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 : 14838 (5070 unt;5235 typ; 0 def)
% Number of atoms : 24508 (12656 equ)
% Maximal formula atoms : 912 ( 1 avg)
% Number of connectives : 15898 ( 993 ~; 640 |;5536 &)
% (4055 <=>;4674 =>; 0 <=; 0 <~>)
% Maximal formula depth : 360 ( 6 avg)
% Maximal term depth : 27 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 4400 (2573 >;1827 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 1755 (1755 usr; 208 con; 0-8 aty)
% Number of variables : 54586 (36957 !;12788 ?;54586 :)
% (4841 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_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').
%------------------------------------------------------------------------------
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Ewellorder_2Ewellorder,type,
tyop_2Ewellorder_2Ewellorder: $tType > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2ECURRY_2E0,type,
c_2Epair_2ECURRY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))) ).
tff(c_2Epair_2ECURRY_2E1,type,
c_2Epair_2ECURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) ) ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2ESUBSET_2E0,type,
c_2Epred__set_2ESUBSET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2ESUBSET_2E2,type,
c_2Epred__set_2ESUBSET_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EUNION_2E0,type,
c_2Epred__set_2EUNION_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EUNION_2E2,type,
c_2Epred__set_2EUNION_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWF_2E1,type,
c_2Erelation_2EWF_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Eset__relation_2Eantisym_2E0,type,
c_2Eset__relation_2Eantisym_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Eset__relation_2Eantisym_2E1,type,
c_2Eset__relation_2Eantisym_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Eset__relation_2Edomain_2E0,type,
c_2Eset__relation_2Edomain_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Eset__relation_2Edomain_2E1,type,
c_2Eset__relation_2Edomain_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Ewellorder_2EelsOf_2E0,type,
c_2Ewellorder_2EelsOf_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Ewellorder_2EelsOf_2E1,type,
c_2Ewellorder_2EelsOf_2E1:
!>[A_27a: $tType] : ( tyop_2Ewellorder_2Ewellorder(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eset__relation_2Elinear__order_2E0,type,
c_2Eset__relation_2Elinear__order_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Eset__relation_2Elinear__order_2E2,type,
c_2Eset__relation_2Elinear__order_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eset__relation_2Erange_2E0,type,
c_2Eset__relation_2Erange_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Eset__relation_2Erange_2E1,type,
c_2Eset__relation_2Erange_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eset__relation_2Ereflexive_2E0,type,
c_2Eset__relation_2Ereflexive_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Eset__relation_2Ereflexive_2E2,type,
c_2Eset__relation_2Ereflexive_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eset__relation_2Errestrict_2E0,type,
c_2Eset__relation_2Errestrict_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))) ).
tff(c_2Eset__relation_2Errestrict_2E2,type,
c_2Eset__relation_2Errestrict_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Eset__relation_2Estrict_2E0,type,
c_2Eset__relation_2Estrict_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Eset__relation_2Estrict_2E1,type,
c_2Eset__relation_2Estrict_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Eset__relation_2Etransitive_2E0,type,
c_2Eset__relation_2Etransitive_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Eset__relation_2Etransitive_2E1,type,
c_2Eset__relation_2Etransitive_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewellorder_2Ewellfounded_2E0,type,
c_2Ewellorder_2Ewellfounded_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ewellorder_2Ewellfounded_2E1,type,
c_2Ewellorder_2Ewellfounded_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewellorder_2Ewellorder_2E0,type,
c_2Ewellorder_2Ewellorder_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ewellorder_2Ewellorder_2E1,type,
c_2Ewellorder_2Ewellorder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewellorder_2Ewellorder__ABS_2E0,type,
c_2Ewellorder_2Ewellorder__ABS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a)) ).
tff(c_2Ewellorder_2Ewellorder__ABS_2E1,type,
c_2Ewellorder_2Ewellorder__ABS_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Ewellorder_2Ewellorder(A_27a) ) ).
