ITP001 Axioms: ITP050+5.ax
%------------------------------------------------------------------------------
% File : ITP050+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, 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 : quotient+2.ax [Gau20]
% : HL4050+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 120 ( 1 unt; 0 def)
% Number of atoms : 1194 ( 51 equ)
% Maximal formula atoms : 28 ( 9 avg)
% Number of connectives : 1076 ( 2 ~; 2 |; 57 &)
% ( 35 <=>; 980 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 16 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 45 ( 45 usr; 3 con; 0-7 aty)
% Number of variables : 834 ( 833 !; 1 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Equotient_2E_2D_2D_3E,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> mem(c_2Equotient_2E_2D_2D_3E(A_27a,A_27b,A_27c,A_27d),arr(arr(A_27a,A_27c),arr(arr(A_27b,A_27d),arr(arr(A_27c,A_27b),arr(A_27a,A_27d))))) ) ) ) ) ).
fof(mem_c_2Equotient_2E_3D_3D_3D_3E,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27b,bool)),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),bool))))) ) ) ).
fof(mem_c_2Equotient_2E_3F_21_21,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Equotient_2E_3F_21_21(A_27a),arr(arr(A_27a,bool),bool)) ) ).
fof(mem_c_2Equotient_2EEQUIV,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Equotient_2EEQUIV(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) ).
fof(mem_c_2Equotient_2EPARTIAL__EQUIV,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Equotient_2EPARTIAL__EQUIV(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) ).
fof(mem_c_2Equotient_2EQUOTIENT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Equotient_2EQUOTIENT(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,A_27b),arr(arr(A_27b,A_27a),bool)))) ) ) ).
fof(mem_c_2Equotient_2ERES__EXISTS__EQUIV,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Equotient_2ERES__EXISTS__EQUIV(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),bool))) ) ).
fof(mem_c_2Equotient_2Erespects,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Equotient_2Erespects(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,A_27b)),arr(A_27a,A_27b))) ) ) ).
fof(ax_thm_2Equotient_2EEQUIV__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0E] :
( mem(V0E,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Equotient_2EEQUIV(A_27a),V0E))
<=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(V0E,V1x),V2y))
<=> ap(V0E,V1x) = ap(V0E,V2y) ) ) ) ) ) ) ).
fof(ax_thm_2Equotient_2EPARTIAL__EQUIV__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Equotient_2EPARTIAL__EQUIV(A_27a),V0R))
<=> ( ? [V1x] :
( mem(V1x,A_27a)
& p(ap(ap(V0R,V1x),V1x)) )
& ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(V0R,V2x),V3y))
<=> ( p(ap(ap(V0R,V2x),V2x))
& p(ap(ap(V0R,V3y),V3y))
& ap(V0R,V2x) = ap(V0R,V3y) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUIV__IMP__PARTIAL__EQUIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Equotient_2EEQUIV(A_27a),V0R))
=> p(ap(c_2Equotient_2EPARTIAL__EQUIV(A_27a),V0R)) ) ) ) ).
fof(ax_thm_2Equotient_2EQUOTIENT__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
<=> ( ! [V3a] :
( mem(V3a,A_27b)
=> ap(V1abs,ap(V2rep,V3a)) = V3a )
& ! [V4a] :
( mem(V4a,A_27b)
=> p(ap(ap(V0R,ap(V2rep,V4a)),ap(V2rep,V4a))) )
& ! [V5r] :
( mem(V5r,A_27a)
=> ! [V6s] :
( mem(V6s,A_27a)
=> ( p(ap(ap(V0R,V5r),V6s))
<=> ( p(ap(ap(V0R,V5r),V5r))
& p(ap(ap(V0R,V6s),V6s))
& ap(V1abs,V5r) = ap(V1abs,V6s) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EQUOTIENT__ABS__REP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3a] :
( mem(V3a,A_27b)
=> ap(V1abs,ap(V2rep,V3a)) = V3a ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EQUOTIENT__REP__REFL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3a] :
( mem(V3a,A_27b)
=> p(ap(ap(V0R,ap(V2rep,V3a)),ap(V2rep,V3a))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EQUOTIENT__REL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3r] :
( mem(V3r,A_27a)
=> ! [V4s] :
( mem(V4s,A_27a)
=> ( p(ap(ap(V0R,V3r),V4s))
<=> ( p(ap(ap(V0R,V3r),V3r))
& p(ap(ap(V0R,V4s),V4s))
& ap(V1abs,V3r) = ap(V1abs,V4s) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EQUOTIENT__REL__ABS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3r] :
( mem(V3r,A_27a)
=> ! [V4s] :
( mem(V4s,A_27a)
=> ( p(ap(ap(V0R,V3r),V4s))
=> ap(V1abs,V3r) = ap(V1abs,V4s) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EQUOTIENT__REL__ABS__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3r] :
( mem(V3r,A_27a)
=> ! [V4s] :
( mem(V4s,A_27a)
=> ( p(ap(ap(V0R,V3r),V3r))
=> ( p(ap(ap(V0R,V4s),V4s))
=> ( p(ap(ap(V0R,V3r),V4s))
<=> ap(V1abs,V3r) = ap(V1abs,V4s) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EQUOTIENT__REL__REP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3a] :
( mem(V3a,A_27b)
=> ! [V4b] :
( mem(V4b,A_27b)
=> ( p(ap(ap(V0R,ap(V2rep,V3a)),ap(V2rep,V4b)))
<=> V3a = V4b ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EQUOTIENT__REP__ABS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3r] :
( mem(V3r,A_27a)
=> ( p(ap(ap(V0R,V3r),V3r))
=> p(ap(ap(V0R,ap(V2rep,ap(V1abs,V3r))),V3r)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EIDENTITY__EQUIV,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(c_2Equotient_2EEQUIV(A_27a),c_2Emin_2E_3D(A_27a))) ) ).
