ITP001 Axioms: ITP065_5.ax
%------------------------------------------------------------------------------
% File : ITP065_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 : finite_map_2.ax [Gau20]
% : HL4065_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 441 ( 44 unt; 84 typ; 0 def)
% Number of atoms : 6087 ( 360 equ)
% Maximal formula atoms : 13 ( 13 avg)
% Number of connectives : 1290 ( 30 ~; 9 |; 136 &)
% ( 62 <=>;1053 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4470 (4470 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 315 ( 84 >; 231 *; 0 +; 0 <<)
% Number of predicates : 93 ( 92 usr; 17 prp; 0-3 aty)
% Number of functors : 84 ( 84 usr; 0 con; 1-10 aty)
% Number of variables : 1803 (1780 !; 23 ?;1803 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_ty_2Efinite__map_2Efmap,type,
ty_2Efinite__map_2Efmap: ( del * del ) > del ).
tff(tp_c_2Efinite__map_2EDRESTRICT,type,
c_2Efinite__map_2EDRESTRICT: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EDRESTRICT,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(arr(A_27a,bool),ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ).
tff(tp_c_2Efinite__map_2EFAPPLY,type,
c_2Efinite__map_2EFAPPLY: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFAPPLY,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(A_27a,A_27b))) ).
tff(tp_c_2Efinite__map_2EFCARD,type,
c_2Efinite__map_2EFCARD: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFCARD,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFCARD(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Enum_2Enum)) ).
tff(tp_c_2Efinite__map_2EFDOM,type,
c_2Efinite__map_2EFDOM: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFDOM,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFDOM(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(A_27a,bool))) ).
tff(tp_c_2Efinite__map_2EFEMPTY,type,
c_2Efinite__map_2EFEMPTY: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFEMPTY,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFEMPTY(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b)) ).
tff(tp_c_2Efinite__map_2EFEVERY,type,
c_2Efinite__map_2EFEVERY: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFEVERY,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFEVERY(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),bool),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),bool))) ).
tff(tp_c_2Efinite__map_2EFLOOKUP,type,
c_2Efinite__map_2EFLOOKUP: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFLOOKUP,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(A_27a,ty_2Eoption_2Eoption(A_27b)))) ).
tff(tp_c_2Efinite__map_2EFMAP__MAP2,type,
c_2Efinite__map_2EFMAP__MAP2: ( del * del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFMAP__MAP2,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efinite__map_2EFMAP__MAP2(A_27a,A_27b,A_27c),arr(arr(ty_2Epair_2Eprod(A_27a,A_27c),A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27c),ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ).
tff(tp_c_2Efinite__map_2EFMERGE,type,
c_2Efinite__map_2EFMERGE: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFMERGE,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFMERGE(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,A_27a)),arr(ty_2Efinite__map_2Efmap(A_27b,A_27a),arr(ty_2Efinite__map_2Efmap(A_27b,A_27a),ty_2Efinite__map_2Efmap(A_27b,A_27a))))) ).
tff(tp_c_2Efinite__map_2EFRANGE,type,
c_2Efinite__map_2EFRANGE: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFRANGE,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFRANGE(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(A_27b,bool))) ).
tff(tp_c_2Efinite__map_2EFUNION,type,
c_2Efinite__map_2EFUNION: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFUNION,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFUNION(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ).
tff(tp_c_2Efinite__map_2EFUN__FMAP,type,
c_2Efinite__map_2EFUN__FMAP: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFUN__FMAP,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ).
tff(tp_c_2Efinite__map_2EFUPDATE,type,
c_2Efinite__map_2EFUPDATE: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFUPDATE,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ).
tff(tp_c_2Efinite__map_2EFUPDATE__LIST,type,
c_2Efinite__map_2EFUPDATE__LIST: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2EFUPDATE__LIST,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ).
tff(tp_c_2Efinite__map_2EMAP__KEYS,type,
c_2Efinite__map_2EMAP__KEYS: ( del * del * del ) > $i ).
tff(mem_c_2Efinite__map_2EMAP__KEYS,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),arr(arr(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27c),ty_2Efinite__map_2Efmap(A_27b,A_27c)))) ).
tff(tp_c_2Efinite__map_2ERRESTRICT,type,
c_2Efinite__map_2ERRESTRICT: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2ERRESTRICT,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2ERRESTRICT(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(arr(A_27b,bool),ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ).
tff(tp_c_2Efinite__map_2ESUBMAP,type,
c_2Efinite__map_2ESUBMAP: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2ESUBMAP,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),bool))) ).
tff(tp_c_2Efinite__map_2Ef__o,type,
c_2Efinite__map_2Ef__o: ( del * del * del ) > $i ).
tff(mem_c_2Efinite__map_2Ef__o,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efinite__map_2Ef__o(A_27a,A_27b,A_27c),arr(ty_2Efinite__map_2Efmap(A_27b,A_27c),arr(arr(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27c)))) ).
tff(tp_c_2Efinite__map_2Ef__o__f,type,
c_2Efinite__map_2Ef__o__f: ( del * del * del ) > $i ).
tff(mem_c_2Efinite__map_2Ef__o__f,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efinite__map_2Ef__o__f(A_27a,A_27b,A_27c),arr(ty_2Efinite__map_2Efmap(A_27b,A_27c),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27c)))) ).
tff(tp_c_2Efinite__map_2Efdomsub,type,
c_2Efinite__map_2Efdomsub: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2Efdomsub,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2Efdomsub(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(A_27a,ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ).
tff(tp_c_2Efinite__map_2Efmap__ABS,type,
c_2Efinite__map_2Efmap__ABS: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2Efmap__ABS,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2Efmap__ABS(A_27a,A_27b),arr(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),ty_2Efinite__map_2Efmap(A_27a,A_27b))) ).
tff(tp_c_2Efinite__map_2Efmap__EQ__UPTO,type,
c_2Efinite__map_2Efmap__EQ__UPTO: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2Efmap__EQ__UPTO,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(arr(A_27a,bool),bool)))) ).
tff(tp_c_2Efinite__map_2Efmap__REP,type,
c_2Efinite__map_2Efmap__REP: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2Efmap__REP,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2Efmap__REP(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))) ).
tff(tp_c_2Efinite__map_2Efmap__inverse,type,
c_2Efinite__map_2Efmap__inverse: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2Efmap__inverse,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2Efmap__inverse(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27b,A_27a),bool))) ).
tff(tp_c_2Efinite__map_2Efmap__rel,type,
c_2Efinite__map_2Efmap__rel: ( del * del * del ) > $i ).
tff(mem_c_2Efinite__map_2Efmap__rel,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,bool)),arr(ty_2Efinite__map_2Efmap(A_27c,A_27a),arr(ty_2Efinite__map_2Efmap(A_27c,A_27b),bool)))) ).
tff(tp_c_2Efinite__map_2Efmap__size,type,
c_2Efinite__map_2Efmap__size: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2Efmap__size,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2Efmap__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Enum_2Enum)))) ).
tff(tp_c_2Efinite__map_2Eis__fmap,type,
c_2Efinite__map_2Eis__fmap: ( del * del ) > $i ).
tff(mem_c_2Efinite__map_2Eis__fmap,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),arr(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),bool)) ).
tff(tp_c_2Efinite__map_2Eo__f,type,
c_2Efinite__map_2Eo__f: ( del * del * del ) > $i ).
tff(mem_c_2Efinite__map_2Eo__f,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),arr(arr(A_27b,A_27c),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27c)))) ).
tff(lamtp_f1894,type,
f1894: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f1894,axiom,
! [A_27b: del,A_27a: del,V6b: $i] :
( mem(V6b,A_27b)
=> ! [V5a: $i] :
( mem(V5a,A_27a)
=> ! [V4f: $i] :
( mem(V4f,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V7x: $i] : ( ap(f1894(A_27b,A_27a,V6b,V5a,V4f),V7x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),ap(ap(c_2Emin_2E_3D(A_27a),V7x),V5a)),ap(c_2Esum_2EINL(A_27b,ty_2Eone_2Eone),V6b)),ap(V4f,V7x)) ) ) ) ) ).
tff(lamtp_f1895,type,
f1895: ( del * del * $i * $i * $i * $i ) > $i ).
tff(lameq_f1895,axiom,
! [A_27a: del,A_27b: del,V5a: $i] :
( mem(V5a,A_27a)
=> ! [V2a0: $i] :
( mem(V2a0,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V1is__fmap_27: $i] :
( mem(V1is__fmap_27,arr(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),bool))
=> ! [V4f: $i] :
( mem(V4f,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V6b: $i] : ( ap(f1895(A_27a,A_27b,V5a,V2a0,V1is__fmap_27,V4f),V6b) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone))),V2a0),f1894(A_27b,A_27a,V6b,V5a,V4f))),ap(V1is__fmap_27,V4f)) ) ) ) ) ) ).
tff(lamtp_f1896,type,
f1896: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f1896,axiom,
! [A_27b: del,A_27a: del,V4f: $i] :
( mem(V4f,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V1is__fmap_27: $i] :
( mem(V1is__fmap_27,arr(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),bool))
=> ! [V2a0: $i] :
( mem(V2a0,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V5a: $i] : ( ap(f1896(A_27b,A_27a,V4f,V1is__fmap_27,V2a0),V5a) = ap(c_2Ebool_2E_3F(A_27b),f1895(A_27a,A_27b,V5a,V2a0,V1is__fmap_27,V4f)) ) ) ) ) ).
tff(lamtp_f1897,type,
f1897: ( del * del * $i * $i ) > $i ).
tff(lameq_f1897,axiom,
! [A_27b: del,A_27a: del,V2a0: $i] :
( mem(V2a0,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V1is__fmap_27: $i] :
( mem(V1is__fmap_27,arr(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),bool))
=> ! [V4f: $i] : ( ap(f1897(A_27b,A_27a,V2a0,V1is__fmap_27),V4f) = ap(c_2Ebool_2E_3F(A_27a),f1896(A_27b,A_27a,V4f,V1is__fmap_27,V2a0)) ) ) ) ).
tff(lamtp_f1898,type,
f1898: ( del * del * $i ) > $i ).
tff(lameq_f1898,axiom,
! [A_27a: del,A_27b: del,V1is__fmap_27: $i] :
( mem(V1is__fmap_27,arr(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),bool))
=> ! [V2a0: $i] : ( ap(f1898(A_27a,A_27b,V1is__fmap_27),V2a0) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone))),V2a0),k(A_27a,ap(c_2Esum_2EINR(A_27b,ty_2Eone_2Eone),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone))))),ap(c_2Ebool_2E_3F(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone))),f1897(A_27b,A_27a,V2a0,V1is__fmap_27)))),ap(V1is__fmap_27,V2a0)) ) ) ).
tff(lamtp_f1899,type,
f1899: ( del * del * $i ) > $i ).
tff(lameq_f1899,axiom,
! [A_27a: del,A_27b: del,V0a0: $i] :
( mem(V0a0,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V1is__fmap_27: $i] : ( ap(f1899(A_27a,A_27b,V0a0),V1is__fmap_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone))),f1898(A_27a,A_27b,V1is__fmap_27))),ap(V1is__fmap_27,V0a0)) ) ) ).
tff(lamtp_f1900,type,
f1900: ( del * del ) > $i ).
tff(lameq_f1900,axiom,
! [A_27a: del,A_27b: del,V0a0: $i] : ( ap(f1900(A_27a,A_27b),V0a0) = ap(c_2Ebool_2E_21(arr(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),bool)),f1899(A_27a,A_27b,V0a0)) ) ).
tff(ax_thm_2Efinite__map_2Eis__fmap__def,axiom,
! [A_27a: del,A_27b: del] : ( c_2Efinite__map_2Eis__fmap(A_27a,A_27b) = f1900(A_27a,A_27b) ) ).
tff(lamtp_f1901,type,
f1901: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f1901,axiom,
! [A_27b: del,A_27a: del,V3b: $i] :
( mem(V3b,A_27b)
=> ! [V2a: $i] :
( mem(V2a,A_27a)
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V4x: $i] : ( ap(f1901(A_27b,A_27a,V3b,V2a,V1f),V4x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),ap(ap(c_2Emin_2E_3D(A_27a),V4x),V2a)),ap(c_2Esum_2EINL(A_27b,ty_2Eone_2Eone),V3b)),ap(V1f,V4x)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eis__fmap__rules,axiom,
! [A_27a: del,A_27b: del] :
( p(ap(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),k(A_27a,ap(c_2Esum_2EINR(A_27b,ty_2Eone_2Eone),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone)))))
& ! [V1f: $i] :
( mem(V1f,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V2a: $i] :
( mem(V2a,A_27a)
=> ! [V3b: $i] :
( mem(V3b,A_27b)
=> ( p(ap(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),V1f))
=> p(ap(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),f1901(A_27b,A_27a,V3b,V2a,V1f))) ) ) ) ) ) ).
tff(lamtp_f1902,type,
f1902: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f1902,axiom,
! [A_27b: del,A_27a: del,V4b: $i] :
( mem(V4b,A_27b)
=> ! [V3a: $i] :
( mem(V3a,A_27a)
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V5x: $i] : ( ap(f1902(A_27b,A_27a,V4b,V3a,V2f),V5x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),ap(ap(c_2Emin_2E_3D(A_27a),V5x),V3a)),ap(c_2Esum_2EINL(A_27b,ty_2Eone_2Eone),V4b)),ap(V2f,V5x)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eis__fmap__ind,axiom,
! [A_27a: del,A_27b: del,V0is__fmap_27: $i] :
( mem(V0is__fmap_27,arr(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),bool))
=> ( ( p(ap(V0is__fmap_27,k(A_27a,ap(c_2Esum_2EINR(A_27b,ty_2Eone_2Eone),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone)))))
& ! [V2f: $i] :
( mem(V2f,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V3a: $i] :
( mem(V3a,A_27a)
=> ! [V4b: $i] :
( mem(V4b,A_27b)
=> ( p(ap(V0is__fmap_27,V2f))
=> p(ap(V0is__fmap_27,f1902(A_27b,A_27a,V4b,V3a,V2f))) ) ) ) ) )
=> ! [V6a0: $i] :
( mem(V6a0,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ( p(ap(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),V6a0))
=> p(ap(V0is__fmap_27,V6a0)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eis__fmap__strongind,axiom,
! [A_27a: del,A_27b: del,V0is__fmap_27: $i] :
( mem(V0is__fmap_27,arr(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),bool))
=> ( ( p(ap(V0is__fmap_27,k(A_27a,ap(c_2Esum_2EINR(A_27b,ty_2Eone_2Eone),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone)))))
& ! [V2f: $i] :
( mem(V2f,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ! [V3a: $i] :
( mem(V3a,A_27a)
=> ! [V4b: $i] :
( mem(V4b,A_27b)
=> ( ( p(ap(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),V2f))
& p(ap(V0is__fmap_27,V2f)) )
=> p(ap(V0is__fmap_27,f1902(A_27b,A_27a,V4b,V3a,V2f))) ) ) ) ) )
=> ! [V6a0: $i] :
( mem(V6a0,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ( p(ap(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),V6a0))
=> p(ap(V0is__fmap_27,V6a0)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eis__fmap__cases,axiom,
! [A_27a: del,A_27b: del,V0a0: $i] :
( mem(V0a0,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ( p(ap(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),V0a0))
<=> ( ( V0a0 = k(A_27a,ap(c_2Esum_2EINR(A_27b,ty_2Eone_2Eone),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone))) )
| ? [V2f: $i] :
( mem(V2f,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
& ? [V3a: $i] :
( mem(V3a,A_27a)
& ? [V4b: $i] :
( mem(V4b,A_27b)
& ( V0a0 = f1902(A_27b,A_27a,V4b,V3a,V2f) )
& p(ap(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),V2f)) ) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2Efmap__TY__DEF,axiom,
! [A_27a: del,A_27b: del] :
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone))))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),ty_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2Eis__fmap(A_27a,A_27b)),V0rep)) ) ).
