ITP001 Axioms: ITP088_5.ax
%------------------------------------------------------------------------------
% File : ITP088_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_pred_set_2.ax [Gau20]
% : HL4088_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 104 ( 8 unt; 28 typ; 0 def)
% Number of atoms : 2311 ( 32 equ)
% Maximal formula atoms : 15 ( 22 avg)
% Number of connectives : 364 ( 3 ~; 1 |; 13 &)
% ( 24 <=>; 323 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 11 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1874 (1874 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 84 ( 28 >; 56 *; 0 +; 0 <<)
% Number of predicates : 39 ( 38 usr; 7 prp; 0-4 aty)
% Number of functors : 28 ( 28 usr; 0 con; 1-6 aty)
% Number of variables : 420 ( 420 !; 0 ?; 420 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2Equotient__pred__set_2EDELETER,type,
c_2Equotient__pred__set_2EDELETER: del > $i ).
tff(mem_c_2Equotient__pred__set_2EDELETER,axiom,
! [A_27a: del] : mem(c_2Equotient__pred__set_2EDELETER(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))))) ).
tff(tp_c_2Equotient__pred__set_2EDISJOINTR,type,
c_2Equotient__pred__set_2EDISJOINTR: del > $i ).
tff(mem_c_2Equotient__pred__set_2EDISJOINTR,axiom,
! [A_27a: del] : mem(c_2Equotient__pred__set_2EDISJOINTR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool)))) ).
tff(tp_c_2Equotient__pred__set_2EFINITER,type,
c_2Equotient__pred__set_2EFINITER: del > $i ).
tff(mem_c_2Equotient__pred__set_2EFINITER,axiom,
! [A_27a: del] : mem(c_2Equotient__pred__set_2EFINITER(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),bool))) ).
tff(tp_c_2Equotient__pred__set_2EGSPECR,type,
c_2Equotient__pred__set_2EGSPECR: ( del * del ) > $i ).
tff(mem_c_2Equotient__pred__set_2EGSPECR,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Equotient__pred__set_2EGSPECR(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27b,bool)),arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,bool)),arr(A_27b,bool))))) ).
tff(tp_c_2Equotient__pred__set_2EIMAGER,type,
c_2Equotient__pred__set_2EIMAGER: ( del * del ) > $i ).
tff(mem_c_2Equotient__pred__set_2EIMAGER,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Equotient__pred__set_2EIMAGER(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,bool),arr(A_27b,bool)))))) ).
tff(tp_c_2Equotient__pred__set_2EINSERTR,type,
c_2Equotient__pred__set_2EINSERTR: del > $i ).
tff(mem_c_2Equotient__pred__set_2EINSERTR,axiom,
! [A_27a: del] : mem(c_2Equotient__pred__set_2EINSERTR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(arr(A_27a,bool),arr(A_27a,bool))))) ).
tff(tp_c_2Equotient__pred__set_2EPSUBSETR,type,
c_2Equotient__pred__set_2EPSUBSETR: del > $i ).
tff(mem_c_2Equotient__pred__set_2EPSUBSETR,axiom,
! [A_27a: del] : mem(c_2Equotient__pred__set_2EPSUBSETR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool)))) ).
tff(tp_c_2Equotient__pred__set_2ESUBSETR,type,
c_2Equotient__pred__set_2ESUBSETR: del > $i ).
tff(mem_c_2Equotient__pred__set_2ESUBSETR,axiom,
! [A_27a: del] : mem(c_2Equotient__pred__set_2ESUBSETR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool)))) ).
