93/1.52 => ( ( finite_card_a @ ( insert_a @ X_17 @ A_51 ) )
% 2.93/1.52 = ( suc @ ( finite_card_a @ A_51 ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_110_finite__Collect__conjI,axiom,
% 2.93/1.52 ! [Q_1: ( nat > $o ) > $o,P_4: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( ( finite_finite_nat_o @ ( collect_nat_o @ P_4 ) )
% 2.93/1.52 | ( finite_finite_nat_o @ ( collect_nat_o @ Q_1 ) ) )
% 2.93/1.52 => ( finite_finite_nat_o
% 2.93/1.52 @ ( collect_nat_o
% 2.93/1.52 @ ^ [X: nat > $o] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_111_finite__Collect__conjI,axiom,
% 2.93/1.52 ! [Q_1: ( pname > $o ) > $o,P_4: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_4 ) )
% 2.93/1.52 | ( finite297249702name_o @ ( collect_pname_o @ Q_1 ) ) )
% 2.93/1.52 => ( finite297249702name_o
% 2.93/1.52 @ ( collect_pname_o
% 2.93/1.52 @ ^ [X: pname > $o] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_112_finite__Collect__conjI,axiom,
% 2.93/1.52 ! [Q_1: ( x_a > $o ) > $o,P_4: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( ( finite_finite_a_o @ ( collect_a_o @ P_4 ) )
% 2.93/1.52 | ( finite_finite_a_o @ ( collect_a_o @ Q_1 ) ) )
% 2.93/1.52 => ( finite_finite_a_o
% 2.93/1.52 @ ( collect_a_o
% 2.93/1.52 @ ^ [X: x_a > $o] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_113_finite__Collect__conjI,axiom,
% 2.93/1.52 ! [Q_1: x_a > $o,P_4: x_a > $o] :
% 2.93/1.52 ( ( ( finite_finite_a @ ( collect_a @ P_4 ) )
% 2.93/1.52 | ( finite_finite_a @ ( collect_a @ Q_1 ) ) )
% 2.93/1.52 => ( finite_finite_a
% 2.93/1.52 @ ( collect_a
% 2.93/1.52 @ ^ [X: x_a] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_114_finite__Collect__conjI,axiom,
% 2.93/1.52 ! [Q_1: pname > $o,P_4: pname > $o] :
% 2.93/1.52 ( ( ( finite_finite_pname @ ( collect_pname @ P_4 ) )
% 2.93/1.52 | ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
% 2.93/1.52 => ( finite_finite_pname
% 2.93/1.52 @ ( collect_pname
% 2.93/1.52 @ ^ [X: pname] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_115_finite__Collect__conjI,axiom,
% 2.93/1.52 ! [Q_1: nat > $o,P_4: nat > $o] :
% 2.93/1.52 ( ( ( finite_finite_nat @ ( collect_nat @ P_4 ) )
% 2.93/1.52 | ( finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
% 2.93/1.52 => ( finite_finite_nat
% 2.93/1.52 @ ( collect_nat
% 2.93/1.52 @ ^ [X: nat] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_116_Suc__diff__le,axiom,
% 2.93/1.52 ! [N_1: nat,M_2: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ N_1 @ M_2 )
% 2.93/1.52 => ( ( minus_minus_nat @ ( suc @ M_2 ) @ N_1 )
% 2.93/1.52 = ( suc @ ( minus_minus_nat @ M_2 @ N_1 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_117_finite__Collect__le__nat,axiom,
% 2.93/1.52 ! [K: nat] :
% 2.93/1.52 ( finite_finite_nat
% 2.93/1.52 @ ( collect_nat
% 2.93/1.52 @ ^ [N_2: nat] : ( ord_less_eq_nat @ N_2 @ K ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_118_card__Collect__le__nat,axiom,
% 2.93/1.52 ! [N_1: nat] :
% 2.93/1.52 ( ( finite_card_nat
% 2.93/1.52 @ ( collect_nat
% 2.93/1.52 @ ^ [I_1: nat] : ( ord_less_eq_nat @ I_1 @ N_1 ) ) )
% 2.93/1.52 = ( suc @ N_1 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_119_Suc__inject,axiom,
% 2.93/1.52 ! [X_16: nat,Y_3: nat] :
% 2.93/1.52 ( ( ( suc @ X_16 )
% 2.93/1.52 = ( suc @ Y_3 ) )
% 2.93/1.52 => ( X_16 = Y_3 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_120_nat_Oinject,axiom,
% 2.93/1.52 ! [Nat_1: nat,Nat: nat] :
% 2.93/1.52 ( ( ( suc @ Nat_1 )
% 2.93/1.52 = ( suc @ Nat ) )
% 2.93/1.52 <=> ( Nat_1 = Nat ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_121_Suc__n__not__n,axiom,
% 2.93/1.52 ! [N_1: nat] :
% 2.93/1.52 ( ( suc @ N_1 )
% 2.93/1.52 != N_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_122_n__not__Suc__n,axiom,
% 2.93/1.52 ! [N_1: nat] :
% 2.93/1.52 ( N_1
% 2.93/1.52 != ( suc @ N_1 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_123_le__antisym,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 2.93/1.52 => ( ( ord_less_eq_nat @ N_1 @ M_2 )
% 2.93/1.52 => ( M_2 = N_1 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_124_le__trans,axiom,
% 2.93/1.52 ! [K: nat,I: nat,J: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ I @ J )
% 2.93/1.52 => ( ( ord_less_eq_nat @ J @ K )
% 2.93/1.52 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_125_eq__imp__le,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( M_2 = N_1 )
% 2.93/1.52 => ( ord_less_eq_nat @ M_2 @ N_1 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_126_nat__le__linear,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 2.93/1.52 | ( ord_less_eq_nat @ N_1 @ M_2 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_127_le__refl,axiom,
% 2.93/1.52 ! [N_1: nat] : ( ord_less_eq_nat @ N_1 @ N_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_128_diff__commute,axiom,
% 2.93/1.52 ! [I: nat,J: nat,K: nat] :
% 2.93/1.52 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 2.93/1.52 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_129_finite__Collect__disjI,axiom,
% 2.93/1.52 ! [P_3: pname > $o,Q: pname > $o] :
% 2.93/1.52 ( ( finite_finite_pname
% 2.93/1.52 @ ( collect_pname
% 2.93/1.52 @ ^ [X: pname] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 2.93/1.52 <=> ( ( finite_finite_pname @ ( collect_pname @ P_3 ) )
% 2.93/1.52 & ( finite_finite_pname @ ( collect_pname @ Q ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_130_finite__Collect__disjI,axiom,
% 2.93/1.52 ! [P_3: ( nat > $o ) > $o,Q: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_nat_o
% 2.93/1.52 @ ( collect_nat_o
% 2.93/1.52 @ ^ [X: nat > $o] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 2.93/1.52 <=> ( ( finite_finite_nat_o @ ( collect_nat_o @ P_3 ) )
% 2.93/1.52 & ( finite_finite_nat_o @ ( collect_nat_o @ Q ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_131_finite__Collect__disjI,axiom,
% 2.93/1.52 ! [P_3: ( pname > $o ) > $o,Q: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( finite297249702name_o
% 2.93/1.52 @ ( collect_pname_o
% 2.93/1.52 @ ^ [X: pname > $o] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 2.93/1.52 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_3 ) )
% 2.93/1.52 & ( finite297249702name_o @ ( collect_pname_o @ Q ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_132_finite__Collect__disjI,axiom,
% 2.93/1.52 ! [P_3: ( x_a > $o ) > $o,Q: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_a_o
% 2.93/1.52 @ ( collect_a_o
% 2.93/1.52 @ ^ [X: x_a > $o] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 2.93/1.52 <=> ( ( finite_finite_a_o @ ( collect_a_o @ P_3 ) )
% 2.93/1.52 & ( finite_finite_a_o @ ( collect_a_o @ Q ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_133_finite__Collect__disjI,axiom,
% 2.93/1.52 ! [P_3: nat > $o,Q: nat > $o] :
% 2.93/1.52 ( ( finite_finite_nat
% 2.93/1.52 @ ( collect_nat
% 2.93/1.52 @ ^ [X: nat] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 2.93/1.52 <=> ( ( finite_finite_nat @ ( collect_nat @ P_3 ) )
% 2.93/1.52 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_134_finite__Collect__disjI,axiom,
% 2.93/1.52 ! [P_3: x_a > $o,Q: x_a > $o] :
% 2.93/1.52 ( ( finite_finite_a
% 2.93/1.52 @ ( collect_a
% 2.93/1.52 @ ^ [X: x_a] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 2.93/1.52 <=> ( ( finite_finite_a @ ( collect_a @ P_3 ) )
% 2.93/1.52 & ( finite_finite_a @ ( collect_a @ Q ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_135_finite__insert,axiom,
% 2.93/1.52 ! [A_50: nat,A_49: nat > $o] :
% 2.93/1.52 ( ( finite_finite_nat @ ( insert_nat @ A_50 @ A_49 ) )
% 2.93/1.52 <=> ( finite_finite_nat @ A_49 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_136_finite__insert,axiom,
% 2.93/1.52 ! [A_50: pname,A_49: pname > $o] :
% 2.93/1.52 ( ( finite_finite_pname @ ( insert_pname @ A_50 @ A_49 ) )
% 2.93/1.52 <=> ( finite_finite_pname @ A_49 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_137_finite__insert,axiom,
% 2.93/1.52 ! [A_50: x_a,A_49: x_a > $o] :
% 2.93/1.52 ( ( finite_finite_a @ ( insert_a @ A_50 @ A_49 ) )
% 2.93/1.52 <=> ( finite_finite_a @ A_49 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_138_finite__insert,axiom,
% 2.93/1.52 ! [A_50: nat > $o,A_49: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_nat_o @ ( insert_nat_o @ A_50 @ A_49 ) )
% 2.93/1.52 <=> ( finite_finite_nat_o @ A_49 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_139_finite__insert,axiom,
% 2.93/1.52 ! [A_50: pname > $o,A_49: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( finite297249702name_o @ ( insert_pname_o @ A_50 @ A_49 ) )
% 2.93/1.52 <=> ( finite297249702name_o @ A_49 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_140_finite__insert,axiom,
% 2.93/1.52 ! [A_50: x_a > $o,A_49: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_a_o @ ( insert_a_o @ A_50 @ A_49 ) )
% 2.93/1.52 <=> ( finite_finite_a_o @ A_49 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_141_finite__subset,axiom,
% 2.93/1.52 ! [A_48: ( nat > $o ) > $o,B_35: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o_o @ A_48 @ B_35 )
% 2.93/1.52 => ( ( finite_finite_nat_o @ B_35 )
% 2.93/1.52 => ( finite_finite_nat_o @ A_48 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_142_finite__subset,axiom,
% 2.93/1.52 ! [A_48: ( pname > $o ) > $o,B_35: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( ord_le1205211808me_o_o @ A_48 @ B_35 )
% 2.93/1.52 => ( ( finite297249702name_o @ B_35 )
% 2.93/1.52 => ( finite297249702name_o @ A_48 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_143_finite__subset,axiom,
% 2.93/1.52 ! [A_48: x_a > $o,B_35: x_a > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ A_48 @ B_35 )
% 2.93/1.52 => ( ( finite_finite_a @ B_35 )
% 2.93/1.52 => ( finite_finite_a @ A_48 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_144_finite__subset,axiom,
% 2.93/1.52 ! [A_48: ( x_a > $o ) > $o,B_35: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o_o @ A_48 @ B_35 )
% 2.93/1.52 => ( ( finite_finite_a_o @ B_35 )
% 2.93/1.52 => ( finite_finite_a_o @ A_48 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_145_finite__subset,axiom,
% 2.93/1.52 ! [A_48: nat > $o,B_35: nat > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o @ A_48 @ B_35 )
% 2.93/1.52 => ( ( finite_finite_nat @ B_35 )
% 2.93/1.52 => ( finite_finite_nat @ A_48 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_146_finite__subset,axiom,
% 2.93/1.52 ! [A_48: pname > $o,B_35: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ A_48 @ B_35 )
% 2.93/1.52 => ( ( finite_finite_pname @ B_35 )