tff(ax_thm_2Efinite__map_2Efmap__ISO__DEF,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0a: $i] :
( mem(V0a,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(c_2Efinite__map_2Efmap__ABS(A_27a,A_27b),ap(c_2Efinite__map_2Efmap__REP(A_27a,A_27b),V0a)) = V0a ) )
& ! [V1r: $i] :
( mem(V1r,arr(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)))
=> ( p(ap(c_2Efinite__map_2Eis__fmap(A_27a,A_27b),V1r))
<=> ( ap(c_2Efinite__map_2Efmap__REP(A_27a,A_27b),ap(c_2Efinite__map_2Efmap__ABS(A_27a,A_27b),V1r)) = V1r ) ) ) ) ).
tff(lamtp_f1903,type,
f1903: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f1903,axiom,
! [A_27b: del,A_27a: del,V2y: $i] :
( mem(V2y,A_27b)
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3a: $i] : ( ap(f1903(A_27b,A_27a,V2y,V1x,V0f),V3a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),ap(ap(c_2Emin_2E_3D(A_27a),V3a),V1x)),ap(c_2Esum_2EINL(A_27b,ty_2Eone_2Eone),V2y)),ap(ap(c_2Efinite__map_2Efmap__REP(A_27a,A_27b),V0f),V3a)) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2EFUPDATE__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) = ap(c_2Efinite__map_2Efmap__ABS(A_27a,A_27b),f1903(A_27b,A_27a,V2y,V1x,V0f)) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2EFEMPTY__DEF,axiom,
! [A_27a: del,A_27b: del] : ( c_2Efinite__map_2EFEMPTY(A_27a,A_27b) = ap(c_2Efinite__map_2Efmap__ABS(A_27a,A_27b),k(A_27a,ap(c_2Esum_2EINR(A_27b,ty_2Eone_2Eone),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone)))) ) ).
tff(ax_thm_2Efinite__map_2EFAPPLY__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V1x) = ap(c_2Esum_2EOUTL(A_27b,ty_2Eone_2Eone),ap(ap(c_2Efinite__map_2Efmap__REP(A_27a,A_27b),V0f),V1x)) ) ) ) ).
tff(ax_thm_2Efinite__map_2EFDOM__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f),V1x))
<=> p(ap(c_2Esum_2EISL(A_27b,ty_2Eone_2Eone),ap(ap(c_2Efinite__map_2Efmap__REP(A_27a,A_27b),V0f),V1x))) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFAPPLY__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y))),V1x) = V2y ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ENOT__EQ__FAPPLY,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( ( V1a != V2x )
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),V1a) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V1a) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__COMMUTES,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2b: $i] :
( mem(V2b,A_27b)
=> ! [V3c: $i] :
( mem(V3c,A_27a)
=> ! [V4d: $i] :
( mem(V4d,A_27b)
=> ( ( V1a != V3c )
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V2b))),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3c),V4d)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3c),V4d))),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V2b)) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__EQ,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2b: $i] :
( mem(V2b,A_27b)
=> ! [V3c: $i] :
( mem(V3c,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V2b))),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V3c)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V3c)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__FEMPTY,axiom,
! [A_27a: del,A_27b: del] : ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)) = c_2Epred__set_2EEMPTY(A_27a) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2b: $i] :
( mem(V2b,A_27b)
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V2b))) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFAPPLY__FUPDATE__THM,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2b: $i] :
( mem(V2b,A_27b)
=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V2b))),V3x) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V1a)),V2b),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V3x)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ENOT__EQ__FEMPTY__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2b: $i] :
( mem(V2b,A_27b)
=> ( c_2Efinite__map_2EFEMPTY(A_27a,A_27b) != ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V2b)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__EQ__FDOM__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
=> ! [V2y: $i] :
( mem(V2y,A_27b)
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y))) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__SIMPLE__INDUCT,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),bool))
=> ( ( p(ap(V0P,c_2Efinite__map_2EFEMPTY(A_27a,A_27b)))
& ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(V0P,V1f))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> p(ap(V0P,ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)))) ) ) ) ) )
=> ! [V4f: $i] :
( mem(V4f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> p(ap(V0P,V4f)) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__EQ__EMPTY,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f) = c_2Epred__set_2EEMPTY(A_27a) )
<=> ( V0f = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__EQ__EMPTY__SYM,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( c_2Epred__set_2EEMPTY(A_27a) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f) )
<=> ( V0f = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__F__FEMPTY1,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ! [V1a: $i] :
( mem(V1a,A_27a)
=> ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))) )
<=> ( V0f = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__FINITE,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0fm))) ) ).
tff(ax_thm_2Efinite__map_2EFCARD__DEF,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( surj__ty_2Enum_2Enum(ap(c_2Efinite__map_2EFCARD(A_27a,A_27b),V0fm)) = surj__ty_2Enum_2Enum(ap(c_2Epred__set_2ECARD(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0fm))) ) ) ).
tff(conj_thm_2Efinite__map_2EFCARD__FEMPTY,axiom,
! [A_27a: del,A_27b: del] : ( surj__ty_2Enum_2Enum(ap(c_2Efinite__map_2EFCARD(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b))) = fo__c_2Enum_2E0 ) ).
tff(conj_thm_2Efinite__map_2EFCARD__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ! [V2b: $i] :
( mem(V2b,A_27b)
=> ( surj__ty_2Enum_2Enum(ap(c_2Efinite__map_2EFCARD(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V2b)))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2EIN(A_27a),V1a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0fm))),ap(c_2Efinite__map_2EFCARD(A_27a,A_27b),V0fm)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Efinite__map_2EFCARD(A_27a,A_27b),V0fm)))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFCARD__0__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( surj__ty_2Enum_2Enum(ap(c_2Efinite__map_2EFCARD(A_27a,A_27b),V0f)) = fo__c_2Enum_2E0 )
<=> ( V0f = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFCARD__SUC,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum(ap(c_2Efinite__map_2EFCARD(A_27a,A_27b),V0f)) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n))) )
<=> ? [V2f_27: $i] :
( mem(V2f_27,ty_2Efinite__map_2Efmap(A_27a,A_27b))
& ? [V3x: $i] :
( mem(V3x,A_27a)
& ? [V4y: $i] :
( mem(V4y,A_27b)
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2f_27)))
& ( surj__ty_2Enum_2Enum(ap(c_2Efinite__map_2EFCARD(A_27a,A_27b),V2f_27)) = V1n )
& ( V0f = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V2f_27),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V4y)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__INDUCT,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),bool))
=> ( ( p(ap(V0P,c_2Efinite__map_2EFEMPTY(A_27a,A_27b)))
& ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(V0P,V1f))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f)))
=> p(ap(V0P,ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)))) ) ) ) ) ) )
=> ! [V4f: $i] :
( mem(V4f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> p(ap(V0P,V4f)) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFM__PULL__APART,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1k),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0fm)))
=> ? [V2fm0: $i] :
( mem(V2fm0,ty_2Efinite__map_2Efmap(A_27a,A_27b))
& ? [V3v: $i] :
( mem(V3v,A_27b)
& ( V0fm = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V2fm0),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V3v)) )
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1k),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2fm0))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ENOT__FDOM__FAPPLY__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V1x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V1x) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__EQ,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g) )
& ( ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f) = ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g) ) )
<=> ( V0f = V1g ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__EQ__THM,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g) )
& ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V2x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g),V2x) ) ) ) )
<=> ( V0f = V1g ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__EXT,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( V0f = V1g )
<=> ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g) )
& ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V2x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g),V2x) ) ) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2ESUBMAP__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V1g))
<=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g)))
& ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V2x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g),V2x) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V0f)) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__REFL,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V0f)) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__ANTISYM,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V1g))
& p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V1g),V0f)) )
<=> ( V0f = V1g ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__TRANS,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2h: $i] :
( mem(V2h,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V1g))
& p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V1g),V2h)) )
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V2h)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EEQ__FDOM__SUBMAP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( V0f = V1g )
<=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V1g))
& ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__FUPDATE__EQN,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27b)
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y))))
<=> ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
| ( ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V1x) = V2y )
& p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))) ) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2EDRESTRICT__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1r: $i] :
( mem(V1r,arr(A_27a,bool))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1r)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)),V1r) )
& ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1r)),V2x) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)),V1r))),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V2x)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V2x)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0r: $i] :
( mem(V0r,arr(A_27a,bool))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V0r) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1r: $i] :
( mem(V1r,arr(A_27a,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),V1r) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1r)),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1r)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1r)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESTRONG__DRESTRICT__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1r: $i] :
( mem(V1r,arr(A_27a,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1r))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),V1r) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1r),V2x))),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__DRESTRICT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1r: $i] :
( mem(V1r,arr(A_27a,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27c)
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1r)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)),V1r) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ENOT__FDOM__DRESTRICT,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a)))) = V0f ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__SUBMAP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1r: $i] :
( mem(V1r,arr(A_27a,bool))
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1r)),V0f)) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__DRESTRICT,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1P: $i] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2Q: $i] :
( mem(V2Q,arr(A_27a,bool))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1P)),V2Q) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINTER(A_27a),V1P),V2Q)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__IS__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__DRESTRICT,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a))))),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESTRONG__DRESTRICT__FUPDATE__THM,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1r: $i] :
( mem(V1r,arr(A_27a,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),V1r) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1r)),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),c_2Epred__set_2EEMPTY(A_27a)))),V1r))),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),c_2Epred__set_2EEMPTY(A_27a)))),V1r))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__UNIV,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),c_2Epred__set_2EUNIV(A_27a)) = V0f ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__DRESTRICT,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1P: $i] :
( mem(V1P,arr(A_27a,bool))
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1P)),V0f)) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__EQ__DRESTRICT,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2s1: $i] :
( mem(V2s1,arr(A_27a,bool))
=> ! [V3s2: $i] :
( mem(V3s2,arr(A_27a,bool))
=> ( ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f1),V2s1) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f2),V3s2) )
<=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f1),V2s1)),V1f2))
& p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f2),V3s2)),V0f1))
& ( ap(ap(c_2Epred__set_2EINTER(A_27a),V2s1),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)) = ap(ap(c_2Epred__set_2EINTER(A_27a),V3s2),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f2)) ) ) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2EFUNION__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g)) )
& ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g)),V2x) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V2x)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g),V2x)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__FEMPTY__1,axiom,
! [A_27a: del,A_27b: del,V0g: $i] :
( mem(V0g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V0g) = V0g ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__FEMPTY__2,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)) = V0f ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__FUPDATE__1,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),V1g) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__FUPDATE__2,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1g),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g)),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__FUNION,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27c)
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__IDEMPOT,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0fm),V0fm) = V0fm ) ) ).
tff(ax_thm_2Efinite__map_2EFMERGE__DEF,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27a,arr(A_27a,A_27a)))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V2g: $i] :
( mem(V2g,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27b,A_27a),ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27a,A_27b),V0m),V1f),V2g)) = ap(ap(c_2Epred__set_2EUNION(A_27b),ap(c_2Efinite__map_2EFDOM(A_27b,A_27a),V1f)),ap(c_2Efinite__map_2EFDOM(A_27b,A_27a),V2g)) )
& ! [V3x: $i] :
( mem(V3x,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27a),ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27a,A_27b),V0m),V1f),V2g)),V3x) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27b),V3x),ap(c_2Efinite__map_2EFDOM(A_27b,A_27a),V1f)))),ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27a),V2g),V3x)),ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27b),V3x),ap(c_2Efinite__map_2EFDOM(A_27b,A_27a),V2g)))),ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27a),V1f),V3x)),ap(ap(V0m,ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27a),V1f),V3x)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27a),V2g),V3x)))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFMERGE__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27b,arr(A_27b,A_27b)))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V0m),V1f),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)) = V1f )
& ( ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V0m),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V1f) = V1f ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__FMERGE,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27a,arr(A_27a,A_27a)))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V2g: $i] :
( mem(V2g,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( ap(c_2Efinite__map_2EFDOM(A_27b,A_27a),ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27a,A_27b),V0m),V1f),V2g)) = ap(ap(c_2Epred__set_2EUNION(A_27b),ap(c_2Efinite__map_2EFDOM(A_27b,A_27a),V1f)),ap(c_2Efinite__map_2EFDOM(A_27b,A_27a),V2g)) ) ) ) ) ).
tff(lamtp_f1904,type,
f1904: del > $i ).
tff(lameq_f1904,axiom,
! [A_27b: del,V0x: $i] : ( ap(f1904(A_27b),V0x) = k(A_27b,V0x) ) ).
tff(conj_thm_2Efinite__map_2EFMERGE__FUNION,axiom,
! [A_27a: del,A_27b: del] : ( c_2Efinite__map_2EFUNION(A_27a,A_27b) = ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),f1904(A_27b)) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__FMERGE,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2m: $i] :
( mem(V2m,arr(A_27b,arr(A_27b,A_27b)))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f2)))
=> ( ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V2m),V0f1),V1f2) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f1),V1f2) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFMERGE__NO__CHANGE,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27b,arr(A_27b,A_27b)))
=> ! [V1f1: $i] :
( mem(V1f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ( ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V0m),V1f1),V2f2) = V1f1 )
<=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2f2)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f1)))
& ( ap(ap(V0m,ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1f1),V3x)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V2f2),V3x)) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1f1),V3x) ) ) ) ) )
& ( ( ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V0m),V1f1),V2f2) = V2f2 )
<=> ! [V4x: $i] :
( mem(V4x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f1)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2f2)))
& ( ap(ap(V0m,ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1f1),V4x)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V2f2),V4x)) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V2f2),V4x) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFMERGE__COMM,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27b,arr(A_27b,A_27b)))
=> ( p(ap(c_2Ecombin_2ECOMM(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V0m)))
<=> p(ap(c_2Ecombin_2ECOMM(A_27b,A_27b),V0m)) ) ) ).
tff(conj_thm_2Efinite__map_2EFMERGE__ASSOC,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27b,arr(A_27b,A_27b)))
=> ( p(ap(c_2Ecombin_2EASSOC(ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V0m)))
<=> p(ap(c_2Ecombin_2EASSOC(A_27b),V0m)) ) ) ).
tff(conj_thm_2Efinite__map_2EFMERGE__DRESTRICT,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27b,arr(A_27b,A_27b)))
=> ! [V1st1: $i] :
( mem(V1st1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2st2: $i] :
( mem(V2st2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3vs: $i] :
( mem(V3vs,arr(A_27a,bool))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V0f),V1st1),V2st2)),V3vs) = ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V0f),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1st1),V3vs)),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V2st2),V3vs)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFMERGE__EQ__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27b,arr(A_27b,A_27b)))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2g: $i] :
( mem(V2g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27b,A_27a),V0m),V1f),V2g) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) )
<=> ( ( V1f = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) )
& ( V2g = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2EFLOOKUP__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0f),V1x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))),ap(c_2Eoption_2ESOME(A_27b),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V1x))),c_2Eoption_2ENONE(A_27b)) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__EMPTY,axiom,
! [A_27a: del,A_27b: del,V0k: $i] :
( mem(V0k,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27a),c_2Efinite__map_2EFEMPTY(A_27b,A_27a)),V0k) = c_2Eoption_2ENONE(A_27a) ) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__UPDATE,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1k1: $i] :
( mem(V1k1,A_27b)
=> ! [V2v: $i] :
( mem(V2v,A_27a)
=> ! [V3k2: $i] :
( mem(V3k2,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27a),ap(ap(c_2Efinite__map_2EFUPDATE(A_27b,A_27a),V0fm),ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V1k1),V2v))),V3k2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(A_27b),V1k1),V3k2)),ap(c_2Eoption_2ESOME(A_27a),V2v)),ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27a),V0fm),V3k2)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__SUBMAP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V1g))
& ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0f),V2k) = ap(c_2Eoption_2ESOME(A_27b),V3v) ) )
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V1g),V2k) = ap(c_2Eoption_2ESOME(A_27b),V3v) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__FUPDATE__FLOOKUP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27b)
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y))))
<=> ( ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0f),V1x) = c_2Eoption_2ENONE(A_27b) )
| ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0f),V1x) = ap(c_2Eoption_2ESOME(A_27b),V2y) ) ) ) ) ) ) ).
