ITP001 Axioms: ITP032_5.ax
%------------------------------------------------------------------------------
% File : ITP032_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 : res_quan_2.ax [Gau20]
% : HL4032_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 117 ( 0 unt; 30 typ; 0 def)
% Number of atoms : 1211 ( 49 equ)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 260 ( 12 ~; 4 |; 13 &)
% ( 38 <=>; 193 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 876 ( 876 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 86 ( 30 >; 56 *; 0 +; 0 <<)
% Number of predicates : 39 ( 38 usr; 9 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 0 con; 2-4 aty)
% Number of variables : 336 ( 332 !; 4 ?; 336 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(conj_thm_2Eres__quan_2ERES__FORALL,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),V1f))
<=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P))
=> p(ap(V1f,V2x)) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),V1f))
<=> ? [V2x: $i] :
( mem(V2x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P))
& p(ap(V1f,V2x)) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0P),V1f))
<=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f61(A_27a,V1f)))
& p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f63(A_27a,V1f,V0P))) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__SELECT,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,bool))
=> ( ap(ap(c_2Ebool_2ERES__SELECT(A_27a),V0P),V1f) = ap(c_2Emin_2E_40(A_27a),f64(A_27a,V0P,V1f)) ) ) ) ).
tff(lamtp_f467,type,
f467: ( del * $i * $i ) > $i ).
tff(lameq_f467,axiom,
! [A_27a: del,V1Q: $i] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2R: $i] :
( mem(V2R,arr(A_27a,bool))
=> ! [V3i: $i] : ( ap(f467(A_27a,V1Q,V2R),V3i) = ap(ap(c_2Ebool_2E_2F_5C,ap(V1Q,V3i)),ap(V2R,V3i)) ) ) ) ).
tff(lamtp_f468,type,
f468: ( del * $i ) > $i ).
tff(lameq_f468,axiom,
! [A_27a: del,V1Q: $i] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V4i: $i] : ( ap(f468(A_27a,V1Q),V4i) = ap(V1Q,V4i) ) ) ).
tff(lamtp_f469,type,
f469: ( del * $i ) > $i ).
tff(lameq_f469,axiom,
! [A_27a: del,V2R: $i] :
( mem(V2R,arr(A_27a,bool))
=> ! [V5i: $i] : ( ap(f469(A_27a,V2R),V5i) = ap(V2R,V5i) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__CONJ__DIST,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2R: $i] :
( mem(V2R,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f467(A_27a,V1Q,V2R)))
<=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f468(A_27a,V1Q)))
& p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f469(A_27a,V2R))) ) ) ) ) ) ).
tff(lamtp_f470,type,
f470: ( del * $i * $i ) > $i ).
tff(lameq_f470,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V3j: $i] : ( ap(f470(A_27a,V0P,V1Q),V3j) = ap(ap(c_2Ebool_2E_5C_2F,ap(V0P,V3j)),ap(V1Q,V3j)) ) ) ) ).
tff(lamtp_f471,type,
f471: ( del * $i ) > $i ).
tff(lameq_f471,axiom,
! [A_27a: del,V2R: $i] :
( mem(V2R,arr(A_27a,bool))
=> ! [V4i: $i] : ( ap(f471(A_27a,V2R),V4i) = ap(V2R,V4i) ) ) ).
tff(lamtp_f472,type,
f472: ( del * $i ) > $i ).
tff(lameq_f472,axiom,
! [A_27a: del,V2R: $i] :
( mem(V2R,arr(A_27a,bool))
=> ! [V6i: $i] : ( ap(f472(A_27a,V2R),V6i) = ap(V2R,V6i) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__DISJ__DIST,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2R: $i] :
( mem(V2R,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),f470(A_27a,V0P,V1Q)),f471(A_27a,V2R)))
<=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f469(A_27a,V2R)))
& p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1Q),f472(A_27a,V2R))) ) ) ) ) ) ).
tff(lamtp_f473,type,
f473: ( del * $i ) > $i ).