fof(conj_thm_2Equotient_2EIDENTITY__QUOTIENT,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27a),c_2Emin_2E_3D(A_27a)),c_2Ecombin_2EI(A_27a)),c_2Ecombin_2EI(A_27a))) ) ).
fof(conj_thm_2Equotient_2EEQUIV__REFL__SYM__TRANS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(V0R,V1x),V2y))
<=> ap(V0R,V1x) = ap(V0R,V2y) ) ) )
<=> ( ! [V3x] :
( mem(V3x,A_27a)
=> p(ap(ap(V0R,V3x),V3x)) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( p(ap(ap(V0R,V4x),V5y))
=> p(ap(ap(V0R,V5y),V4x)) ) ) )
& ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27a)
=> ! [V8z] :
( mem(V8z,A_27a)
=> ( ( p(ap(ap(V0R,V6x),V7y))
& p(ap(ap(V0R,V7y),V8z)) )
=> p(ap(ap(V0R,V6x),V8z)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EQUOTIENT__SYM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( p(ap(ap(V0R,V3x),V4y))
=> p(ap(ap(V0R,V4y),V3x)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EQUOTIENT__TRANS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ! [V5z] :
( mem(V5z,A_27a)
=> ( ( p(ap(ap(V0R,V3x),V4y))
& p(ap(ap(V0R,V4y),V5z)) )
=> p(ap(ap(V0R,V3x),V5z)) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f1248,axiom,
! [A_27d,A_27b,A_27c,A_27a,V2h] :
( mem(V2h,arr(A_27c,A_27b))
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27c))
=> ! [V1g] :
( mem(V1g,arr(A_27b,A_27d))
=> ! [V3x] : ap(f1248(A_27d,A_27b,A_27c,A_27a,V2h,V0f,V1g),V3x) = ap(V1g,ap(V2h,ap(V0f,V3x))) ) ) ) ).
fof(lameq_f1249,axiom,
! [A_27a,A_27d,A_27c,A_27b,V0f] :
( mem(V0f,arr(A_27a,A_27c))
=> ! [V1g] :
( mem(V1g,arr(A_27b,A_27d))
=> ! [V2h] : ap(f1249(A_27a,A_27d,A_27c,A_27b,V0f,V1g),V2h) = f1248(A_27d,A_27b,A_27c,A_27a,V2h,V0f,V1g) ) ) ).
fof(ax_thm_2Equotient_2EFUN__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27c))
=> ! [V1g] :
( mem(V1g,arr(A_27b,A_27d))
=> ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27b,A_27c,A_27d),V0f),V1g) = f1249(A_27a,A_27d,A_27c,A_27b,V0f,V1g) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EFUN__MAP__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27c))
=> ! [V1g] :
( mem(V1g,arr(A_27b,A_27d))
=> ! [V2h] :
( mem(V2h,arr(A_27c,A_27b))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ap(ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27b,A_27c,A_27d),V0f),V1g),V2h),V3x) = ap(V1g,ap(V2h,ap(V0f,V3x))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EFUN__MAP__I,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27b,A_27a,A_27b),c_2Ecombin_2EI(A_27a)),c_2Ecombin_2EI(A_27b)) = c_2Ecombin_2EI(arr(A_27a,A_27b)) ) ) ).
fof(conj_thm_2Equotient_2EIN__FUN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1g] :
( mem(V1g,arr(bool,bool))
=> ! [V2s] :
( mem(V2s,arr(A_27b,bool))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V0f),V1g),V2s)))
<=> p(ap(V1g,ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2s))) ) ) ) ) ) ) ) ).
fof(ax_thm_2Equotient_2EFUN__REL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f] :
( mem(V2f,arr(A_27a,A_27b))
=> ! [V3g] :
( mem(V3g,arr(A_27a,A_27b))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V1R2),V2f),V3g))
<=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( p(ap(ap(V0R1,V4x),V5y))
=> p(ap(ap(V1R2,ap(V2f,V4x)),ap(V3g,V5y))) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EFUN__REL__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),c_2Emin_2E_3D(A_27a)),c_2Emin_2E_3D(A_27b)) = c_2Emin_2E_3D(arr(A_27a,A_27b)) ) ) ).
fof(conj_thm_2Equotient_2EFUN__QUOTIENT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(A_27a,A_27b),arr(A_27c,A_27d)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2)),ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Equotient_2Erespects__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Equotient_2Erespects(A_27a,A_27b) = c_2Ecombin_2EW(A_27a,A_27b) ) ) ).
fof(conj_thm_2Equotient_2ERESPECTS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Equotient_2Erespects(A_27a,bool),V0R),V1x))
<=> p(ap(ap(V0R,V1x),V1x)) ) ) ) ) ).
