TPTP Problem File: ITP008^7.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP008^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Ewellorder_2EWIN__WF2.p, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Ewellorder_2EWIN__WF2.p [Gau20]
% : HL403501^7.p [TPAP]
% Status : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 8016 (2032 unt;2577 typ; 0 def)
% Number of atoms : 20640 (7730 equ; 726 cnn)
% Maximal formula atoms : 912 ( 3 avg)
% Number of connectives : 142766 ( 726 ~; 461 |;5285 &;129983 @)
% (3162 <=>;3149 =>; 0 <=; 0 <~>)
% Maximal formula depth : 364 ( 8 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 15180 (15180 >; 0 *; 0 +; 0 <<)
% Number of symbols : 808 ( 806 usr; 8 con; 0-9 aty)
% Number of variables : 36864 (1711 ^;20370 !;12692 ?;36864 :)
% (2091 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP002^7.ax').
include('Axioms/ITP001/ITP003^7.ax').
include('Axioms/ITP001/ITP004^7.ax').
include('Axioms/ITP001/ITP005^7.ax').
include('Axioms/ITP001/ITP006^7.ax').
include('Axioms/ITP001/ITP007^7.ax').
include('Axioms/ITP001/ITP008^7.ax').
include('Axioms/ITP001/ITP009^7.ax').
include('Axioms/ITP001/ITP010^7.ax').
include('Axioms/ITP001/ITP011^7.ax').
include('Axioms/ITP001/ITP012^7.ax').
include('Axioms/ITP001/ITP013^7.ax').
include('Axioms/ITP001/ITP014^7.ax').
include('Axioms/ITP001/ITP015^7.ax').
include('Axioms/ITP001/ITP016^7.ax').
include('Axioms/ITP001/ITP017^7.ax').
include('Axioms/ITP001/ITP018^7.ax').
include('Axioms/ITP001/ITP019^7.ax').
include('Axioms/ITP001/ITP020^7.ax').
include('Axioms/ITP001/ITP021^7.ax').
include('Axioms/ITP001/ITP022^7.ax').
include('Axioms/ITP001/ITP023^7.ax').
include('Axioms/ITP001/ITP024^7.ax').
include('Axioms/ITP001/ITP025^7.ax').
include('Axioms/ITP001/ITP026^7.ax').
include('Axioms/ITP001/ITP027^7.ax').
include('Axioms/ITP001/ITP028^7.ax').
include('Axioms/ITP001/ITP029^7.ax').
include('Axioms/ITP001/ITP030^7.ax').
include('Axioms/ITP001/ITP031^7.ax').
include('Axioms/ITP001/ITP032^7.ax').
include('Axioms/ITP001/ITP033^7.ax').
include('Axioms/ITP001/ITP034^7.ax').
include('Axioms/ITP001/ITP035^7.ax').
include('Axioms/ITP001/ITP036^7.ax').
include('Axioms/ITP001/ITP037^7.ax').
include('Axioms/ITP001/ITP038^7.ax').
include('Axioms/ITP001/ITP039^7.ax').
include('Axioms/ITP001/ITP040^7.ax').
include('Axioms/ITP001/ITP041^7.ax').
include('Axioms/ITP001/ITP042^7.ax').
include('Axioms/ITP001/ITP043^7.ax').
include('Axioms/ITP001/ITP044^7.ax').
include('Axioms/ITP001/ITP045^7.ax').
include('Axioms/ITP001/ITP046^7.ax').
include('Axioms/ITP001/ITP047^7.ax').
include('Axioms/ITP001/ITP048^7.ax').
include('Axioms/ITP001/ITP049^7.ax').
include('Axioms/ITP001/ITP050^7.ax').
include('Axioms/ITP001/ITP051^7.ax').
include('Axioms/ITP001/ITP052^7.ax').
include('Axioms/ITP001/ITP053^7.ax').
include('Axioms/ITP001/ITP054^7.ax').
include('Axioms/ITP001/ITP055^7.ax').
include('Axioms/ITP001/ITP056^7.ax').