tff(c_2Ewellorder_2Ewellorder__REP_2E0,type,
c_2Ewellorder_2Ewellorder__REP_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ewellorder_2Ewellorder__REP_2E1,type,
c_2Ewellorder_2Ewellorder__REP_2E1:
!>[A_27a: $tType] : ( tyop_2Ewellorder_2Ewellorder(A_27a) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] : c_2Epair_2E_2C_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2E_2C_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Epair_2ECURRY_2E1(A_27a,A_27a,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epair_2ECURRY_2E0(A_27a,A_27a,tyop_2Emin_2Ebool),X0_2E0) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Epred__set_2EINSERT_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ewellorder_2Ewellorder_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] : c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EUNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : c_2Erelation_2EWF_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(A_27a),X0_2E0) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Eset__relation_2Eantisym_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Eset__relation_2Eantisym_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E0(A_27a,A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewellorder_2EelsOf_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : c_2Ewellorder_2EelsOf_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ewellorder_2EelsOf_2E0(A_27a),X0_2E0) ).
tff(arityeq2_2Ec_2Eset__relation_2Elinear__order_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Eset__relation_2Elinear__order_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Elinear__order_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Eset__relation_2Erange_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E0(A_27a,A_27a),X0_2E0) ).
tff(arityeq2_2Ec_2Eset__relation_2Ereflexive_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Eset__relation_2Ereflexive_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Ereflexive_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Eset__relation_2Errestrict_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Eset__relation_2Errestrict_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Errestrict_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Eset__relation_2Estrict_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Eset__relation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Eset__relation_2Etransitive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewellorder_2Ewellfounded_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Ewellorder_2Ewellfounded_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Ewellfounded_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewellorder_2Ewellorder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Ewellorder_2Ewellorder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Ewellorder_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewellorder_2Ewellorder__ABS_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a),c_2Ewellorder_2Ewellorder__ABS_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewellorder_2Ewellorder__REP_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2Ewellorder__REP_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Ewellorder_2Ewellfounded__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ewellorder_2Ewellfounded_2E1(A_27a,V0R_2E0))
<=> ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V2w_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V2w_2E0,V1s_2E0))
=> ? [V3min_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3min_2E0,V1s_2E0))
& ! [V4w_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V4w_2E0,V3min_2E0),V0R_2E0))
=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V4w_2E0,V1s_2E0)) ) ) ) ) ).
tff(thm_2Ewellorder_2Ewellorder__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,V0R_2E0))
<=> ( p(c_2Ewellorder_2Ewellfounded_2E1(A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0R_2E0)))
& p(c_2Eset__relation_2Elinear__order_2E2(A_27a,V0R_2E0,c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0R_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0R_2E0))))
& p(c_2Eset__relation_2Ereflexive_2E2(A_27a,V0R_2E0,c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,V0R_2E0),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,V0R_2E0)))) ) ) ).
tff(thm_2Ewellorder_2Ewellorder__TY__DEF,axiom,
! [A_27a: $tType] :
? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a),c_2Ewellorder_2Ewellorder_2E0(A_27a),V0rep_2E0)) ).
tff(thm_2Ewellorder_2Ewellorder__ABSREP,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0a_2E0)) = V0a_2E0
& ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,V1r_2E0))
<=> ( c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Ewellorder_2EelsOf__def,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Eset__relation_2Edomain_2E1(A_27a,A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0)),c_2Eset__relation_2Erange_2E1(A_27a,A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0))) ).
tff(thm_2Ewellorder_2Ewellfounded__WF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Ewellorder_2Ewellfounded_2E1(A_27a,V0R_2E0) = c_2Erelation_2EWF_2E1(A_27a,c_2Epair_2ECURRY_2E1(A_27a,A_27a,tyop_2Emin_2Ebool,V0R_2E0)) ).
tff(thm_2Ewellorder_2Ewellorder__EMPTY,axiom,
! [A_27a: $tType] : p(c_2Ewellorder_2Ewellorder_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)))) ).