fof(conj_thm_2Equotient_2EIN__RESPECTS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)))
<=> p(ap(ap(V0R,V1x),V1x)) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERESPECTS__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f] :
( mem(V2f,arr(A_27a,A_27b))
=> ( p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V1R2)),V2f))
<=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( p(ap(ap(V0R1,V3x),V4y))
=> p(ap(ap(V1R2,ap(V2f,V3x)),ap(V2f,V4y))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERESPECTS__MP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f] :
( mem(V2f,arr(A_27a,A_27b))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( ( p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V1R2)),V2f))
& p(ap(ap(V0R1,V3x),V4y)) )
=> p(ap(ap(V1R2,ap(V2f,V3x)),ap(V2f,V4y))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERESPECTS__REP__ABS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4f] :
( mem(V4f,arr(A_27a,A_27b))
=> ! [V5x] :
( mem(V5x,A_27a)
=> ( ( p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),V4f))
& p(ap(ap(V0R1,V5x),V5x)) )
=> p(ap(ap(V3R2,ap(V4f,ap(V2rep1,ap(V1abs1,V5x)))),ap(V4f,V5x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERESPECTS__o,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2R3] :
( mem(V2R3,arr(A_27c,arr(A_27c,bool)))
=> ! [V3f] :
( mem(V3f,arr(A_27b,A_27c))
=> ! [V4g] :
( mem(V4g,arr(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Equotient_2Erespects(arr(A_27b,A_27c),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27b,A_27c),V1R2),V2R3)),V3f))
& p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V1R2)),V4g)) )
=> p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27c),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27c),V0R1),V2R3)),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V3f),V4g))) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Equotient_2E_3F_21_21,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ( p(ap(c_2Equotient_2E_3F_21_21(A_27a),V0P))
<=> p(ap(c_2Ebool_2E_3F_21(A_27a),V0P)) ) ) ) ).
fof(lameq_f1250,axiom,
! [A_27a,V1P] :
( mem(V1P,arr(A_27a,bool))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V4y] : ap(f1250(A_27a,V1P,V3x,V0R),V4y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V3x)),ap(V1P,V4y))),ap(ap(V0R,V3x),V4y)) ) ) ) ).
fof(lameq_f1251,axiom,
! [A_27a,V1P] :
( mem(V1P,arr(A_27a,bool))
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V3x] : ap(f1251(A_27a,V1P,V0R),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f1250(A_27a,V1P,V3x,V0R)) ) ) ).
fof(lameq_f1252,axiom,
! [A_27a,V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1P] : ap(f1252(A_27a,V0R),V1P) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f252(A_27a,V1P))),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f1251(A_27a,V1P,V0R))) ) ).
fof(lameq_f1253,axiom,
! [A_27a,V0R] : ap(f1253(A_27a),V0R) = f1252(A_27a,V0R) ).
fof(ax_thm_2Equotient_2ERES__EXISTS__EQUIV__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Equotient_2ERES__EXISTS__EQUIV(A_27a) = f1253(A_27a) ) ).
fof(lameq_f1254,axiom,
! [A_27a,V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V4y] : ap(f1254(A_27a,V1m,V3x,V0R),V4y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1m,V3x)),ap(V1m,V4y))),ap(ap(V0R,V3x),V4y)) ) ) ) ).
fof(lameq_f1255,axiom,
! [A_27a,V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V3x] : ap(f1255(A_27a,V1m,V0R),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f1254(A_27a,V1m,V3x,V0R)) ) ) ).
fof(conj_thm_2Equotient_2ERES__EXISTS__EQUIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1m] :
( mem(V1m,arr(A_27a,bool))
=> ( p(ap(ap(c_2Equotient_2ERES__EXISTS__EQUIV(A_27a),V0R),V1m))
<=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f40(A_27a,V1m)))
& p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f1255(A_27a,V1m,V0R))) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EFUN__REL__EQ__REL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27a,A_27b))
=> ! [V7g] :
( mem(V7g,arr(A_27a,A_27b))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V6f),V7g))
<=> ( p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),V6f))
& p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),V7g))
& ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),V6f) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),V7g) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EFUN__REL__MP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27a,A_27b))
=> ! [V7g] :
( mem(V7g,arr(A_27a,A_27b))
=> ! [V8x] :
( mem(V8x,A_27a)
=> ! [V9y] :
( mem(V9y,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V6f),V7g))
& p(ap(ap(V0R1,V8x),V9y)) )
=> p(ap(ap(V3R2,ap(V6f,V8x)),ap(V7g,V9y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EFUN__REL__EQUALS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27a,A_27b))
=> ! [V7g] :
( mem(V7g,arr(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),V6f))
& p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),V7g)) )
=> ( ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),V6f) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),V7g)
<=> ! [V8x] :
( mem(V8x,A_27a)
=> ! [V9y] :
( mem(V9y,A_27a)
=> ( p(ap(ap(V0R1,V8x),V9y))
=> p(ap(ap(V3R2,ap(V6f,V8x)),ap(V7g,V9y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EFUN__REL__IMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27a,A_27b))
=> ! [V7g] :
( mem(V7g,arr(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),V6f))
& p(ap(ap(c_2Equotient_2Erespects(arr(A_27a,A_27b),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),V7g))
& ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),V6f) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),V7g) )
=> ! [V8x] :
( mem(V8x,A_27a)
=> ! [V9y] :
( mem(V9y,A_27a)
=> ( p(ap(ap(V0R1,V8x),V9y))
=> p(ap(ap(V3R2,ap(V6f,V8x)),ap(V7g,V9y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUALS__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3x] :
( mem(V3x,A_27b)
=> ! [V4y] :
( mem(V4y,A_27b)
=> ( V3x = V4y
<=> p(ap(ap(V0R,ap(V2rep,V3x)),ap(V2rep,V4y))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUALS__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3x1] :
( mem(V3x1,A_27a)
=> ! [V4x2] :
( mem(V4x2,A_27a)
=> ! [V5y1] :
( mem(V5y1,A_27a)
=> ! [V6y2] :
( mem(V6y2,A_27a)
=> ( ( p(ap(ap(V0R,V3x1),V4x2))
& p(ap(ap(V0R,V5y1),V6y2)) )
=> ( p(ap(ap(V0R,V3x1),V5y1))
<=> p(ap(ap(V0R,V4x2),V6y2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f1256,axiom,
! [A_27d,A_27c,V6f] :
( mem(V6f,arr(A_27c,A_27d))
=> ! [V7x] : ap(f1256(A_27d,A_27c,V6f),V7x) = ap(V6f,V7x) ) ).