tff(lamtp_f1905,type,
f1905: del > $i ).
tff(lameq_f1905,axiom,
! [A_27a: del,V3v: $i] : ( ap(f1905(A_27a),V3v) = ap(c_2Eoption_2ESOME(A_27a),V3v) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__FUNION,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V2k: $i] :
( mem(V2k,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27a),ap(ap(c_2Efinite__map_2EFUNION(A_27b,A_27a),V0f1),V1f2)),V2k) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27a),V0f1),V2k)),ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27a),V1f2),V2k)),f1905(A_27a)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__EXT,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( V0f1 = V1f2 )
<=> ( ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0f1) = ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V1f2) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__eq__flookup,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( V0f1 = V1f2 )
<=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0f1),V2x) = ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V1f2),V2x) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__DRESTRICT,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0fm),V1s)),V2k) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Ebool_2EIN(A_27a),V2k),V1s)),ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0fm),V2k)),c_2Eoption_2ENONE(A_27b)) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2EFEVERY__DEF,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),V1f))
<=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f)))
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1f),V2x)))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFEVERY__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),c_2Efinite__map_2EFEMPTY(A_27a,A_27b))) ) ).
tff(conj_thm_2Efinite__map_2EFEVERY__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))))
<=> ( p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)))
& p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),c_2Epred__set_2EEMPTY(A_27a)))))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFEVERY__FLOOKUP,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),V1f))
& ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V1f),V2k) = ap(c_2Eoption_2ESOME(A_27b),V3v) ) )
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v))) ) ) ) ) ) ).
tff(lamtp_f1906,type,
f1906: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1906,axiom,
! [A_27b: del,A_27c: del,A_27a: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] : ( ap(f1906(A_27b,A_27c,A_27a,V0f,V1g),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2EIN(A_27b),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g),V2x)),ap(c_2Efinite__map_2EFDOM(A_27b,A_27c),V0f))) ) ) ) ).
tff(ax_thm_2Efinite__map_2Ef__o__f__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),ap(ap(c_2Efinite__map_2Ef__o__f(A_27a,A_27b,A_27c),V0f),V1g)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g)),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f1906(A_27b,A_27c,A_27a,V0f,V1g))) )
& ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),ap(ap(c_2Efinite__map_2Ef__o__f(A_27a,A_27b,A_27c),V0f),V1g))))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27c),ap(ap(c_2Efinite__map_2Ef__o__f(A_27a,A_27b,A_27c),V0f),V1g)),V3x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27c),V0f),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g),V3x)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Ef__o__f__FEMPTY__1,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2Ef__o__f(A_27a,A_27b,A_27c),c_2Efinite__map_2EFEMPTY(A_27b,A_27c)),V0f) = c_2Efinite__map_2EFEMPTY(A_27a,A_27c) ) ) ).
tff(conj_thm_2Efinite__map_2Ef__o__f__FEMPTY__2,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ( ap(ap(c_2Efinite__map_2Ef__o__f(A_27a,A_27b,A_27c),V0f),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)) = c_2Efinite__map_2EFEMPTY(A_27a,A_27c) ) ) ).
tff(ax_thm_2Efinite__map_2Eo__f__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),V0f),V1g)) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g) )
& ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),V0f),V1g))))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27c),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),V0f),V1g)),V2x) = ap(V0f,ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g),V2x)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eo__f__FDOM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),V0f),V1g)) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__o__f,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),V0f),V1g)) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eo__f__FAPPLY,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g)))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27c),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),V0f),V1g)),V2x) = ap(V0f,ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g),V2x)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eo__f__FEMPTY,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27c,A_27b))
=> ( ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27c,A_27b),V0f),c_2Efinite__map_2EFEMPTY(A_27a,A_27c)) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ).
tff(lamtp_f1907,type,
f1907: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1907,axiom,
! [A_27c: del,A_27a: del,A_27b: del,V2f: $i] :
( mem(V2f,arr(A_27b,A_27c))
=> ! [V1P: $i] :
( mem(V1P,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool))
=> ! [V3x: $i] : ( ap(f1907(A_27c,A_27a,A_27b,V2f,V1P),V3x) = ap(V1P,ap(ap(c_2Epair_2E_2C(A_27a,A_27c),ap(c_2Epair_2EFST(A_27a,A_27b),V3x)),ap(V2f,ap(c_2Epair_2ESND(A_27a,A_27b),V3x)))) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFEVERY__o__f,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0m: $i] :
( mem(V0m,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1P: $i] :
( mem(V1P,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27b,A_27c))
=> ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27c),V1P),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),V2f),V0m)))
<=> p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),f1907(A_27c,A_27a,A_27b,V2f,V1P)),V0m)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eo__f__o__f,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
( mem(V0f,arr(A_27c,A_27b))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27d,A_27c))
=> ! [V2h: $i] :
( mem(V2h,ty_2Efinite__map_2Efmap(A_27a,A_27d))
=> ( ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27c,A_27b),V0f),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27d,A_27c),V1g),V2h)) = ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27d,A_27b),ap(ap(c_2Ecombin_2Eo(A_27d,A_27b,A_27c),V0f),V1g)),V2h) ) ) ) ) ).
tff(lamtp_f1908,type,
f1908: ( del * del * $i ) > $i ).
tff(lameq_f1908,axiom,
! [A_27a: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27c,A_27a))
=> ! [V3v: $i] : ( ap(f1908(A_27a,A_27c,V0f),V3v) = ap(c_2Eoption_2ESOME(A_27a),ap(V0f,V3v)) ) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__o__f,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27c,A_27a))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V2k: $i] :
( mem(V2k,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27a),ap(ap(c_2Efinite__map_2Eo__f(A_27b,A_27c,A_27a),V0f),V1fm)),V2k) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27c,ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27c),V1fm),V2k)),c_2Eoption_2ENONE(A_27a)),f1908(A_27a,A_27c,V0f)) ) ) ) ) ).
tff(lamtp_f1909,type,
f1909: ( del * del * $i * $i ) > $i ).
tff(lameq_f1909,axiom,
! [A_27b: del,A_27a: del,V1y: $i] :
( mem(V1y,A_27b)
=> ! [V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] : ( ap(f1909(A_27b,A_27a,V1y,V0f),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))),ap(ap(c_2Emin_2E_3D(A_27b),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V2x)),V1y)) ) ) ) ).
tff(lamtp_f1910,type,
f1910: ( del * del * $i ) > $i ).
tff(lameq_f1910,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1y: $i] : ( ap(f1910(A_27a,A_27b,V0f),V1y) = ap(ap(c_2Epair_2E_2C(A_27b,bool),V1y),ap(c_2Ebool_2E_3F(A_27a),f1909(A_27b,A_27a,V1y,V0f))) ) ) ).
tff(ax_thm_2Efinite__map_2EFRANGE__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),V0f) = ap(c_2Epred__set_2EGSPEC(A_27b,A_27b),f1910(A_27a,A_27b,V0f)) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__FEMPTY,axiom,
! [A_27a: del,A_27b: del] : ( ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),c_2Efinite__map_2EFEMPTY(A_27b,A_27a)) = c_2Epred__set_2EEMPTY(A_27a) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27b)
=> ( ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y))) = ap(ap(c_2Epred__set_2EINSERT(A_27b),V2y),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a)))))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__FRANGE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V1g))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),V0f)),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),V1g))) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFINITE__FRANGE,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> p(ap(c_2Epred__set_2EFINITE(A_27b),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),V0fm))) ) ).
tff(conj_thm_2Efinite__map_2Eo__f__FRANGE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,A_27c))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V1g)))
=> p(ap(ap(c_2Ebool_2EIN(A_27c),ap(V2f,V0x)),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27c),ap(ap(c_2Efinite__map_2Eo__f(A_27b,A_27a,A_27c),V2f),V1g)))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__FLOOKUP,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( mem(V0v,A_27a)
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V1f)))
<=> ? [V2k: $i] :
( mem(V2k,A_27b)
& ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27a),V1f),V2k) = ap(c_2Eoption_2ESOME(A_27a),V0v) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__FUNION,axiom,
! [A_27a: del,A_27b: del,V0fm1: $i] :
( mem(V0fm1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1fm2: $i] :
( mem(V1fm2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0fm1)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1fm2)))
=> ( ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0fm1),V1fm2)) = ap(ap(c_2Epred__set_2EUNION(A_27b),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),V0fm1)),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),V1fm2)) ) ) ) ) ).
tff(lamtp_f1911,type,
f1911: ( del * del * $i * $i ) > $i ).
tff(lameq_f1911,axiom,
! [A_27b: del,A_27a: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1r: $i] :
( mem(V1r,arr(A_27b,bool))
=> ! [V2x: $i] : ( ap(f1911(A_27b,A_27a,V0f,V1r),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))),ap(ap(c_2Ebool_2EIN(A_27b),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V2x)),V1r))) ) ) ) ).
tff(ax_thm_2Efinite__map_2ERRESTRICT__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1r: $i] :
( mem(V1r,arr(A_27b,bool))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2ERRESTRICT(A_27a,A_27b),V0f),V1r)) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f1911(A_27b,A_27a,V0f,V1r)) )
& ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2ERRESTRICT(A_27a,A_27b),V0f),V1r)),V3x) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))),ap(ap(c_2Ebool_2EIN(A_27b),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V3x)),V1r))),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V3x)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V3x)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ERRESTRICT__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0r: $i] :
( mem(V0r,arr(A_27a,bool))
=> ( ap(ap(c_2Efinite__map_2ERRESTRICT(A_27b,A_27a),c_2Efinite__map_2EFEMPTY(A_27b,A_27a)),V0r) = c_2Efinite__map_2EFEMPTY(A_27b,A_27a) ) ) ).
tff(conj_thm_2Efinite__map_2ERRESTRICT__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1r: $i] :
( mem(V1r,arr(A_27b,bool))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( ap(ap(c_2Efinite__map_2ERRESTRICT(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),V1r) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(ap(c_2Ebool_2EIN(A_27b),V3y),V1r)),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2ERRESTRICT(A_27a,A_27b),V0f),V1r)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),ap(ap(c_2Efinite__map_2ERRESTRICT(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),c_2Epred__set_2EEMPTY(A_27a))))),V1r)) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2EFUN__FMAP__DEF,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1P: $i] :
( mem(V1P,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1P))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),V0f),V1P)) = V1P )
& ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1P))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),V0f),V1P)),V2x) = ap(V0f,V2x) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUN__FMAP__EMPTY,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__FMAP,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0P))
=> ( ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),V1f),V0P)) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1f),V0P) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__FMAP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),V0f),V1s)) = V1s ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__FUN__FMAP,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0P))
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),V1f),V0P)),V2k) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Ebool_2EIN(A_27a),V2k),V0P)),ap(c_2Eoption_2ESOME(A_27b),ap(V1f,V2k))),c_2Eoption_2ENONE(A_27b)) ) ) ) ) ) ).
tff(lamtp_f1912,type,
f1912: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1912,axiom,
! [A_27b: del,A_27c: del,A_27a: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27a,A_27b))
=> ! [V2x: $i] : ( ap(f1912(A_27b,A_27c,A_27a,V0f,V1g),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2EIN(A_27b),ap(V1g,V2x)),ap(c_2Efinite__map_2EFDOM(A_27b,A_27c),V0f))) ) ) ) ).
tff(ax_thm_2Efinite__map_2Ef__o__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2Ef__o(A_27a,A_27b,A_27c),V0f),V1g) = ap(ap(c_2Efinite__map_2Ef__o__f(A_27a,A_27b,A_27c),V0f),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),V1g),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f1912(A_27b,A_27c,A_27a,V0f,V1g)))) ) ) ) ).
tff(lamtp_f1913,type,
f1913: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1913,axiom,
! [A_27b: del,A_27c: del,A_27a: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27a,A_27b))
=> ! [V3x: $i] : ( ap(f1913(A_27b,A_27c,A_27a,V0f,V1g),V3x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V3x),ap(ap(c_2Ebool_2EIN(A_27b),ap(V1g,V3x)),ap(c_2Efinite__map_2EFDOM(A_27b,A_27c),V0f))) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__f__o,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27a,A_27b))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f1912(A_27b,A_27c,A_27a,V0f,V1g))))
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),ap(ap(c_2Efinite__map_2Ef__o(A_27a,A_27b,A_27c),V0f),V1g)) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f1913(A_27b,A_27c,A_27a,V0f,V1g)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Ef__o__FEMPTY,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0g: $i] :
( mem(V0g,arr(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2Ef__o(A_27a,A_27b,A_27c),c_2Efinite__map_2EFEMPTY(A_27b,A_27c)),V0g) = c_2Efinite__map_2EFEMPTY(A_27a,A_27c) ) ) ).
tff(lamtp_f1914,type,
f1914: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1914,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3g: $i] :
( mem(V3g,arr(A_27c,A_27a))
=> ! [V4x: $i] : ( ap(f1914(A_27a,A_27b,A_27c,V0fm,V3g),V4x) = ap(ap(c_2Epair_2E_2C(A_27c,bool),V4x),ap(ap(c_2Ebool_2EIN(A_27a),ap(V3g,V4x)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0fm))) ) ) ) ).
tff(lamtp_f1915,type,
f1915: ( del * del * $i * $i ) > $i ).
tff(lameq_f1915,axiom,
! [A_27a: del,A_27c: del,V1k: $i] :
( mem(V1k,A_27a)
=> ! [V3g: $i] :
( mem(V3g,arr(A_27c,A_27a))
=> ! [V5x: $i] : ( ap(f1915(A_27a,A_27c,V1k,V3g),V5x) = ap(ap(c_2Epair_2E_2C(A_27c,bool),V5x),ap(ap(c_2Emin_2E_3D(A_27a),ap(V3g,V5x)),V1k)) ) ) ) ).
tff(lamtp_f1916,type,
f1916: ( del * del * $i * $i ) > $i ).
tff(lameq_f1916,axiom,
! [A_27a: del,A_27c: del,V1k: $i] :
( mem(V1k,A_27a)
=> ! [V3g: $i] :
( mem(V3g,arr(A_27c,A_27a))
=> ! [V6x: $i] : ( ap(f1916(A_27a,A_27c,V1k,V3g),V6x) = ap(ap(c_2Epair_2E_2C(A_27c,bool),V6x),ap(ap(c_2Emin_2E_3D(A_27a),ap(V3g,V6x)),V1k)) ) ) ) ).