% 2.93/1.52 => ( finite_finite_pname @ A_48 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_147_rev__finite__subset,axiom,
% 2.93/1.52 ! [A_47: ( nat > $o ) > $o,B_34: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_nat_o @ B_34 )
% 2.93/1.52 => ( ( ord_less_eq_nat_o_o @ A_47 @ B_34 )
% 2.93/1.52 => ( finite_finite_nat_o @ A_47 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_148_rev__finite__subset,axiom,
% 2.93/1.52 ! [A_47: ( pname > $o ) > $o,B_34: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( finite297249702name_o @ B_34 )
% 2.93/1.52 => ( ( ord_le1205211808me_o_o @ A_47 @ B_34 )
% 2.93/1.52 => ( finite297249702name_o @ A_47 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_149_rev__finite__subset,axiom,
% 2.93/1.52 ! [A_47: x_a > $o,B_34: x_a > $o] :
% 2.93/1.52 ( ( finite_finite_a @ B_34 )
% 2.93/1.52 => ( ( ord_less_eq_a_o @ A_47 @ B_34 )
% 2.93/1.52 => ( finite_finite_a @ A_47 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_150_rev__finite__subset,axiom,
% 2.93/1.52 ! [A_47: ( x_a > $o ) > $o,B_34: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( finite_finite_a_o @ B_34 )
% 2.93/1.52 => ( ( ord_less_eq_a_o_o @ A_47 @ B_34 )
% 2.93/1.52 => ( finite_finite_a_o @ A_47 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_151_rev__finite__subset,axiom,
% 2.93/1.52 ! [A_47: nat > $o,B_34: nat > $o] :
% 2.93/1.52 ( ( finite_finite_nat @ B_34 )
% 2.93/1.52 => ( ( ord_less_eq_nat_o @ A_47 @ B_34 )
% 2.93/1.52 => ( finite_finite_nat @ A_47 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_152_rev__finite__subset,axiom,
% 2.93/1.52 ! [A_47: pname > $o,B_34: pname > $o] :
% 2.93/1.52 ( ( finite_finite_pname @ B_34 )
% 2.93/1.52 => ( ( ord_less_eq_pname_o @ A_47 @ B_34 )
% 2.93/1.52 => ( finite_finite_pname @ A_47 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_153_Suc__leD,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ ( suc @ M_2 ) @ N_1 )
% 2.93/1.52 => ( ord_less_eq_nat @ M_2 @ N_1 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_154_le__SucE,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ M_2 @ ( suc @ N_1 ) )
% 2.93/1.52 => ( ~ ( ord_less_eq_nat @ M_2 @ N_1 )
% 2.93/1.52 => ( M_2
% 2.93/1.52 = ( suc @ N_1 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_155_le__SucI,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 2.93/1.52 => ( ord_less_eq_nat @ M_2 @ ( suc @ N_1 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_156_Suc__le__mono,axiom,
% 2.93/1.52 ! [N_1: nat,M_2: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ ( suc @ N_1 ) @ ( suc @ M_2 ) )
% 2.93/1.52 <=> ( ord_less_eq_nat @ N_1 @ M_2 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_157_le__Suc__eq,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ M_2 @ ( suc @ N_1 ) )
% 2.93/1.52 <=> ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 2.93/1.52 | ( M_2
% 2.93/1.52 = ( suc @ N_1 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_158_not__less__eq__eq,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] :
% 2.93/1.52 ( ~ ( ord_less_eq_nat @ M_2 @ N_1 )
% 2.93/1.52 <=> ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_2 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_159_Suc__n__not__le__n,axiom,
% 2.93/1.52 ! [N_1: nat] :
% 2.93/1.52 ~ ( ord_less_eq_nat @ ( suc @ N_1 ) @ N_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_160_Suc__diff__diff,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat,K: nat] :
% 2.93/1.52 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M_2 ) @ N_1 ) @ ( suc @ K ) )
% 2.93/1.52 = ( minus_minus_nat @ ( minus_minus_nat @ M_2 @ N_1 ) @ K ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_161_diff__Suc__Suc,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( minus_minus_nat @ ( suc @ M_2 ) @ ( suc @ N_1 ) )
% 2.93/1.52 = ( minus_minus_nat @ M_2 @ N_1 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_162_le__diff__iff,axiom,
% 2.93/1.52 ! [N_1: nat,K: nat,M_2: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ K @ M_2 )
% 2.93/1.52 => ( ( ord_less_eq_nat @ K @ N_1 )
% 2.93/1.52 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M_2 @ K ) @ ( minus_minus_nat @ N_1 @ K ) )
% 2.93/1.52 <=> ( ord_less_eq_nat @ M_2 @ N_1 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_163_Nat_Odiff__diff__eq,axiom,
% 2.93/1.52 ! [N_1: nat,K: nat,M_2: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ K @ M_2 )
% 2.93/1.52 => ( ( ord_less_eq_nat @ K @ N_1 )
% 2.93/1.52 => ( ( minus_minus_nat @ ( minus_minus_nat @ M_2 @ K ) @ ( minus_minus_nat @ N_1 @ K ) )
% 2.93/1.52 = ( minus_minus_nat @ M_2 @ N_1 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_164_eq__diff__iff,axiom,
% 2.93/1.52 ! [N_1: nat,K: nat,M_2: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ K @ M_2 )
% 2.93/1.52 => ( ( ord_less_eq_nat @ K @ N_1 )
% 2.93/1.52 => ( ( ( minus_minus_nat @ M_2 @ K )
% 2.93/1.52 = ( minus_minus_nat @ N_1 @ K ) )
% 2.93/1.52 <=> ( M_2 = N_1 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_165_diff__diff__cancel,axiom,
% 2.93/1.52 ! [I: nat,N_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ I @ N_1 )
% 2.93/1.52 => ( ( minus_minus_nat @ N_1 @ ( minus_minus_nat @ N_1 @ I ) )
% 2.93/1.52 = I ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_166_diff__le__mono,axiom,
% 2.93/1.52 ! [L: nat,M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 2.93/1.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ M_2 @ L ) @ ( minus_minus_nat @ N_1 @ L ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_167_diff__le__mono2,axiom,
% 2.93/1.52 ! [L: nat,M_2: nat,N_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 2.93/1.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N_1 ) @ ( minus_minus_nat @ L @ M_2 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_168_diff__le__self,axiom,
% 2.93/1.52 ! [M_2: nat,N_1: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M_2 @ N_1 ) @ M_2 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_169_finite__surj,axiom,
% 2.93/1.52 ! [B_33: x_a > $o,F_13: pname > x_a,A_46: pname > $o] :
% 2.93/1.52 ( ( finite_finite_pname @ A_46 )
% 2.93/1.52 => ( ( ord_less_eq_a_o @ B_33 @ ( image_pname_a @ F_13 @ A_46 ) )
% 2.93/1.52 => ( finite_finite_a @ B_33 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_170_finite__subset__image,axiom,
% 2.93/1.52 ! [F_12: pname > x_a,A_45: pname > $o,B_32: x_a > $o] :
% 2.93/1.52 ( ( finite_finite_a @ B_32 )
% 2.93/1.52 => ( ( ord_less_eq_a_o @ B_32 @ ( image_pname_a @ F_12 @ A_45 ) )
% 2.93/1.52 => ? [C_3: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ C_3 @ A_45 )
% 2.93/1.52 & ( finite_finite_pname @ C_3 )
% 2.93/1.52 & ( B_32
% 2.93/1.52 = ( image_pname_a @ F_12 @ C_3 ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_171_lift__Suc__mono__le,axiom,
% 2.93/1.52 ! [N_4: nat,N_3: nat,F_11: nat > nat > $o] :
% 2.93/1.52 ( ! [N_2: nat] : ( ord_less_eq_nat_o @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 2.93/1.52 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 2.93/1.52 => ( ord_less_eq_nat_o @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_172_lift__Suc__mono__le,axiom,
% 2.93/1.52 ! [N_4: nat,N_3: nat,F_11: nat > pname > $o] :
% 2.93/1.52 ( ! [N_2: nat] : ( ord_less_eq_pname_o @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 2.93/1.52 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 2.93/1.52 => ( ord_less_eq_pname_o @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_173_lift__Suc__mono__le,axiom,
% 2.93/1.52 ! [N_4: nat,N_3: nat,F_11: nat > nat] :
% 2.93/1.52 ( ! [N_2: nat] : ( ord_less_eq_nat @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 2.93/1.52 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 2.93/1.52 => ( ord_less_eq_nat @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_174_lift__Suc__mono__le,axiom,
% 2.93/1.52 ! [N_4: nat,N_3: nat,F_11: nat > x_a > $o] :
% 2.93/1.52 ( ! [N_2: nat] : ( ord_less_eq_a_o @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 2.93/1.52 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 2.93/1.52 => ( ord_less_eq_a_o @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_175_pigeonhole__infinite,axiom,
% 2.93/1.52 ! [F_10: pname > x_a,A_43: pname > $o] :
% 2.93/1.52 ( ~ ( finite_finite_pname @ A_43 )
% 2.93/1.52 => ( ( finite_finite_a @ ( image_pname_a @ F_10 @ A_43 ) )
% 2.93/1.52 => ? [X: pname] :
% 2.93/1.52 ( ( member_pname @ X @ A_43 )
% 2.93/1.52 & ~ ( finite_finite_pname
% 2.93/1.52 @ ( collect_pname
% 2.93/1.52 @ ^ [A_44: pname] :
% 2.93/1.52 ( (&) @ ( member_pname @ A_44 @ A_43 )
% 2.93/1.52 @ ( ( F_10 @ A_44 )
% 2.93/1.52 = ( F_10 @ X ) ) ) ) ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_176_image__eqI,axiom,
% 2.93/1.52 ! [A_42: pname > $o,B_31: x_a,F_9: pname > x_a,X_15: pname] :
% 2.93/1.52 ( ( B_31
% 2.93/1.52 = ( F_9 @ X_15 ) )
% 2.93/1.52 => ( ( member_pname @ X_15 @ A_42 )
% 2.93/1.52 => ( member_a @ B_31 @ ( image_pname_a @ F_9 @ A_42 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_177_equalityI,axiom,
% 2.93/1.52 ! [A_41: nat > $o,B_30: nat > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o @ A_41 @ B_30 )
% 2.93/1.52 => ( ( ord_less_eq_nat_o @ B_30 @ A_41 )
% 2.93/1.52 => ( A_41 = B_30 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_178_equalityI,axiom,
% 2.93/1.52 ! [A_41: pname > $o,B_30: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ A_41 @ B_30 )
% 2.93/1.52 => ( ( ord_less_eq_pname_o @ B_30 @ A_41 )
% 2.93/1.52 => ( A_41 = B_30 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_179_equalityI,axiom,
% 2.93/1.52 ! [A_41: x_a > $o,B_30: x_a > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ A_41 @ B_30 )
% 2.93/1.52 => ( ( ord_less_eq_a_o @ B_30 @ A_41 )
% 2.93/1.52 => ( A_41 = B_30 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_180_subsetD,axiom,
% 2.93/1.52 ! [C_2: nat,A_40: nat > $o,B_29: nat > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o @ A_40 @ B_29 )
% 2.93/1.52 => ( ( member_nat @ C_2 @ A_40 )
% 2.93/1.52 => ( member_nat @ C_2 @ B_29 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_181_subsetD,axiom,
% 2.93/1.52 ! [C_2: x_a,A_40: x_a > $o,B_29: x_a > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ A_40 @ B_29 )
% 2.93/1.52 => ( ( member_a @ C_2 @ A_40 )
% 2.93/1.52 => ( member_a @ C_2 @ B_29 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_182_subsetD,axiom,
% 2.93/1.52 ! [C_2: pname,A_40: pname > $o,B_29: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ A_40 @ B_29 )