fof(lameq_f1257,axiom,
! [A_27b,A_27d,A_27c,A_27a,V6f] :
( mem(V6f,arr(A_27c,A_27d))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ! [V8x] : ap(f1257(A_27b,A_27d,A_27c,A_27a,V6f,V1abs1,V5rep2),V8x) = ap(V5rep2,ap(V6f,ap(V1abs1,V8x))) ) ) ) ).
fof(conj_thm_2Equotient_2ELAMBDA__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27c,A_27d))
=> f1256(A_27d,A_27c,V6f) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),f1257(A_27b,A_27d,A_27c,A_27a,V6f,V1abs1,V5rep2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f1258,axiom,
! [A_27b,A_27c,A_27d,A_27a,V6f] :
( mem(V6f,arr(A_27c,A_27d))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ! [V8x] : ap(f1258(A_27b,A_27c,A_27d,A_27a,V6f,V1abs1,V5rep2),V8x) = ap(ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2),V6f),V8x) ) ) ) ).
fof(conj_thm_2Equotient_2ELAMBDA__PRS1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27c,A_27d))
=> f1256(A_27d,A_27c,V6f) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),f1258(A_27b,A_27c,A_27d,A_27a,V6f,V1abs1,V5rep2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f1259,axiom,
! [A_27b,A_27a,V6f1] :
( mem(V6f1,arr(A_27a,A_27b))
=> ! [V8x] : ap(f1259(A_27b,A_27a,V6f1),V8x) = ap(V6f1,V8x) ) ).
fof(lameq_f1260,axiom,
! [A_27b,A_27a,V7f2] :
( mem(V7f2,arr(A_27a,A_27b))
=> ! [V9y] : ap(f1260(A_27b,A_27a,V7f2),V9y) = ap(V7f2,V9y) ) ).
fof(conj_thm_2Equotient_2ELAMBDA__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f1] :
( mem(V6f1,arr(A_27a,A_27b))
=> ! [V7f2] :
( mem(V7f2,arr(A_27a,A_27b))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V6f1),V7f2))
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),f1259(A_27b,A_27a,V6f1)),f1260(A_27b,A_27a,V7f2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EABSTRACT__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27c,A_27d))
=> V6f = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2),V6f))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__ABSTRACT__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f1] :
( mem(V6f1,arr(A_27a,A_27b))
=> ! [V7f2] :
( mem(V7f2,arr(A_27a,A_27b))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V6f1),V7f2))
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),V6f1)),ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),V7f2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ELET__RES__ABSTRACT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0r] :
( mem(V0r,arr(A_27a,bool))
=> ! [V1lam] :
( mem(V1lam,arr(A_27a,A_27b))
=> ! [V2v] :
( mem(V2v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2v),V0r))
=> ap(ap(c_2Ebool_2ELET(A_27a,A_27b),ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0r),V1lam)),V2v) = ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V1lam),V2v) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ELAMBDA__REP__ABS__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0REL1] :
( mem(V0REL1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ! [V3REL2] :
( mem(V3REL2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ! [V6f1] :
( mem(V6f1,arr(A_27a,A_27b))
=> ! [V7f2] :
( mem(V7f2,arr(A_27a,A_27b))
=> ( ( ! [V8r] :
( mem(V8r,A_27a)
=> ! [V9r_27] :
( mem(V9r_27,A_27a)
=> ( p(ap(ap(V0REL1,V8r),V9r_27))
=> p(ap(ap(V0REL1,V8r),ap(V2rep1,ap(V1abs1,V9r_27)))) ) ) )
& ! [V10r] :
( mem(V10r,A_27b)
=> ! [V11r_27] :
( mem(V11r_27,A_27b)
=> ( p(ap(ap(V3REL2,V10r),V11r_27))
=> p(ap(ap(V3REL2,V10r),ap(V5rep2,ap(V4abs2,V11r_27)))) ) ) )
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0REL1),V3REL2),V6f1),V7f2)) )
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0REL1),V3REL2),V6f1),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),V7f2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EREP__ABS__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0REL] :
( mem(V0REL,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0REL),V1abs),V2rep))
=> ! [V3x1] :
( mem(V3x1,A_27a)
=> ! [V4x2] :
( mem(V4x2,A_27a)
=> ( p(ap(ap(V0REL,V3x1),V4x2))
=> p(ap(ap(V0REL,V3x1),ap(V2rep,ap(V1abs,V4x2)))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EFORALL__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3f] :
( mem(V3f,arr(A_27b,bool))
=> ( p(ap(c_2Ebool_2E_21(A_27b),V3f))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3f))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__FORALL__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3f] :
( mem(V3f,arr(A_27a,bool))
=> ! [V4g] :
( mem(V4g,arr(A_27a,bool))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V3f),V4g))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),V3f))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),V4g)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__FORALL__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3P] :
( mem(V3P,arr(A_27b,bool))
=> ! [V4f] :
( mem(V4f,arr(A_27b,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27b),V3P),V4f))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3P)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V4f))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEXISTS__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3f] :
( mem(V3f,arr(A_27b,bool))
=> ( p(ap(c_2Ebool_2E_3F(A_27b),V3f))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3f))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__EXISTS__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3f] :