tff(conj_thm_2Efinite__map_2Ef__o__FUPDATE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ! [V2v: $i] :
( mem(V2v,A_27b)
=> ! [V3g: $i] :
( mem(V3g,arr(A_27c,A_27a))
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27c),ap(c_2Epred__set_2EGSPEC(A_27c,A_27c),f1914(A_27a,A_27b,A_27c,V0fm,V3g))))
& p(ap(c_2Epred__set_2EFINITE(A_27c),ap(c_2Epred__set_2EGSPEC(A_27c,A_27c),f1915(A_27a,A_27c,V1k,V3g)))) )
=> ( ap(ap(c_2Efinite__map_2Ef__o(A_27c,A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V2v))),V3g) = ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27b,A_27c),ap(c_2Ecombin_2EC(A_27b,A_27b,A_27b),c_2Ecombin_2EK(A_27b,A_27b))),ap(ap(c_2Efinite__map_2Ef__o(A_27c,A_27a,A_27b),V0fm),V3g)),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27c,A_27b),ap(c_2Ecombin_2EK(A_27b,A_27c),V2v)),ap(c_2Epred__set_2EGSPEC(A_27c,A_27c),f1916(A_27a,A_27c,V1k,V3g)))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFAPPLY__f__o,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27a,A_27b))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f1912(A_27b,A_27c,A_27a,V0f,V1g))))
=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),ap(ap(c_2Efinite__map_2Ef__o(A_27a,A_27b,A_27c),V0f),V1g))))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27c),ap(ap(c_2Efinite__map_2Ef__o(A_27a,A_27b,A_27c),V0f),V1g)),V3x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27c),V0f),ap(V1g,V3x)) ) ) ) ) ) ) ).
tff(lamtp_f1917,type,
f1917: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1917,axiom,
! [A_27b: del,A_27c: del,A_27a: del,V3f: $i] :
( mem(V3f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V0g: $i] :
( mem(V0g,arr(A_27a,A_27b))
=> ! [V4x: $i] : ( ap(f1917(A_27b,A_27c,A_27a,V3f,V0g),V4x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V4x),ap(ap(c_2Ebool_2EIN(A_27b),ap(V0g,V4x)),ap(c_2Efinite__map_2EFDOM(A_27b,A_27c),V3f))) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFINITE__PRED__11,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0g: $i] :
( mem(V0g,arr(A_27a,A_27b))
=> ( ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( ap(V0g,V1x) = ap(V0g,V2y) )
<=> ( V1x = V2y ) ) ) )
=> ! [V3f: $i] :
( mem(V3f,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f1917(A_27b,A_27c,A_27a,V3f,V0g)))) ) ) ) ).
tff(conj_thm_2Efinite__map_2Ef__o__ASSOC,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0g: $i] :
( mem(V0g,arr(A_27a,A_27b))
=> ! [V1h: $i] :
( mem(V1h,arr(A_27c,A_27a))
=> ! [V2f: $i] :
( mem(V2f,ty_2Efinite__map_2Efmap(A_27b,A_27d))
=> ( ( ! [V3x: $i] :
( mem(V3x,A_27a)
=> ! [V4y: $i] :
( mem(V4y,A_27a)
=> ( ( ap(V0g,V3x) = ap(V0g,V4y) )
<=> ( V3x = V4y ) ) ) )
& ! [V5x: $i] :
( mem(V5x,A_27c)
=> ! [V6y: $i] :
( mem(V6y,A_27c)
=> ( ( ap(V1h,V5x) = ap(V1h,V6y) )
<=> ( V5x = V6y ) ) ) ) )
=> ( ap(ap(c_2Efinite__map_2Ef__o(A_27c,A_27a,A_27d),ap(ap(c_2Efinite__map_2Ef__o(A_27a,A_27b,A_27d),V2f),V0g)),V1h) = ap(ap(c_2Efinite__map_2Ef__o(A_27c,A_27b,A_27d),V2f),ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0g),V1h)) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2Efmap__domsub,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0fm),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1k),c_2Epred__set_2EEMPTY(A_27a)))) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0k: $i] :
( mem(V0k,A_27a)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V0k) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ! [V2v: $i] :
( mem(V2v,A_27b)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V2v))),V1k) = ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FUPDATE__NEQ,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k1: $i] :
( mem(V1k1,A_27a)
=> ! [V2k2: $i] :
( mem(V2k2,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ( V1k1 != V2k2 )
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k1),V3v))),V2k2) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V2k2)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k1),V3v)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FUPDATE__THM,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k1: $i] :
( mem(V1k1,A_27a)
=> ! [V2k2: $i] :
( mem(V2k2,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k1),V3v))),V2k2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(ap(c_2Emin_2E_3D(A_27a),V1k1),V2k2)),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V2k2)),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V2k2)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k1),V3v))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__DOMSUB,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k)) = ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0fm)),V1k) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FAPPLY,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k)),V1k) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V1k) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FAPPLY__NEQ,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k1: $i] :
( mem(V1k1,A_27a)
=> ! [V2k2: $i] :
( mem(V2k2,A_27a)
=> ( ( V1k1 != V2k2 )
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k1)),V2k2) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0fm),V2k2) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FAPPLY__THM,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k1: $i] :
( mem(V1k1,A_27a)
=> ! [V2k2: $i] :
( mem(V2k2,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k1)),V2k2) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V1k1),V2k2)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V2k2)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0fm),V2k2)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FLOOKUP,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k)),V1k) = c_2Eoption_2ENONE(A_27b) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FLOOKUP__NEQ,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k1: $i] :
( mem(V1k1,A_27a)
=> ! [V2k2: $i] :
( mem(V2k2,A_27a)
=> ( ( V1k1 != V2k2 )
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k1)),V2k2) = ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0fm),V2k2) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FLOOKUP__THM,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k1: $i] :
( mem(V1k1,A_27a)
=> ! [V2k2: $i] :
( mem(V2k2,A_27a)
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k1)),V2k2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Emin_2E_3D(A_27a),V1k1),V2k2)),c_2Eoption_2ENONE(A_27b)),ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0fm),V2k2)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__FUPDATE__DOMSUB,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ! [V2v: $i] :
( mem(V2v,A_27b)
=> ( ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V2v))) = ap(ap(c_2Epred__set_2EINSERT(A_27b),V2v),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eo__f__DOMSUB,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0g: $i] :
( mem(V0g,arr(A_27c,A_27b))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27c,A_27b),V0g),V1fm)),V2k) = ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27c,A_27b),V0g),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27c),V1fm),V2k)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__IDEM,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k)),V1k) = ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__COMMUTES,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k1: $i] :
( mem(V1k1,A_27a)
=> ! [V2k2: $i] :
( mem(V2k2,A_27a)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V1k1)),V2k2) = ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0fm),V2k2)),V1k1) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eo__f__FUPDATE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27c,A_27b))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27c)
=> ( ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27c,A_27b),V0f),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27c),V1fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2k),V3v))) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27c,A_27b),V0f),V1fm)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),ap(V0f,V3v))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__NOT__IN__DOM,axiom,
! [A_27a: del,A_27b: del,V0k: $i] :
( mem(V0k,A_27a)
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0k),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1fm)))
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V1fm),V0k) = V1fm ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__CASES,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( V0f = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) )
| ? [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
& ? [V2x: $i] :
( mem(V2x,A_27a)
& ? [V3y: $i] :
( mem(V3y,A_27b)
& ( V0f = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1g),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__DOMSUB,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0f),V1k)),V0f)) ) ) ).
tff(conj_thm_2Efinite__map_2EFMERGE__DOMSUB,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27a,arr(A_27a,A_27a)))
=> ! [V1m1: $i] :
( mem(V1m1,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V2m2: $i] :
( mem(V2m2,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V3k: $i] :
( mem(V3k,A_27b)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27b,A_27a),ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27a,A_27b),V0m),V1m1),V2m2)),V3k) = ap(ap(ap(c_2Efinite__map_2EFMERGE(A_27a,A_27b),V0m),ap(ap(c_2Efinite__map_2Efdomsub(A_27b,A_27a),V1m1),V3k)),ap(ap(c_2Efinite__map_2Efdomsub(A_27b,A_27a),V2m2),V3k)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),V1g))
<=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g)))
& ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1g),V2x) = V3y )
& p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0f),V2x)),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V1g),V2x))) ) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2EFUPDATE__LIST,axiom,
! [A_27a: del,A_27b: del] : ( c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b) = ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFUPDATE(A_27a,A_27b)) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__THM,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V0f),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))) = V0f )
& ! [V1h: $i] :
( mem(V1h,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V2t: $i] :
( mem(V2t,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V0f),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),V1h),V2t)) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),V1h)),V2t) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__APPLY__NOT__MEM,axiom,
! [A_27a: del,A_27b: del,V0kvl: $i] :
( mem(V0kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2k),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl))))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1f),V0kvl)),V2k) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1f),V2k) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__APPEND,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1kvl1: $i] :
( mem(V1kvl1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2kvl2: $i] :
( mem(V2kvl2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V0fm),ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(A_27a,A_27b)),V1kvl1),V2kvl2)) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V0fm),V1kvl1)),V2kvl2) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__FUPDATE__LIST__COMMUTES,axiom,
! [A_27a: del,A_27b: del,V0k: $i] :
( mem(V0k,A_27a)
=> ! [V1kvl: $i] :
( mem(V1kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2fm: $i] :
( mem(V2fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0k),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V1kvl))))
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V2fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0k),V3v))),V1kvl) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm),V1kvl)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0k),V3v)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__FUPDATE__LIST__MEM,axiom,
! [A_27a: del,A_27b: del,V0k: $i] :
( mem(V0k,A_27a)
=> ! [V1kvl: $i] :
( mem(V1kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2fm: $i] :
( mem(V2fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0k),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V1kvl))))
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V2fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0k),V3v))),V1kvl) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm),V1kvl) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFEVERY__FUPDATE__LIST,axiom,
! [A_27a: del,A_27b: del,V0kvl: $i] :
( mem(V0kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1P: $i] :
( mem(V1P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V2fm: $i] :
( mem(V2fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl)))
=> ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V1P),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm),V0kvl)))
<=> ( p(ap(ap(c_2Elist_2EEVERY(ty_2Epair_2Eprod(A_27a,A_27b)),V1P),V0kvl))
& p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V1P),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V2fm),ap(c_2Epred__set_2ECOMPL(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl)))))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__APPLY__MEM,axiom,
! [A_27a: del,A_27b: del,V0kvl: $i] :
( mem(V0kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ! [V4n: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4n)),ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),V0kvl)))
& ( V2k = ap(ap(c_2Elist_2EEL(A_27a),inj__ty_2Enum_2Enum(V4n)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl)) )
& ( V3v = ap(ap(c_2Elist_2EEL(A_27b),inj__ty_2Enum_2Enum(V4n)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),V0kvl)) )
& ! [V5m: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4n)),inj__ty_2Enum_2Enum(V5m)))
& p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V5m)),ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),V0kvl))) )
=> ( ap(ap(c_2Elist_2EEL(A_27a),inj__ty_2Enum_2Enum(V5m)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl)) != V2k ) ) )
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1f),V0kvl)),V2k) = V3v ) ) ) ) ) ) ).
tff(lamtp_f1918,type,
f1918: ( del * del * del * $i * $i * $i ) > $i ).
tff(lameq_f1918,axiom,
! [A_27c: del,A_27b: del,A_27a: del,V1f2: $i] :
( mem(V1f2,arr(A_27a,A_27c))
=> ! [V0f1: $i] :
( mem(V0f1,arr(A_27a,A_27b))
=> ! [V4fm: $i] :
( mem(V4fm,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ! [V5k: $i] : ( ap(f1918(A_27c,A_27b,A_27a,V1f2,V0f1,V4fm),V5k) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27b,A_27c),V4fm),ap(ap(c_2Epair_2E_2C(A_27b,A_27c),ap(V0f1,V5k)),ap(V1f2,V5k))) ) ) ) ) ).
tff(lamtp_f1919,type,
f1919: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1919,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V1f2: $i] :
( mem(V1f2,arr(A_27a,A_27c))
=> ! [V0f1: $i] :
( mem(V0f1,arr(A_27a,A_27b))
=> ! [V4fm: $i] : ( ap(f1919(A_27a,A_27b,A_27c,V1f2,V0f1),V4fm) = f1918(A_27c,A_27b,A_27a,V1f2,V0f1,V4fm) ) ) ) ).
tff(lamtp_f1920,type,
f1920: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1920,axiom,
! [A_27c: del,A_27b: del,A_27a: del,V0f1: $i] :
( mem(V0f1,arr(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,arr(A_27a,A_27c))
=> ! [V6k: $i] : ( ap(f1920(A_27c,A_27b,A_27a,V0f1,V1f2),V6k) = ap(ap(c_2Epair_2E_2C(A_27b,A_27c),ap(V0f1,V6k)),ap(V1f2,V6k)) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFOLDL__FUPDATE__LIST,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f1: $i] :
( mem(V0f1,arr(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,arr(A_27a,A_27c))
=> ! [V2ls: $i] :
( mem(V2ls,ty_2Elist_2Elist(A_27a))
=> ! [V3a: $i] :
( mem(V3a,ty_2Efinite__map_2Efmap(A_27b,A_27c))
=> ( ap(ap(ap(c_2Elist_2EFOLDL(A_27a,ty_2Efinite__map_2Efmap(A_27b,A_27c)),f1919(A_27a,A_27b,A_27c,V1f2,V0f1)),V3a),V2ls) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27b,A_27c),V3a),ap(ap(c_2Elist_2EMAP(A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),f1920(A_27c,A_27b,A_27a,V0f1,V1f2)),V2ls)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__SNOC,axiom,
! [A_27a: del,A_27b: del,V0xs: $i] :
( mem(V0xs,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1x: $i] :
( mem(V1x,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V2fm: $i] :
( mem(V2fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm),ap(ap(c_2Elist_2ESNOC(ty_2Epair_2Eprod(A_27a,A_27b)),V1x),V0xs)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm),V0xs)),V1x) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPD11__SAME__KEY__AND__BASE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ! [V2v1: $i] :
( mem(V2v1,A_27b)
=> ! [V3v2: $i] :
( mem(V3v2,A_27b)
=> ( ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V2v1)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V3v2)) )
<=> ( V2v1 = V3v2 ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPD11__SAME__NEW__KEY,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v1: $i] :
( mem(V3v1,A_27b)
=> ! [V4v2: $i] :
( mem(V4v2,A_27b)
=> ( ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2k),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)))
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2k),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f2))) )
=> ( ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v1)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f2),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V4v2)) )
<=> ( ( V0f1 = V1f2 )
& ( V3v1 = V4v2 ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESAME__KEY__UPDATES__DIFFER,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v1: $i] :
( mem(V3v1,A_27b)
=> ! [V4v2: $i] :
( mem(V4v2,A_27b)
=> ( ( V3v1 != V4v2 )
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v1)) != ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f2),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V4v2)) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPD11__SAME__BASE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k1: $i] :
( mem(V1k1,A_27a)
=> ! [V2v1: $i] :
( mem(V2v1,A_27b)
=> ! [V3k2: $i] :
( mem(V3k2,A_27a)
=> ! [V4v2: $i] :
( mem(V4v2,A_27b)
=> ( ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k1),V2v1)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3k2),V4v2)) )
<=> ( ( ( V1k1 = V3k2 )
& ( V2v1 = V4v2 ) )
| ( ( V1k1 != V3k2 )
& p(ap(ap(c_2Ebool_2EIN(A_27a),V1k1),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3k2),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
& ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k1),V2v1)) = V0f )
& ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3k2),V4v2)) = V0f ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPD__SAME__KEY__UNWIND,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v1: $i] :
( mem(V3v1,A_27b)
=> ! [V4v2: $i] :
( mem(V4v2,A_27b)
=> ( ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v1)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f2),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V4v2)) )
=> ( ( V3v1 = V4v2 )
& ! [V5v: $i] :
( mem(V5v,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V5v)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f2),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V5v)) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPD11__SAME__UPDATE,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f2),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v)) )
<=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f1),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2k),c_2Epred__set_2EEMPTY(A_27a)))) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f2),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2k),c_2Epred__set_2EEMPTY(A_27a)))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__FUPDATE__LIST,axiom,
! [A_27a: del,A_27b: del,V0kvl: $i] :
( mem(V0kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1fm),V0kvl)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1fm)),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl))) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__SAME__UPDATE,axiom,
! [A_27a: del,A_27b: del,V0kvl: $i] :
( mem(V0kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1f1: $i] :
( mem(V1f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1f1),V0kvl) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2f2),V0kvl) )
<=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f1),ap(c_2Epred__set_2ECOMPL(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl)))) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V2f2),ap(c_2Epred__set_2ECOMPL(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl)))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__SAME__KEYS__UNWIND,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2kvl1: $i] :
( mem(V2kvl1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3kvl2: $i] :
( mem(V3kvl2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V0f1),V2kvl1) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1f2),V3kvl2) )
& ( ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V2kvl1) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V3kvl2) )
& p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V2kvl1))) )
=> ( ( V2kvl1 = V3kvl2 )
& ! [V4kvl: $i] :
( mem(V4kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V4kvl) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V2kvl1) )
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V0f1),V4kvl) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1f2),V4kvl) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFMEQ__ENUMERATE__CASES,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1kvl: $i] :
( mem(V1kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2p: $i] :
( mem(V2p,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),V2p) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V1kvl) )
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V2p),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),V1kvl))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFMEQ__SINGLE__SIMPLE__ELIM,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),bool))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ! [V2v: $i] :
( mem(V2v,A_27b)
=> ! [V3ck: $i] :
( mem(V3ck,A_27a)
=> ! [V4cv: $i] :
( mem(V4cv,A_27b)
=> ! [V5nv: $i] :
( mem(V5nv,A_27b)
=> ( ? [V6fm: $i] :
( mem(V6fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
& ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V6fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V2v)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3ck),V4cv)) )
& p(ap(V0P,ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V6fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V5nv)))) )
<=> ( ( V1k = V3ck )
& ( V2v = V4cv )
& p(ap(V0P,ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3ck),V5nv)))) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFMEQ__SINGLE__SIMPLE__DISJ__ELIM,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1k: $i] :
( mem(V1k,A_27a)
=> ! [V2v: $i] :
( mem(V2v,A_27b)
=> ! [V3ck: $i] :
( mem(V3ck,A_27a)
=> ! [V4cv: $i] :
( mem(V4cv,A_27b)
=> ( ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V2v)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3ck),V4cv)) )
<=> ( ( V1k = V3ck )
& ( V2v = V4cv )
& ( ( V0fm = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) )
| ? [V5v_27: $i] :
( mem(V5v_27,A_27b)
& ( V0fm = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1k),V5v_27)) ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__PURGE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27b)
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0f),V1x)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) ) ) ) ) ).