% 2.93/1.52 => ( ( member_pname @ C_2 @ A_40 )
% 2.93/1.52 => ( member_pname @ C_2 @ B_29 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_183_insertCI,axiom,
% 2.93/1.52 ! [B_28: nat,A_39: nat,B_27: nat > $o] :
% 2.93/1.52 ( ( ~ ( member_nat @ A_39 @ B_27 )
% 2.93/1.52 => ( A_39 = B_28 ) )
% 2.93/1.52 => ( member_nat @ A_39 @ ( insert_nat @ B_28 @ B_27 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_184_insertCI,axiom,
% 2.93/1.52 ! [B_28: pname,A_39: pname,B_27: pname > $o] :
% 2.93/1.52 ( ( ~ ( member_pname @ A_39 @ B_27 )
% 2.93/1.52 => ( A_39 = B_28 ) )
% 2.93/1.52 => ( member_pname @ A_39 @ ( insert_pname @ B_28 @ B_27 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_185_insertCI,axiom,
% 2.93/1.52 ! [B_28: x_a,A_39: x_a,B_27: x_a > $o] :
% 2.93/1.52 ( ( ~ ( member_a @ A_39 @ B_27 )
% 2.93/1.52 => ( A_39 = B_28 ) )
% 2.93/1.52 => ( member_a @ A_39 @ ( insert_a @ B_28 @ B_27 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_186_insertE,axiom,
% 2.93/1.52 ! [A_38: nat,B_26: nat,A_37: nat > $o] :
% 2.93/1.52 ( ( member_nat @ A_38 @ ( insert_nat @ B_26 @ A_37 ) )
% 2.93/1.52 => ( ( A_38 != B_26 )
% 2.93/1.52 => ( member_nat @ A_38 @ A_37 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_187_insertE,axiom,
% 2.93/1.52 ! [A_38: pname,B_26: pname,A_37: pname > $o] :
% 2.93/1.52 ( ( member_pname @ A_38 @ ( insert_pname @ B_26 @ A_37 ) )
% 2.93/1.52 => ( ( A_38 != B_26 )
% 2.93/1.52 => ( member_pname @ A_38 @ A_37 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_188_insertE,axiom,
% 2.93/1.52 ! [A_38: x_a,B_26: x_a,A_37: x_a > $o] :
% 2.93/1.52 ( ( member_a @ A_38 @ ( insert_a @ B_26 @ A_37 ) )
% 2.93/1.52 => ( ( A_38 != B_26 )
% 2.93/1.52 => ( member_a @ A_38 @ A_37 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_189_insertI1,axiom,
% 2.93/1.52 ! [A_36: nat,B_25: nat > $o] : ( member_nat @ A_36 @ ( insert_nat @ A_36 @ B_25 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_190_insertI1,axiom,
% 2.93/1.52 ! [A_36: pname,B_25: pname > $o] : ( member_pname @ A_36 @ ( insert_pname @ A_36 @ B_25 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_191_insertI1,axiom,
% 2.93/1.52 ! [A_36: x_a,B_25: x_a > $o] : ( member_a @ A_36 @ ( insert_a @ A_36 @ B_25 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_192_insert__compr,axiom,
% 2.93/1.52 ! [A_35: nat,B_24: nat > $o] :
% 2.93/1.52 ( ( insert_nat @ A_35 @ B_24 )
% 2.93/1.52 = ( collect_nat
% 2.93/1.52 @ ^ [X: nat] : ( (|) @ ( X = A_35 ) @ ( member_nat @ X @ B_24 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_193_insert__compr,axiom,
% 2.93/1.52 ! [A_35: pname,B_24: pname > $o] :
% 2.93/1.52 ( ( insert_pname @ A_35 @ B_24 )
% 2.93/1.52 = ( collect_pname
% 2.93/1.52 @ ^ [X: pname] : ( (|) @ ( X = A_35 ) @ ( member_pname @ X @ B_24 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_194_insert__compr,axiom,
% 2.93/1.52 ! [A_35: x_a,B_24: x_a > $o] :
% 2.93/1.52 ( ( insert_a @ A_35 @ B_24 )
% 2.93/1.52 = ( collect_a
% 2.93/1.52 @ ^ [X: x_a] : ( (|) @ ( X = A_35 ) @ ( member_a @ X @ B_24 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_195_insert__compr,axiom,
% 2.93/1.52 ! [A_35: nat > $o,B_24: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( insert_nat_o @ A_35 @ B_24 )
% 2.93/1.52 = ( collect_nat_o
% 2.93/1.52 @ ^ [X: nat > $o] : ( (|) @ ( X = A_35 ) @ ( member_nat_o @ X @ B_24 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_196_insert__compr,axiom,
% 2.93/1.52 ! [A_35: pname > $o,B_24: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( insert_pname_o @ A_35 @ B_24 )
% 2.93/1.52 = ( collect_pname_o
% 2.93/1.52 @ ^ [X: pname > $o] : ( (|) @ ( X = A_35 ) @ ( member_pname_o @ X @ B_24 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_197_insert__compr,axiom,
% 2.93/1.52 ! [A_35: x_a > $o,B_24: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( insert_a_o @ A_35 @ B_24 )
% 2.93/1.52 = ( collect_a_o
% 2.93/1.52 @ ^ [X: x_a > $o] : ( (|) @ ( X = A_35 ) @ ( member_a_o @ X @ B_24 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_198_insert__Collect,axiom,
% 2.93/1.52 ! [A_34: nat,P_2: nat > $o] :
% 2.93/1.52 ( ( insert_nat @ A_34 @ ( collect_nat @ P_2 ) )
% 2.93/1.52 = ( collect_nat
% 2.93/1.52 @ ^ [U: nat] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_199_insert__Collect,axiom,
% 2.93/1.52 ! [A_34: pname,P_2: pname > $o] :
% 2.93/1.52 ( ( insert_pname @ A_34 @ ( collect_pname @ P_2 ) )
% 2.93/1.52 = ( collect_pname
% 2.93/1.52 @ ^ [U: pname] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_200_insert__Collect,axiom,
% 2.93/1.52 ! [A_34: x_a,P_2: x_a > $o] :
% 2.93/1.52 ( ( insert_a @ A_34 @ ( collect_a @ P_2 ) )
% 2.93/1.52 = ( collect_a
% 2.93/1.52 @ ^ [U: x_a] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_201_insert__Collect,axiom,
% 2.93/1.52 ! [A_34: nat > $o,P_2: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( insert_nat_o @ A_34 @ ( collect_nat_o @ P_2 ) )
% 2.93/1.52 = ( collect_nat_o
% 2.93/1.52 @ ^ [U: nat > $o] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_202_insert__Collect,axiom,
% 2.93/1.52 ! [A_34: pname > $o,P_2: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( insert_pname_o @ A_34 @ ( collect_pname_o @ P_2 ) )
% 2.93/1.52 = ( collect_pname_o
% 2.93/1.52 @ ^ [U: pname > $o] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_203_insert__Collect,axiom,
% 2.93/1.52 ! [A_34: x_a > $o,P_2: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( insert_a_o @ A_34 @ ( collect_a_o @ P_2 ) )
% 2.93/1.52 = ( collect_a_o
% 2.93/1.52 @ ^ [U: x_a > $o] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_204_insert__absorb2,axiom,
% 2.93/1.52 ! [X_14: nat,A_33: nat > $o] :
% 2.93/1.52 ( ( insert_nat @ X_14 @ ( insert_nat @ X_14 @ A_33 ) )
% 2.93/1.52 = ( insert_nat @ X_14 @ A_33 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_205_insert__absorb2,axiom,
% 2.93/1.52 ! [X_14: pname,A_33: pname > $o] :
% 2.93/1.52 ( ( insert_pname @ X_14 @ ( insert_pname @ X_14 @ A_33 ) )
% 2.93/1.52 = ( insert_pname @ X_14 @ A_33 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_206_insert__absorb2,axiom,
% 2.93/1.52 ! [X_14: x_a,A_33: x_a > $o] :
% 2.93/1.52 ( ( insert_a @ X_14 @ ( insert_a @ X_14 @ A_33 ) )
% 2.93/1.52 = ( insert_a @ X_14 @ A_33 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_207_insert__commute,axiom,
% 2.93/1.52 ! [X_13: nat,Y_2: nat,A_32: nat > $o] :
% 2.93/1.52 ( ( insert_nat @ X_13 @ ( insert_nat @ Y_2 @ A_32 ) )
% 2.93/1.52 = ( insert_nat @ Y_2 @ ( insert_nat @ X_13 @ A_32 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_208_insert__commute,axiom,
% 2.93/1.52 ! [X_13: pname,Y_2: pname,A_32: pname > $o] :
% 2.93/1.52 ( ( insert_pname @ X_13 @ ( insert_pname @ Y_2 @ A_32 ) )
% 2.93/1.52 = ( insert_pname @ Y_2 @ ( insert_pname @ X_13 @ A_32 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_209_insert__commute,axiom,
% 2.93/1.52 ! [X_13: x_a,Y_2: x_a,A_32: x_a > $o] :
% 2.93/1.52 ( ( insert_a @ X_13 @ ( insert_a @ Y_2 @ A_32 ) )
% 2.93/1.52 = ( insert_a @ Y_2 @ ( insert_a @ X_13 @ A_32 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_210_insert__iff,axiom,
% 2.93/1.52 ! [A_31: nat,B_23: nat,A_30: nat > $o] :
% 2.93/1.52 ( ( member_nat @ A_31 @ ( insert_nat @ B_23 @ A_30 ) )
% 2.93/1.52 <=> ( ( A_31 = B_23 )
% 2.93/1.52 | ( member_nat @ A_31 @ A_30 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_211_insert__iff,axiom,
% 2.93/1.52 ! [A_31: pname,B_23: pname,A_30: pname > $o] :
% 2.93/1.52 ( ( member_pname @ A_31 @ ( insert_pname @ B_23 @ A_30 ) )
% 2.93/1.52 <=> ( ( A_31 = B_23 )
% 2.93/1.52 | ( member_pname @ A_31 @ A_30 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_212_insert__iff,axiom,
% 2.93/1.52 ! [A_31: x_a,B_23: x_a,A_30: x_a > $o] :
% 2.93/1.52 ( ( member_a @ A_31 @ ( insert_a @ B_23 @ A_30 ) )
% 2.93/1.52 <=> ( ( A_31 = B_23 )
% 2.93/1.52 | ( member_a @ A_31 @ A_30 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_213_insert__code,axiom,
% 2.93/1.52 ! [Y_1: nat,A_29: nat > $o,X_12: nat] :
% 2.93/1.52 ( ( insert_nat @ Y_1 @ A_29 @ X_12 )
% 2.93/1.52 <=> ( ( Y_1 = X_12 )
% 2.93/1.52 | ( A_29 @ X_12 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_214_insert__code,axiom,
% 2.93/1.52 ! [Y_1: pname,A_29: pname > $o,X_12: pname] :
% 2.93/1.52 ( ( insert_pname @ Y_1 @ A_29 @ X_12 )
% 2.93/1.52 <=> ( ( Y_1 = X_12 )
% 2.93/1.52 | ( A_29 @ X_12 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_215_insert__code,axiom,
% 2.93/1.52 ! [Y_1: x_a,A_29: x_a > $o,X_12: x_a] :
% 2.93/1.52 ( ( insert_a @ Y_1 @ A_29 @ X_12 )
% 2.93/1.52 <=> ( ( Y_1 = X_12 )
% 2.93/1.52 | ( A_29 @ X_12 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_216_insert__ident,axiom,
% 2.93/1.52 ! [B_22: nat > $o,X_11: nat,A_28: nat > $o] :
% 2.93/1.52 ( ~ ( member_nat @ X_11 @ A_28 )
% 2.93/1.52 => ( ~ ( member_nat @ X_11 @ B_22 )
% 2.93/1.52 => ( ( ( insert_nat @ X_11 @ A_28 )
% 2.93/1.52 = ( insert_nat @ X_11 @ B_22 ) )
% 2.93/1.52 <=> ( A_28 = B_22 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_217_insert__ident,axiom,
% 2.93/1.52 ! [B_22: pname > $o,X_11: pname,A_28: pname > $o] :
% 2.93/1.52 ( ~ ( member_pname @ X_11 @ A_28 )
% 2.93/1.52 => ( ~ ( member_pname @ X_11 @ B_22 )
% 2.93/1.52 => ( ( ( insert_pname @ X_11 @ A_28 )
% 2.93/1.52 = ( insert_pname @ X_11 @ B_22 ) )
% 2.93/1.52 <=> ( A_28 = B_22 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_218_insert__ident,axiom,
% 2.93/1.52 ! [B_22: x_a > $o,X_11: x_a,A_28: x_a > $o] :
% 2.93/1.52 ( ~ ( member_a @ X_11 @ A_28 )
% 2.93/1.52 => ( ~ ( member_a @ X_11 @ B_22 )
% 2.93/1.52 => ( ( ( insert_a @ X_11 @ A_28 )
% 2.93/1.52 = ( insert_a @ X_11 @ B_22 ) )
% 2.93/1.52 <=> ( A_28 = B_22 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_219_insertI2,axiom,
% 2.93/1.52 ! [B_21: nat,A_27: nat,B_20: nat > $o] :
% 2.93/1.52 ( ( member_nat @ A_27 @ B_20 )
% 2.93/1.52 => ( member_nat @ A_27 @ ( insert_nat @ B_21 @ B_20 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_220_insertI2,axiom,
% 2.93/1.52 ! [B_21: pname,A_27: pname,B_20: pname > $o] :
% 2.93/1.52 ( ( member_pname @ A_27 @ B_20 )
% 2.93/1.52 => ( member_pname @ A_27 @ ( insert_pname @ B_21 @ B_20 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_221_insertI2,axiom,
% 2.93/1.52 ! [B_21: x_a,A_27: x_a,B_20: x_a > $o] :
% 2.93/1.52 ( ( member_a @ A_27 @ B_20 )
% 2.93/1.52 => ( member_a @ A_27 @ ( insert_a @ B_21 @ B_20 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_222_insert__absorb,axiom,
% 2.93/1.52 ! [A_26: nat,A_25: nat > $o] :
% 2.93/1.52 ( ( member_nat @ A_26 @ A_25 )