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(tyop_2Ewellorder_2Ewellorder,type,
tyop_2Ewellorder_2Ewellorder: $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Epair_2E_2C,type,
c_2Epair_2E_2C:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Epair_2ECURRY,type,
c_2Epair_2ECURRY:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27c ) > A_27a > A_27b > A_27c ) ).
thf(c_2Epred__set_2EEMPTY,type,
c_2Epred__set_2EEMPTY:
!>[A_27a: $tType] : ( A_27a > $o ) ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2Ebool_2EIN,type,
c_2Ebool_2EIN:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
thf(c_2Epred__set_2EINSERT,type,
c_2Epred__set_2EINSERT:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > A_27a > $o ) ).
thf(c_2Epred__set_2ESUBSET,type,
c_2Epred__set_2ESUBSET:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2ETYPE__DEFINITION,type,
c_2Ebool_2ETYPE__DEFINITION:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > A_27a ) > $o ) ).
thf(c_2Epred__set_2EUNION,type,
c_2Epred__set_2EUNION:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > $o ) > A_27a > $o ) ).
thf(c_2Erelation_2EWF,type,
c_2Erelation_2EWF:
!>[A_27a: $tType] : ( ( A_27a > A_27a > $o ) > $o ) ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Eset__relation_2Eantisym,type,
c_2Eset__relation_2Eantisym:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > $o ) ).
thf(c_2Eset__relation_2Edomain,type,
c_2Eset__relation_2Edomain:
!>[A_27a: $tType,A_27b: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o ) > A_27a > $o ) ).
thf(c_2Ewellorder_2EelsOf,type,
c_2Ewellorder_2EelsOf:
!>[A_27a: $tType] : ( ( tyop_2Ewellorder_2Ewellorder @ A_27a ) > A_27a > $o ) ).
thf(c_2Eset__relation_2Elinear__order,type,
c_2Eset__relation_2Elinear__order:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > ( A_27a > $o ) > $o ) ).
thf(c_2Eset__relation_2Erange,type,
c_2Eset__relation_2Erange:
!>[A_27a: $tType,A_27b: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) > $o ) > A_27a > $o ) ).
thf(c_2Eset__relation_2Ereflexive,type,
c_2Eset__relation_2Ereflexive:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > ( A_27a > $o ) > $o ) ).
thf(c_2Eset__relation_2Errestrict,type,
c_2Eset__relation_2Errestrict:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > ( A_27a > $o ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) ).
thf(c_2Eset__relation_2Estrict,type,
c_2Eset__relation_2Estrict:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) ).
thf(c_2Eset__relation_2Etransitive,type,
c_2Eset__relation_2Etransitive:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > $o ) ).
thf(c_2Ewellorder_2Ewellfounded,type,
c_2Ewellorder_2Ewellfounded:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > $o ) ).
thf(c_2Ewellorder_2Ewellorder,type,
c_2Ewellorder_2Ewellorder:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > $o ) ).
thf(c_2Ewellorder_2Ewellorder__ABS,type,
c_2Ewellorder_2Ewellorder__ABS:
!>[A_27a: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) > ( tyop_2Ewellorder_2Ewellorder @ A_27a ) ) ).
thf(c_2Ewellorder_2Ewellorder__REP,type,
c_2Ewellorder_2Ewellorder__REP:
!>[A_27a: $tType] : ( ( tyop_2Ewellorder_2Ewellorder @ A_27a ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2Ewellorder_2Ewellfounded__def,axiom,
! [A_27a: $tType,V0R: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o] :
( ( c_2Ewellorder_2Ewellfounded @ A_27a @ V0R )
<=> ! [V1s: A_27a > $o] :
( ? [V2w: A_27a] : ( c_2Ebool_2EIN @ A_27a @ V2w @ V1s )
=> ? [V3min: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V3min @ V1s )
& ! [V4w: A_27a] :
( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V4w @ V3min ) @ V0R )
=> ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V4w @ V1s ) ) ) ) ) ) ).