tff(lamtp_f1921,type,
f1921: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1921,axiom,
! [A_27c: del,A_27b: del,A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V0f: $i] :
( mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27c),A_27b))
=> ! [V2x: $i] : ( ap(f1921(A_27c,A_27b,A_27a,V1m,V0f),V2x) = ap(V0f,ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2x),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27c),V1m),V2x))) ) ) ) ).
tff(ax_thm_2Efinite__map_2EFMAP__MAP2__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27c),A_27b))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ( ap(ap(c_2Efinite__map_2EFMAP__MAP2(A_27a,A_27b,A_27c),V0f),V1m) = ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),f1921(A_27c,A_27b,A_27a,V1m,V0f)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1m)) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFMAP__MAP2__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27c),A_27b))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFMAP__MAP2(A_27a,A_27b,A_27c),V0f),V1m)) = ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1m) )
& ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1m)))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFMAP__MAP2(A_27a,A_27b,A_27c),V0f),V1m)),V2x) = ap(V0f,ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2x),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27c),V1m),V2x))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFMAP__MAP2__FEMPTY,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27c),A_27b))
=> ( ap(ap(c_2Efinite__map_2EFMAP__MAP2(A_27a,A_27b,A_27c),V0f),c_2Efinite__map_2EFEMPTY(A_27a,A_27c)) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ).
tff(conj_thm_2Efinite__map_2EFMAP__MAP2__FUPDATE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27c),A_27b))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27c)
=> ( ap(ap(c_2Efinite__map_2EFMAP__MAP2(A_27a,A_27b,A_27c),V0f),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27c),V1m),ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2x),V3v))) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFMAP__MAP2(A_27a,A_27b,A_27c),V0f),V1m)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),ap(V0f,ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2x),V3v)))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFEVERY__STRENGTHEN__THM,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)))
& ( ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),V1f))
& p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))) )
=> p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__ELIM,axiom,
! [A_27a: del,A_27b: del,V0k: $i] :
( mem(V0k,A_27a)
=> ! [V1v: $i] :
( mem(V1v,A_27b)
=> ! [V2f: $i] :
( mem(V2f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0k),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2f)))
& ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V2f),V0k) = V1v ) )
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V2f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0k),V1v)) = V2f ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFEVERY__DRESTRICT__COMPL,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ! [V4s: $i] :
( mem(V4s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v))),ap(c_2Epred__set_2ECOMPL(A_27a),V4s))))
<=> ( ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2k),V4s))
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v))) )
& p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f),ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2k),V4s))))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__EQ__FEMPTY,axiom,
! [A_27a: del,A_27b: del,V0h1: $i] :
( mem(V0h1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1h2: $i] :
( mem(V1h2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0h1),V1h2) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) )
<=> ( ( V0h1 = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) )
& ( V1h2 = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__FUNION__EQ,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] :
( ! [V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2f3: $i] :
( mem(V2f3,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f2)))
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f1),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V1f2),V2f3)))
<=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f1),V2f3)) ) ) ) ) )
& ! [V3f1: $i] :
( mem(V3f1,ty_2Efinite__map_2Efmap(A_27c,A_27d))
=> ! [V4f2: $i] :
( mem(V4f2,ty_2Efinite__map_2Efmap(A_27c,A_27d))
=> ! [V5f3: $i] :
( mem(V5f3,ty_2Efinite__map_2Efmap(A_27c,A_27d))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27c),ap(c_2Efinite__map_2EFDOM(A_27c,A_27d),V3f1)),ap(ap(c_2Epred__set_2EDIFF(A_27c),ap(c_2Efinite__map_2EFDOM(A_27c,A_27d),V5f3)),ap(c_2Efinite__map_2EFDOM(A_27c,A_27d),V4f2))))
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27c,A_27d),V3f1),ap(ap(c_2Efinite__map_2EFUNION(A_27c,A_27d),V4f2),V5f3)))
<=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27c,A_27d),V3f1),V4f2)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__FUNION,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2f3: $i] :
( mem(V2f3,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f1),V1f2))
| ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f2)))
& p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f1),V2f3)) ) )
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f1),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V1f2),V2f3))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__FUNION__ID,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] :
( ! [V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f1),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f1),V1f2))) ) )
& ! [V2f1: $i] :
( mem(V2f1,ty_2Efinite__map_2Efmap(A_27c,A_27d))
=> ! [V3f2: $i] :
( mem(V3f2,ty_2Efinite__map_2Efmap(A_27c,A_27d))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27c),ap(c_2Efinite__map_2EFDOM(A_27c,A_27d),V2f1)),ap(c_2Efinite__map_2EFDOM(A_27c,A_27d),V3f2)))
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27c,A_27d),V3f2),ap(ap(c_2Efinite__map_2EFUNION(A_27c,A_27d),V2f1),V3f2))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFEMPTY__SUBMAP,axiom,
! [A_27a: del,A_27b: del,V0h: $i] :
( mem(V0h,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0h),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)))
<=> ( V0h = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__EQ,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2f3: $i] :
( mem(V2f3,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f2)))
& p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2f3))) )
=> ( ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f1),V1f2) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f1),V2f3) )
<=> ( V1f2 = V2f3 ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__EQ__IMPL,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2f3: $i] :
( mem(V2f3,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f2)))
& p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2f3)))
& ( V1f2 = V2f3 ) )
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f1),V1f2) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f1),V2f3) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__FUNION,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g)),V2k) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0f),V2k)),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V1g),V2k)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__COMM,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1g)))
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V1g),V0f) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUNION__ASSOC,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2h: $i] :
( mem(V2h,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V1g),V2h)) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g)),V2h) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__FUNION,axiom,
! [A_27a: del,A_27b: del,V0h: $i] :
( mem(V0h,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1s1: $i] :
( mem(V1s1,arr(A_27a,bool))
=> ! [V2s2: $i] :
( mem(V2s2,arr(A_27a,bool))
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0h),V1s1)),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0h),V2s2)) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0h),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s1),V2s2)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__EQ__FUNION,axiom,
! [A_27a: del,A_27b: del,V0h: $i] :
( mem(V0h,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1h1: $i] :
( mem(V1h1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2h2: $i] :
( mem(V2h2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1h1)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2h2)))
& ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V1h1),V2h2) = V0h ) )
=> ( V2h2 = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0h),ap(c_2Epred__set_2ECOMPL(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1h1))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EIN__FDOM__FOLDR__UNION,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1hL: $i] :
( mem(V1hL,ty_2Elist_2Elist(ty_2Efinite__map_2Efmap(A_27a,A_27b)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(ap(c_2Elist_2EFOLDR(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFUNION(A_27a,A_27b)),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V1hL))))
<=> ? [V2h: $i] :
( mem(V2h,ty_2Efinite__map_2Efmap(A_27a,A_27b))
& p(ap(ap(c_2Ebool_2EIN(ty_2Efinite__map_2Efmap(A_27a,A_27b)),V2h),ap(c_2Elist_2ELIST__TO__SET(ty_2Efinite__map_2Efmap(A_27a,A_27b)),V1hL)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2h))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__FUNION__DRESTRICT__COMPL,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(c_2Epred__set_2ECOMPL(A_27a),V1s))) = V0f ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__IDEMPOT,axiom,
! [A_27a: del,A_27b: del,V0s: $i] :
( mem(V0s,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1vs: $i] :
( mem(V1vs,arr(A_27a,bool))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0s),V1vs)),V1vs) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0s),V1vs) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__FUNION__ABSORPTION,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V1g))
<=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f),V1g) = V1g ) ) ) ) ).
tff(lamtp_f1922,type,
f1922: ( del * del * del * $i * $i * $i ) > $i ).
tff(lameq_f1922,axiom,
! [A_27c: del,A_27b: del,A_27a: del,V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V0m: $i] :
( mem(V0m,arr(arr(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27c),ty_2Efinite__map_2Efmap(A_27b,A_27c))))
=> ! [V2fm: $i] :
( mem(V2fm,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V3x: $i] : ( ap(f1922(A_27c,A_27b,A_27a,V1f,V0m,V2fm),V3x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V2fm))),ap(ap(c_2Emin_2E_3D(A_27c),ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27c),ap(ap(V0m,V1f),V2fm)),ap(V1f,V3x))),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27c),V2fm),V3x))) ) ) ) ) ).
tff(lamtp_f1923,type,
f1923: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1923,axiom,
! [A_27b: del,A_27a: del,A_27c: del,V0m: $i] :
( mem(V0m,arr(arr(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27c),ty_2Efinite__map_2Efmap(A_27b,A_27c))))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2fm: $i] : ( ap(f1923(A_27b,A_27a,A_27c,V0m,V1f),V2fm) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(arr(A_27b,bool)),ap(c_2Efinite__map_2EFDOM(A_27b,A_27c),ap(ap(V0m,V1f),V2fm))),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V2fm)))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V1f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V2fm)),c_2Epred__set_2EUNIV(A_27b))),ap(c_2Ebool_2E_21(A_27a),f1922(A_27c,A_27b,A_27a,V1f,V0m,V2fm)))) ) ) ) ).
tff(lamtp_f1924,type,
f1924: ( del * del * del * $i ) > $i ).
tff(lameq_f1924,axiom,
! [A_27c: del,A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(arr(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27c),ty_2Efinite__map_2Efmap(A_27b,A_27c))))
=> ! [V1f: $i] : ( ap(f1924(A_27c,A_27a,A_27b,V0m),V1f) = ap(c_2Ebool_2E_21(ty_2Efinite__map_2Efmap(A_27a,A_27c)),f1923(A_27b,A_27a,A_27c,V0m,V1f)) ) ) ).
tff(lamtp_f1925,type,
f1925: ( del * del * del ) > $i ).
tff(lameq_f1925,axiom,
! [A_27c: del,A_27b: del,A_27a: del,V0m: $i] : ( ap(f1925(A_27c,A_27b,A_27a),V0m) = ap(c_2Ebool_2E_21(arr(A_27a,A_27b)),f1924(A_27c,A_27a,A_27b,V0m)) ) ).
tff(lamtp_f1926,type,
f1926: ( del * del * del * $i ) > $i ).
tff(lameq_f1926,axiom,
! [A_27b: del,A_27a: del,A_27c: del,V4f: $i] :
( mem(V4f,arr(A_27a,A_27b))
=> ! [V5fm: $i] : ( ap(f1926(A_27b,A_27a,A_27c,V4f),V5fm) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efinite__map_2Efmap(A_27b,A_27c)),ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V4f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V5fm)),c_2Epred__set_2EUNIV(A_27b))),ap(ap(c_2Efinite__map_2Ef__o__f(A_27b,A_27a,A_27c),V5fm),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27b,A_27a),ap(ap(c_2Epred__set_2ELINV(A_27a,A_27b),V4f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V5fm))),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V4f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V5fm))))),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27b,A_27c),c_2Ebool_2EARB(arr(A_27b,A_27c))),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V4f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V5fm)))) ) ) ).
tff(lamtp_f1927,type,
f1927: ( del * del * del ) > $i ).
tff(lameq_f1927,axiom,
! [A_27c: del,A_27a: del,A_27b: del,V4f: $i] : ( ap(f1927(A_27c,A_27a,A_27b),V4f) = f1926(A_27b,A_27a,A_27c,V4f) ) ).
tff(conj_thm_2Efinite__map_2EMAP__KEYS__witness,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : p(ap(ap(c_2Ebool_2ELET(arr(arr(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27c),ty_2Efinite__map_2Efmap(A_27b,A_27c))),bool),f1925(A_27c,A_27b,A_27a)),f1927(A_27c,A_27a,A_27b))) ).
tff(ax_thm_2Efinite__map_2EMAP__KEYS__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ( ( ap(c_2Efinite__map_2EFDOM(A_27b,A_27c),ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),V1fm)) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1fm)) )
& ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1fm)),c_2Epred__set_2EUNIV(A_27b)))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1fm)))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27c),ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),V1fm)),ap(V0f,V2x)) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27c),V1fm),V2x) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EMAP__KEYS__FEMPTY,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),c_2Efinite__map_2EFEMPTY(A_27a,A_27c)) = c_2Efinite__map_2EFEMPTY(A_27b,A_27c) ) ) ).
tff(conj_thm_2Efinite__map_2EMAP__KEYS__FUPDATE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27c)
=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2k),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1fm))),c_2Epred__set_2EUNIV(A_27b)))
=> ( ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27c),V1fm),ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2k),V3v))) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27b,A_27c),ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),V1fm)),ap(ap(c_2Epair_2E_2C(A_27b,A_27c),ap(V0f,V2k)),V3v)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EMAP__KEYS__using__LINV,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1fm)),c_2Epred__set_2EUNIV(A_27b)))
=> ( ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),V1fm) = ap(ap(c_2Efinite__map_2Ef__o__f(A_27b,A_27a,A_27c),V1fm),ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27b,A_27a),ap(ap(c_2Epred__set_2ELINV(A_27a,A_27b),V0f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1fm))),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1fm)))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EMAP__KEYS__BIJ__LINV,axiom,
! [A_27a: del,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1t: $i] :
( mem(V1t,ty_2Efinite__map_2Efmap(ty_2Enum_2Enum,A_27a))
=> ( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
=> ( ap(ap(c_2Efinite__map_2EMAP__KEYS(ty_2Enum_2Enum,ty_2Enum_2Enum,A_27a),V0f),ap(ap(c_2Efinite__map_2EMAP__KEYS(ty_2Enum_2Enum,ty_2Enum_2Enum,A_27a),ap(ap(c_2Epred__set_2ELINV(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),V1t)) = V1t ) ) ) ) ).