tff(conj_thm_2Equotient__pred__set_2EIN__SET__MAP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V0f),c_2Ecombin_2EI(bool)),V1s)))
<=> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V2x)),V1s)) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2ESET__REL,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,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)),V1s),V2t))
<=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> ! [V4y: $i] :
( mem(V4y,A_27a)
=> ( p(ap(ap(V0R,V3x),V4y))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s))
<=> p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V2t)) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2ESET__REL__MP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27a,bool))
=> ! [V4t: $i] :
( mem(V4t,arr(A_27a,bool))
=> ! [V5x: $i] :
( mem(V5x,A_27a)
=> ! [V6y: $i] :
( mem(V6y,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V3s),V4t))
& p(ap(ap(V0R,V5x),V6y)) )
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V5x),V3s))
<=> p(ap(ap(c_2Ebool_2EIN(A_27a),V6y),V4t)) ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EIN__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3x: $i] :
( mem(V3x,A_27b)
=> ! [V4s: $i] :
( mem(V4s,arr(A_27b,bool))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27b),V3x),V4s))
<=> p(ap(ap(c_2Ebool_2EIN(A_27a),ap(V2rep,V3x)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V4s))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EIN__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3x1: $i] :
( mem(V3x1,A_27a)
=> ! [V4x2: $i] :
( mem(V4x2,A_27a)
=> ! [V5s1: $i] :
( mem(V5s1,arr(A_27a,bool))
=> ! [V6s2: $i] :
( mem(V6s2,arr(A_27a,bool))
=> ( ( p(ap(ap(V0R,V3x1),V4x2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V5s1),V6s2)) )
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x1),V5s1))
<=> p(ap(ap(c_2Ebool_2EIN(A_27a),V4x2),V6s2)) ) ) ) ) ) ) ) ) ) ) ).
tff(lamtp_f2063,type,
f2063: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2063,axiom,
! [A_27b: del,A_27a: del,V3v: $i] :
( mem(V3v,A_27b)
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,ty_2Epair_2Eprod(A_27b,bool)))
=> ! [V4x: $i] : ( ap(f2063(A_27b,A_27a,V3v,V1R2,V2f),V4x) = ap(ap(ap(ap(c_2Equotient__pair_2E_23_23_23(A_27b,bool,A_27b,bool),V1R2),c_2Emin_2E_3D(bool)),ap(ap(c_2Epair_2E_2C(A_27b,bool),V3v),inj__o(fo__c_2Ebool_2ET))),ap(V2f,V4x)) ) ) ) ) ).
tff(ax_thm_2Equotient__pred__set_2EGSPECR__def,axiom,
! [A_27a: del,A_27b: del,V0R1: $i] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,ty_2Epair_2Eprod(A_27b,bool)))
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( p(ap(ap(ap(ap(c_2Equotient__pred__set_2EGSPECR(A_27a,A_27b),V0R1),V1R2),V2f),V3v))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),f2063(A_27b,A_27a,V3v,V1R2,V2f))) ) ) ) ) ) ).
tff(lamtp_f2064,type,
f2064: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2064,axiom,
! [A_27a: del,A_27b: del,V3v: $i] :
( mem(V3v,A_27a)
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27a,arr(A_27a,bool)))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)))
=> ! [V4x: $i] : ( ap(f2064(A_27a,A_27b,V3v,V1R2,V2f),V4x) = ap(ap(ap(ap(c_2Equotient__pair_2E_23_23_23(A_27a,bool,A_27a,bool),V1R2),c_2Emin_2E_3D(bool)),ap(ap(c_2Epair_2E_2C(A_27a,bool),V3v),inj__o(fo__c_2Ebool_2ET))),ap(V2f,V4x)) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EIN__GSPECR,axiom,
! [A_27a: del,A_27b: del,V0R1: $i] :
( mem(V0R1,arr(A_27b,arr(A_27b,bool)))
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27a,arr(A_27a,bool)))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)))
=> ! [V3v: $i] :
( mem(V3v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3v),ap(ap(ap(c_2Equotient__pred__set_2EGSPECR(A_27b,A_27a),V0R1),V1R2),V2f)))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27b),ap(c_2Equotient_2Erespects(A_27b,bool),V0R1)),f2064(A_27a,A_27b,V3v,V1R2,V2f))) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EGSPEC__PRS,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1: $i] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1: $i] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2: $i] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2: $i] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2: $i] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f: $i] :
( mem(V6f,arr(A_27c,ty_2Epair_2Eprod(A_27d,bool)))