tff(lameq_f473,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V2i: $i] : ( ap(f473(A_27a,V0P),V2i) = ap(V0P,V2i) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__UNIQUE,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1j: $i] :
( mem(V1j,A_27a)
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Emin_2E_3D(A_27a),V1j)),f473(A_27a,V0P)))
<=> p(ap(V0P,V1j)) ) ) ) ).
tff(lamtp_f474,type,
f474: ( del * del * $i * $i ) > $i ).
tff(lameq_f474,axiom,
! [A_27b: del,A_27a: del,V1R: $i] :
( mem(V1R,arr(A_27a,arr(A_27b,bool)))
=> ! [V3x: $i] :
( mem(V3x,A_27b)
=> ! [V4i: $i] : ( ap(f474(A_27b,A_27a,V1R,V3x),V4i) = ap(ap(V1R,V4i),V3x) ) ) ) ).
tff(lamtp_f475,type,
f475: ( del * del * $i * $i ) > $i ).
tff(lameq_f475,axiom,
! [A_27a: del,A_27b: del,V5i: $i] :
( mem(V5i,A_27a)
=> ! [V1R: $i] :
( mem(V1R,arr(A_27a,arr(A_27b,bool)))
=> ! [V6x: $i] : ( ap(f475(A_27a,A_27b,V5i,V1R),V6x) = ap(ap(V1R,V5i),V6x) ) ) ) ).
tff(lamtp_f476,type,
f476: ( del * del * $i ) > $i ).
tff(lameq_f476,axiom,
! [A_27b: del,A_27a: del,V1R: $i] :
( mem(V1R,arr(A_27a,arr(A_27b,bool)))
=> ! [V5i: $i] : ( ap(f476(A_27b,A_27a,V1R),V5i) = ap(c_2Ebool_2E_21(A_27b),f475(A_27a,A_27b,V5i,V1R)) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__FORALL,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1R: $i] :
( mem(V1R,arr(A_27a,arr(A_27b,bool)))
=> ! [V2x: $i] :
( mem(V2x,A_27b)
=> ( ! [V3x: $i] :
( mem(V3x,A_27b)
=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f474(A_27b,A_27a,V1R,V3x))) )
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f476(A_27b,A_27a,V1R))) ) ) ) ) ).
tff(lamtp_f477,type,
f477: ( del * del * $i * $i ) > $i ).
tff(lameq_f477,axiom,
! [A_27a: del,A_27b: del,V3i: $i] :
( mem(V3i,A_27a)
=> ! [V2R: $i] :
( mem(V2R,arr(A_27a,arr(A_27b,bool)))
=> ! [V4j: $i] : ( ap(f477(A_27a,A_27b,V3i,V2R),V4j) = ap(ap(V2R,V3i),V4j) ) ) ) ).
tff(lamtp_f478,type,
f478: ( del * del * $i * $i ) > $i ).
tff(lameq_f478,axiom,
! [A_27b: del,A_27a: del,V2R: $i] :
( mem(V2R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27b,bool))
=> ! [V3i: $i] : ( ap(f478(A_27b,A_27a,V2R,V1Q),V3i) = ap(ap(c_2Ebool_2ERES__FORALL(A_27b),V1Q),f477(A_27a,A_27b,V3i,V2R)) ) ) ) ).
tff(lamtp_f479,type,
f479: ( del * del * $i * $i ) > $i ).
tff(lameq_f479,axiom,
! [A_27b: del,A_27a: del,V2R: $i] :
( mem(V2R,arr(A_27a,arr(A_27b,bool)))
=> ! [V5j: $i] :
( mem(V5j,A_27b)
=> ! [V6i: $i] : ( ap(f479(A_27b,A_27a,V2R,V5j),V6i) = ap(ap(V2R,V6i),V5j) ) ) ) ).
tff(lamtp_f480,type,
f480: ( del * del * $i * $i ) > $i ).