tff(lamtp_f1928,type,
f1928: ( del * del * del * $i * $i * $i ) > $i ).
tff(lameq_f1928,axiom,
! [A_27c: del,A_27b: del,A_27a: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27b)
=> ! [V1m: $i] :
( mem(V1m,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V3x: $i] : ( ap(f1928(A_27c,A_27b,A_27a,V0f,V2k,V1m),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27b),V2k),ap(V0f,V3x))),ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1m))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__MAP__KEYS,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V2k: $i] :
( mem(V2k,A_27b)
=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27c),V1m)),c_2Epred__set_2EUNIV(A_27b)))
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27c),ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),V1m)),V2k) = ap(ap(c_2Eoption_2EOPTION__BIND(A_27c,A_27a),ap(c_2Eoption_2Esome(A_27a),f1928(A_27c,A_27b,A_27a,V0f,V2k,V1m))),ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27c),V1m)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFLOOKUP__MAP__KEYS__MAPPED,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),c_2Epred__set_2EUNIV(A_27a)),c_2Epred__set_2EUNIV(A_27b)))
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27c),ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),V1m)),ap(V0f,V2k)) = ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27c),V1m),V2k) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__MAP__KEYS__IMAGE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V2s: $i] :
( mem(V2s,arr(A_27a,bool))
=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),c_2Epred__set_2EUNIV(A_27a)),c_2Epred__set_2EUNIV(A_27b)))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27b,A_27c),ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),V1fm)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s)) = ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27c),V1fm),V2s)) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__MAP__KEYS,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V2s: $i] :
( mem(V2s,A_27a)
=> ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),c_2Epred__set_2EUNIV(A_27a)),c_2Epred__set_2EUNIV(A_27b)))
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27b,A_27c),ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),V1fm)),ap(V0f,V2s)) = ap(ap(c_2Efinite__map_2EMAP__KEYS(A_27a,A_27b,A_27c),V0f),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27c),V1fm),V2s)) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2Efmap__rel__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f1: $i] :
( mem(V1f1,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27c,A_27b))
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),V1f1),V2f2))
<=> ( ( ap(c_2Efinite__map_2EFDOM(A_27c,A_27b),V2f2) = ap(c_2Efinite__map_2EFDOM(A_27c,A_27a),V1f1) )
& ! [V3x: $i] :
( mem(V3x,A_27c)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27c),V3x),ap(c_2Efinite__map_2EFDOM(A_27c,A_27a),V1f1)))
=> p(ap(ap(V0R,ap(ap(c_2Efinite__map_2EFAPPLY(A_27c,A_27a),V1f1),V3x)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27c,A_27b),V2f2),V3x))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__FUPDATE__same,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f1: $i] :
( mem(V1f1,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27c,A_27b))
=> ! [V3v1: $i] :
( mem(V3v1,A_27a)
=> ! [V4v2: $i] :
( mem(V4v2,A_27b)
=> ! [V5k: $i] :
( mem(V5k,A_27c)
=> ( ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),V1f1),V2f2))
& p(ap(ap(V0R,V3v1),V4v2)) )
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),ap(ap(c_2Efinite__map_2EFUPDATE(A_27c,A_27a),V1f1),ap(ap(c_2Epair_2E_2C(A_27c,A_27a),V5k),V3v1))),ap(ap(c_2Efinite__map_2EFUPDATE(A_27c,A_27b),V2f2),ap(ap(c_2Epair_2E_2C(A_27c,A_27b),V5k),V4v2)))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__FUPDATE__LIST__same,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1ls1: $i] :
( mem(V1ls1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27c,A_27a)))
=> ! [V2ls2: $i] :
( mem(V2ls2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27c,A_27b)))
=> ! [V3f1: $i] :
( mem(V3f1,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V4f2: $i] :
( mem(V4f2,ty_2Efinite__map_2Efmap(A_27c,A_27b))
=> ( ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),V3f1),V4f2))
& ( ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27c,A_27a),A_27c),c_2Epair_2EFST(A_27c,A_27a)),V1ls1) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27c,A_27b),A_27c),c_2Epair_2EFST(A_27c,A_27b)),V2ls2) )
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27c,A_27a),A_27a),c_2Epair_2ESND(A_27c,A_27a)),V1ls1)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27c,A_27b),A_27b),c_2Epair_2ESND(A_27c,A_27b)),V2ls2))) )
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27c,A_27a),V3f1),V1ls1)),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27c,A_27b),V4f2),V2ls2))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__FEMPTY,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),c_2Efinite__map_2EFEMPTY(A_27c,A_27a)),c_2Efinite__map_2EFEMPTY(A_27c,A_27b))) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__FEMPTY2,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27a,A_27b),V0R),c_2Efinite__map_2EFEMPTY(A_27b,A_27a)),V1f))
<=> ( V1f = c_2Efinite__map_2EFEMPTY(A_27b,A_27a) ) )
& ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27a,A_27b),V0R),V1f),c_2Efinite__map_2EFEMPTY(A_27b,A_27a)))
<=> ( V1f = c_2Efinite__map_2EFEMPTY(A_27b,A_27a) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__refl,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x: $i] :
( mem(V1x,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( ! [V2x: $i] :
( mem(V2x,A_27a)
=> p(ap(ap(V0R,V2x),V2x)) )
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27a,A_27b),V0R),V1x),V1x)) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__FUNION__rels,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f1: $i] :
( mem(V1f1,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27c,A_27b))
=> ! [V3f3: $i] :
( mem(V3f3,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V4f4: $i] :
( mem(V4f4,ty_2Efinite__map_2Efmap(A_27c,A_27b))
=> ( ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),V1f1),V2f2))
& p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),V3f3),V4f4)) )
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),ap(ap(c_2Efinite__map_2EFUNION(A_27c,A_27a),V1f1),V3f3)),ap(ap(c_2Efinite__map_2EFUNION(A_27c,A_27b),V2f2),V4f4))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__FUPDATE__I,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f1: $i] :
( mem(V1f1,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V2k: $i] :
( mem(V2k,A_27c)
=> ! [V3f2: $i] :
( mem(V3f2,ty_2Efinite__map_2Efmap(A_27c,A_27b))
=> ! [V4v1: $i] :
( mem(V4v1,A_27a)
=> ! [V5v2: $i] :
( mem(V5v2,A_27b)
=> ( ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),ap(ap(c_2Efinite__map_2Efdomsub(A_27c,A_27a),V1f1),V2k)),ap(ap(c_2Efinite__map_2Efdomsub(A_27c,A_27b),V3f2),V2k)))
& p(ap(ap(V0R,V4v1),V5v2)) )
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),ap(ap(c_2Efinite__map_2EFUPDATE(A_27c,A_27a),V1f1),ap(ap(c_2Epair_2E_2C(A_27c,A_27a),V2k),V4v1))),ap(ap(c_2Efinite__map_2EFUPDATE(A_27c,A_27b),V3f2),ap(ap(c_2Epair_2E_2C(A_27c,A_27b),V2k),V5v2)))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__mono,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0R1: $i] :
( mem(V0R1,arr(A_27a,arr(A_27b,bool)))
=> ! [V1R2: $i] :
( mem(V1R2,arr(A_27a,arr(A_27b,bool)))
=> ! [V2f1: $i] :
( mem(V2f1,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V3f2: $i] :
( mem(V3f2,ty_2Efinite__map_2Efmap(A_27c,A_27b))
=> ( ! [V4x: $i] :
( mem(V4x,A_27a)
=> ! [V5y: $i] :
( mem(V5y,A_27b)
=> ( p(ap(ap(V0R1,V4x),V5y))
=> p(ap(ap(V1R2,V4x),V5y)) ) ) )
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R1),V2f1),V3f2))
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V1R2),V2f1),V3f2)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__OPTREL__FLOOKUP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f1: $i] :
( mem(V1f1,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27c,A_27b))
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),V1f1),V2f2))
<=> ! [V3k: $i] :
( mem(V3k,A_27c)
=> p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27b),V0R),ap(ap(c_2Efinite__map_2EFLOOKUP(A_27c,A_27a),V1f1),V3k)),ap(ap(c_2Efinite__map_2EFLOOKUP(A_27c,A_27b),V2f2),V3k))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__FLOOKUP__imp,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f1: $i] :
( mem(V1f1,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27c,A_27b))
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27b,A_27c),V0R),V1f1),V2f2))
=> ( ! [V3k: $i] :
( mem(V3k,A_27c)
=> ( ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27c,A_27a),V1f1),V3k) = c_2Eoption_2ENONE(A_27a) )
=> ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27c,A_27b),V2f2),V3k) = c_2Eoption_2ENONE(A_27b) ) ) )
& ! [V4k: $i] :
( mem(V4k,A_27c)
=> ! [V5v1: $i] :
( mem(V5v1,A_27a)
=> ( ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27c,A_27a),V1f1),V4k) = ap(c_2Eoption_2ESOME(A_27a),V5v1) )
=> ? [V6v2: $i] :
( mem(V6v2,A_27b)
& ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27c,A_27b),V2f2),V4k) = ap(c_2Eoption_2ESOME(A_27b),V6v2) )
& p(ap(ap(V0R,V5v1),V6v2)) ) ) ) ) ) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2Efmap__EQ__UPTO__def,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2vs: $i] :
( mem(V2vs,arr(A_27a,bool))
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),V0f1),V1f2),V2vs))
<=> ( ( ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)),ap(c_2Epred__set_2ECOMPL(A_27a),V2vs)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f2)),ap(c_2Epred__set_2ECOMPL(A_27a),V2vs)) )
& ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)),ap(c_2Epred__set_2ECOMPL(A_27a),V2vs))))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f1),V3x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1f2),V3x) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__EQ__UPTO______EMPTY,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),V0f1),V1f2),c_2Epred__set_2EEMPTY(A_27a)))
<=> ( V0f1 = V1f2 ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__EQ__UPTO______EQ,axiom,
! [A_27a: del,A_27b: del,V0vs: $i] :
( mem(V0vs,arr(A_27a,bool))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),V1f),V1f),V0vs)) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__BOTH,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2ks: $i] :
( mem(V2ks,arr(A_27a,bool))
=> ! [V3k: $i] :
( mem(V3k,A_27a)
=> ! [V4v: $i] :
( mem(V4v,A_27b)
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),V0f1),V1f2),V2ks))
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3k),V4v))),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f2),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3k),V4v))),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2ks),V3k))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__BOTH______NO__DELETE,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2ks: $i] :
( mem(V2ks,arr(A_27a,bool))
=> ! [V3k: $i] :
( mem(V3k,A_27a)
=> ! [V4v: $i] :
( mem(V4v,A_27b)
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),V0f1),V1f2),V2ks))
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3k),V4v))),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1f2),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3k),V4v))),V2ks)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__SING,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2ks: $i] :
( mem(V2ks,arr(A_27a,bool))
=> ! [V3k: $i] :
( mem(V3k,A_27a)
=> ! [V4v: $i] :
( mem(V4v,A_27b)
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),V0f1),V1f2),V2ks))
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__EQ__UPTO(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3k),V4v))),V1f2),ap(ap(c_2Epred__set_2EINSERT(A_27a),V3k),V2ks))) ) ) ) ) ) ) ).
tff(lamtp_f1929,type,
f1929: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f1929,axiom,
! [A_27b: del,A_27a: del,V1vz: $i] :
( mem(V1vz,arr(A_27b,ty_2Enum_2Enum))
=> ! [V2fm: $i] :
( mem(V2fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V0kz: $i] :
( mem(V0kz,arr(A_27a,ty_2Enum_2Enum))
=> ! [V3k: $i] : ( ap(f1929(A_27b,A_27a,V1vz,V2fm,V0kz),V3k) = ap(ap(c_2Earithmetic_2E_2B,ap(V0kz,V3k)),ap(V1vz,ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V2fm),V3k))) ) ) ) ) ).
tff(ax_thm_2Efinite__map_2Efmap__size__def,axiom,
! [A_27a: del,A_27b: del,V0kz: $i] :
( mem(V0kz,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1vz: $i] :
( mem(V1vz,arr(A_27b,ty_2Enum_2Enum))
=> ! [V2fm: $i] :
( mem(V2fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( surj__ty_2Enum_2Enum(ap(ap(ap(c_2Efinite__map_2Efmap__size(A_27a,A_27b),V0kz),V1vz),V2fm)) = surj__ty_2Enum_2Enum(ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),f1929(A_27b,A_27a,V1vz,V2fm,V0kz)),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2fm))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eo__f__FUNION,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27c,A_27b))
=> ! [V1f1: $i] :
( mem(V1f1,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27a,A_27c))
=> ( ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27c,A_27b),V0f),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27c),V1f1),V2f2)) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27c,A_27b),V0f),V1f1)),ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27c,A_27b),V0f),V2f2)) ) ) ) ) ).
tff(lamtp_f1930,type,
f1930: ( del * del * $i ) > $i ).
tff(lameq_f1930,axiom,
! [A_27b: del,A_27a: del,V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3m: $i] : ( ap(f1930(A_27b,A_27a,V2k),V3m) = ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V3m),V2k) ) ) ).
tff(lamtp_f1931,type,
f1931: ( del * del ) > $i ).
tff(lameq_f1931,axiom,
! [A_27b: del,A_27a: del,V2k: $i] : ( ap(f1931(A_27b,A_27a),V2k) = f1930(A_27b,A_27a,V2k) ) ).
tff(conj_thm_2Efinite__map_2EFDOM__FOLDR__DOMSUB,axiom,
! [A_27a: del,A_27b: del,V0ls: $i] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(ap(c_2Elist_2EFOLDR(A_27a,ty_2Efinite__map_2Efmap(A_27a,A_27b)),f1931(A_27b,A_27a)),V1fm),V0ls)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1fm)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls)) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFEVERY__SUBMAP,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2fm0: $i] :
( mem(V2fm0,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),V1fm))
& p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V2fm0),V1fm)) )
=> p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),V2fm0)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFEVERY__ALL__FLOOKUP,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),V1f))
<=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V1f),V2k) = ap(c_2Eoption_2ESOME(A_27b),V3v) )
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__CANCEL,axiom,
! [A_27a: del,A_27b: del,V0ls1: $i] :
( mem(V0ls1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2ls2: $i] :
( mem(V2ls2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ! [V3k: $i] :
( mem(V3k,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3k),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0ls1))))
=> p(ap(ap(c_2Ebool_2EIN(A_27a),V3k),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V2ls2)))) ) )
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1fm),V0ls1)),V2ls2) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1fm),V2ls2) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__EQ__FUNION,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1kv: $i] :
( mem(V1kv,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0fm),V1kv) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V1kv)),V0fm) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__APPEND__COMMUTES,axiom,
! [A_27a: del,A_27b: del,V0l1: $i] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1l2: $i] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2fm: $i] :
( mem(V2fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0l1))),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V1l2))))
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm),V0l1)),V1l2) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm),V1l2)),V0l1) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EIMAGE__FRANGE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(c_2Efinite__map_2EFRANGE(A_27c,A_27a),V1fm)) = ap(c_2Efinite__map_2EFRANGE(A_27c,A_27b),ap(ap(c_2Efinite__map_2Eo__f(A_27c,A_27a,A_27b),V0f),V1fm)) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__mono__FUPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27b)
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0f),V2x)),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V1g),V2x)))
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y))),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V1g),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2ESUBMAP__DOMSUB__gen,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0f),V2k)),V1g))
<=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V0f),V2k)),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V1g),V2k))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDOMSUB__SUBMAP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V1g))
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))) )
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),V1g),V2x))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__DOMSUB,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ( ap(ap(c_2Efinite__map_2Efdomsub(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V1s)),V2k) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V2k)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__SUBSET__SUBMAP__gen,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2s: $i] :
( mem(V2s,arr(A_27a,bool))
=> ! [V3t: $i] :
( mem(V3t,arr(A_27a,bool))
=> ( ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f1),V2s)),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f2),V2s)))
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V3t),V2s)) )
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f1),V3t)),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f2),V3t))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__FUNION__SAME,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0fm),V1s)),V0fm) = V0fm ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__EQ__DRESTRICT__SAME,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f1),V1s) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V2f2),V1s) )
<=> ( ( ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)) = ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2f2)) )
& ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) )
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f1),V3x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V2f2),V3x) ) ) ) ) ) ) ) ) ).