% 2.93/1.52 => ( ( insert_nat @ A_26 @ A_25 )
% 2.93/1.52 = A_25 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_223_insert__absorb,axiom,
% 2.93/1.52 ! [A_26: pname,A_25: pname > $o] :
% 2.93/1.52 ( ( member_pname @ A_26 @ A_25 )
% 2.93/1.52 => ( ( insert_pname @ A_26 @ A_25 )
% 2.93/1.52 = A_25 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_224_insert__absorb,axiom,
% 2.93/1.52 ! [A_26: x_a,A_25: x_a > $o] :
% 2.93/1.52 ( ( member_a @ A_26 @ A_25 )
% 2.93/1.52 => ( ( insert_a @ A_26 @ A_25 )
% 2.93/1.52 = A_25 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_225_subset__refl,axiom,
% 2.93/1.52 ! [A_24: nat > $o] : ( ord_less_eq_nat_o @ A_24 @ A_24 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_226_subset__refl,axiom,
% 2.93/1.52 ! [A_24: pname > $o] : ( ord_less_eq_pname_o @ A_24 @ A_24 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_227_subset__refl,axiom,
% 2.93/1.52 ! [A_24: x_a > $o] : ( ord_less_eq_a_o @ A_24 @ A_24 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_228_set__eq__subset,axiom,
% 2.93/1.52 ! [A_23: nat > $o,B_19: nat > $o] :
% 2.93/1.52 ( ( A_23 = B_19 )
% 2.93/1.52 <=> ( ( ord_less_eq_nat_o @ A_23 @ B_19 )
% 2.93/1.52 & ( ord_less_eq_nat_o @ B_19 @ A_23 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_229_set__eq__subset,axiom,
% 2.93/1.52 ! [A_23: pname > $o,B_19: pname > $o] :
% 2.93/1.52 ( ( A_23 = B_19 )
% 2.93/1.52 <=> ( ( ord_less_eq_pname_o @ A_23 @ B_19 )
% 2.93/1.52 & ( ord_less_eq_pname_o @ B_19 @ A_23 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_230_set__eq__subset,axiom,
% 2.93/1.52 ! [A_23: x_a > $o,B_19: x_a > $o] :
% 2.93/1.52 ( ( A_23 = B_19 )
% 2.93/1.52 <=> ( ( ord_less_eq_a_o @ A_23 @ B_19 )
% 2.93/1.52 & ( ord_less_eq_a_o @ B_19 @ A_23 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_231_equalityD1,axiom,
% 2.93/1.52 ! [A_22: nat > $o,B_18: nat > $o] :
% 2.93/1.52 ( ( A_22 = B_18 )
% 2.93/1.52 => ( ord_less_eq_nat_o @ A_22 @ B_18 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_232_equalityD1,axiom,
% 2.93/1.52 ! [A_22: pname > $o,B_18: pname > $o] :
% 2.93/1.52 ( ( A_22 = B_18 )
% 2.93/1.52 => ( ord_less_eq_pname_o @ A_22 @ B_18 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_233_equalityD1,axiom,
% 2.93/1.52 ! [A_22: x_a > $o,B_18: x_a > $o] :
% 2.93/1.52 ( ( A_22 = B_18 )
% 2.93/1.52 => ( ord_less_eq_a_o @ A_22 @ B_18 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_234_equalityD2,axiom,
% 2.93/1.52 ! [A_21: nat > $o,B_17: nat > $o] :
% 2.93/1.52 ( ( A_21 = B_17 )
% 2.93/1.52 => ( ord_less_eq_nat_o @ B_17 @ A_21 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_235_equalityD2,axiom,
% 2.93/1.52 ! [A_21: pname > $o,B_17: pname > $o] :
% 2.93/1.52 ( ( A_21 = B_17 )
% 2.93/1.52 => ( ord_less_eq_pname_o @ B_17 @ A_21 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_236_equalityD2,axiom,
% 2.93/1.52 ! [A_21: x_a > $o,B_17: x_a > $o] :
% 2.93/1.52 ( ( A_21 = B_17 )
% 2.93/1.52 => ( ord_less_eq_a_o @ B_17 @ A_21 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_237_in__mono,axiom,
% 2.93/1.52 ! [X_10: nat,A_20: nat > $o,B_16: nat > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o @ A_20 @ B_16 )
% 2.93/1.52 => ( ( member_nat @ X_10 @ A_20 )
% 2.93/1.52 => ( member_nat @ X_10 @ B_16 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_238_in__mono,axiom,
% 2.93/1.52 ! [X_10: x_a,A_20: x_a > $o,B_16: x_a > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ A_20 @ B_16 )
% 2.93/1.52 => ( ( member_a @ X_10 @ A_20 )
% 2.93/1.52 => ( member_a @ X_10 @ B_16 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_239_in__mono,axiom,
% 2.93/1.52 ! [X_10: pname,A_20: pname > $o,B_16: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ A_20 @ B_16 )
% 2.93/1.52 => ( ( member_pname @ X_10 @ A_20 )
% 2.93/1.52 => ( member_pname @ X_10 @ B_16 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_240_set__rev__mp,axiom,
% 2.93/1.52 ! [B_15: nat > $o,X_9: nat,A_19: nat > $o] :
% 2.93/1.52 ( ( member_nat @ X_9 @ A_19 )
% 2.93/1.52 => ( ( ord_less_eq_nat_o @ A_19 @ B_15 )
% 2.93/1.52 => ( member_nat @ X_9 @ B_15 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_241_set__rev__mp,axiom,
% 2.93/1.52 ! [B_15: x_a > $o,X_9: x_a,A_19: x_a > $o] :
% 2.93/1.52 ( ( member_a @ X_9 @ A_19 )
% 2.93/1.52 => ( ( ord_less_eq_a_o @ A_19 @ B_15 )
% 2.93/1.52 => ( member_a @ X_9 @ B_15 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_242_set__rev__mp,axiom,
% 2.93/1.52 ! [B_15: pname > $o,X_9: pname,A_19: pname > $o] :
% 2.93/1.52 ( ( member_pname @ X_9 @ A_19 )
% 2.93/1.52 => ( ( ord_less_eq_pname_o @ A_19 @ B_15 )
% 2.93/1.52 => ( member_pname @ X_9 @ B_15 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_243_set__mp,axiom,
% 2.93/1.52 ! [X_8: nat,A_18: nat > $o,B_14: nat > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o @ A_18 @ B_14 )
% 2.93/1.52 => ( ( member_nat @ X_8 @ A_18 )
% 2.93/1.52 => ( member_nat @ X_8 @ B_14 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_244_set__mp,axiom,
% 2.93/1.52 ! [X_8: x_a,A_18: x_a > $o,B_14: x_a > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ A_18 @ B_14 )
% 2.93/1.52 => ( ( member_a @ X_8 @ A_18 )
% 2.93/1.52 => ( member_a @ X_8 @ B_14 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_245_set__mp,axiom,
% 2.93/1.52 ! [X_8: pname,A_18: pname > $o,B_14: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ A_18 @ B_14 )
% 2.93/1.52 => ( ( member_pname @ X_8 @ A_18 )
% 2.93/1.52 => ( member_pname @ X_8 @ B_14 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_246_subset__trans,axiom,
% 2.93/1.52 ! [C_1: nat > $o,A_17: nat > $o,B_13: nat > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o @ A_17 @ B_13 )
% 2.93/1.52 => ( ( ord_less_eq_nat_o @ B_13 @ C_1 )
% 2.93/1.52 => ( ord_less_eq_nat_o @ A_17 @ C_1 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_247_subset__trans,axiom,
% 2.93/1.52 ! [C_1: pname > $o,A_17: pname > $o,B_13: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ A_17 @ B_13 )
% 2.93/1.52 => ( ( ord_less_eq_pname_o @ B_13 @ C_1 )
% 2.93/1.52 => ( ord_less_eq_pname_o @ A_17 @ C_1 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_248_subset__trans,axiom,
% 2.93/1.52 ! [C_1: x_a > $o,A_17: x_a > $o,B_13: x_a > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ A_17 @ B_13 )
% 2.93/1.52 => ( ( ord_less_eq_a_o @ B_13 @ C_1 )
% 2.93/1.52 => ( ord_less_eq_a_o @ A_17 @ C_1 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_249_equalityE,axiom,
% 2.93/1.52 ! [A_16: nat > $o,B_12: nat > $o] :
% 2.93/1.52 ( ( A_16 = B_12 )
% 2.93/1.52 => ~ ( ( ord_less_eq_nat_o @ A_16 @ B_12 )
% 2.93/1.52 => ~ ( ord_less_eq_nat_o @ B_12 @ A_16 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_250_equalityE,axiom,
% 2.93/1.52 ! [A_16: pname > $o,B_12: pname > $o] :
% 2.93/1.52 ( ( A_16 = B_12 )
% 2.93/1.52 => ~ ( ( ord_less_eq_pname_o @ A_16 @ B_12 )
% 2.93/1.52 => ~ ( ord_less_eq_pname_o @ B_12 @ A_16 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_251_equalityE,axiom,
% 2.93/1.52 ! [A_16: x_a > $o,B_12: x_a > $o] :
% 2.93/1.52 ( ( A_16 = B_12 )
% 2.93/1.52 => ~ ( ( ord_less_eq_a_o @ A_16 @ B_12 )
% 2.93/1.52 => ~ ( ord_less_eq_a_o @ B_12 @ A_16 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_252_mem__def,axiom,
% 2.93/1.52 ! [X_7: nat,A_15: nat > $o] :
% 2.93/1.52 ( ( member_nat @ X_7 @ A_15 )
% 2.93/1.52 <=> ( A_15 @ X_7 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_253_mem__def,axiom,
% 2.93/1.52 ! [X_7: x_a,A_15: x_a > $o] :
% 2.93/1.52 ( ( member_a @ X_7 @ A_15 )
% 2.93/1.52 <=> ( A_15 @ X_7 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_254_mem__def,axiom,
% 2.93/1.52 ! [X_7: pname,A_15: pname > $o] :
% 2.93/1.52 ( ( member_pname @ X_7 @ A_15 )
% 2.93/1.52 <=> ( A_15 @ X_7 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_255_Collect__def,axiom,
% 2.93/1.52 ! [P_1: pname > $o] :
% 2.93/1.52 ( ( collect_pname @ P_1 )
% 2.93/1.52 = P_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_256_Collect__def,axiom,
% 2.93/1.52 ! [P_1: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( collect_nat_o @ P_1 )
% 2.93/1.52 = P_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_257_Collect__def,axiom,
% 2.93/1.52 ! [P_1: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( collect_pname_o @ P_1 )
% 2.93/1.52 = P_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_258_Collect__def,axiom,
% 2.93/1.52 ! [P_1: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( collect_a_o @ P_1 )
% 2.93/1.52 = P_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_259_Collect__def,axiom,
% 2.93/1.52 ! [P_1: nat > $o] :
% 2.93/1.52 ( ( collect_nat @ P_1 )
% 2.93/1.52 = P_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_260_image__iff,axiom,
% 2.93/1.52 ! [Z: x_a,F_8: pname > x_a,A_14: pname > $o] :
% 2.93/1.52 ( ( member_a @ Z @ ( image_pname_a @ F_8 @ A_14 ) )
% 2.93/1.52 <=> ? [X: pname] :
% 2.93/1.52 ( ( member_pname @ X @ A_14 )
% 2.93/1.52 & ( Z
% 2.93/1.52 = ( F_8 @ X ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_261_imageI,axiom,
% 2.93/1.52 ! [F_7: pname > x_a,X_6: pname,A_13: pname > $o] :
% 2.93/1.52 ( ( member_pname @ X_6 @ A_13 )
% 2.93/1.52 => ( member_a @ ( F_7 @ X_6 ) @ ( image_pname_a @ F_7 @ A_13 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_262_rev__image__eqI,axiom,
% 2.93/1.52 ! [B_11: x_a,F_6: pname > x_a,X_5: pname,A_12: pname > $o] :
% 2.93/1.52 ( ( member_pname @ X_5 @ A_12 )
% 2.93/1.52 => ( ( B_11
% 2.93/1.52 = ( F_6 @ X_5 ) )
% 2.93/1.52 => ( member_a @ B_11 @ ( image_pname_a @ F_6 @ A_12 ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_263_insert__compr__raw,axiom,
% 2.93/1.52 ! [X: nat,Xa: nat > $o] :
% 2.93/1.52 ( ( insert_nat @ X @ Xa )
% 2.93/1.52 = ( collect_nat
% 2.93/1.52 @ ^ [Y: nat] : ( (|) @ ( Y = X ) @ ( member_nat @ Y @ Xa ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_264_insert__compr__raw,axiom,
% 2.93/1.52 ! [X: pname,Xa: pname > $o] :
% 2.93/1.52 ( ( insert_pname @ X @ Xa )
% 2.93/1.52 = ( collect_pname
% 2.93/1.52 @ ^ [Y: pname] : ( (|) @ ( Y = X ) @ ( member_pname @ Y @ Xa ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_265_insert__compr__raw,axiom,
% 2.93/1.52 ! [X: x_a,Xa: x_a > $o] :
% 2.93/1.52 ( ( insert_a @ X @ Xa )
% 2.93/1.52 = ( collect_a
% 2.93/1.52 @ ^ [Y: x_a] : ( (|) @ ( Y = X ) @ ( member_a @ Y @ Xa ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_266_insert__compr__raw,axiom,
% 2.93/1.52 ! [X: nat > $o,Xa: ( nat > $o ) > $o] :