=> ( ap(c_2Epred__set_2EGSPEC(A_27d,A_27c),V6f) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27d,bool,A_27b,bool),V5rep2),c_2Ecombin_2EI(bool)),ap(ap(ap(c_2Equotient__pred__set_2EGSPECR(A_27a,A_27b),V0R1),V3R2),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,ty_2Epair_2Eprod(A_27d,bool),A_27c,ty_2Epair_2Eprod(A_27b,bool)),V1abs1),ap(ap(c_2Epair_2E_23_23(A_27d,bool,A_27b,bool),V5rep2),c_2Ecombin_2EI(bool))),V6f))) ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EGSPECR__RSP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1: $i] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1: $i] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2: $i] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2: $i] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2: $i] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f1: $i] :
( mem(V6f1,arr(A_27a,ty_2Epair_2Eprod(A_27b,bool)))
=> ! [V7f2: $i] :
( mem(V7f2,arr(A_27a,ty_2Epair_2Eprod(A_27b,bool)))
=> ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,ty_2Epair_2Eprod(A_27b,bool)),V0R1),ap(ap(c_2Equotient__pair_2E_23_23_23(A_27b,bool,A_27b,bool),V3R2),c_2Emin_2E_3D(bool))),V6f1),V7f2))
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27b,bool),V3R2),c_2Emin_2E_3D(bool)),ap(ap(ap(c_2Equotient__pred__set_2EGSPECR(A_27a,A_27b),V0R1),V3R2),V6f1)),ap(ap(ap(c_2Equotient__pred__set_2EGSPECR(A_27a,A_27b),V0R1),V3R2),V7f2))) ) ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EEMPTY__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ( c_2Epred__set_2EEMPTY(A_27b) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27b,bool,A_27a,bool),V2rep),c_2Ecombin_2EI(bool)),c_2Epred__set_2EEMPTY(A_27a)) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EEMPTY__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),c_2Epred__set_2EEMPTY(A_27a)),c_2Epred__set_2EEMPTY(A_27a))) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EUNIV__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ( c_2Epred__set_2EUNIV(A_27b) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27b,bool,A_27a,bool),V2rep),c_2Ecombin_2EI(bool)),c_2Epred__set_2EUNIV(A_27a)) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EUNIV__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),c_2Epred__set_2EUNIV(A_27a)),c_2Epred__set_2EUNIV(A_27a))) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EUNION__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27b,bool))
=> ! [V4t: $i] :
( mem(V4t,arr(A_27b,bool))
=> ( ap(ap(c_2Epred__set_2EUNION(A_27b),V3s),V4t) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27b,bool,A_27a,bool),V2rep),c_2Ecombin_2EI(bool)),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3s)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V4t))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EUNION__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s1: $i] :
( mem(V3s1,arr(A_27a,bool))
=> ! [V4s2: $i] :
( mem(V4s2,arr(A_27a,bool))
=> ! [V5t1: $i] :
( mem(V5t1,arr(A_27a,bool))
=> ! [V6t2: $i] :
( mem(V6t2,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)),V3s1),V4s2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V5t1),V6t2)) )
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),ap(ap(c_2Epred__set_2EUNION(A_27a),V3s1),V5t1)),ap(ap(c_2Epred__set_2EUNION(A_27a),V4s2),V6t2))) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EINTER__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27b,bool))
=> ! [V4t: $i] :
( mem(V4t,arr(A_27b,bool))
=> ( ap(ap(c_2Epred__set_2EINTER(A_27b),V3s),V4t) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27b,bool,A_27a,bool),V2rep),c_2Ecombin_2EI(bool)),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3s)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V4t))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EINTER__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s1: $i] :
( mem(V3s1,arr(A_27a,bool))
=> ! [V4s2: $i] :
( mem(V4s2,arr(A_27a,bool))
=> ! [V5t1: $i] :
( mem(V5t1,arr(A_27a,bool))
=> ! [V6t2: $i] :
( mem(V6t2,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)),V3s1),V4s2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V5t1),V6t2)) )
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),ap(ap(c_2Epred__set_2EINTER(A_27a),V3s1),V5t1)),ap(ap(c_2Epred__set_2EINTER(A_27a),V4s2),V6t2))) ) ) ) ) ) ) ) ) ) ).
tff(lamtp_f2065,type,
f2065: ( del * $i * $i ) > $i ).
tff(lameq_f2065,axiom,
! [A_27a: del,V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ! [V3x: $i] : ( ap(f2065(A_27a,V1s,V2t),V3x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)),ap(ap(c_2Ebool_2EIN(A_27a),V3x),V2t)) ) ) ) ).