tff(lamtp_f1932,type,
f1932: ( del * del * del * del * $i * $i * $i * $i ) > $i ).
tff(lameq_f1932,axiom,
! [A_27d: del,A_27c: del,A_27a: del,A_27b: del,V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,A_27d)))
=> ! [V6b: $i] :
( mem(V6b,A_27a)
=> ! [V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,A_27c)))
=> ! [V5fm: $i] :
( mem(V5fm,ty_2Efinite__map_2Efmap(A_27c,A_27d))
=> ! [V7c: $i] : ( ap(f1932(A_27d,A_27c,A_27a,A_27b,V1f2,V6b,V0f1,V5fm),V7c) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27c,A_27d),V5fm),ap(ap(c_2Epair_2E_2C(A_27c,A_27d),ap(ap(V0f1,V6b),V7c)),ap(ap(V1f2,V6b),V7c))) ) ) ) ) ) ).
tff(lamtp_f1933,type,
f1933: ( del * del * del * del * $i * $i * $i ) > $i ).
tff(lameq_f1933,axiom,
! [A_27b: del,A_27c: del,A_27d: del,A_27a: del,V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,A_27d)))
=> ! [V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,A_27c)))
=> ! [V5fm: $i] :
( mem(V5fm,ty_2Efinite__map_2Efmap(A_27c,A_27d))
=> ! [V6b: $i] : ( ap(f1933(A_27b,A_27c,A_27d,A_27a,V1f2,V0f1,V5fm),V6b) = f1932(A_27d,A_27c,A_27a,A_27b,V1f2,V6b,V0f1,V5fm) ) ) ) ) ).
tff(lamtp_f1934,type,
f1934: ( del * del * del * del * $i * $i ) > $i ).
tff(lameq_f1934,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,A_27d)))
=> ! [V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,A_27c)))
=> ! [V5fm: $i] : ( ap(f1934(A_27a,A_27b,A_27c,A_27d,V1f2,V0f1),V5fm) = f1933(A_27b,A_27c,A_27d,A_27a,V1f2,V0f1,V5fm) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFOLDL2__FUPDATE__LIST,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,A_27c)))
=> ! [V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,A_27d)))
=> ! [V2bs: $i] :
( mem(V2bs,ty_2Elist_2Elist(A_27a))
=> ! [V3cs: $i] :
( mem(V3cs,ty_2Elist_2Elist(A_27b))
=> ! [V4a: $i] :
( mem(V4a,ty_2Efinite__map_2Efmap(A_27c,A_27d))
=> ( ( surj__ty_2Enum_2Enum(ap(c_2Elist_2ELENGTH(A_27a),V2bs)) = surj__ty_2Enum_2Enum(ap(c_2Elist_2ELENGTH(A_27b),V3cs)) )
=> ( ap(ap(ap(ap(c_2Elist_2EFOLDL2(ty_2Efinite__map_2Efmap(A_27c,A_27d),A_27a,A_27b),f1934(A_27a,A_27b,A_27c,A_27d,V1f2,V0f1)),V4a),V2bs),V3cs) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27c,A_27d),V4a),ap(c_2Elist_2EZIP(A_27c,A_27d),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27d)),ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V0f1),V2bs),V3cs)),ap(ap(ap(c_2Elist_2EMAP2(A_27d,A_27a,A_27b),V1f2),V2bs),V3cs)))) ) ) ) ) ) ) ) ).
tff(lamtp_f1935,type,
f1935: ( del * del * del * del * del * $i * $i * $i * $i * $i ) > $i ).
tff(lameq_f1935,axiom,
! [A_27e: del,A_27d: del,A_27b: del,A_27a: del,A_27c: del,V6b: $i] :
( mem(V6b,A_27a)
=> ! [V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,arr(A_27c,A_27e))))
=> ! [V7c: $i] :
( mem(V7c,A_27b)
=> ! [V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,arr(A_27c,A_27d))))
=> ! [V5fm: $i] :
( mem(V5fm,ty_2Efinite__map_2Efmap(A_27d,A_27e))
=> ! [V8d: $i] : ( ap(f1935(A_27e,A_27d,A_27b,A_27a,A_27c,V6b,V1f2,V7c,V0f1,V5fm),V8d) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27d,A_27e),V5fm),ap(ap(c_2Epair_2E_2C(A_27d,A_27e),ap(ap(ap(V0f1,V6b),V7c),V8d)),ap(ap(ap(V1f2,V6b),V7c),V8d))) ) ) ) ) ) ) ).
tff(lamtp_f1936,type,
f1936: ( del * del * del * del * del * $i * $i * $i * $i ) > $i ).
tff(lameq_f1936,axiom,
! [A_27c: del,A_27a: del,A_27d: del,A_27e: del,A_27b: del,V6b: $i] :
( mem(V6b,A_27a)
=> ! [V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,arr(A_27c,A_27e))))
=> ! [V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,arr(A_27c,A_27d))))
=> ! [V5fm: $i] :
( mem(V5fm,ty_2Efinite__map_2Efmap(A_27d,A_27e))
=> ! [V7c: $i] : ( ap(f1936(A_27c,A_27a,A_27d,A_27e,A_27b,V6b,V1f2,V0f1,V5fm),V7c) = f1935(A_27e,A_27d,A_27b,A_27a,A_27c,V6b,V1f2,V7c,V0f1,V5fm) ) ) ) ) ) ).
tff(lamtp_f1937,type,
f1937: ( del * del * del * del * del * $i * $i * $i ) > $i ).
tff(lameq_f1937,axiom,
! [A_27b: del,A_27d: del,A_27e: del,A_27c: del,A_27a: del,V5fm: $i] :
( mem(V5fm,ty_2Efinite__map_2Efmap(A_27d,A_27e))
=> ! [V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,arr(A_27c,A_27d))))
=> ! [V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,arr(A_27c,A_27e))))
=> ! [V6b: $i] : ( ap(f1937(A_27b,A_27d,A_27e,A_27c,A_27a,V5fm,V0f1,V1f2),V6b) = ap(c_2Epair_2EUNCURRY(A_27b,A_27c,ty_2Efinite__map_2Efmap(A_27d,A_27e)),f1936(A_27c,A_27a,A_27d,A_27e,A_27b,V6b,V1f2,V0f1,V5fm)) ) ) ) ) ).
tff(lamtp_f1938,type,
f1938: ( del * del * del * del * del * $i * $i ) > $i ).
tff(lameq_f1938,axiom,
! [A_27a: del,A_27c: del,A_27b: del,A_27d: del,A_27e: del,V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,arr(A_27c,A_27d))))
=> ! [V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,arr(A_27c,A_27e))))
=> ! [V5fm: $i] : ( ap(f1938(A_27a,A_27c,A_27b,A_27d,A_27e,V0f1,V1f2),V5fm) = f1937(A_27b,A_27d,A_27e,A_27c,A_27a,V5fm,V0f1,V1f2) ) ) ) ).
tff(lamtp_f1939,type,
f1939: ( del * del * del * del * $i ) > $i ).
tff(lameq_f1939,axiom,
! [A_27b: del,A_27d: del,A_27c: del,A_27a: del,V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,arr(A_27c,A_27d))))
=> ! [V9b: $i] : ( ap(f1939(A_27b,A_27d,A_27c,A_27a,V0f1),V9b) = ap(c_2Epair_2EUNCURRY(A_27b,A_27c,A_27d),ap(V0f1,V9b)) ) ) ).
tff(lamtp_f1940,type,
f1940: ( del * del * del * del * $i ) > $i ).
tff(lameq_f1940,axiom,
! [A_27b: del,A_27e: del,A_27c: del,A_27a: del,V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,arr(A_27c,A_27e))))
=> ! [V10b: $i] : ( ap(f1940(A_27b,A_27e,A_27c,A_27a,V1f2),V10b) = ap(c_2Epair_2EUNCURRY(A_27b,A_27c,A_27e),ap(V1f2,V10b)) ) ) ).
tff(conj_thm_2Efinite__map_2EFOLDL2__FUPDATE__LIST__paired,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,V0f1: $i] :
( mem(V0f1,arr(A_27a,arr(A_27b,arr(A_27c,A_27d))))
=> ! [V1f2: $i] :
( mem(V1f2,arr(A_27a,arr(A_27b,arr(A_27c,A_27e))))
=> ! [V2bs: $i] :
( mem(V2bs,ty_2Elist_2Elist(A_27a))
=> ! [V3cs: $i] :
( mem(V3cs,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27b,A_27c)))
=> ! [V4a: $i] :
( mem(V4a,ty_2Efinite__map_2Efmap(A_27d,A_27e))
=> ( ( surj__ty_2Enum_2Enum(ap(c_2Elist_2ELENGTH(A_27a),V2bs)) = surj__ty_2Enum_2Enum(ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27b,A_27c)),V3cs)) )
=> ( ap(ap(ap(ap(c_2Elist_2EFOLDL2(ty_2Efinite__map_2Efmap(A_27d,A_27e),A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),f1938(A_27a,A_27c,A_27b,A_27d,A_27e,V0f1,V1f2)),V4a),V2bs),V3cs) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27d,A_27e),V4a),ap(c_2Elist_2EZIP(A_27d,A_27e),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27d),ty_2Elist_2Elist(A_27e)),ap(ap(ap(c_2Elist_2EMAP2(A_27d,A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),f1939(A_27b,A_27d,A_27c,A_27a,V0f1)),V2bs),V3cs)),ap(ap(ap(c_2Elist_2EMAP2(A_27e,A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),f1940(A_27b,A_27e,A_27c,A_27a,V1f2)),V2bs),V3cs)))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__FUNION__SUBSET,axiom,
! [A_27a: del,A_27b: del,V0s2: $i] :
( mem(V0s2,arr(A_27a,bool))
=> ! [V1s1: $i] :
( mem(V1s1,arr(A_27a,bool))
=> ! [V2f: $i] :
( mem(V2f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3g: $i] :
( mem(V3g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s2),V1s1))
=> ? [V4h: $i] :
( mem(V4h,ty_2Efinite__map_2Efmap(A_27a,A_27b))
& ( ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V2f),V1s1)),V3g) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V2f),V0s2)),V4h) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__APPLY__NOT__MEM__matchable,axiom,
! [A_27a: del,A_27b: del,V0kvl: $i] :
( mem(V0kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2k),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl))))
& ( V3v = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V1f),V2k) ) )
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1f),V0kvl)),V2k) = V3v ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__APPLY__HO__THM,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V2kvl: $i] :
( mem(V2kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V3k: $i] :
( mem(V3k,A_27b)
=> ( ( ? [V4n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4n)),ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27b,A_27a)),V2kvl)))
& ( V3k = ap(ap(c_2Elist_2EEL(A_27b),inj__ty_2Enum_2Enum(V4n)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST(A_27b,A_27a)),V2kvl)) )
& p(ap(V0P,ap(ap(c_2Elist_2EEL(A_27a),inj__ty_2Enum_2Enum(V4n)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27b,A_27a),A_27a),c_2Epair_2ESND(A_27b,A_27a)),V2kvl))))
& ! [V5m: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4n)),inj__ty_2Enum_2Enum(V5m)))
& p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V5m)),ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27b,A_27a)),V2kvl))) )
=> ( ap(ap(c_2Elist_2EEL(A_27b),inj__ty_2Enum_2Enum(V5m)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST(A_27b,A_27a)),V2kvl)) != V3k ) ) )
| ( ~ p(ap(ap(c_2Ebool_2EIN(A_27b),V3k),ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST(A_27b,A_27a)),V2kvl))))
& p(ap(V0P,ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27a),V1f),V3k))) ) )
=> p(ap(V0P,ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27a),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27b,A_27a),V1f),V2kvl)),V3k))) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__SAME__APPLY,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1kv: $i] :
( mem(V1kv,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V2fm1: $i] :
( mem(V2fm1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3fm2: $i] :
( mem(V3fm2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( ( V0x = ap(c_2Epair_2EFST(A_27a,A_27b),V1kv) )
| ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V2fm1),V0x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V3fm2),V0x) ) )
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V2fm1),V1kv)),V0x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V3fm2),V1kv)),V0x) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__SAME__LIST__APPLY,axiom,
! [A_27a: del,A_27b: del,V0kvl: $i] :
( mem(V0kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1fm1: $i] :
( mem(V1fm1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2fm2: $i] :
( mem(V2fm2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl))))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1fm1),V0kvl)),V3x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm2),V0kvl)),V3x) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__APPLY__MEM,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1ls: $i] :
( mem(V1ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V2k: $i] :
( mem(V2k,A_27b)
=> ! [V3v: $i] :
( mem(V3v,A_27a)
=> ! [V4fm: $i] :
( mem(V4fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( ( p(ap(c_2Elist_2EALL__DISTINCT(A_27b),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST(A_27b,A_27a)),V1ls)))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27b,A_27a)),ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V2k),V3v)),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27b,A_27a)),V1ls)))
& p(ap(V0P,V3v)) )
=> p(ap(V0P,ap(ap(c_2Efinite__map_2EFAPPLY(A_27b,A_27a),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27b,A_27a),V4fm),V1ls)),V2k))) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__REVERSE,axiom,
! [A_27a: del,A_27b: del,V0ls: $i] :
( mem(V0ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0ls)))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1fm),ap(c_2Elist_2EREVERSE(ty_2Epair_2Eprod(A_27a,A_27b)),V0ls)) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1fm),V0ls) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EIN__FRANGE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1v: $i] :
( mem(V1v,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27b),V1v),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),V0f)))
<=> ? [V2k: $i] :
( mem(V2k,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2k),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
& ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V2k) = V1v ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EIN__FRANGE__FLOOKUP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1v: $i] :
( mem(V1v,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27b),V1v),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),V0f)))
<=> ? [V2k: $i] :
( mem(V2k,A_27a)
& ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0f),V2k) = ap(c_2Eoption_2ESOME(A_27b),V1v) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__FUPDATE__LIST__SUBSET,axiom,
! [A_27a: del,A_27b: del,V0ls: $i] :
( mem(V0ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1fm),V0ls))),ap(ap(c_2Epred__set_2EUNION(A_27b),ap(c_2Efinite__map_2EFRANGE(A_27a,A_27b),V1fm)),ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),V0ls))))) ) ) ).