tff(lameq_f480,axiom,
! [A_27a: del,A_27b: del,V2R: $i] :
( mem(V2R,arr(A_27a,arr(A_27b,bool)))
=> ! [V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V5j: $i] : ( ap(f480(A_27a,A_27b,V2R,V0P),V5j) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f479(A_27b,A_27a,V2R,V5j)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__REORDER,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27b,bool))
=> ! [V2R: $i] :
( mem(V2R,arr(A_27a,arr(A_27b,bool)))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f478(A_27b,A_27a,V2R,V1Q)))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27b),V1Q),f480(A_27a,A_27b,V2R,V0P))) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__T,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
( mem(V0P,A_27a)
=> ! [V1s: $i] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27c)
=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27b),V1s),k(A_27b,c_2Ebool_2ET))) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__F,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
( mem(V0P,A_27a)
=> ! [V1s: $i] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27c)
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27b),V1s),k(A_27b,c_2Ebool_2EF)))
<=> ( V1s = c_2Epred__set_2EEMPTY(A_27b) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__EMPTY,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0p)) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__UNIV,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0p))
<=> p(ap(c_2Ebool_2E_21(A_27a),V0p)) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__NULL,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m: tp__o] :
( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),k(A_27a,inj__o(V1m))))
<=> ( ( V0p = c_2Epred__set_2EEMPTY(A_27a) )
| p(inj__o(V1m)) ) ) ) ).
tff(lamtp_f481,type,
f481: ( del * $i ) > $i ).
tff(lameq_f481,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V3x: $i] : ( ap(f481(A_27a,V0P),V3x) = ap(c_2Ebool_2E_7E,ap(V0P,V3x)) ) ) ).
tff(conj_thm_2Eres__quan_2ENOT__RES__FORALL,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( ~ p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),f108(A_27a,V0P)))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),f481(A_27a,V0P))) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__NOT__EMPTY,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( ~ p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),V0P))
=> ( V1s != c_2Epred__set_2EEMPTY(A_27a) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__SUBSET,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V2t),V0P))
=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),V0P)) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__UNION,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)),V0P))
<=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),V0P))
& p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V2t),V0P)) ) ) ) ) ) ).
tff(lamtp_f482,type,
f482: ( del * $i ) > $i ).
tff(lameq_f482,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V4x: $i] : ( ap(f482(A_27a,V0P),V4x) = ap(V0P,V4x) ) ) ).
tff(lamtp_f483,type,
f483: ( del * $i * $i ) > $i ).
tff(lameq_f483,axiom,
! [A_27a: del,V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ! [V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V5x: $i] : ( ap(f483(A_27a,V2t,V0P),V5x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V5x),V2t))),ap(V0P,V5x)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__DIFF,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ! [V3x: $i] :
( mem(V3x,A_27b)
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1s),V2t)),f482(A_27a,V0P)))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),f483(A_27a,V2t,V0P))) ) ) ) ) ) ).
tff(lamtp_f484,type,
f484: ( del * $i ) > $i ).
tff(lameq_f484,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V2s: $i] : ( ap(f484(A_27a,V0x),V2s) = ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s) ) ) ).
tff(conj_thm_2Eres__quan_2EIN__BIGINTER__RES__FORALL,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1sos: $i] :
( mem(V1sos,arr(arr(A_27a,bool),bool))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EBIGINTER(A_27a),V1sos)))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),V1sos),f484(A_27a,V0x))) ) ) ) ).
tff(lamtp_f485,type,
f485: ( del * $i ) > $i ).
tff(lameq_f485,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V3s: $i] : ( ap(f485(A_27a,V0P),V3s) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V3s),f482(A_27a,V0P)) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__BIGUNION,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1sos: $i] :
( mem(V1sos,arr(arr(A_27a,bool),bool))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V1sos)),f108(A_27a,V0P)))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),V1sos),f485(A_27a,V0P))) ) ) ) ).
tff(lamtp_f486,type,
f486: ( del * $i ) > $i ).