( mem(V3f,arr(A_27a,bool))
=> ! [V4g] :
( mem(V4g,arr(A_27a,bool))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V3f),V4g))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),V3f))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),V4g)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__EXISTS__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3P] :
( mem(V3P,arr(A_27b,bool))
=> ! [V4f] :
( mem(V4f,arr(A_27b,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27b),V3P),V4f))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3P)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V4f))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEXISTS__UNIQUE__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3f] :
( mem(V3f,arr(A_27b,bool))
=> ( p(ap(c_2Ebool_2E_3F_21(A_27b),V3f))
<=> p(ap(ap(c_2Equotient_2ERES__EXISTS__EQUIV(A_27a),V0R),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3f))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__EXISTS__EQUIV__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3f] :
( mem(V3f,arr(A_27a,bool))
=> ! [V4g] :
( mem(V4g,arr(A_27a,bool))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V3f),V4g))
=> ( p(ap(ap(c_2Equotient_2ERES__EXISTS__EQUIV(A_27a),V0R),V3f))
<=> p(ap(ap(c_2Equotient_2ERES__EXISTS__EQUIV(A_27a),V0R),V4g)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ECOND__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3a] :
( mem(V3a,bool)
=> ! [V4b] :
( mem(V4b,A_27b)
=> ! [V5c] :
( mem(V5c,A_27b)
=> ap(ap(ap(c_2Ebool_2ECOND(A_27b),V3a),V4b),V5c) = ap(V1abs,ap(ap(ap(c_2Ebool_2ECOND(A_27a),V3a),ap(V2rep,V4b)),ap(V2rep,V5c))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ECOND__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3a1] :
( mem(V3a1,bool)
=> ! [V4a2] :
( mem(V4a2,bool)
=> ! [V5b1] :
( mem(V5b1,A_27a)
=> ! [V6b2] :
( mem(V6b2,A_27a)
=> ! [V7c1] :
( mem(V7c1,A_27a)
=> ! [V8c2] :
( mem(V8c2,A_27a)
=> ( ( ( p(V3a1)
<=> p(V4a2) )
& p(ap(ap(V0R,V5b1),V6b2))
& p(ap(ap(V0R,V7c1),V8c2)) )
=> p(ap(ap(V0R,ap(ap(ap(c_2Ebool_2ECOND(A_27a),V3a1),V5b1),V7c1)),ap(ap(ap(c_2Ebool_2ECOND(A_27a),V4a2),V6b2),V8c2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ELET__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27c,A_27d))
=> ! [V7x] :
( mem(V7x,A_27c)
=> ap(ap(c_2Ebool_2ELET(A_27c,A_27d),V6f),V7x) = ap(V4abs2,ap(ap(c_2Ebool_2ELET(A_27a,A_27b),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2),V6f)),ap(V2rep1,V7x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ELET__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27a,A_27b))
=> ! [V7g] :
( mem(V7g,arr(A_27a,A_27b))
=> ! [V8x] :
( mem(V8x,A_27a)
=> ! [V9y] :
( mem(V9y,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V6f),V7g))
& p(ap(ap(V0R1,V8x),V9y)) )
=> p(ap(ap(V3R2,ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V6f),V8x)),ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V7g),V9y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2Eliteral__case__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27c,A_27d))
=> ! [V7x] :
( mem(V7x,A_27c)
=> ap(ap(c_2Ebool_2Eliteral__case(A_27c,A_27d),V6f),V7x) = ap(V4abs2,ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2),V6f)),ap(V2rep1,V7x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2Eliteral__case__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27a,A_27b))
=> ! [V7g] :
( mem(V7g,arr(A_27a,A_27b))
=> ! [V8x] :
( mem(V8x,A_27a)
=> ! [V9y] :
( mem(V9y,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V6f),V7g))
& p(ap(ap(V0R1,V8x),V9y)) )
=> p(ap(ap(V3R2,ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V6f),V8x)),ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V7g),V9y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EAPPLY__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27c,A_27d))
=> ! [V7x] :
( mem(V7x,A_27c)
=> ap(V6f,V7x) = ap(V4abs2,ap(ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2),V6f),ap(V2rep1,V7x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EAPPLY__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27a,A_27b))
=> ! [V7g] :
( mem(V7g,arr(A_27a,A_27b))
=> ! [V8x] :
( mem(V8x,A_27a)
=> ! [V9y] :
( mem(V9y,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V6f),V7g))
& p(ap(ap(V0R1,V8x),V9y)) )
=> p(ap(ap(V3R2,ap(V6f,V8x)),ap(V7g,V9y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EI__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3e] :
( mem(V3e,A_27b)
=> ap(c_2Ecombin_2EI(A_27b),V3e) = ap(V1abs,ap(c_2Ecombin_2EI(A_27a),ap(V2rep,V3e))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EI__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3e1] :
( mem(V3e1,A_27a)
=> ! [V4e2] :
( mem(V4e2,A_27a)
=> ( p(ap(ap(V0R,V3e1),V4e2))
=> p(ap(ap(V0R,ap(c_2Ecombin_2EI(A_27a),V3e1)),ap(c_2Ecombin_2EI(A_27a),V4e2))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EK__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6x] :
( mem(V6x,A_27c)
=> ! [V7y] :
( mem(V7y,A_27d)
=> ap(ap(c_2Ecombin_2EK(A_27c,A_27d),V6x),V7y) = ap(V1abs1,ap(ap(c_2Ecombin_2EK(A_27a,A_27b),ap(V2rep1,V6x)),ap(V5rep2,V7y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EK__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6x1] :