% 2.93/1.52 ( ( insert_nat_o @ X @ Xa )
% 2.93/1.52 = ( collect_nat_o
% 2.93/1.52 @ ^ [Y: nat > $o] : ( (|) @ ( Y = X ) @ ( member_nat_o @ Y @ Xa ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_267_insert__compr__raw,axiom,
% 2.93/1.52 ! [X: pname > $o,Xa: ( pname > $o ) > $o] :
% 2.93/1.52 ( ( insert_pname_o @ X @ Xa )
% 2.93/1.52 = ( collect_pname_o
% 2.93/1.52 @ ^ [Y: pname > $o] : ( (|) @ ( Y = X ) @ ( member_pname_o @ Y @ Xa ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_268_insert__compr__raw,axiom,
% 2.93/1.52 ! [X: x_a > $o,Xa: ( x_a > $o ) > $o] :
% 2.93/1.52 ( ( insert_a_o @ X @ Xa )
% 2.93/1.52 = ( collect_a_o
% 2.93/1.52 @ ^ [Y: x_a > $o] : ( (|) @ ( Y = X ) @ ( member_a_o @ Y @ Xa ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_269_subset__insertI,axiom,
% 2.93/1.52 ! [B_10: nat > $o,A_11: nat] : ( ord_less_eq_nat_o @ B_10 @ ( insert_nat @ A_11 @ B_10 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_270_subset__insertI,axiom,
% 2.93/1.52 ! [B_10: pname > $o,A_11: pname] : ( ord_less_eq_pname_o @ B_10 @ ( insert_pname @ A_11 @ B_10 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_271_subset__insertI,axiom,
% 2.93/1.52 ! [B_10: x_a > $o,A_11: x_a] : ( ord_less_eq_a_o @ B_10 @ ( insert_a @ A_11 @ B_10 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_272_insert__subset,axiom,
% 2.93/1.52 ! [X_4: nat,A_10: nat > $o,B_9: nat > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o @ ( insert_nat @ X_4 @ A_10 ) @ B_9 )
% 2.93/1.52 <=> ( ( member_nat @ X_4 @ B_9 )
% 2.93/1.52 & ( ord_less_eq_nat_o @ A_10 @ B_9 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_273_insert__subset,axiom,
% 2.93/1.52 ! [X_4: pname,A_10: pname > $o,B_9: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_4 @ A_10 ) @ B_9 )
% 2.93/1.52 <=> ( ( member_pname @ X_4 @ B_9 )
% 2.93/1.52 & ( ord_less_eq_pname_o @ A_10 @ B_9 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_274_insert__subset,axiom,
% 2.93/1.52 ! [X_4: x_a,A_10: x_a > $o,B_9: x_a > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ ( insert_a @ X_4 @ A_10 ) @ B_9 )
% 2.93/1.52 <=> ( ( member_a @ X_4 @ B_9 )
% 2.93/1.52 & ( ord_less_eq_a_o @ A_10 @ B_9 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_275_subset__insert,axiom,
% 2.93/1.52 ! [B_8: nat > $o,X_3: nat,A_9: nat > $o] :
% 2.93/1.52 ( ~ ( member_nat @ X_3 @ A_9 )
% 2.93/1.52 => ( ( ord_less_eq_nat_o @ A_9 @ ( insert_nat @ X_3 @ B_8 ) )
% 2.93/1.52 <=> ( ord_less_eq_nat_o @ A_9 @ B_8 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_276_subset__insert,axiom,
% 2.93/1.52 ! [B_8: pname > $o,X_3: pname,A_9: pname > $o] :
% 2.93/1.52 ( ~ ( member_pname @ X_3 @ A_9 )
% 2.93/1.52 => ( ( ord_less_eq_pname_o @ A_9 @ ( insert_pname @ X_3 @ B_8 ) )
% 2.93/1.52 <=> ( ord_less_eq_pname_o @ A_9 @ B_8 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_277_subset__insert,axiom,
% 2.93/1.52 ! [B_8: x_a > $o,X_3: x_a,A_9: x_a > $o] :
% 2.93/1.52 ( ~ ( member_a @ X_3 @ A_9 )
% 2.93/1.52 => ( ( ord_less_eq_a_o @ A_9 @ ( insert_a @ X_3 @ B_8 ) )
% 2.93/1.52 <=> ( ord_less_eq_a_o @ A_9 @ B_8 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_278_subset__insertI2,axiom,
% 2.93/1.52 ! [B_7: nat,A_8: nat > $o,B_6: nat > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o @ A_8 @ B_6 )
% 2.93/1.52 => ( ord_less_eq_nat_o @ A_8 @ ( insert_nat @ B_7 @ B_6 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_279_subset__insertI2,axiom,
% 2.93/1.52 ! [B_7: pname,A_8: pname > $o,B_6: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ A_8 @ B_6 )
% 2.93/1.52 => ( ord_less_eq_pname_o @ A_8 @ ( insert_pname @ B_7 @ B_6 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_280_subset__insertI2,axiom,
% 2.93/1.52 ! [B_7: x_a,A_8: x_a > $o,B_6: x_a > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ A_8 @ B_6 )
% 2.93/1.52 => ( ord_less_eq_a_o @ A_8 @ ( insert_a @ B_7 @ B_6 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_281_insert__mono,axiom,
% 2.93/1.52 ! [A_7: nat,C: nat > $o,D: nat > $o] :
% 2.93/1.52 ( ( ord_less_eq_nat_o @ C @ D )
% 2.93/1.52 => ( ord_less_eq_nat_o @ ( insert_nat @ A_7 @ C ) @ ( insert_nat @ A_7 @ D ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_282_insert__mono,axiom,
% 2.93/1.52 ! [A_7: pname,C: pname > $o,D: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ C @ D )
% 2.93/1.52 => ( ord_less_eq_pname_o @ ( insert_pname @ A_7 @ C ) @ ( insert_pname @ A_7 @ D ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_283_insert__mono,axiom,
% 2.93/1.52 ! [A_7: x_a,C: x_a > $o,D: x_a > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ C @ D )
% 2.93/1.52 => ( ord_less_eq_a_o @ ( insert_a @ A_7 @ C ) @ ( insert_a @ A_7 @ D ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_284_image__insert,axiom,
% 2.93/1.52 ! [F_5: pname > x_a,A_6: pname,B_5: pname > $o] :
% 2.93/1.52 ( ( image_pname_a @ F_5 @ ( insert_pname @ A_6 @ B_5 ) )
% 2.93/1.52 = ( insert_a @ ( F_5 @ A_6 ) @ ( image_pname_a @ F_5 @ B_5 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_285_insert__image,axiom,
% 2.93/1.52 ! [F_4: pname > x_a,X_2: pname,A_5: pname > $o] :
% 2.93/1.52 ( ( member_pname @ X_2 @ A_5 )
% 2.93/1.52 => ( ( insert_a @ ( F_4 @ X_2 ) @ ( image_pname_a @ F_4 @ A_5 ) )
% 2.93/1.52 = ( image_pname_a @ F_4 @ A_5 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_286_subset__image__iff,axiom,
% 2.93/1.52 ! [B_4: x_a > $o,F_3: pname > x_a,A_4: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_a_o @ B_4 @ ( image_pname_a @ F_3 @ A_4 ) )
% 2.93/1.52 <=> ? [AA: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ AA @ A_4 )
% 2.93/1.52 & ( B_4
% 2.93/1.52 = ( image_pname_a @ F_3 @ AA ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_287_image__mono,axiom,
% 2.93/1.52 ! [F_2: pname > x_a,A_3: pname > $o,B_3: pname > $o] :
% 2.93/1.52 ( ( ord_less_eq_pname_o @ A_3 @ B_3 )
% 2.93/1.52 => ( ord_less_eq_a_o @ ( image_pname_a @ F_2 @ A_3 ) @ ( image_pname_a @ F_2 @ B_3 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_288_imageE,axiom,
% 2.93/1.52 ! [B_2: x_a,F_1: pname > x_a,A_2: pname > $o] :
% 2.93/1.52 ( ( member_a @ B_2 @ ( image_pname_a @ F_1 @ A_2 ) )
% 2.93/1.52 => ~ ! [X: pname] :
% 2.93/1.52 ( ( B_2
% 2.93/1.52 = ( F_1 @ X ) )
% 2.93/1.52 => ~ ( member_pname @ X @ A_2 ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_289_subsetI,axiom,
% 2.93/1.52 ! [B_1: nat > $o,A_1: nat > $o] :
% 2.93/1.52 ( ! [X: nat] :
% 2.93/1.52 ( ( member_nat @ X @ A_1 )
% 2.93/1.52 => ( member_nat @ X @ B_1 ) )
% 2.93/1.52 => ( ord_less_eq_nat_o @ A_1 @ B_1 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_290_subsetI,axiom,
% 2.93/1.52 ! [B_1: x_a > $o,A_1: x_a > $o] :
% 2.93/1.52 ( ! [X: x_a] :
% 2.93/1.52 ( ( member_a @ X @ A_1 )
% 2.93/1.52 => ( member_a @ X @ B_1 ) )
% 2.93/1.52 => ( ord_less_eq_a_o @ A_1 @ B_1 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_291_subsetI,axiom,
% 2.93/1.52 ! [B_1: pname > $o,A_1: pname > $o] :
% 2.93/1.52 ( ! [X: pname] :
% 2.93/1.52 ( ( member_pname @ X @ A_1 )
% 2.93/1.52 => ( member_pname @ X @ B_1 ) )
% 2.93/1.52 => ( ord_less_eq_pname_o @ A_1 @ B_1 ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_292_zero__induct__lemma,axiom,
% 2.93/1.52 ! [I: nat,P: nat > $o,K: nat] :
% 2.93/1.52 ( ( P @ K )
% 2.93/1.52 => ( ! [N_2: nat] :
% 2.93/1.52 ( ( P @ ( suc @ N_2 ) )
% 2.93/1.52 => ( P @ N_2 ) )
% 2.93/1.52 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_293_Suc__le__D,axiom,
% 2.93/1.52 ! [N_1: nat,M_1: nat] :
% 2.93/1.52 ( ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_1 )
% 2.93/1.52 => ? [M: nat] :
% 2.93/1.52 ( M_1
% 2.93/1.52 = ( suc @ M ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_294_image__subsetI,axiom,
% 2.93/1.52 ! [F: pname > x_a,B: x_a > $o,A: pname > $o] :
% 2.93/1.52 ( ! [X: pname] :
% 2.93/1.52 ( ( member_pname @ X @ A )
% 2.93/1.52 => ( member_a @ ( F @ X ) @ B ) )
% 2.93/1.52 => ( ord_less_eq_a_o @ ( image_pname_a @ F @ A ) @ B ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_295_order__refl,axiom,
% 2.93/1.52 ! [X_1: nat > $o] : ( ord_less_eq_nat_o @ X_1 @ X_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_296_order__refl,axiom,
% 2.93/1.52 ! [X_1: pname > $o] : ( ord_less_eq_pname_o @ X_1 @ X_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_297_order__refl,axiom,
% 2.93/1.52 ! [X_1: nat] : ( ord_less_eq_nat @ X_1 @ X_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_298_order__refl,axiom,
% 2.93/1.52 ! [X_1: x_a > $o] : ( ord_less_eq_a_o @ X_1 @ X_1 ) ).
% 2.93/1.52
% 2.93/1.52 thf(fact_299_finite__nat__set__iff__bounded__le,axiom,
% 2.93/1.52 ! [N: nat > $o] :
% 2.93/1.52 ( ( finite_finite_nat @ N )
% 2.93/1.52 <=> ? [M: nat] :
% 2.93/1.52 ! [X: nat] :
% 2.93/1.52 ( ( member_nat @ X @ N )
% 2.93/1.52 => ( ord_less_eq_nat @ X @ M ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(conj_0,hypothesis,
% 2.93/1.52 finite_finite_pname @ u ).
% 2.93/1.52
% 2.93/1.52 thf(conj_1,hypothesis,
% 2.93/1.52 ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) ).
% 2.93/1.52
% 2.93/1.52 thf(conj_2,hypothesis,
% 2.93/1.52 ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(conj_3,hypothesis,
% 2.93/1.52 ( ( finite_card_a @ g )
% 2.93/1.52 = ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ) ).
% 2.93/1.52
% 2.93/1.52 thf(conj_4,hypothesis,
% 2.93/1.52 member_pname @ pn @ u ).
% 2.93/1.52
% 2.93/1.52 thf(conj_5,hypothesis,
% 2.93/1.52 ~ ( member_a @ ( mgt_call @ pn ) @ g ) ).
% 2.93/1.52
% 2.93/1.52 thf(conj_6,conjecture,
% 2.93/1.52 ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ).
% 2.93/1.52 ------------------------
% 2.93/1.54 % (30868)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/183Mi)
% 2.93/1.54 % (30869)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_30594 for (2999ds/4Mi)
% 2.93/1.54 % (30870)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_30594 for (2999ds/27Mi)
% 2.93/1.54 % (30871)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/2Mi)
% 2.93/1.54 % (30871)Instruction limit reached!
% 2.93/1.54 % (30871)------------------------------
% 2.93/1.54 % (30871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.54 % (30871)Termination reason: Unknown
% 2.93/1.54 % (30871)Termination phase: shuffling
% 2.93/1.54
% 2.93/1.54 % (30871)Memory used [KB]: 1535
% 2.93/1.54 % (30871)Time elapsed: 0.002 s
% 2.93/1.54 % (30871)Instructions burned: 2 (million)
% 2.93/1.54 % (30871)------------------------------
% 2.93/1.54 % (30871)------------------------------
% 2.93/1.54 % (30869)Instruction limit reached!