tff(ax_thm_2Equotient__pred__set_2ESUBSETR__def,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ( p(ap(ap(ap(c_2Equotient__pred__set_2ESUBSETR(A_27a),V0R),V1s),V2t))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f2065(A_27a,V1s,V2t))) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2ESUBSET__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27b,bool))
=> ! [V4t: $i] :
( mem(V4t,arr(A_27b,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),V3s),V4t))
<=> p(ap(ap(ap(c_2Equotient__pred__set_2ESUBSETR(A_27a),V0R),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3s)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V4t))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2ESUBSETR__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s1: $i] :
( mem(V3s1,arr(A_27a,bool))
=> ! [V4s2: $i] :
( mem(V4s2,arr(A_27a,bool))
=> ! [V5t1: $i] :
( mem(V5t1,arr(A_27a,bool))
=> ! [V6t2: $i] :
( mem(V6t2,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)),V3s1),V4s2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V5t1),V6t2)) )
=> ( p(ap(ap(ap(c_2Equotient__pred__set_2ESUBSETR(A_27a),V0R),V3s1),V5t1))
<=> p(ap(ap(ap(c_2Equotient__pred__set_2ESUBSETR(A_27a),V0R),V4s2),V6t2)) ) ) ) ) ) ) ) ) ) ) ).
tff(ax_thm_2Equotient__pred__set_2EPSUBSETR__def,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ( p(ap(ap(ap(c_2Equotient__pred__set_2EPSUBSETR(A_27a),V0R),V1s),V2t))
<=> ( p(ap(ap(ap(c_2Equotient__pred__set_2ESUBSETR(A_27a),V0R),V1s),V2t))
& ~ p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V1s),V2t)) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EPSUBSET__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27b,bool))
=> ! [V4t: $i] :
( mem(V4t,arr(A_27b,bool))
=> ( p(ap(ap(c_2Epred__set_2EPSUBSET(A_27b),V3s),V4t))
<=> p(ap(ap(ap(c_2Equotient__pred__set_2EPSUBSETR(A_27a),V0R),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3s)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V4t))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EPSUBSETR__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s1: $i] :
( mem(V3s1,arr(A_27a,bool))
=> ! [V4s2: $i] :
( mem(V4s2,arr(A_27a,bool))
=> ! [V5t1: $i] :
( mem(V5t1,arr(A_27a,bool))
=> ! [V6t2: $i] :
( mem(V6t2,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)),V3s1),V4s2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V5t1),V6t2)) )
=> ( p(ap(ap(ap(c_2Equotient__pred__set_2EPSUBSETR(A_27a),V0R),V3s1),V5t1))
<=> p(ap(ap(ap(c_2Equotient__pred__set_2EPSUBSETR(A_27a),V0R),V4s2),V6t2)) ) ) ) ) ) ) ) ) ) ) ).
tff(lamtp_f2066,type,
f2066: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2066,axiom,
! [A_27a: del,V2s: $i] :
( mem(V2s,arr(A_27a,bool))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V3y: $i] : ( ap(f2066(A_27a,V2s,V1x,V0R),V3y) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V3y),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(V0R,V3y),V1x)),ap(ap(c_2Ebool_2EIN(A_27a),V3y),V2s))) ) ) ) ) ).
tff(ax_thm_2Equotient__pred__set_2EINSERTR__def,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2s: $i] :
( mem(V2s,arr(A_27a,bool))
=> ( ap(ap(ap(c_2Equotient__pred__set_2EINSERTR(A_27a),V0R),V1x),V2s) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2066(A_27a,V2s,V1x,V0R)) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EIN__INSERTR,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2s: $i] :
( mem(V2s,arr(A_27a,bool))
=> ! [V3y: $i] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(ap(c_2Equotient__pred__set_2EINSERTR(A_27a),V0R),V1x),V2s)))
<=> ( p(ap(ap(V0R,V3y),V1x))
| p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V2s)) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EINSERT__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27b,bool))
=> ! [V4x: $i] :
( mem(V4x,A_27b)
=> ( ap(ap(c_2Epred__set_2EINSERT(A_27b),V4x),V3s) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27b,bool,A_27a,bool),V2rep),c_2Ecombin_2EI(bool)),ap(ap(ap(c_2Equotient__pred__set_2EINSERTR(A_27a),V0R),ap(V2rep,V4x)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3s))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EINSERTR__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3x1: $i] :
( mem(V3x1,A_27a)
=> ! [V4x2: $i] :
( mem(V4x2,A_27a)
=> ! [V5s1: $i] :
( mem(V5s1,arr(A_27a,bool))
=> ! [V6s2: $i] :
( mem(V6s2,arr(A_27a,bool))
=> ( ( p(ap(ap(V0R,V3x1),V4x2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V5s1),V6s2)) )
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),ap(ap(ap(c_2Equotient__pred__set_2EINSERTR(A_27a),V0R),V3x1),V5s1)),ap(ap(ap(c_2Equotient__pred__set_2EINSERTR(A_27a),V0R),V4x2),V6s2))) ) ) ) ) ) ) ) ) ) ).