( mem(V6x1,A_27a)
=> ! [V7x2] :
( mem(V7x2,A_27a)
=> ! [V8y1] :
( mem(V8y1,A_27b)
=> ! [V9y2] :
( mem(V9y2,A_27b)
=> ( ( p(ap(ap(V0R1,V6x1),V7x2))
& p(ap(ap(V3R2,V8y1),V9y2)) )
=> p(ap(ap(V0R1,ap(ap(c_2Ecombin_2EK(A_27a,A_27b),V6x1),V8y1)),ap(ap(c_2Ecombin_2EK(A_27a,A_27b),V7x2),V9y2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2Eo__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27d))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27d,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27d),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27e))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27e,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27e),V3R2),V4abs2),V5rep2))
=> ! [V6R3] :
( mem(V6R3,arr(A_27c,arr(A_27c,bool)))
=> ! [V7abs3] :
( mem(V7abs3,arr(A_27c,A_27f))
=> ! [V8rep3] :
( mem(V8rep3,arr(A_27f,A_27c))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27c,A_27f),V6R3),V7abs3),V8rep3))
=> ! [V9f] :
( mem(V9f,arr(A_27e,A_27f))
=> ! [V10g] :
( mem(V10g,arr(A_27d,A_27e))
=> ap(ap(c_2Ecombin_2Eo(A_27d,A_27f,A_27e),V9f),V10g) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27d,A_27c,A_27a,A_27f),V2rep1),V7abs3),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27b,A_27f,A_27e,A_27c),V4abs2),V8rep3),V9f)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27e,A_27d,A_27b),V1abs1),V5rep2),V10g))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2Eo__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27d))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27d,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27d),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27e))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27e,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27e),V3R2),V4abs2),V5rep2))
=> ! [V6R3] :
( mem(V6R3,arr(A_27c,arr(A_27c,bool)))
=> ! [V7abs3] :
( mem(V7abs3,arr(A_27c,A_27f))
=> ! [V8rep3] :
( mem(V8rep3,arr(A_27f,A_27c))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27c,A_27f),V6R3),V7abs3),V8rep3))
=> ! [V9f1] :
( mem(V9f1,arr(A_27b,A_27c))
=> ! [V10f2] :
( mem(V10f2,arr(A_27b,A_27c))
=> ! [V11g1] :
( mem(V11g1,arr(A_27a,A_27b))
=> ! [V12g2] :
( mem(V12g2,arr(A_27a,A_27b))
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27b,A_27c),V3R2),V6R3),V9f1),V10f2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V11g1),V12g2)) )
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27c),V0R1),V6R3),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V9f1),V11g1)),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V10f2),V12g2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EC__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27d))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27d,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27d),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27e))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27e,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27e),V3R2),V4abs2),V5rep2))
=> ! [V6R3] :
( mem(V6R3,arr(A_27c,arr(A_27c,bool)))
=> ! [V7abs3] :
( mem(V7abs3,arr(A_27c,A_27f))
=> ! [V8rep3] :
( mem(V8rep3,arr(A_27f,A_27c))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27c,A_27f),V6R3),V7abs3),V8rep3))
=> ! [V9f] :
( mem(V9f,arr(A_27d,arr(A_27e,A_27f)))
=> ! [V10x] :
( mem(V10x,A_27e)
=> ! [V11y] :
( mem(V11y,A_27d)
=> ap(ap(ap(c_2Ecombin_2EC(A_27d,A_27e,A_27f),V9f),V10x),V11y) = ap(V7abs3,ap(ap(ap(c_2Ecombin_2EC(A_27a,A_27b,A_27c),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,arr(A_27e,A_27f),A_27d,arr(A_27b,A_27c)),V1abs1),ap(ap(c_2Equotient_2E_2D_2D_3E(A_27b,A_27f,A_27e,A_27c),V4abs2),V8rep3)),V9f)),ap(V5rep2,V10x)),ap(V2rep1,V11y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EC__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27d))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27d,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27d),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27e))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27e,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27e),V3R2),V4abs2),V5rep2))
=> ! [V6R3] :
( mem(V6R3,arr(A_27c,arr(A_27c,bool)))
=> ! [V7abs3] :
( mem(V7abs3,arr(A_27c,A_27f))
=> ! [V8rep3] :
( mem(V8rep3,arr(A_27f,A_27c))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27c,A_27f),V6R3),V7abs3),V8rep3))
=> ! [V9f1] :
( mem(V9f1,arr(A_27a,arr(A_27b,A_27c)))
=> ! [V10f2] :
( mem(V10f2,arr(A_27a,arr(A_27b,A_27c)))
=> ! [V11x1] :
( mem(V11x1,A_27b)
=> ! [V12x2] :
( mem(V12x2,A_27b)
=> ! [V13y1] :
( mem(V13y1,A_27a)
=> ! [V14y2] :
( mem(V14y2,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,arr(A_27b,A_27c)),V0R1),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27b,A_27c),V3R2),V6R3)),V9f1),V10f2))
& p(ap(ap(V3R2,V11x1),V12x2))
& p(ap(ap(V0R1,V13y1),V14y2)) )
=> p(ap(ap(V6R3,ap(ap(ap(c_2Ecombin_2EC(A_27a,A_27b,A_27c),V9f1),V11x1),V13y1)),ap(ap(ap(c_2Ecombin_2EC(A_27a,A_27b,A_27c),V10f2),V12x2),V14y2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EW__PRS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f] :
( mem(V6f,arr(A_27c,arr(A_27c,A_27d)))
=> ! [V7x] :
( mem(V7x,A_27c)