% 2.93/1.54 % (30869)------------------------------
% 2.93/1.54 % (30869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.54 % (30869)Termination reason: Unknown
% 2.93/1.54 % (30869)Termination phase: shuffling
% 2.93/1.54
% 2.93/1.54 % (30869)Memory used [KB]: 1663
% 2.93/1.54 % (30869)Time elapsed: 0.003 s
% 2.93/1.54 % (30869)Instructions burned: 6 (million)
% 2.93/1.54 % (30869)------------------------------
% 2.93/1.54 % (30869)------------------------------
% 2.93/1.54 % (30872)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_30594 for (2999ds/2Mi)
% 2.93/1.54 % (30873)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_30594 for (2999ds/275Mi)
% 2.93/1.54 % (30874)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/18Mi)
% 2.93/1.55 % (30872)Instruction limit reached!
% 2.93/1.55 % (30872)------------------------------
% 2.93/1.55 % (30872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.55 % (30872)Termination reason: Unknown
% 2.93/1.55 % (30872)Termination phase: shuffling
% 2.93/1.55
% 2.93/1.55 % (30872)Memory used [KB]: 1535
% 2.93/1.55 % (30872)Time elapsed: 0.004 s
% 2.93/1.55 % (30872)Instructions burned: 3 (million)
% 2.93/1.55 % (30872)------------------------------
% 2.93/1.55 % (30872)------------------------------
% 2.93/1.55 % (30870)Instruction limit reached!
% 2.93/1.55 % (30870)------------------------------
% 2.93/1.55 % (30870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.55 % (30870)Termination reason: Unknown
% 2.93/1.55 % (30870)Termination phase: Property scanning
% 2.93/1.55
% 2.93/1.55 % (30870)Memory used [KB]: 1918
% 2.93/1.55 % (30870)Time elapsed: 0.011 s
% 2.93/1.55 % (30870)Instructions burned: 28 (million)
% 2.93/1.55 % (30870)------------------------------
% 2.93/1.55 % (30870)------------------------------
% 2.93/1.55 % (30875)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/3Mi)
% 2.93/1.55 % (30876)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_30594 for (2999ds/37Mi)
% 2.93/1.55 % (30875)Instruction limit reached!
% 2.93/1.55 % (30875)------------------------------
% 2.93/1.55 % (30875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.55 % (30875)Termination reason: Unknown
% 2.93/1.55 % (30875)Termination phase: shuffling
% 2.93/1.55
% 2.93/1.55 % (30875)Memory used [KB]: 1535
% 2.93/1.55 % (30875)Time elapsed: 0.002 s
% 2.93/1.55 % (30875)Instructions burned: 3 (million)
% 2.93/1.55 % (30875)------------------------------
% 2.93/1.55 % (30875)------------------------------
% 2.93/1.56 % (30874)Instruction limit reached!
% 2.93/1.56 % (30874)------------------------------
% 2.93/1.56 % (30874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.56 % (30874)Termination reason: Unknown
% 2.93/1.56 % (30874)Termination phase: shuffling
% 2.93/1.56
% 2.93/1.56 % (30874)Memory used [KB]: 1791
% 2.93/1.56 % (30874)Time elapsed: 0.014 s
% 2.93/1.56 % (30874)Instructions burned: 19 (million)
% 2.93/1.56 % (30874)------------------------------
% 2.93/1.56 % (30874)------------------------------
% 2.93/1.56 % (30878)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_30594 for (2999ds/3Mi)
% 2.93/1.56 % (30878)Instruction limit reached!
% 2.93/1.56 % (30878)------------------------------
% 2.93/1.56 % (30878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.56 % (30878)Termination reason: Unknown
% 2.93/1.56 % (30878)Termination phase: shuffling
% 2.93/1.56
% 2.93/1.56 % (30878)Memory used [KB]: 1535
% 2.93/1.56 % (30878)Time elapsed: 0.003 s
% 2.93/1.56 % (30878)Instructions burned: 3 (million)
% 2.93/1.56 % (30878)------------------------------
% 2.93/1.56 % (30878)------------------------------
% 2.93/1.56 % (30876)Instruction limit reached!
% 2.93/1.56 % (30876)------------------------------
% 2.93/1.56 % (30876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.56 % (30876)Termination reason: Unknown
% 2.93/1.56 % (30876)Termination phase: shuffling
% 2.93/1.56
% 2.93/1.56 % (30876)Memory used [KB]: 2430
% 2.93/1.56 % (30876)Time elapsed: 0.012 s
% 2.93/1.56 % (30876)Instructions burned: 40 (million)
% 2.93/1.56 % (30876)------------------------------
% 2.93/1.56 % (30876)------------------------------
% 2.93/1.56 % (30879)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_30594 for (2999ds/1041Mi)
% 2.93/1.56 % (30877)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_30594 for (2999ds/15Mi)
% 2.93/1.57 % (30881)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/16Mi)
% 2.93/1.57 % (30882)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_30594 for (2999ds/3Mi)
% 2.93/1.57 % (30882)Instruction limit reached!
% 2.93/1.57 % (30882)------------------------------
% 2.93/1.57 % (30882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.57 % (30882)Termination reason: Unknown
% 2.93/1.57 % (30882)Termination phase: shuffling
% 2.93/1.57
% 2.93/1.57 % (30882)Memory used [KB]: 1535
% 2.93/1.57 % (30882)Time elapsed: 0.002 s
% 2.93/1.57 % (30882)Instructions burned: 3 (million)
% 2.93/1.57 % (30882)------------------------------
% 2.93/1.57 % (30882)------------------------------
% 2.93/1.57 % (30877)Instruction limit reached!
% 2.93/1.57 % (30877)------------------------------
% 2.93/1.57 % (30877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.57 % (30877)Termination reason: Unknown
% 2.93/1.57 % (30877)Termination phase: shuffling
% 2.93/1.57
% 2.93/1.57 % (30877)Memory used [KB]: 1791
% 2.93/1.57 % (30877)Time elapsed: 0.011 s
% 2.93/1.57 % (30877)Instructions burned: 15 (million)
% 2.93/1.57 % (30877)------------------------------
% 2.93/1.57 % (30877)------------------------------
% 2.93/1.57 % (30880)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/7Mi)
% 2.93/1.58 % (30881)Instruction limit reached!
% 2.93/1.58 % (30881)------------------------------
% 2.93/1.58 % (30881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.58 % (30881)Termination reason: Unknown
% 2.93/1.58 % (30881)Termination phase: shuffling
% 2.93/1.58
% 2.93/1.58 % (30881)Memory used [KB]: 1791
% 2.93/1.58 % (30881)Time elapsed: 0.008 s
% 2.93/1.58 % (30881)Instructions burned: 18 (million)
% 2.93/1.58 % (30881)------------------------------
% 2.93/1.58 % (30881)------------------------------
% 2.93/1.58 % (30880)Instruction limit reached!
% 2.93/1.58 % (30880)------------------------------
% 2.93/1.58 % (30880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.58 % (30880)Termination reason: Unknown
% 2.93/1.58 % (30880)Termination phase: shuffling
% 2.93/1.58
% 2.93/1.58 % (30880)Memory used [KB]: 1663
% 2.93/1.58 % (30880)Time elapsed: 0.006 s
% 2.93/1.58 % (30880)Instructions burned: 8 (million)
% 2.93/1.58 % (30880)------------------------------
% 2.93/1.58 % (30880)------------------------------
% 2.93/1.58 % (30883)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_30594 for (2999ds/3Mi)
% 2.93/1.58 % (30883)Instruction limit reached!
% 2.93/1.58 % (30883)------------------------------
% 2.93/1.58 % (30883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.58 % (30883)Termination reason: Unknown
% 2.93/1.58 % (30883)Termination phase: shuffling
% 2.93/1.58
% 2.93/1.58 % (30883)Memory used [KB]: 1535
% 2.93/1.58 % (30883)Time elapsed: 0.002 s
% 2.93/1.58 % (30883)Instructions burned: 3 (million)
% 2.93/1.58 % (30883)------------------------------
% 2.93/1.58 % (30883)------------------------------
% 2.93/1.59 % (30885)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/3Mi)
% 2.93/1.59 % (30885)Instruction limit reached!
% 2.93/1.59 % (30885)------------------------------
% 2.93/1.59 % (30885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.59 % (30885)Termination reason: Unknown
% 2.93/1.59 % (30885)Termination phase: shuffling
% 2.93/1.59
% 2.93/1.59 % (30885)Memory used [KB]: 1535
% 2.93/1.59 % (30885)Time elapsed: 0.003 s
% 2.93/1.59 % (30885)Instructions burned: 4 (million)
% 2.93/1.59 % (30885)------------------------------
% 2.93/1.59 % (30885)------------------------------
% 2.93/1.59 % (30887)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/18Mi)
% 2.93/1.59 % (30884)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/7Mi)
% 2.93/1.59 % (30886)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/4Mi)
% 2.93/1.59 % (30886)Instruction limit reached!
% 2.93/1.59 % (30886)------------------------------
% 2.93/1.59 % (30886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.59 % (30886)Termination reason: Unknown
% 2.93/1.59 % (30886)Termination phase: shuffling
% 2.93/1.59
% 2.93/1.59 % (30886)Memory used [KB]: 1663
% 2.93/1.59 % (30886)Time elapsed: 0.003 s
% 2.93/1.59 % (30886)Instructions burned: 5 (million)
% 2.93/1.59 % (30886)------------------------------
% 2.93/1.59 % (30886)------------------------------
% 2.93/1.60 % (30884)Instruction limit reached!
% 2.93/1.60 % (30884)------------------------------
% 2.93/1.60 % (30884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (30884)Termination reason: Unknown
% 2.93/1.60 % (30884)Termination phase: shuffling
% 2.93/1.60
% 2.93/1.60 % (30884)Memory used [KB]: 1663
% 2.93/1.60 % (30884)Time elapsed: 0.007 s
% 2.93/1.60 % (30884)Instructions burned: 8 (million)
% 2.93/1.60 % (30884)------------------------------
% 2.93/1.60 % (30884)------------------------------
% 2.97/1.60 % (30887)Instruction limit reached!
% 2.97/1.60 % (30887)------------------------------
% 2.97/1.60 % (30887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.60 % (30887)Termination reason: Unknown
% 2.97/1.60 % (30887)Termination phase: shuffling
% 2.97/1.60
% 2.97/1.60 % (30887)Memory used [KB]: 1918
% 2.97/1.60 % (30887)Time elapsed: 0.008 s
% 2.97/1.60 % (30887)Instructions burned: 20 (million)
% 2.97/1.60 % (30887)------------------------------
% 2.97/1.60 % (30887)------------------------------
% 2.97/1.60 % (30888)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/710Mi)
% 2.97/1.60 % (30868)Instruction limit reached!
% 2.97/1.60 % (30868)------------------------------
% 2.97/1.60 % (30868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.60 % (30868)Termination reason: Unknown
% 2.97/1.60 % (30868)Termination phase: Saturation
% 2.97/1.60
% 2.97/1.60 % (30868)Memory used [KB]: 7291
% 2.97/1.60 % (30868)Time elapsed: 0.061 s
% 2.97/1.60 % (30868)Instructions burned: 183 (million)
% 2.97/1.60 % (30868)------------------------------
% 2.97/1.60 % (30868)------------------------------
% 2.97/1.60 % (30889)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/6Mi)
% 2.97/1.60 % (30889)Instruction limit reached!
% 2.97/1.60 % (30889)------------------------------
% 2.97/1.60 % (30889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.60 % (30889)Termination reason: Unknown
% 2.97/1.61 % (30889)Termination phase: shuffling
% 2.97/1.61
% 2.97/1.61 % (30889)Memory used [KB]: 1663
% 2.97/1.61 % (30889)Time elapsed: 0.004 s
% 2.97/1.61 % (30889)Instructions burned: 8 (million)
% 2.97/1.61 % (30889)------------------------------
% 2.97/1.61 % (30889)------------------------------
% 2.97/1.61 % (30891)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_30594 for (2999ds/21Mi)
% 2.97/1.61 % (30873)First to succeed.
% 2.97/1.61 % (30892)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30594 for (2999ds/5Mi)
% 2.97/1.61 % (30873)Refutation found. Thanks to Tanya!
% 2.97/1.61 % SZS status Theorem for DTF2THF_30594
% 2.97/1.61 % SZS output start Proof for DTF2THF_30594
% 2.97/1.61 thf(type_def_5, type, x_a: $tType).
% 2.97/1.61 thf(type_def_7, type, nat: $tType).
% 2.97/1.61 thf(type_def_8, type, pname: $tType).
% 2.97/1.61 thf(func_def_0, type, x_a: $tType).
% 2.97/1.61 thf(func_def_1, type, pname: $tType).