tff(lamtp_f2067,type,
f2067: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2067,axiom,
! [A_27a: del,V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] : ( ap(f2067(A_27a,V1s,V0R,V2x),V3y) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V3y),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)),ap(c_2Ebool_2E_7E,ap(ap(V0R,V2x),V3y)))) ) ) ) ) ).
tff(ax_thm_2Equotient__pred__set_2EDELETER__def,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( ap(ap(ap(c_2Equotient__pred__set_2EDELETER(A_27a),V0R),V1s),V2x) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2067(A_27a,V1s,V0R,V2x)) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EIN__DELETER,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(ap(c_2Equotient__pred__set_2EDELETER(A_27a),V0R),V1s),V2x)))
<=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s))
& ~ p(ap(ap(V0R,V2x),V3y)) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EDELETE__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27b,bool))
=> ! [V4x: $i] :
( mem(V4x,A_27b)
=> ( ap(ap(c_2Epred__set_2EDELETE(A_27b),V3s),V4x) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27b,bool,A_27a,bool),V2rep),c_2Ecombin_2EI(bool)),ap(ap(ap(c_2Equotient__pred__set_2EDELETER(A_27a),V0R),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3s)),ap(V2rep,V4x))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EDELETER__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s1: $i] :
( mem(V3s1,arr(A_27a,bool))
=> ! [V4s2: $i] :
( mem(V4s2,arr(A_27a,bool))
=> ! [V5x1: $i] :
( mem(V5x1,A_27a)
=> ! [V6x2: $i] :
( mem(V6x2,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V3s1),V4s2))
& p(ap(ap(V0R,V5x1),V6x2)) )
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),ap(ap(ap(c_2Equotient__pred__set_2EDELETER(A_27a),V0R),V3s1),V5x1)),ap(ap(ap(c_2Equotient__pred__set_2EDELETER(A_27a),V0R),V4s2),V6x2))) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EDIFF__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27b,bool))
=> ! [V4t: $i] :
( mem(V4t,arr(A_27b,bool))
=> ( ap(ap(c_2Epred__set_2EDIFF(A_27b),V3s),V4t) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27b,bool,A_27a,bool),V2rep),c_2Ecombin_2EI(bool)),ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3s)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V4t))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EDIFF__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s1: $i] :
( mem(V3s1,arr(A_27a,bool))
=> ! [V4s2: $i] :
( mem(V4s2,arr(A_27a,bool))
=> ! [V5t1: $i] :
( mem(V5t1,arr(A_27a,bool))
=> ! [V6t2: $i] :
( mem(V6t2,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)),V3s1),V4s2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V5t1),V6t2)) )
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),ap(ap(c_2Epred__set_2EDIFF(A_27a),V3s1),V5t1)),ap(ap(c_2Epred__set_2EDIFF(A_27a),V4s2),V6t2))) ) ) ) ) ) ) ) ) ) ).
tff(lamtp_f2068,type,
f2068: ( del * $i * $i ) > $i ).
tff(lameq_f2068,axiom,
! [A_27a: del,V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ! [V3x: $i] : ( ap(f2068(A_27a,V1s,V2t),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)),ap(ap(c_2Ebool_2EIN(A_27a),V3x),V2t)) ) ) ) ).