=> ap(ap(c_2Ecombin_2EW(A_27c,A_27d),V6f),V7x) = ap(V4abs2,ap(ap(c_2Ecombin_2EW(A_27a,A_27b),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,arr(A_27c,A_27d),A_27c,arr(A_27a,A_27b)),V1abs1),ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2)),V6f)),ap(V2rep1,V7x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EW__RSP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f1] :
( mem(V6f1,arr(A_27a,arr(A_27a,A_27b)))
=> ! [V7f2] :
( mem(V7f2,arr(A_27a,arr(A_27a,A_27b)))
=> ! [V8x1] :
( mem(V8x1,A_27a)
=> ! [V9x2] :
( mem(V9x2,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,arr(A_27a,A_27b)),V0R1),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),V6f1),V7f2))
& p(ap(ap(V0R1,V8x1),V9x2)) )
=> p(ap(ap(V3R2,ap(ap(c_2Ecombin_2EW(A_27a,A_27b),V6f1),V8x1)),ap(ap(c_2Ecombin_2EW(A_27a,A_27b),V7f2),V9x2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQ__IMPLIES,axiom,
! [V0P] :
( mem(V0P,bool)
=> ! [V1Q] :
( mem(V1Q,bool)
=> ( ( p(V0P)
<=> p(V1Q) )
=> ( p(V0P)
=> p(V1Q) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUALS__IMPLIES,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,A_27a)
=> ! [V1P_27] :
( mem(V1P_27,A_27a)
=> ! [V2Q] :
( mem(V2Q,A_27a)
=> ! [V3Q_27] :
( mem(V3Q_27,A_27a)
=> ( ( V0P = V2Q
& V1P_27 = V3Q_27 )
=> ( V0P = V1P_27
=> V2Q = V3Q_27 ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ECONJ__IMPLIES,axiom,
! [V0P] :
( mem(V0P,bool)
=> ! [V1P_27] :
( mem(V1P_27,bool)
=> ! [V2Q] :
( mem(V2Q,bool)
=> ! [V3Q_27] :
( mem(V3Q_27,bool)
=> ( ( ( p(V0P)
=> p(V2Q) )
& ( p(V1P_27)
=> p(V3Q_27) ) )
=> ( ( p(V0P)
& p(V1P_27) )
=> ( p(V2Q)
& p(V3Q_27) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EDISJ__IMPLIES,axiom,
! [V0P] :
( mem(V0P,bool)
=> ! [V1P_27] :
( mem(V1P_27,bool)
=> ! [V2Q] :
( mem(V2Q,bool)
=> ! [V3Q_27] :
( mem(V3Q_27,bool)
=> ( ( ( p(V0P)
=> p(V2Q) )
& ( p(V1P_27)
=> p(V3Q_27) ) )
=> ( ( p(V0P)
| p(V1P_27) )
=> ( p(V2Q)
| p(V3Q_27) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EIMP__IMPLIES,axiom,
! [V0P] :
( mem(V0P,bool)
=> ! [V1P_27] :
( mem(V1P_27,bool)
=> ! [V2Q] :
( mem(V2Q,bool)
=> ! [V3Q_27] :
( mem(V3Q_27,bool)
=> ( ( ( p(V2Q)
=> p(V0P) )
& ( p(V1P_27)
=> p(V3Q_27) ) )
=> ( ( p(V0P)
=> p(V1P_27) )
=> ( p(V2Q)
=> p(V3Q_27) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ENOT__IMPLIES,axiom,
! [V0P] :
( mem(V0P,bool)
=> ! [V1Q] :
( mem(V1Q,bool)
=> ( ( p(V1Q)
=> p(V0P) )
=> ( ~ p(V0P)
=> ~ p(V1Q) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUALS__EQUIV__IMPLIES,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a1] :
( mem(V0a1,A_27a)
=> ! [V1a2] :
( mem(V1a2,A_27a)
=> ! [V2b1] :
( mem(V2b1,A_27a)
=> ! [V3b2] :
( mem(V3b2,A_27a)
=> ! [V4R] :
( mem(V4R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Equotient_2EEQUIV(A_27a),V4R))
=> ( ( p(ap(ap(V4R,V0a1),V1a2))
& p(ap(ap(V4R,V2b1),V3b2)) )
=> ( V0a1 = V2b1
=> p(ap(ap(V4R,V1a2),V3b2)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EABSTRACT__RES__ABSTRACT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4f] :
( mem(V4f,arr(A_27a,A_27b))
=> ! [V5g] :
( mem(V5g,arr(A_27a,A_27b))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V4f),V5g))
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V4f),ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),V5g))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__ABSTRACT__ABSTRACT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4f] :
( mem(V4f,arr(A_27a,A_27b))
=> ! [V5g] :
( mem(V5g,arr(A_27a,A_27b))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V4f),V5g))
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),V4f)),V5g)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUIV__RES__ABSTRACT__LEFT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f1] :
( mem(V2f1,arr(A_27a,A_27b))
=> ! [V3f2] :
( mem(V3f2,arr(A_27a,A_27b))
=> ! [V4x1] :
( mem(V4x1,A_27a)
=> ! [V5x2] :
( mem(V5x2,A_27a)
=> ( ( p(ap(ap(V1R2,ap(V2f1,V4x1)),ap(V3f2,V5x2)))
& p(ap(ap(V0R1,V4x1),V4x1)) )
=> p(ap(ap(V1R2,ap(ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),V2f1),V4x1)),ap(V3f2,V5x2))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUIV__RES__ABSTRACT__RIGHT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f1] :
( mem(V2f1,arr(A_27a,A_27b))
=> ! [V3f2] :
( mem(V3f2,arr(A_27a,A_27b))
=> ! [V4x1] :
( mem(V4x1,A_27a)
=> ! [V5x2] :
( mem(V5x2,A_27a)
=> ( ( p(ap(ap(V1R2,ap(V2f1,V4x1)),ap(V3f2,V5x2)))
& p(ap(ap(V0R1,V5x2),V5x2)) )
=> p(ap(ap(V1R2,ap(V2f1,V4x1)),ap(ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),V3f2),V5x2))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUIV__RES__FORALL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0E] :
( mem(V0E,arr(A_27a,arr(A_27a,bool)))
=> ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ( p(ap(c_2Equotient_2EEQUIV(A_27a),V0E))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0E)),V1P))
<=> p(ap(c_2Ebool_2E_21(A_27a),V1P)) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUIV__RES__EXISTS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0E] :
( mem(V0E,arr(A_27a,arr(A_27a,bool)))
=> ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ( p(ap(c_2Equotient_2EEQUIV(A_27a),V0E))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0E)),V1P))
<=> p(ap(c_2Ebool_2E_3F(A_27a),V1P)) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEQUIV__RES__EXISTS__UNIQUE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0E] :