tff(lameq_f486,axiom,
! [A_27a: del,V3x: $i] :
( mem(V3x,A_27a)
=> ! [V4s: $i] : ( ap(f486(A_27a,V3x),V4s) = ap(ap(c_2Ebool_2EIN(A_27a),V3x),V4s) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__FORALL__BIGINTER,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1sos: $i] :
( mem(V1sos,arr(arr(A_27a,bool),bool))
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Epred__set_2EBIGINTER(A_27a),V1sos)),f108(A_27a,V0P)))
<=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),V1sos),f486(A_27a,V3x)))
=> p(ap(V0P,V3x)) ) ) ) ) ) ).
tff(lamtp_f487,type,
f487: ( del * $i * $i ) > $i ).
tff(lameq_f487,axiom,
! [A_27a: del,V1Q: $i] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2R: $i] :
( mem(V2R,arr(A_27a,bool))
=> ! [V3i: $i] : ( ap(f487(A_27a,V1Q,V2R),V3i) = ap(ap(c_2Ebool_2E_5C_2F,ap(V1Q,V3i)),ap(V2R,V3i)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__DISJ__DIST,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2R: $i] :
( mem(V2R,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f487(A_27a,V1Q,V2R)))
<=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f468(A_27a,V1Q)))
| p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f469(A_27a,V2R))) ) ) ) ) ) ).
tff(lamtp_f488,type,
f488: ( del * $i * $i ) > $i ).
tff(lameq_f488,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V3i: $i] : ( ap(f488(A_27a,V0P,V1Q),V3i) = ap(ap(c_2Ebool_2E_5C_2F,ap(V0P,V3i)),ap(V1Q,V3i)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__DISJ__EXISTS__DIST,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2R: $i] :
( mem(V2R,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),f488(A_27a,V0P,V1Q)),f471(A_27a,V2R)))
<=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f469(A_27a,V2R)))
| p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1Q),f472(A_27a,V2R))) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__EQUAL,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1j: $i] :
( mem(V1j,A_27a)
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Emin_2E_3D(A_27a),V1j)),f473(A_27a,V0P)))
<=> p(ap(V0P,V1j)) ) ) ) ).
tff(lamtp_f489,type,
f489: ( del * del * $i * $i ) > $i ).
tff(lameq_f489,axiom,
! [A_27b: del,A_27a: del,V2R: $i] :
( mem(V2R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27b,bool))
=> ! [V3i: $i] : ( ap(f489(A_27b,A_27a,V2R,V1Q),V3i) = ap(ap(c_2Ebool_2ERES__EXISTS(A_27b),V1Q),f477(A_27a,A_27b,V3i,V2R)) ) ) ) ).
tff(lamtp_f490,type,
f490: ( del * del * $i * $i ) > $i ).
tff(lameq_f490,axiom,
! [A_27a: del,A_27b: del,V2R: $i] :
( mem(V2R,arr(A_27a,arr(A_27b,bool)))
=> ! [V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V5j: $i] : ( ap(f490(A_27a,A_27b,V2R,V0P),V5j) = ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f479(A_27b,A_27a,V2R,V5j)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__REORDER,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q: $i] :
( mem(V1Q,arr(A_27b,bool))
=> ! [V2R: $i] :
( mem(V2R,arr(A_27a,arr(A_27b,bool)))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f489(A_27b,A_27a,V2R,V1Q)))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27b),V1Q),f490(A_27a,A_27b,V2R,V0P))) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__F,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
( mem(V0P,A_27a)
=> ! [V1s: $i] :
( mem(V1s,A_27b)
=> ! [V2x: $i] :
( mem(V2x,arr(A_27c,bool))
=> ~ p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27c),V2x),k(A_27c,c_2Ebool_2EF))) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__T,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
( mem(V0P,A_27a)
=> ! [V1s: $i] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27c)
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27b),V1s),k(A_27b,c_2Ebool_2ET)))
<=> ( V1s != c_2Epred__set_2EEMPTY(A_27b) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__EMPTY,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ~ p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0p)) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIV,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0p))
<=> p(ap(c_2Ebool_2E_3F(A_27a),V0p)) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__NULL,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m: tp__o] :
( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),k(A_27a,inj__o(V1m))))
<=> ( ( V0p != c_2Epred__set_2EEMPTY(A_27a) )
& p(inj__o(V1m)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__ALT,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m: $i] :
( mem(V1m,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),V1m))
<=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),ap(ap(c_2Ebool_2ERES__SELECT(A_27a),V0p),V1m)),V0p))
& p(ap(V1m,ap(ap(c_2Ebool_2ERES__SELECT(A_27a),V0p),V1m))) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ENOT__RES__EXISTS,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( ~ p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),f108(A_27a,V0P)))
<=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),f481(A_27a,V0P))) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__NOT__EMPTY,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),V0P))
=> ( V1s != c_2Epred__set_2EEMPTY(A_27a) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__SUBSET,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),V0P))
=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V2t),V0P)) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNION,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)),V0P))
<=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),V0P))
| p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V2t),V0P)) ) ) ) ) ) ).