tff(ax_thm_2Equotient__pred__set_2EDISJOINTR__def,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ( p(ap(ap(ap(c_2Equotient__pred__set_2EDISJOINTR(A_27a),V0R),V1s),V2t))
<=> ~ p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f2068(A_27a,V1s,V2t))) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EDISJOINT__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27b,bool))
=> ! [V4t: $i] :
( mem(V4t,arr(A_27b,bool))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27b),V3s),V4t))
<=> p(ap(ap(ap(c_2Equotient__pred__set_2EDISJOINTR(A_27a),V0R),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3s)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V4t))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EDISJOINTR__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s1: $i] :
( mem(V3s1,arr(A_27a,bool))
=> ! [V4s2: $i] :
( mem(V4s2,arr(A_27a,bool))
=> ! [V5t1: $i] :
( mem(V5t1,arr(A_27a,bool))
=> ! [V6t2: $i] :
( mem(V6t2,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)),V3s1),V4s2))
& p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V5t1),V6t2)) )
=> ( p(ap(ap(ap(c_2Equotient__pred__set_2EDISJOINTR(A_27a),V0R),V3s1),V5t1))
<=> p(ap(ap(ap(c_2Equotient__pred__set_2EDISJOINTR(A_27a),V0R),V4s2),V6t2)) ) ) ) ) ) ) ) ) ) ) ).
tff(lamtp_f2069,type,
f2069: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2069,axiom,
! [A_27a: del,V3s: $i] :
( mem(V3s,arr(A_27a,bool))
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2P: $i] :
( mem(V2P,arr(arr(A_27a,bool),bool))
=> ! [V4e: $i] : ( ap(f2069(A_27a,V3s,V0R,V2P),V4e) = ap(V2P,ap(ap(ap(c_2Equotient__pred__set_2EINSERTR(A_27a),V0R),V4e),V3s)) ) ) ) ) ).
tff(lamtp_f2070,type,
f2070: ( del * $i * $i ) > $i ).
tff(lameq_f2070,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2P: $i] :
( mem(V2P,arr(arr(A_27a,bool),bool))
=> ! [V3s: $i] : ( ap(f2070(A_27a,V0R,V2P),V3s) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V2P,V3s)),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f2069(A_27a,V3s,V0R,V2P))) ) ) ) ).
tff(lamtp_f2071,type,
f2071: ( del * $i * $i ) > $i ).
tff(lameq_f2071,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2P: $i] : ( ap(f2071(A_27a,V0R,V1s),V2P) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V2P,c_2Epred__set_2EEMPTY(A_27a))),ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),ap(c_2Equotient_2Erespects(arr(A_27a,bool),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)))),f2070(A_27a,V0R,V2P)))),ap(V2P,V1s)) ) ) ) ).
tff(ax_thm_2Equotient__pred__set_2EFINITER__def,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),V1s))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(arr(arr(A_27a,bool),bool)),ap(c_2Equotient_2Erespects(arr(arr(A_27a,bool),bool),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(arr(A_27a,bool),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool))),c_2Emin_2E_3D(bool)))),f2071(A_27a,V0R,V1s))) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EFINITE__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27b,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27b),V3s))
<=> p(ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3s))) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EFINITER__EQ,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s1: $i] :
( mem(V1s1,arr(A_27a,bool))
=> ! [V2s2: $i] :
( mem(V2s2,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)),V1s1),V2s2))
=> ( p(ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),V1s1))
<=> p(ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),V2s2)) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EFINITER__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs: $i] :
( mem(V1abs,arr(A_27a,A_27b))
=> ! [V2rep: $i] :
( mem(V2rep,arr(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep))
=> ! [V3s1: $i] :
( mem(V3s1,arr(A_27a,bool))
=> ! [V4s2: $i] :
( mem(V4s2,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)),V3s1),V4s2))
=> ( p(ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),V3s1))
<=> p(ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),V4s2)) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EFINITER__EMPTY,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> p(ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),c_2Epred__set_2EEMPTY(A_27a))) ) ).
tff(lamtp_f2072,type,
f2072: ( del * $i * $i ) > $i ).
tff(lameq_f2072,axiom,
! [A_27a: del,V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2x: $i] : ( ap(f2072(A_27a,V1s,V0R),V2x) = ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),ap(ap(ap(c_2Equotient__pred__set_2EINSERTR(A_27a),V0R),V2x),V1s)) ) ) ) ).
tff(lamtp_f2073,type,
f2073: ( del * $i ) > $i ).