thf(thm_2Ewellorder_2Ewellorder__def,axiom,
! [A_27a: $tType,V0R: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o] :
( ( c_2Ewellorder_2Ewellorder @ A_27a @ V0R )
<=> ( ( c_2Ewellorder_2Ewellfounded @ A_27a @ ( c_2Eset__relation_2Estrict @ A_27a @ V0R ) )
& ( c_2Eset__relation_2Elinear__order @ A_27a @ V0R @ ( c_2Epred__set_2EUNION @ A_27a @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a @ V0R ) @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a @ V0R ) ) )
& ( c_2Eset__relation_2Ereflexive @ A_27a @ V0R @ ( c_2Epred__set_2EUNION @ A_27a @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a @ V0R ) @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a @ V0R ) ) ) ) ) ).
thf(thm_2Ewellorder_2Ewellorder__TY__DEF,axiom,
! [A_27a: $tType] :
? [V0rep: ( tyop_2Ewellorder_2Ewellorder @ A_27a ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o] : ( c_2Ebool_2ETYPE__DEFINITION @ ( ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o ) @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( c_2Ewellorder_2Ewellorder @ A_27a ) @ V0rep ) ).
thf(thm_2Ewellorder_2Ewellorder__ABSREP,axiom,
! [A_27a: $tType] :
( ! [V0a: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( c_2Ewellorder_2Ewellorder__ABS @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0a ) )
= V0a )
& ! [V1r: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o] :
( ( c_2Ewellorder_2Ewellorder @ A_27a @ V1r )
<=> ( ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ ( c_2Ewellorder_2Ewellorder__ABS @ A_27a @ V1r ) )
= V1r ) ) ) ).
thf(thm_2Ewellorder_2EelsOf__def,axiom,
! [A_27a: $tType,V0w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( c_2Ewellorder_2EelsOf @ A_27a @ V0w )
= ( c_2Epred__set_2EUNION @ A_27a @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0w ) ) @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0w ) ) ) ) ).
thf(thm_2Ewellorder_2Ewellfounded__WF,axiom,
! [A_27a: $tType,V0R: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o] :
( ( c_2Ewellorder_2Ewellfounded @ A_27a @ V0R )
= ( c_2Erelation_2EWF @ A_27a @ ( c_2Epair_2ECURRY @ A_27a @ A_27a @ $o @ V0R ) ) ) ).
thf(thm_2Ewellorder_2Ewellorder__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Ewellorder_2Ewellorder @ A_27a @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) ).
thf(thm_2Ewellorder_2Ewellorder__SING,axiom,
! [A_27a: $tType,V0x: A_27a,V1y: A_27a] :
( ( c_2Ewellorder_2Ewellorder @ A_27a @ ( c_2Epred__set_2EINSERT @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V0x @ V1y ) @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) )
<=> ( V0x = V1y ) ) ).
thf(thm_2Ewellorder_2Errestrict__SUBSET,axiom,
! [A_27a: $tType,V0r: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o,V1s: A_27a > $o] : ( c_2Epred__set_2ESUBSET @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Eset__relation_2Errestrict @ A_27a @ V0r @ V1s ) @ V0r ) ).
thf(thm_2Ewellorder_2Ewellfounded__subset,axiom,
! [A_27a: $tType,V0r0: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o,V1r: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o] :
( ( ( c_2Ewellorder_2Ewellfounded @ A_27a @ V1r )
& ( c_2Epred__set_2ESUBSET @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ V0r0 @ V1r ) )
=> ( c_2Ewellorder_2Ewellfounded @ A_27a @ V0r0 ) ) ).
thf(thm_2Ewellorder_2EmkWO__destWO,axiom,
! [A_27a: $tType,V0a: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( c_2Ewellorder_2Ewellorder__ABS @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0a ) )
= V0a ) ).
thf(thm_2Ewellorder_2EdestWO__mkWO,axiom,
! [A_27a: $tType,V0r: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o] :
( ( c_2Ewellorder_2Ewellorder @ A_27a @ V0r )
=> ( ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ ( c_2Ewellorder_2Ewellorder__ABS @ A_27a @ V0r ) )
= V0r ) ) ).
thf(thm_2Ewellorder_2EWIN__elsOf,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1x @ V0y ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V2w ) ) )
=> ( ( c_2Ebool_2EIN @ A_27a @ V1x @ ( c_2Ewellorder_2EelsOf @ A_27a @ V2w ) )
& ( c_2Ebool_2EIN @ A_27a @ V0y @ ( c_2Ewellorder_2EelsOf @ A_27a @ V2w ) ) ) ) ).