tff(conj_thm_2Efinite__map_2EIN__FRANGE__FUPDATE__LIST__suff,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1P: $i] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2ls: $i] :
( mem(V2ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27b,A_27a)))
=> ( ( ! [V3v: $i] :
( mem(V3v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0fm)))
=> p(ap(V1P,V3v)) ) )
& ! [V4v: $i] :
( mem(V4v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4v),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27b,A_27a),A_27a),c_2Epair_2ESND(A_27b,A_27a)),V2ls))))
=> p(ap(V1P,V4v)) ) ) )
=> ! [V5v: $i] :
( mem(V5v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V5v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27b,A_27a),V0fm),V2ls))))
=> p(ap(V1P,V5v)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__FUNION__SUBSET,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),ap(ap(c_2Efinite__map_2EFUNION(A_27b,A_27a),V0f1),V1f2))),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0f1)),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V1f2)))) ) ) ).
tff(conj_thm_2Efinite__map_2EIN__FRANGE__FUNION__suff,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1P: $i] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2f2: $i] :
( mem(V2f2,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( ( ! [V3v: $i] :
( mem(V3v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0f1)))
=> p(ap(V1P,V3v)) ) )
& ! [V4v: $i] :
( mem(V4v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V2f2)))
=> p(ap(V1P,V4v)) ) ) )
=> ! [V5v: $i] :
( mem(V5v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V5v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),ap(ap(c_2Efinite__map_2EFUNION(A_27b,A_27a),V0f1),V2f2))))
=> p(ap(V1P,V5v)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__DOMSUB__SUBSET,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1k: $i] :
( mem(V1k,A_27b)
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),ap(ap(c_2Efinite__map_2Efdomsub(A_27b,A_27a),V0fm),V1k))),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0fm))) ) ) ).
tff(conj_thm_2Efinite__map_2EIN__FRANGE__DOMSUB__suff,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1P: $i] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2k: $i] :
( mem(V2k,A_27b)
=> ( ! [V3v: $i] :
( mem(V3v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0fm)))
=> p(ap(V1P,V3v)) ) )
=> ! [V4v: $i] :
( mem(V4v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),ap(ap(c_2Efinite__map_2Efdomsub(A_27b,A_27a),V0fm),V2k))))
=> p(ap(V1P,V4v)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EIN__FRANGE__DRESTRICT__suff,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1P: $i] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2s: $i] :
( mem(V2s,arr(A_27b,bool))
=> ( ! [V3v: $i] :
( mem(V3v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0fm)))
=> p(ap(V1P,V3v)) ) )
=> ! [V4v: $i] :
( mem(V4v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27b,A_27a),V0fm),V2s))))
=> p(ap(V1P,V4v)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__FUPDATE__SUBSET,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1kv: $i] :
( mem(V1kv,ty_2Epair_2Eprod(A_27b,A_27a))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),ap(ap(c_2Efinite__map_2EFUPDATE(A_27b,A_27a),V0fm),V1kv))),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0fm)),ap(ap(c_2Epred__set_2EINSERT(A_27a),ap(c_2Epair_2ESND(A_27b,A_27a),V1kv)),c_2Epred__set_2EEMPTY(A_27a))))) ) ) ).
tff(conj_thm_2Efinite__map_2EIN__FRANGE__FUPDATE__suff,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1P: $i] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2kv: $i] :
( mem(V2kv,ty_2Epair_2Eprod(A_27b,A_27a))
=> ( ( ! [V3v: $i] :
( mem(V3v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0fm)))
=> p(ap(V1P,V3v)) ) )
& p(ap(V1P,ap(c_2Epair_2ESND(A_27b,A_27a),V2kv))) )
=> ! [V4v: $i] :
( mem(V4v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),ap(ap(c_2Efinite__map_2EFUPDATE(A_27b,A_27a),V0fm),V2kv))))
=> p(ap(V1P,V4v)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EIN__FRANGE__o__f__suff,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1P: $i] :
( mem(V1P,arr(A_27c,bool))
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,A_27c))
=> ( ! [V3v: $i] :
( mem(V3v,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0fm)))
=> p(ap(V1P,ap(V2f,V3v))) ) )
=> ! [V4v: $i] :
( mem(V4v,A_27c)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27c),V4v),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27c),ap(ap(c_2Efinite__map_2Eo__f(A_27b,A_27a,A_27c),V2f),V0fm))))
=> p(ap(V1P,V4v)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__SUBMAP__gen,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2P: $i] :
( mem(V2P,arr(A_27a,bool))
=> ( p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),V0f),V1g))
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),V2P)),V1g)) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__SUBSET__SUBMAP,axiom,
! [A_27a: del,A_27b: del,V0s1: $i] :
( mem(V0s1,arr(A_27a,bool))
=> ! [V1s2: $i] :
( mem(V1s2,arr(A_27a,bool))
=> ! [V2f: $i] :
( mem(V2f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s1),V1s2))
=> p(ap(ap(c_2Efinite__map_2ESUBMAP(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V2f),V0s1)),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V2f),V1s2))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICTED__FUNION,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2s: $i] :
( mem(V2s,arr(A_27a,bool))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V0f1),V1f2)),V2s) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f1),V2s)),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f2),ap(ap(c_2Epred__set_2EDIFF(A_27a),V2s),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFRANGE__DRESTRICT__SUBSET,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V1s: $i] :
( mem(V1s,arr(A_27b,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27b,A_27a),V0fm),V1s))),ap(c_2Efinite__map_2EFRANGE(A_27b,A_27a),V0fm))) ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__FDOM,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)) = V0f ) ) ).
tff(conj_thm_2Efinite__map_2EDRESTRICT__SUBSET,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2s: $i] :
( mem(V2s,arr(A_27a,bool))
=> ! [V3t: $i] :
( mem(V3t,arr(A_27a,bool))
=> ( ( ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f1),V2s) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f2),V2s) )
& p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V3t),V2s)) )
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0f1),V3t) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f2),V3t) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Ef__o__f__FUPDATE__compose,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f1: $i] :
( mem(V0f1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1f2: $i] :
( mem(V1f2,ty_2Efinite__map_2Efmap(A_27c,A_27a))
=> ! [V2k: $i] :
( mem(V2k,A_27c)
=> ! [V3x: $i] :
( mem(V3x,A_27a)
=> ! [V4v: $i] :
( mem(V4v,A_27b)
=> ( ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f1)))
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFRANGE(A_27c,A_27a),V1f2))) )
=> ( ap(ap(c_2Efinite__map_2Ef__o__f(A_27c,A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0f1),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V4v))),ap(ap(c_2Efinite__map_2EFUPDATE(A_27c,A_27a),V1f2),ap(ap(c_2Epair_2E_2C(A_27c,A_27a),V2k),V3x))) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27c,A_27b),ap(ap(c_2Efinite__map_2Ef__o__f(A_27c,A_27a,A_27b),V0f1),V1f2)),ap(ap(c_2Epair_2E_2C(A_27c,A_27b),V2k),V4v)) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__trans,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,A_27a)
=> ( ( p(ap(ap(V0R,V1x),V2y))
& p(ap(ap(V0R,V2y),V3z)) )
=> p(ap(ap(V0R,V1x),V3z)) ) ) ) )
=> ! [V4x: $i] :
( mem(V4x,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V5y: $i] :
( mem(V5y,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V6z: $i] :
( mem(V6z,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27a,A_27b),V0R),V4x),V5y))
& p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27a,A_27b),V0R),V5y),V6z)) )
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27a,A_27b),V0R),V4x),V6z)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__rel__sym,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( p(ap(ap(V0R,V1x),V2y))
=> p(ap(ap(V0R,V2y),V1x)) ) ) )
=> ! [V3x: $i] :
( mem(V3x,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ! [V4y: $i] :
( mem(V4y,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27a,A_27b),V0R),V3x),V4y))
=> p(ap(ap(ap(c_2Efinite__map_2Efmap__rel(A_27a,A_27a,A_27b),V0R),V4y),V3x)) ) ) ) ) ) ).
tff(lamtp_f1941,type,
f1941: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1941,axiom,
! [A_27c: del,A_27a: del,A_27b: del,V1f: $i] :
( mem(V1f,arr(A_27b,A_27c))
=> ! [V4a: $i] :
( mem(V4a,A_27a)
=> ! [V5b: $i] : ( ap(f1941(A_27c,A_27a,A_27b,V1f,V4a),V5b) = ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V4a),ap(V1f,V5b)) ) ) ) ).
tff(lamtp_f1942,type,
f1942: ( del * del * del * $i ) > $i ).
tff(lameq_f1942,axiom,
! [A_27b: del,A_27c: del,A_27a: del,V1f: $i] :
( mem(V1f,arr(A_27b,A_27c))
=> ! [V4a: $i] : ( ap(f1942(A_27b,A_27c,A_27a,V1f),V4a) = f1941(A_27c,A_27a,A_27b,V1f,V4a) ) ) ).
tff(conj_thm_2Efinite__map_2Efupdate__list__map,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0l: $i] :
( mem(V0l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27b,A_27c))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27d)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V0l))))
=> ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27c),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27c),c_2Efinite__map_2EFEMPTY(A_27a,A_27c)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27c)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(A_27a,A_27c)),f1942(A_27b,A_27c,A_27a,V1f))),V0l))),V2x) = ap(V1f,ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V0l)),V2x)) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efdom__fupdate__list2,axiom,
! [A_27a: del,A_27b: del,V0kvl: $i] :
( mem(V0kvl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1fm: $i] :
( mem(V1fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V1fm),V0kvl)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1fm)),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl)))),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0kvl))) ) ) ) ).
tff(conj_thm_2Efinite__map_2Eflookup__thm,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2v: $i] :
( mem(V2v,A_27b)
=> ( ( ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0f),V1x) = c_2Eoption_2ENONE(A_27b) )
<=> ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f))) )
& ( ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0f),V1x) = ap(c_2Eoption_2ESOME(A_27b),V2v) )
<=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0f)))
& ( ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),V0f),V1x) = V2v ) ) ) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__EQ__FUPDATE__LIST,axiom,
! [A_27a: del,A_27b: del,V0fm: $i] :
( mem(V0fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1kv: $i] :
( mem(V1kv,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V0fm),V1kv) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V0fm),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),V1kv),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)))) ) ) ) ).
tff(ax_thm_2Efinite__map_2Efmap__inverse__def,axiom,
! [A_27a: del,A_27b: del,V0m1: $i] :
( mem(V0m1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1m2: $i] :
( mem(V1m2,ty_2Efinite__map_2Efmap(A_27b,A_27a))
=> ( p(ap(ap(c_2Efinite__map_2Efmap__inverse(A_27a,A_27b),V0m1),V1m2))
<=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2k),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V0m1)))
=> ? [V3v: $i] :
( mem(V3v,A_27b)
& ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27a,A_27b),V0m1),V2k) = ap(c_2Eoption_2ESOME(A_27b),V3v) )
& ( ap(ap(c_2Efinite__map_2EFLOOKUP(A_27b,A_27a),V1m2),V3v) = ap(c_2Eoption_2ESOME(A_27a),V2k) ) ) ) ) ) ) ) ).
tff(lamtp_f1943,type,
f1943: ( del * del * $i * $i ) > $i ).
tff(lameq_f1943,axiom,
! [A_27a: del,A_27b: del,V3v: $i] :
( mem(V3v,A_27b)
=> ! [V2k: $i] :
( mem(V2k,A_27a)
=> ! [V4env: $i] : ( ap(f1943(A_27a,A_27b,V3v,V2k),V4env) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V4env),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2k),V3v)) ) ) ) ).
tff(lamtp_f1944,type,
f1944: ( del * del * $i ) > $i ).
tff(lameq_f1944,axiom,
! [A_27a: del,A_27b: del,V2k: $i] :
( mem(V2k,A_27a)
=> ! [V3v: $i] : ( ap(f1944(A_27a,A_27b,V2k),V3v) = f1943(A_27a,A_27b,V3v,V2k) ) ) ).
tff(lamtp_f1945,type,
f1945: ( del * del ) > $i ).
tff(lameq_f1945,axiom,
! [A_27b: del,A_27a: del,V2k: $i] : ( ap(f1945(A_27b,A_27a),V2k) = f1944(A_27a,A_27b,V2k) ) ).
tff(conj_thm_2Efinite__map_2Efupdate__list__foldr,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1l: $i] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ap(ap(ap(c_2Elist_2EFOLDR(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b))),f1945(A_27b,A_27a))),V0m),V1l) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V0m),ap(c_2Elist_2EREVERSE(ty_2Epair_2Eprod(A_27a,A_27b)),V1l)) ) ) ) ).
tff(lamtp_f1946,type,
f1946: ( del * del * $i * $i ) > $i ).
tff(lameq_f1946,axiom,
! [A_27a: del,A_27b: del,V3k: $i] :
( mem(V3k,A_27a)
=> ! [V2env: $i] :
( mem(V2env,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V4v: $i] : ( ap(f1946(A_27a,A_27b,V3k,V2env),V4v) = ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),V2env),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3k),V4v)) ) ) ) ).
tff(lamtp_f1947,type,
f1947: ( del * del * $i ) > $i ).
tff(lameq_f1947,axiom,
! [A_27b: del,A_27a: del,V2env: $i] :
( mem(V2env,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3k: $i] : ( ap(f1947(A_27b,A_27a,V2env),V3k) = f1946(A_27a,A_27b,V3k,V2env) ) ) ).
tff(lamtp_f1948,type,
f1948: ( del * del ) > $i ).
tff(lameq_f1948,axiom,
! [A_27b: del,A_27a: del,V2env: $i] : ( ap(f1948(A_27b,A_27a),V2env) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Efinite__map_2Efmap(A_27a,A_27b)),f1947(A_27b,A_27a,V2env)) ) ).
tff(conj_thm_2Efinite__map_2Efupdate__list__foldl,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1l: $i] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ap(ap(ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b)),f1948(A_27b,A_27a)),V0m),V1l) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V0m),V1l) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efmap__to__list,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ? [V1l: $i] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
& p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V1l)))
& ( V0m = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V1l) ) ) ) ).
tff(conj_thm_2Efinite__map_2Edisjoint__drestrict,axiom,
! [A_27a: del,A_27b: del,V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1m)))
=> ( ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1m),ap(c_2Epred__set_2ECOMPL(A_27a),V0s)) = V1m ) ) ) ) ).
tff(conj_thm_2Efinite__map_2Edrestrict__iter__list,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V1l: $i] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(ap(c_2Elist_2EFOLDR(A_27a,ty_2Efinite__map_2Efmap(A_27a,A_27b)),f1931(A_27b,A_27a)),V0m),V1l) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V0m),ap(c_2Epred__set_2ECOMPL(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))) ) ) ) ).
tff(conj_thm_2Efinite__map_2Efevery__funion,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))
=> ! [V1m1: $i] :
( mem(V1m1,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2m2: $i] :
( mem(V2m2,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),V1m1))
& p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),V2m2)) )
=> p(ap(ap(c_2Efinite__map_2EFEVERY(A_27a,A_27b),V0P),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V1m1),V2m2))) ) ) ) ) ).
tff(conj_thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__PERM,axiom,
! [A_27a: del,A_27b: del,V0ls: $i] :
( mem(V0ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1ls_27: $i] :
( mem(V1ls_27,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2fm: $i] :
( mem(V2fm,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ( ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0ls)))
& p(ap(ap(c_2Esorting_2EPERM(ty_2Epair_2Eprod(A_27a,A_27b)),V0ls),V1ls_27)) )
=> ( ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm),V0ls) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),V2fm),V1ls_27) ) ) ) ) ) ).
%------------------------------------------------------------------------------