tff(lameq_f2073,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1s: $i] : ( ap(f2073(A_27a,V0R),V1s) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),V1s)),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f2072(A_27a,V1s,V0R))) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EFINITER__INSERTR,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> p(ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),ap(c_2Equotient_2Erespects(arr(A_27a,bool),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)))),f2073(A_27a,V0R))) ) ).
tff(lamtp_f2074,type,
f2074: ( del * $i * $i ) > $i ).
tff(lameq_f2074,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2s: $i] : ( ap(f2074(A_27a,V0R,V1x),V2s) = ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2s)),ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),ap(ap(ap(c_2Equotient__pred__set_2EINSERTR(A_27a),V0R),V1x),V2s)),V2s)) ) ) ) ).
tff(lamtp_f2075,type,
f2075: ( del * $i ) > $i ).
tff(lameq_f2075,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x: $i] : ( ap(f2075(A_27a,V0R),V1x) = ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),ap(c_2Equotient_2Erespects(arr(A_27a,bool),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)))),f2074(A_27a,V0R,V1x)) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EABSORPTIONR,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f2075(A_27a,V0R))) ) ).
tff(lamtp_f2076,type,
f2076: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2076,axiom,
! [A_27a: del,V1P: $i] :
( mem(V1P,arr(arr(A_27a,bool),bool))
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2s: $i] :
( mem(V2s,arr(A_27a,bool))
=> ! [V3e: $i] : ( ap(f2076(A_27a,V1P,V0R,V2s),V3e) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V3e),V2s))),ap(V1P,ap(ap(ap(c_2Equotient__pred__set_2EINSERTR(A_27a),V0R),V3e),V2s))) ) ) ) ) ).
tff(lamtp_f2077,type,
f2077: ( del * $i * $i ) > $i ).
tff(lameq_f2077,axiom,
! [A_27a: del,V1P: $i] :
( mem(V1P,arr(arr(A_27a,bool),bool))
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2s: $i] : ( ap(f2077(A_27a,V1P,V0R),V2s) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),V2s)),ap(V1P,V2s))),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),f2076(A_27a,V1P,V0R,V2s))) ) ) ) ).
tff(lamtp_f2078,type,
f2078: ( del * $i * $i ) > $i ).
tff(lameq_f2078,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1P: $i] :
( mem(V1P,arr(arr(A_27a,bool),bool))
=> ! [V4s: $i] : ( ap(f2078(A_27a,V0R,V1P),V4s) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Equotient__pred__set_2EFINITER(A_27a),V0R),V4s)),ap(V1P,V4s)) ) ) ) ).
tff(lamtp_f2079,type,
f2079: ( del * $i ) > $i ).
tff(lameq_f2079,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1P: $i] : ( ap(f2079(A_27a,V0R),V1P) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,c_2Epred__set_2EEMPTY(A_27a))),ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),ap(c_2Equotient_2Erespects(arr(A_27a,bool),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)))),f2077(A_27a,V1P,V0R)))),ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),ap(c_2Equotient_2Erespects(arr(A_27a,bool),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)))),f2078(A_27a,V0R,V1P))) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EFINITER__INDUCT,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> p(ap(ap(c_2Ebool_2ERES__FORALL(arr(arr(A_27a,bool),bool)),ap(c_2Equotient_2Erespects(arr(arr(A_27a,bool),bool),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(arr(A_27a,bool),bool),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool))),c_2Emin_2E_3D(bool)))),f2079(A_27a,V0R))) ) ).
tff(lamtp_f2080,type,
f2080: ( del * del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2080,axiom,
! [A_27b: del,A_27a: del,V4y: $i] :
( mem(V4y,A_27b)
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,A_27b))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27a,bool))
=> ! [V5x: $i] : ( ap(f2080(A_27b,A_27a,V4y,V1R2,V2f,V3s),V5x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V1R2,V4y),ap(V2f,V5x))),ap(ap(c_2Ebool_2EIN(A_27a),V5x),V3s)) ) ) ) ) ) ).
tff(lamtp_f2081,type,
f2081: ( del * del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2081,axiom,
! [A_27a: del,A_27b: del,V0R1: $i] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,A_27b))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27a,bool))
=> ! [V4y: $i] : ( ap(f2081(A_27a,A_27b,V0R1,V1R2,V2f,V3s),V4y) = ap(ap(c_2Epair_2E_2C(A_27b,bool),V4y),ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),f2080(A_27b,A_27a,V4y,V1R2,V2f,V3s))) ) ) ) ) ) ).