thf(thm_2Ewellorder_2EWLE__elsOf,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1x @ V0y ) @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V2w ) )
=> ( ( c_2Ebool_2EIN @ A_27a @ V1x @ ( c_2Ewellorder_2EelsOf @ A_27a @ V2w ) )
& ( c_2Ebool_2EIN @ A_27a @ V0y @ ( c_2Ewellorder_2EelsOf @ A_27a @ V2w ) ) ) ) ).
thf(thm_2Ewellorder_2EWIN__trichotomy,axiom,
! [A_27a: $tType,V0w: tyop_2Ewellorder_2Ewellorder @ A_27a,V1x: A_27a,V2y: A_27a] :
( ( ( c_2Ebool_2EIN @ A_27a @ V1x @ ( c_2Ewellorder_2EelsOf @ A_27a @ V0w ) )
& ( c_2Ebool_2EIN @ A_27a @ V2y @ ( c_2Ewellorder_2EelsOf @ A_27a @ V0w ) ) )
=> ( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1x @ V2y ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0w ) ) )
| ( V1x = V2y )
| ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V2y @ V1x ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0w ) ) ) ) ) ).
thf(thm_2Ewellorder_2EWIN__REFL,axiom,
! [A_27a: $tType,V0x: A_27a,V1w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V0x @ V0x ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V1w ) ) )
= c_2Ebool_2EF ) ).
thf(thm_2Ewellorder_2EWLE__TRANS,axiom,
! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V2x @ V1y ) @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V3w ) )
& ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1y @ V0z ) @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V3w ) ) )
=> ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V2x @ V0z ) @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V3w ) ) ) ).
thf(thm_2Ewellorder_2EWLE__ANTISYM,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1x @ V0y ) @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V2w ) )
& ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V0y @ V1x ) @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V2w ) ) )
=> ( V1x = V0y ) ) ).
thf(thm_2Ewellorder_2EWIN__WLE,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1x @ V0y ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V2w ) ) )
=> ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1x @ V0y ) @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V2w ) ) ) ).
thf(thm_2Ewellorder_2EelsOf__WLE,axiom,
! [A_27a: $tType,V0x: A_27a,V1w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Ewellorder_2EelsOf @ A_27a @ V1w ) )
= ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V0x @ V0x ) @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V1w ) ) ) ).
thf(thm_2Ewellorder_2Etransitive__strict,axiom,
! [A_27a: $tType,V0r: ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) > $o] :
( ( ( c_2Eset__relation_2Etransitive @ A_27a @ V0r )
& ( c_2Eset__relation_2Eantisym @ A_27a @ V0r ) )
=> ( c_2Eset__relation_2Etransitive @ A_27a @ ( c_2Eset__relation_2Estrict @ A_27a @ V0r ) ) ) ).
thf(thm_2Ewellorder_2EWIN__TRANS,axiom,
! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( ( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V2x @ V1y ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V3w ) ) )
& ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1y @ V0z ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V3w ) ) ) )
=> ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V2x @ V0z ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V3w ) ) ) ) ).
thf(thm_2Ewellorder_2EWIN__WF,axiom,
! [A_27a: $tType,V0w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( c_2Ewellorder_2Ewellfounded @ A_27a
@ ^ [V1p: tyop_2Epair_2Eprod @ A_27a @ A_27a] : ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ V1p @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0w ) ) ) ) ).
thf(thm_2Ewellorder_2EWIN__WF2,conjecture,
! [A_27a: $tType,V0w: tyop_2Ewellorder_2Ewellorder @ A_27a] :
( c_2Erelation_2EWF @ A_27a
@ ^ [V1x: A_27a,V2y: A_27a] : ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C @ A_27a @ A_27a @ V1x @ V2y ) @ ( c_2Eset__relation_2Estrict @ A_27a @ ( c_2Ewellorder_2Ewellorder__REP @ A_27a @ V0w ) ) ) ) ).
%------------------------------------------------------------------------------