% 2.97/1.61 thf(func_def_2, type, nat: $tType).
% 2.97/1.61 thf(func_def_3, type, finite_card_a_o_o: (((x_a > $o) > $o) > $o) > nat).
% 2.97/1.61 thf(func_def_4, type, finite221134632me_o_o: (((pname > $o) > $o) > $o) > nat).
% 2.97/1.61 thf(func_def_5, type, finite_card_nat_o_o: (((nat > $o) > $o) > $o) > nat).
% 2.97/1.61 thf(func_def_6, type, finite_card_a_o: ((x_a > $o) > $o) > nat).
% 2.97/1.61 thf(func_def_7, type, finite_card_pname_o: ((pname > $o) > $o) > nat).
% 2.97/1.61 thf(func_def_8, type, finite_card_nat_o: ((nat > $o) > $o) > nat).
% 2.97/1.61 thf(func_def_9, type, finite_card_a: (x_a > $o) > nat).
% 2.97/1.61 thf(func_def_10, type, finite_card_pname: (pname > $o) > nat).
% 2.97/1.61 thf(func_def_11, type, finite_card_nat: (nat > $o) > nat).
% 2.97/1.61 thf(func_def_12, type, finite1302365357_o_o_o: ((((x_a > $o) > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_13, type, finite1648353812_o_o_o: ((((pname > $o) > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_14, type, finite1237261006_o_o_o: ((((nat > $o) > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_15, type, finite_finite_a_o_o: (((x_a > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_16, type, finite1066544169me_o_o: (((pname > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_17, type, finite1676163439at_o_o: (((nat > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_18, type, finite_finite_a_o: ((x_a > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_19, type, finite297249702name_o: ((pname > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_20, type, finite_finite_nat_o: ((nat > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_21, type, finite_finite_a: (x_a > $o) > $o).
% 2.97/1.61 thf(func_def_22, type, finite_finite_pname: (pname > $o) > $o).
% 2.97/1.61 thf(func_def_23, type, finite_finite_nat: (nat > $o) > $o).
% 2.97/1.61 thf(func_def_24, type, minus_minus_nat: nat > nat > nat).
% 2.97/1.61 thf(func_def_25, type, suc: nat > nat).
% 2.97/1.61 thf(func_def_26, type, ord_less_eq_a_o_o_o: (((x_a > $o) > $o) > $o) > (((x_a > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_27, type, ord_le1828183645_o_o_o: (((pname > $o) > $o) > $o) > (((pname > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_28, type, ord_le124054423_o_o_o: (((nat > $o) > $o) > $o) > (((nat > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_29, type, ord_less_eq_a_o_o: ((x_a > $o) > $o) > ((x_a > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_30, type, ord_le1205211808me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_31, type, ord_less_eq_nat_o_o: ((nat > $o) > $o) > ((nat > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_32, type, ord_less_eq_a_o: (x_a > $o) > (x_a > $o) > $o).
% 2.97/1.61 thf(func_def_33, type, ord_less_eq_pname_o: (pname > $o) > (pname > $o) > $o).
% 2.97/1.61 thf(func_def_34, type, ord_less_eq_nat_o: (nat > $o) > (nat > $o) > $o).
% 2.97/1.61 thf(func_def_35, type, ord_less_eq_nat: nat > nat > $o).
% 2.97/1.61 thf(func_def_36, type, collect_a_o_o_o: ((((x_a > $o) > $o) > $o) > $o) > (((x_a > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_37, type, collect_pname_o_o_o: ((((pname > $o) > $o) > $o) > $o) > (((pname > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_38, type, collect_nat_o_o_o: ((((nat > $o) > $o) > $o) > $o) > (((nat > $o) > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_39, type, collect_a_o_o: (((x_a > $o) > $o) > $o) > ((x_a > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_40, type, collect_pname_o_o: (((pname > $o) > $o) > $o) > ((pname > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_41, type, collect_nat_o_o: (((nat > $o) > $o) > $o) > ((nat > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_42, type, collect_a_o: ((x_a > $o) > $o) > (x_a > $o) > $o).
% 2.97/1.61 thf(func_def_43, type, collect_pname_o: ((pname > $o) > $o) > (pname > $o) > $o).
% 2.97/1.61 thf(func_def_44, type, collect_nat_o: ((nat > $o) > $o) > (nat > $o) > $o).
% 2.97/1.61 thf(func_def_45, type, collect_a: (x_a > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_46, type, collect_pname: (pname > $o) > pname > $o).
% 2.97/1.61 thf(func_def_47, type, collect_nat: (nat > $o) > nat > $o).
% 2.97/1.61 thf(func_def_48, type, image_a_o_o_a: (((x_a > $o) > $o) > x_a) > (((x_a > $o) > $o) > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_49, type, image_a_o_o_pname: (((x_a > $o) > $o) > pname) > (((x_a > $o) > $o) > $o) > pname > $o).
% 2.97/1.61 thf(func_def_50, type, image_a_o_o_nat: (((x_a > $o) > $o) > nat) > (((x_a > $o) > $o) > $o) > nat > $o).
% 2.97/1.61 thf(func_def_51, type, image_pname_o_o_a: (((pname > $o) > $o) > x_a) > (((pname > $o) > $o) > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_52, type, image_471733107_pname: (((pname > $o) > $o) > pname) > (((pname > $o) > $o) > $o) > pname > $o).
% 2.97/1.61 thf(func_def_53, type, image_pname_o_o_nat: (((pname > $o) > $o) > nat) > (((pname > $o) > $o) > $o) > nat > $o).
% 2.97/1.61 thf(func_def_54, type, image_nat_o_o_a: (((nat > $o) > $o) > x_a) > (((nat > $o) > $o) > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_55, type, image_nat_o_o_pname: (((nat > $o) > $o) > pname) > (((nat > $o) > $o) > $o) > pname > $o).
% 2.97/1.61 thf(func_def_56, type, image_nat_o_o_nat: (((nat > $o) > $o) > nat) > (((nat > $o) > $o) > $o) > nat > $o).
% 2.97/1.61 thf(func_def_57, type, image_a_o_a: ((x_a > $o) > x_a) > ((x_a > $o) > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_58, type, image_a_o_pname: ((x_a > $o) > pname) > ((x_a > $o) > $o) > pname > $o).
% 2.97/1.61 thf(func_def_59, type, image_a_o_nat: ((x_a > $o) > nat) > ((x_a > $o) > $o) > nat > $o).
% 2.97/1.61 thf(func_def_60, type, image_pname_o_a: ((pname > $o) > x_a) > ((pname > $o) > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_61, type, image_pname_o_pname: ((pname > $o) > pname) > ((pname > $o) > $o) > pname > $o).
% 2.97/1.61 thf(func_def_62, type, image_pname_o_nat: ((pname > $o) > nat) > ((pname > $o) > $o) > nat > $o).
% 2.97/1.61 thf(func_def_63, type, image_nat_o_a: ((nat > $o) > x_a) > ((nat > $o) > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_64, type, image_nat_o_pname: ((nat > $o) > pname) > ((nat > $o) > $o) > pname > $o).
% 2.97/1.61 thf(func_def_65, type, image_nat_o_nat: ((nat > $o) > nat) > ((nat > $o) > $o) > nat > $o).
% 2.97/1.61 thf(func_def_66, type, image_a_a: (x_a > x_a) > (x_a > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_67, type, image_a_pname: (x_a > pname) > (x_a > $o) > pname > $o).
% 2.97/1.61 thf(func_def_68, type, image_a_nat: (x_a > nat) > (x_a > $o) > nat > $o).
% 2.97/1.61 thf(func_def_69, type, image_pname_a_o_o: (pname > (x_a > $o) > $o) > (pname > $o) > ((x_a > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_70, type, image_504089495me_o_o: (pname > (pname > $o) > $o) > (pname > $o) > ((pname > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_71, type, image_pname_nat_o_o: (pname > (nat > $o) > $o) > (pname > $o) > ((nat > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_72, type, image_pname_a_o: (pname > x_a > $o) > (pname > $o) > (x_a > $o) > $o).
% 2.97/1.61 thf(func_def_73, type, image_pname_pname_o: (pname > pname > $o) > (pname > $o) > (pname > $o) > $o).
% 2.97/1.61 thf(func_def_74, type, image_pname_nat_o: (pname > nat > $o) > (pname > $o) > (nat > $o) > $o).
% 2.97/1.61 thf(func_def_75, type, image_pname_a: (pname > x_a) > (pname > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_76, type, image_pname_pname: (pname > pname) > (pname > $o) > pname > $o).
% 2.97/1.61 thf(func_def_77, type, image_pname_nat: (pname > nat) > (pname > $o) > nat > $o).
% 2.97/1.61 thf(func_def_78, type, image_nat_a_o_o: (nat > (x_a > $o) > $o) > (nat > $o) > ((x_a > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_79, type, image_nat_pname_o_o: (nat > (pname > $o) > $o) > (nat > $o) > ((pname > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_80, type, image_nat_nat_o_o: (nat > (nat > $o) > $o) > (nat > $o) > ((nat > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_81, type, image_nat_a_o: (nat > x_a > $o) > (nat > $o) > (x_a > $o) > $o).
% 2.97/1.61 thf(func_def_82, type, image_nat_pname_o: (nat > pname > $o) > (nat > $o) > (pname > $o) > $o).
% 2.97/1.61 thf(func_def_83, type, image_nat_nat_o: (nat > nat > $o) > (nat > $o) > (nat > $o) > $o).
% 2.97/1.61 thf(func_def_84, type, image_nat_a: (nat > x_a) > (nat > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_85, type, image_nat_pname: (nat > pname) > (nat > $o) > pname > $o).
% 2.97/1.61 thf(func_def_86, type, insert_a_o_o: ((x_a > $o) > $o) > (((x_a > $o) > $o) > $o) > ((x_a > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_87, type, insert_pname_o_o: ((pname > $o) > $o) > (((pname > $o) > $o) > $o) > ((pname > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_88, type, insert_nat_o_o: ((nat > $o) > $o) > (((nat > $o) > $o) > $o) > ((nat > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_89, type, insert_a_o: (x_a > $o) > ((x_a > $o) > $o) > (x_a > $o) > $o).
% 2.97/1.61 thf(func_def_90, type, insert_pname_o: (pname > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 2.97/1.61 thf(func_def_91, type, insert_nat_o: (nat > $o) > ((nat > $o) > $o) > (nat > $o) > $o).
% 2.97/1.61 thf(func_def_92, type, insert_a: x_a > (x_a > $o) > x_a > $o).
% 2.97/1.61 thf(func_def_93, type, insert_pname: pname > (pname > $o) > pname > $o).
% 2.97/1.61 thf(func_def_94, type, insert_nat: nat > (nat > $o) > nat > $o).
% 2.97/1.61 thf(func_def_95, type, member_a_o: (x_a > $o) > ((x_a > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_96, type, member_pname_o: (pname > $o) > ((pname > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_97, type, member_nat_o: (nat > $o) > ((nat > $o) > $o) > $o).
% 2.97/1.61 thf(func_def_98, type, member_a: x_a > (x_a > $o) > $o).
% 2.97/1.61 thf(func_def_99, type, member_pname: pname > (pname > $o) > $o).
% 2.97/1.61 thf(func_def_100, type, member_nat: nat > (nat > $o) > $o).
% 2.97/1.61 thf(func_def_101, type, g: x_a > $o).
% 2.97/1.61 thf(func_def_102, type, p: (x_a > $o) > (x_a > $o) > $o).
% 2.97/1.61 thf(func_def_103, type, u: pname > $o).
% 2.97/1.61 thf(func_def_104, type, mgt_call: pname > x_a).
% 2.97/1.61 thf(func_def_105, type, na: nat).
% 2.97/1.61 thf(func_def_106, type, pn: pname).
% 2.97/1.61 thf(func_def_117, type, sK0: (x_a > $o) > (x_a > $o) > x_a).
% 2.97/1.61 thf(func_def_118, type, sK1: (x_a > $o) > (pname > $o) > (pname > x_a) > pname > $o).
% 2.97/1.61 thf(func_def_119, type, sK2: (pname > $o) > (pname > x_a) > x_a > pname).
% 2.97/1.61 thf(func_def_120, type, sK3: nat > nat).
% 2.97/1.61 thf(func_def_121, type, sK4: (pname > $o) > (x_a > $o) > (pname > x_a) > pname).
% 2.97/1.61 thf(func_def_122, type, sK5: (nat > pname > $o) > nat).
% 2.97/1.61 thf(func_def_123, type, sK6: (pname > x_a) > x_a > (pname > $o) > pname).
% 2.97/1.61 thf(func_def_124, type, sK7: (nat > $o) > nat).
% 2.97/1.61 thf(func_def_125, type, sK8: (pname > x_a) > (x_a > $o) > (pname > $o) > pname > $o).
% 2.97/1.61 thf(func_def_126, type, sK9: (pname > $o) > (pname > $o) > pname).
% 2.97/1.61 thf(func_def_127, type, sK10: (nat > x_a > $o) > nat).