tff(thm_2Ewellorder_2Ewellorder__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V1y_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)))))
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Ewellorder_2Errestrict__SUBSET,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Eset__relation_2Errestrict_2E2(A_27a,V0r_2E0,V1s_2E0),V0r_2E0)) ).
tff(thm_2Ewellorder_2Ewellfounded__subset,axiom,
! [A_27a: $tType,V0r0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Ewellorder_2Ewellfounded_2E1(A_27a,V1r_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V0r0_2E0,V1r_2E0)) )
=> p(c_2Ewellorder_2Ewellfounded_2E1(A_27a,V0r0_2E0)) ) ).
tff(thm_2Ewellorder_2EmkWO__destWO,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0a_2E0)) = V0a_2E0 ).
tff(thm_2Ewellorder_2EdestWO__mkWO,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ewellorder_2Ewellorder_2E1(A_27a,V0r_2E0))
=> ( c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,c_2Ewellorder_2Ewellorder__ABS_2E1(A_27a,V0r_2E0)) = V0r_2E0 ) ) ).
tff(thm_2Ewellorder_2EWIN__elsOf,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V0y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0))))
=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0))) ) ) ).
tff(thm_2Ewellorder_2EWLE__elsOf,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V0y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))
=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V2w_2E0))) ) ) ).
tff(thm_2Ewellorder_2EWIN__trichotomy,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V0w_2E0))) )
=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0))))
| ( V1x_2E0 = V2y_2E0 )
| p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2y_2E0,V1x_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0)))) ) ) ).
tff(thm_2Ewellorder_2EWIN__REFL,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V0x_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0))) = c_2Ebool_2EF_2E0 ).
tff(thm_2Ewellorder_2EWLE__TRANS,axiom,
! [A_27a: $tType,V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V1y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0)))
& p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1y_2E0,V0z_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))) )
=> p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V0z_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))) ) ).
tff(thm_2Ewellorder_2EWLE__ANTISYM,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V0y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))
& p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0y_2E0,V1x_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0))) )
=> ( V1x_2E0 = V0y_2E0 ) ) ).
tff(thm_2Ewellorder_2EWIN__WLE,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V0y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0))))
=> p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V0y_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0))) ) ).
tff(thm_2Ewellorder_2EelsOf__WLE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Ewellorder_2EelsOf_2E1(A_27a,V1w_2E0)) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V0x_2E0,V0x_2E0),c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V1w_2E0)) ).
tff(thm_2Ewellorder_2Etransitive__strict,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Eset__relation_2Etransitive_2E1(A_27a,V0r_2E0))
& p(c_2Eset__relation_2Eantisym_2E1(A_27a,V0r_2E0)) )
=> p(c_2Eset__relation_2Etransitive_2E1(A_27a,c_2Eset__relation_2Estrict_2E1(A_27a,V0r_2E0))) ) ).
tff(thm_2Ewellorder_2EWIN__TRANS,axiom,
! [A_27a: $tType,V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V1y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0))))
& p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1y_2E0,V0z_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0)))) )
=> p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V2x_2E0,V0z_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V3w_2E0)))) ) ).
tff(thm_2Ewellorder_2EWIN__WF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] :
( ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1p_2E0: tyop_2Epair_2Eprod(A_27a,A_27a)] : app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),F0_2E0,V0w_2E0),V1p_2E0) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),V1p_2E0,c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0)))
=> ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : p(c_2Ewellorder_2Ewellfounded_2E1(A_27a,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),F0_2E0,V0w_2E0))) ) ).
tff(thm_2Ewellorder_2EWIN__WF2,conjecture,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] : app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0w_2E0),V1x_2E0),V2y_2E0) = c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V2y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V0w_2E0)))
=> ! [V0w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : p(c_2Erelation_2EWF_2E1(A_27a,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0w_2E0))) ) ).
%------------------------------------------------------------------------------