tff(lamtp_f491,type,
f491: ( del * $i * $i ) > $i ).
tff(lameq_f491,axiom,
! [A_27a: del,V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ! [V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V5x: $i] : ( ap(f491(A_27a,V2t,V0P),V5x) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V5x),V2t))),ap(V0P,V5x)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__DIFF,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2t: $i] :
( mem(V2t,arr(A_27a,bool))
=> ! [V3x: $i] :
( mem(V3x,A_27b)
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1s),V2t)),f482(A_27a,V0P)))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),f491(A_27a,V2t,V0P))) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2EIN__BIGUNION__RES__EXISTS,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1sos: $i] :
( mem(V1sos,arr(arr(A_27a,bool),bool))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EBIGUNION(A_27a),V1sos)))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(arr(A_27a,bool)),V1sos),f484(A_27a,V0x))) ) ) ) ).
tff(lamtp_f492,type,
f492: ( del * $i ) > $i ).
tff(lameq_f492,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V3s: $i] : ( ap(f492(A_27a,V0P),V3s) = ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V3s),f482(A_27a,V0P)) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__BIGUNION,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1sos: $i] :
( mem(V1sos,arr(arr(A_27a,bool),bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V1sos)),f108(A_27a,V0P)))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(arr(A_27a,bool)),V1sos),f492(A_27a,V0P))) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__BIGINTER,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1sos: $i] :
( mem(V1sos,arr(arr(A_27a,bool),bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Epred__set_2EBIGINTER(A_27a),V1sos)),f108(A_27a,V0P)))
<=> ? [V3x: $i] :
( mem(V3x,A_27a)
& p(ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),V1sos),f486(A_27a,V3x)))
& p(ap(V0P,V3x)) ) ) ) ) ).
tff(lamtp_f493,type,
f493: ( del * $i * $i ) > $i ).
tff(lameq_f493,axiom,
! [A_27a: del,V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V3x: $i] : ( ap(f493(A_27a,V1s,V0P),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)),ap(V0P,V3x)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__ELIM,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V1s),f108(A_27a,V0P)))
<=> p(ap(c_2Ebool_2E_3F_21(A_27a),f493(A_27a,V1s,V0P))) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__EXISTS,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0P),V1s))
=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),V1s)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__F,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
( mem(V0P,A_27a)
=> ! [V1s: $i] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27c)
=> ~ p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27b),V1s),k(A_27b,c_2Ebool_2EF))) ) ) ) ).
tff(lamtp_f494,type,
f494: ( del * $i ) > $i ).