tff(ax_thm_2Equotient__pred__set_2EIMAGER__def,axiom,
! [A_27a: del,A_27b: del,V0R1: $i] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,A_27b))
=> ! [V3s: $i] :
( mem(V3s,arr(A_27a,bool))
=> ( ap(ap(ap(ap(c_2Equotient__pred__set_2EIMAGER(A_27a,A_27b),V0R1),V1R2),V2f),V3s) = ap(c_2Epred__set_2EGSPEC(A_27b,A_27b),f2081(A_27a,A_27b,V0R1,V1R2,V2f,V3s)) ) ) ) ) ) ).
tff(lamtp_f2082,type,
f2082: ( del * del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2082,axiom,
! [A_27b: del,A_27a: del,V2y: $i] :
( mem(V2y,A_27b)
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V3f: $i] :
( mem(V3f,arr(A_27a,A_27b))
=> ! [V4s: $i] :
( mem(V4s,arr(A_27a,bool))
=> ! [V5x: $i] : ( ap(f2082(A_27b,A_27a,V2y,V1R2,V3f,V4s),V5x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V1R2,V2y),ap(V3f,V5x))),ap(ap(c_2Ebool_2EIN(A_27a),V5x),V4s)) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EIN__IMAGER,axiom,
! [A_27a: del,A_27b: del,V0R1: $i] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V2y: $i] :
( mem(V2y,A_27b)
=> ! [V3f: $i] :
( mem(V3f,arr(A_27a,A_27b))
=> ! [V4s: $i] :
( mem(V4s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27b),V2y),ap(ap(ap(ap(c_2Equotient__pred__set_2EIMAGER(A_27a,A_27b),V0R1),V1R2),V3f),V4s)))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R1)),f2082(A_27b,A_27a,V2y,V1R2,V3f,V4s))) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EIMAGE__PRS,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1: $i] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1: $i] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2: $i] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2: $i] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2: $i] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f: $i] :
( mem(V6f,arr(A_27c,A_27d))
=> ! [V7s: $i] :
( mem(V7s,arr(A_27c,bool))
=> ( ap(ap(c_2Epred__set_2EIMAGE(A_27c,A_27d),V6f),V7s) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27d,bool,A_27b,bool),V5rep2),c_2Ecombin_2EI(bool)),ap(ap(ap(ap(c_2Equotient__pred__set_2EIMAGER(A_27a,A_27b),V0R1),V3R2),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2),V6f)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27c,bool),V1abs1),c_2Ecombin_2EI(bool)),V7s))) ) ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equotient__pred__set_2EIMAGER__RSP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1abs1: $i] :
( mem(V1abs1,arr(A_27a,A_27c))
=> ! [V2rep1: $i] :
( mem(V2rep1,arr(A_27c,A_27a))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1))
=> ! [V3R2: $i] :
( mem(V3R2,arr(A_27b,arr(A_27b,bool)))
=> ! [V4abs2: $i] :
( mem(V4abs2,arr(A_27b,A_27d))
=> ! [V5rep2: $i] :
( mem(V5rep2,arr(A_27d,A_27b))
=> ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2))
=> ! [V6f1: $i] :
( mem(V6f1,arr(A_27a,A_27b))
=> ! [V7f2: $i] :
( mem(V7f2,arr(A_27a,A_27b))
=> ! [V8s1: $i] :
( mem(V8s1,arr(A_27a,bool))
=> ! [V9s2: $i] :
( mem(V9s2,arr(A_27a,bool))
=> ( ( 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,bool),V0R1),c_2Emin_2E_3D(bool)),V8s1),V9s2)) )
=> p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27b,bool),V3R2),c_2Emin_2E_3D(bool)),ap(ap(ap(ap(c_2Equotient__pred__set_2EIMAGER(A_27a,A_27b),V0R1),V3R2),V6f1),V8s1)),ap(ap(ap(ap(c_2Equotient__pred__set_2EIMAGER(A_27a,A_27b),V0R1),V3R2),V7f2),V9s2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------