( mem(V0E,arr(A_27a,arr(A_27a,bool)))
=> ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ( p(ap(c_2Equotient_2EEQUIV(A_27a),V0E))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0E)),V1P))
<=> p(ap(c_2Ebool_2E_3F_21(A_27a),V1P)) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EFORALL__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ( ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(V0P,V2x))
=> p(ap(V1Q,V2x)) ) )
=> ( p(ap(c_2Ebool_2E_21(A_27a),V0P))
=> p(ap(c_2Ebool_2E_21(A_27a),V1Q)) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEXISTS__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ( ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(V0P,V2x))
=> p(ap(V1Q,V2x)) ) )
=> ( p(ap(c_2Ebool_2E_3F(A_27a),V0P))
=> p(ap(c_2Ebool_2E_3F(A_27a),V1Q)) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__FORALL__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2R] :
( mem(V2R,arr(A_27a,bool))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V2R,V3x))
=> ( p(ap(V0P,V3x))
=> p(ap(V1Q,V3x)) ) ) )
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V2R),V0P))
=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V2R),V1Q)) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__EXISTS__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2R] :
( mem(V2R,arr(A_27a,bool))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V2R,V3x))
=> ( p(ap(V0P,V3x))
=> p(ap(V1Q,V3x)) ) ) )
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V2R),V0P))
=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V2R),V1Q)) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ELEFT__RES__FORALL__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1R] :
( mem(V1R,arr(A_27a,bool))
=> ! [V2Q] :
( mem(V2Q,arr(A_27a,bool))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V1R,V3x))
& ( p(ap(V2Q,V3x))
=> p(ap(V0P,V3x)) ) ) )
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1R),V2Q))
=> p(ap(c_2Ebool_2E_21(A_27a),V0P)) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERIGHT__RES__FORALL__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1R] :
( mem(V1R,arr(A_27a,bool))
=> ! [V2Q] :
( mem(V2Q,arr(A_27a,bool))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V1R,V3x))
=> ( p(ap(V0P,V3x))
=> p(ap(V2Q,V3x)) ) ) )
=> ( p(ap(c_2Ebool_2E_21(A_27a),V0P))
=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1R),V2Q)) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ELEFT__RES__EXISTS__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1R] :
( mem(V1R,arr(A_27a,bool))
=> ! [V2Q] :
( mem(V2Q,arr(A_27a,bool))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V1R,V3x))
=> ( p(ap(V2Q,V3x))
=> p(ap(V0P,V3x)) ) ) )
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1R),V2Q))
=> p(ap(c_2Ebool_2E_3F(A_27a),V0P)) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERIGHT__RES__EXISTS__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1R] :
( mem(V1R,arr(A_27a,bool))
=> ! [V2Q] :
( mem(V2Q,arr(A_27a,bool))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V1R,V3x))
& ( p(ap(V0P,V3x))
=> p(ap(V2Q,V3x)) ) ) )
=> ( p(ap(c_2Ebool_2E_3F(A_27a),V0P))
=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1R),V2Q)) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2EEXISTS__UNIQUE__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1E] :
( mem(V1E,arr(A_27a,arr(A_27a,bool)))
=> ! [V2Q] :
( mem(V2Q,arr(A_27a,bool))
=> ( ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V0P,V3x))
=> ( p(ap(ap(c_2Equotient_2Erespects(A_27a,bool),V1E),V3x))
& p(ap(V2Q,V3x)) ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( ( p(ap(ap(c_2Equotient_2Erespects(A_27a,bool),V1E),V4x))
& p(ap(V2Q,V4x))
& p(ap(ap(c_2Equotient_2Erespects(A_27a,bool),V1E),V5y))
& p(ap(V2Q,V5y)) )
=> p(ap(ap(V1E,V4x),V5y)) ) ) ) )
=> ( p(ap(c_2Ebool_2E_3F_21(A_27a),V0P))
=> p(ap(ap(c_2Equotient_2ERES__EXISTS__EQUIV(A_27a),V1E),V2Q)) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__EXISTS__UNIQUE__RESPECTS__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),V1P))
=> p(ap(ap(c_2Equotient_2ERES__EXISTS__EQUIV(A_27a),V0R),V1P)) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__EXISTS__UNIQUE__REGULAR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1R] :
( mem(V1R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2Q] :
( mem(V2Q,arr(A_27a,bool))
=> ( ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V0P,V3x))
=> p(ap(V2Q,V3x)) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( ( p(ap(ap(c_2Equotient_2Erespects(A_27a,bool),V1R),V4x))
& p(ap(V2Q,V4x))
& p(ap(ap(c_2Equotient_2Erespects(A_27a,bool),V1R),V5y))
& p(ap(V2Q,V5y)) )
=> p(ap(ap(V1R,V4x),V5y)) ) ) ) )
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V1R)),V0P))
=> p(ap(ap(c_2Equotient_2ERES__EXISTS__EQUIV(A_27a),V1R),V2Q)) ) ) ) ) ) ) ).
fof(conj_thm_2Equotient_2ERES__EXISTS__UNIQUE__REGULAR__SAME,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2Q] :
( mem(V2Q,arr(A_27a,bool))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V1P),V2Q))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),V1P))
=> p(ap(ap(c_2Equotient_2ERES__EXISTS__EQUIV(A_27a),V0R),V2Q)) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------