tff(lameq_f494,axiom,
! [A_27b: del,V1s: $i] :
( mem(V1s,arr(A_27b,bool))
=> ! [V4x: $i] : ( ap(f494(A_27b,V1s),V4x) = ap(ap(c_2Ebool_2EIN(A_27b),V4x),V1s) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__T,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
( mem(V0P,A_27a)
=> ! [V1s: $i] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27c)
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27b),V1s),k(A_27b,c_2Ebool_2ET)))
<=> p(ap(c_2Ebool_2E_3F_21(A_27b),f494(A_27b,V1s))) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__EMPTY,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ~ p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0p)) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__NOT__EMPTY,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V1s),V0P))
=> ( V1s != c_2Epred__set_2EEMPTY(A_27a) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__UNIV,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0p))
<=> p(ap(c_2Ebool_2E_3F_21(A_27a),V0p)) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__NULL,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m: tp__o] :
( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0p),k(A_27a,inj__o(V1m))))
<=> ( ? [V3x: $i] :
( mem(V3x,A_27a)
& ( V0p = ap(ap(c_2Epred__set_2EINSERT(A_27a),V3x),c_2Epred__set_2EEMPTY(A_27a)) ) )
& p(inj__o(V1m)) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__SING,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
( mem(V0P,A_27a)
=> ! [V1s: $i] :
( mem(V1s,arr(A_27b,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27c)
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27b),V1s),k(A_27b,c_2Ebool_2ET)))
<=> ? [V4y: $i] :
( mem(V4y,A_27b)
& ( V1s = ap(ap(c_2Epred__set_2EINSERT(A_27b),V4y),c_2Epred__set_2EEMPTY(A_27b)) ) ) ) ) ) ) ).
tff(lamtp_f495,type,
f495: ( del * $i * $i ) > $i ).
tff(lameq_f495,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,arr(A_27a,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] : ( ap(f495(A_27a,V1m,V2x),V3y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1m,V3y)),ap(ap(c_2Emin_2E_3D(A_27a),V3y),V2x)) ) ) ) ).
tff(lamtp_f496,type,
f496: ( del * $i * $i ) > $i ).
tff(lameq_f496,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m: $i] :
( mem(V1m,arr(A_27a,bool))
=> ! [V2x: $i] : ( ap(f496(A_27a,V0p,V1m),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(V1m,V2x)),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f495(A_27a,V1m,V2x))) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__ALT,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m: $i] :
( mem(V1m,arr(A_27a,bool))
=> ( p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0p),V1m))
<=> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),f496(A_27a,V0p,V1m))) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__SELECT__EMPTY,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ( ap(ap(c_2Ebool_2ERES__SELECT(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0p) = ap(c_2Emin_2E_40(A_27a),k(A_27a,c_2Ebool_2EF)) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__SELECT__UNIV,axiom,
! [A_27a: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ( ap(ap(c_2Ebool_2ERES__SELECT(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0p) = ap(c_2Emin_2E_40(A_27a),V0p) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__ABSTRACT,axiom,
! [A_27a: del,A_27b: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m: $i] :
( mem(V1m,arr(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p))
=> ( ap(ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m),V2x) = ap(V1m,V2x) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__ABSTRACT__EQUAL,axiom,
! [A_27a: del,A_27b: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m1: $i] :
( mem(V1m1,arr(A_27a,A_27b))
=> ! [V2m2: $i] :
( mem(V2m2,arr(A_27a,A_27b))
=> ( ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0p))
=> ( ap(V1m1,V3x) = ap(V2m2,V3x) ) ) )
=> ( ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m1) = ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V2m2) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__ABSTRACT__IDEMPOT,axiom,
! [A_27a: del,A_27b: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m: $i] :
( mem(V1m,arr(A_27a,A_27b))
=> ( ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m)) = ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__ABSTRACT__EQUAL__EQ,axiom,
! [A_27a: del,A_27b: del,V0p: $i] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m1: $i] :
( mem(V1m1,arr(A_27a,A_27b))
=> ! [V2m2: $i] :
( mem(V2m2,arr(A_27a,A_27b))
=> ( ( ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m1) = ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V2m2) )
<=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0p))
=> ( ap(V1m1,V3x) = ap(V2m2,V3x) ) ) ) ) ) ) ) ).
tff(conj_thm_2Eres__quan_2ERES__ABSTRACT__UNIV,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27a,A_27b))
=> ( ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),c_2Epred__set_2EUNIV(A_27a)),V0m) = V0m ) ) ).
%------------------------------------------------------------------------------