% 2.97/1.61 thf(func_def_128, type, sK11: (nat > nat) > nat).
% 2.97/1.61 thf(func_def_130, type, ph13: !>[X0: $tType]:(X0)).
% 2.97/1.61 thf(f1384,plain,(
% 2.97/1.61 $false),
% 2.97/1.61 inference(subsumption_resolution,[status(thm)],[f1383,f1082])).
% 2.97/1.61 thf(f1082,plain,(
% 2.97/1.61 ((member_pname @ pn @ u) = $true)),
% 2.97/1.61 inference(cnf_transformation,[status(thm)],[f579])).
% 2.97/1.61 thf(f579,plain,(
% 2.97/1.61 ((member_pname @ pn @ u) = $true)),
% 2.97/1.61 inference(fool_elimination,[status(thm)],[f578])).
% 2.97/1.61 thf(f578,plain,(
% 2.97/1.61 (member_pname @ pn @ u)),
% 2.97/1.61 inference(rectify,[status(thm)],[f305])).
% 2.97/1.61 thf(f305,axiom,(
% 2.97/1.61 (member_pname @ pn @ u)),
% 2.97/1.61 file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',conj_4)).
% 2.97/1.61 thf(f1383,plain,(
% 2.97/1.61 ((member_pname @ pn @ u) != $true)),
% 2.97/1.61 inference(trivial_inequality_removal,[status(thm)],[f1377])).
% 2.97/1.61 thf(f1377,plain,(
% 2.97/1.61 ((member_pname @ pn @ u) != $true) | ($true != $true)),
% 2.97/1.61 inference(superposition,[status(thm)],[f1372,f1252])).
% 2.97/1.61 thf(f1252,plain,(
% 2.97/1.61 ( ! [X2 : pname > x_a,X3 : pname,X0 : pname > $o] : (((member_a @ (X2 @ X3) @ (image_pname_a @ X2 @ X0)) = $true) | ((member_pname @ X3 @ X0) != $true)) )),
% 2.97/1.61 inference(equality_resolution,[status(thm)],[f1163])).
% 2.97/1.61 thf(f1163,plain,(
% 2.97/1.61 ( ! [X2 : pname > x_a,X3 : pname,X0 : pname > $o,X1 : x_a] : (((member_a @ X1 @ (image_pname_a @ X2 @ X0)) = $true) | ((X2 @ X3) != X1) | ((member_pname @ X3 @ X0) != $true)) )),
% 2.97/1.61 inference(cnf_transformation,[status(thm)],[f1050])).
% 2.97/1.61 thf(f1050,plain,(
% 2.97/1.61 ! [X0 : pname > $o,X1 : x_a,X2 : pname > x_a] : ((((member_a @ X1 @ (image_pname_a @ X2 @ X0)) = $true) | ! [X3 : pname] : (((X2 @ X3) != X1) | ((member_pname @ X3 @ X0) != $true))) & ((((X2 @ (sK6 @ X2 @ X1 @ X0)) = X1) & ($true = (member_pname @ (sK6 @ X2 @ X1 @ X0) @ X0))) | ((member_a @ X1 @ (image_pname_a @ X2 @ X0)) != $true)))),
% 2.97/1.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f1048,f1049])).
% 2.97/1.61 thf(f1049,plain,(
% 2.97/1.61 ! [X0 : pname > $o,X1 : x_a,X2 : pname > x_a] : (? [X4 : pname] : (((X2 @ X4) = X1) & ((member_pname @ X4 @ X0) = $true)) => (((X2 @ (sK6 @ X2 @ X1 @ X0)) = X1) & ($true = (member_pname @ (sK6 @ X2 @ X1 @ X0) @ X0))))),
% 2.97/1.61 introduced(definition,[],[choice_axiom])).
% 2.97/1.61 thf(f1048,plain,(
% 2.97/1.61 ! [X0 : pname > $o,X1 : x_a,X2 : pname > x_a] : ((((member_a @ X1 @ (image_pname_a @ X2 @ X0)) = $true) | ! [X3 : pname] : (((X2 @ X3) != X1) | ((member_pname @ X3 @ X0) != $true))) & (? [X4 : pname] : (((X2 @ X4) = X1) & ((member_pname @ X4 @ X0) = $true)) | ((member_a @ X1 @ (image_pname_a @ X2 @ X0)) != $true)))),
% 2.97/1.61 inference(rectify,[status(thm)],[f1047])).
% 2.97/1.61 thf(f1047,plain,(
% 2.97/1.61 ! [X0 : pname > $o,X1 : x_a,X2 : pname > x_a] : ((((member_a @ X1 @ (image_pname_a @ X2 @ X0)) = $true) | ! [X3 : pname] : (((X2 @ X3) != X1) | ((member_pname @ X3 @ X0) != $true))) & (? [X3 : pname] : (((X2 @ X3) = X1) & ((member_pname @ X3 @ X0) = $true)) | ((member_a @ X1 @ (image_pname_a @ X2 @ X0)) != $true)))),
% 2.97/1.61 inference(nnf_transformation,[status(thm)],[f747])).
% 2.97/1.61 thf(f747,plain,(
% 2.97/1.61 ! [X0 : pname > $o,X1 : x_a,X2 : pname > x_a] : (((member_a @ X1 @ (image_pname_a @ X2 @ X0)) = $true) <=> ? [X3 : pname] : (((X2 @ X3) = X1) & ((member_pname @ X3 @ X0) = $true)))),
% 2.97/1.61 inference(fool_elimination,[status(thm)],[f746])).
% 2.97/1.61 thf(f746,plain,(
% 2.97/1.61 ! [X0 : pname > $o,X1 : x_a,X2 : pname > x_a] : ((member_a @ X1 @ (image_pname_a @ X2 @ X0)) <=> ? [X3 : pname] : (((X2 @ X3) = X1) & (member_pname @ X3 @ X0)))),
% 2.97/1.61 inference(rectify,[status(thm)],[f261])).
% 2.97/1.61 thf(f261,axiom,(
% 2.97/1.61 ! [X123 : pname > $o,X121 : x_a,X122 : pname > x_a] : ((member_a @ X121 @ (image_pname_a @ X122 @ X123)) <=> ? [X22 : pname] : (((X122 @ X22) = X121) & (member_pname @ X22 @ X123)))),
% 2.97/1.61 file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',fact_260_image__iff)).
% 2.97/1.61 thf(f1372,plain,(
% 2.97/1.61 ($true != (member_a @ (mgt_call @ pn) @ (image_pname_a @ mgt_call @ u)))),
% 2.97/1.61 inference(subsumption_resolution,[status(thm)],[f1371,f1109])).
% 2.97/1.61 thf(f1109,plain,(
% 2.97/1.61 ((ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u)) = $true)),
% 2.97/1.61 inference(cnf_transformation,[status(thm)],[f317])).
% 2.97/1.61 thf(f317,plain,(
% 2.97/1.61 ((ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u)) = $true)),
% 2.97/1.61 inference(fool_elimination,[status(thm)],[f316])).
% 2.97/1.61 thf(f316,plain,(
% 2.97/1.61 (ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u))),
% 2.97/1.61 inference(rectify,[status(thm)],[f302])).
% 2.97/1.61 thf(f302,axiom,(
% 2.97/1.61 (ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u))),
% 2.97/1.61 file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',conj_1)).
% 2.97/1.61 thf(f1371,plain,(
% 2.97/1.61 ((ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u)) != $true) | ($true != (member_a @ (mgt_call @ pn) @ (image_pname_a @ mgt_call @ u)))),
% 2.97/1.61 inference(trivial_inequality_removal,[status(thm)],[f1368])).
% 2.97/1.61 thf(f1368,plain,(
% 2.97/1.61 ((ord_less_eq_a_o @ g @ (image_pname_a @ mgt_call @ u)) != $true) | ($true != (member_a @ (mgt_call @ pn) @ (image_pname_a @ mgt_call @ u))) | ($true != $true)),
% 2.97/1.61 inference(superposition,[status(thm)],[f1165,f1224])).
% 2.97/1.61 thf(f1224,plain,(
% 2.97/1.61 ( ! [X2 : x_a,X0 : x_a > $o,X1 : x_a > $o] : (($true = (ord_less_eq_a_o @ (insert_a @ X2 @ X1) @ X0)) | ((ord_less_eq_a_o @ X1 @ X0) != $true) | ((member_a @ X2 @ X0) != $true)) )),
% 2.97/1.61 inference(cnf_transformation,[status(thm)],[f1066])).
% 2.97/1.61 thf(f1066,plain,(
% 2.97/1.61 ! [X0 : x_a > $o,X1 : x_a > $o,X2 : x_a] : ((($true = (ord_less_eq_a_o @ (insert_a @ X2 @ X1) @ X0)) | ((ord_less_eq_a_o @ X1 @ X0) != $true) | ((member_a @ X2 @ X0) != $true)) & ((((ord_less_eq_a_o @ X1 @ X0) = $true) & ((member_a @ X2 @ X0) = $true)) | ($true != (ord_less_eq_a_o @ (insert_a @ X2 @ X1) @ X0))))),
% 2.97/1.61 inference(flattening,[status(thm)],[f1065])).
% 2.97/1.61 thf(f1065,plain,(
% 2.97/1.61 ! [X0 : x_a > $o,X1 : x_a > $o,X2 : x_a] : ((($true = (ord_less_eq_a_o @ (insert_a @ X2 @ X1) @ X0)) | (((ord_less_eq_a_o @ X1 @ X0) != $true) | ((member_a @ X2 @ X0) != $true))) & ((((ord_less_eq_a_o @ X1 @ X0) = $true) & ((member_a @ X2 @ X0) = $true)) | ($true != (ord_less_eq_a_o @ (insert_a @ X2 @ X1) @ X0))))),
% 2.97/1.61 inference(nnf_transformation,[status(thm)],[f581])).
% 2.97/1.61 thf(f581,plain,(
% 2.97/1.61 ! [X0 : x_a > $o,X1 : x_a > $o,X2 : x_a] : (($true = (ord_less_eq_a_o @ (insert_a @ X2 @ X1) @ X0)) <=> (((ord_less_eq_a_o @ X1 @ X0) = $true) & ((member_a @ X2 @ X0) = $true)))),
% 2.97/1.61 inference(fool_elimination,[status(thm)],[f580])).
% 2.97/1.61 thf(f580,plain,(
% 2.97/1.61 ! [X0 : x_a > $o,X1 : x_a > $o,X2 : x_a] : (((ord_less_eq_a_o @ X1 @ X0) & (member_a @ X2 @ X0)) <=> (ord_less_eq_a_o @ (insert_a @ X2 @ X1) @ X0))),
% 2.97/1.61 inference(rectify,[status(thm)],[f275])).
% 2.97/1.61 thf(f275,axiom,(
% 2.97/1.61 ! [X137 : x_a > $o,X136 : x_a > $o,X135 : x_a] : (((ord_less_eq_a_o @ X136 @ X137) & (member_a @ X135 @ X137)) <=> (ord_less_eq_a_o @ (insert_a @ X135 @ X136) @ X137))),
% 2.97/1.61 file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',fact_274_insert__subset)).
% 2.97/1.61 thf(f1165,plain,(
% 2.97/1.61 ((ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u)) != $true)),
% 2.97/1.61 inference(cnf_transformation,[status(thm)],[f885])).
% 2.97/1.61 thf(f885,plain,(
% 2.97/1.61 ((ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u)) != $true)),
% 2.97/1.61 inference(flattening,[status(thm)],[f809])).
% 2.97/1.61 thf(f809,plain,(
% 2.97/1.61 ~((ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u)) = $true)),
% 2.97/1.61 inference(fool_elimination,[status(thm)],[f808])).
% 2.97/1.61 thf(f808,plain,(
% 2.97/1.61 ~(ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u))),
% 2.97/1.61 inference(rectify,[status(thm)],[f308])).
% 2.97/1.61 thf(f308,negated_conjecture,(
% 2.97/1.61 ~(ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u))),
% 2.97/1.61 inference(negated_conjecture,[status(cth)],[f307])).
% 2.97/1.61 thf(f307,conjecture,(
% 2.97/1.61 (ord_less_eq_a_o @ (insert_a @ (mgt_call @ pn) @ g) @ (image_pname_a @ mgt_call @ u))),
% 2.97/1.61 file('/export/starexec/sandbox2/tmp/tmp.m2k5194Iiw/DTF2THF_30594.p',conj_6)).
% 2.97/1.61 % SZS output end Proof for DTF2THF_30594
% 2.97/1.61 % (30873)------------------------------
% 2.97/1.61 % (30873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.61 % (30873)Termination reason: Refutation
% 2.97/1.61
% 2.97/1.61 % (30873)Memory used [KB]: 6908
% 2.97/1.61 % (30873)Time elapsed: 0.065 s
% 2.97/1.61 % (30873)Instructions burned: 104 (million)
% 2.97/1.61 % (30873)------------------------------
% 2.97/1.61 % (30873)------------------------------
% 2.97/1.61 % (30867)Success in time 0.083 s
%------------------------------------------------------------------------------