ITP001 Axioms: ITP047_5.ax
%------------------------------------------------------------------------------
% File : ITP047_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 : fcp_2.ax [Gau20]
% : HL4047_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 202 ( 48 unt; 63 typ; 0 def)
% Number of atoms : 1692 ( 139 equ)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 287 ( 7 ~; 7 |; 47 &)
% ( 18 <=>; 208 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1273 (1273 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 134 ( 63 >; 71 *; 0 +; 0 <<)
% Number of predicates : 64 ( 63 usr; 22 prp; 0-2 aty)
% Number of functors : 63 ( 63 usr; 0 con; 1-5 aty)
% Number of variables : 496 ( 480 !; 16 ?; 496 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_ty_2Efcp_2Ebit0,type,
ty_2Efcp_2Ebit0: del > del ).
tff(tp_ty_2Efcp_2Ebit1,type,
ty_2Efcp_2Ebit1: del > del ).
tff(tp_ty_2Efcp_2Ecart,type,
ty_2Efcp_2Ecart: ( del * del ) > del ).
tff(tp_ty_2Efcp_2Efinite__image,type,
ty_2Efcp_2Efinite__image: del > del ).
tff(tp_c_2Efcp_2E_3A_2B,type,
c_2Efcp_2E_3A_2B: ( del * del ) > $i ).
tff(mem_c_2Efcp_2E_3A_2B,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2E_3A_2B(A_27a,A_27b),arr(ty_2Enum_2Enum,arr(A_27a,arr(ty_2Efcp_2Ecart(A_27a,A_27b),ty_2Efcp_2Ecart(A_27a,A_27b))))) ).
tff(tp_c_2Efcp_2EBIT0A,type,
c_2Efcp_2EBIT0A: del > $i ).
tff(mem_c_2Efcp_2EBIT0A,axiom,
! [A_27a: del] : mem(c_2Efcp_2EBIT0A(A_27a),arr(A_27a,ty_2Efcp_2Ebit0(A_27a))) ).
tff(tp_c_2Efcp_2EBIT0B,type,
c_2Efcp_2EBIT0B: del > $i ).
tff(mem_c_2Efcp_2EBIT0B,axiom,
! [A_27a: del] : mem(c_2Efcp_2EBIT0B(A_27a),arr(A_27a,ty_2Efcp_2Ebit0(A_27a))) ).
tff(tp_c_2Efcp_2EBIT1A,type,
c_2Efcp_2EBIT1A: del > $i ).
tff(mem_c_2Efcp_2EBIT1A,axiom,
! [A_27a: del] : mem(c_2Efcp_2EBIT1A(A_27a),arr(A_27a,ty_2Efcp_2Ebit1(A_27a))) ).
tff(tp_c_2Efcp_2EBIT1B,type,
c_2Efcp_2EBIT1B: del > $i ).
tff(mem_c_2Efcp_2EBIT1B,axiom,
! [A_27a: del] : mem(c_2Efcp_2EBIT1B(A_27a),arr(A_27a,ty_2Efcp_2Ebit1(A_27a))) ).
tff(tp_c_2Efcp_2EBIT1C,type,
c_2Efcp_2EBIT1C: del > $i ).
tff(mem_c_2Efcp_2EBIT1C,axiom,
! [A_27a: del] : mem(c_2Efcp_2EBIT1C(A_27a),ty_2Efcp_2Ebit1(A_27a)) ).
tff(tp_c_2Efcp_2EFCP,type,
c_2Efcp_2EFCP: ( del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2EFCP(A_27a,A_27b),arr(arr(ty_2Enum_2Enum,A_27a),ty_2Efcp_2Ecart(A_27a,A_27b))) ).
tff(tp_c_2Efcp_2EFCP__CONCAT,type,
c_2Efcp_2EFCP__CONCAT: ( del * del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP__CONCAT,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efcp_2EFCP__CONCAT(A_27a,A_27b,A_27c),arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(ty_2Efcp_2Ecart(A_27a,A_27c),ty_2Efcp_2Ecart(A_27a,ty_2Esum_2Esum(A_27b,A_27c))))) ).
tff(tp_c_2Efcp_2EFCP__CONS,type,
c_2Efcp_2EFCP__CONS: ( del * del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP__CONS,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efcp_2EFCP__CONS(A_27a,A_27b,A_27c),arr(A_27a,arr(ty_2Efcp_2Ecart(A_27a,A_27b),ty_2Efcp_2Ecart(A_27a,A_27c)))) ).
tff(tp_c_2Efcp_2EFCP__EVERY,type,
c_2Efcp_2EFCP__EVERY: ( del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP__EVERY,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2EFCP__EVERY(A_27a,A_27b),arr(arr(A_27b,bool),arr(ty_2Efcp_2Ecart(A_27b,A_27a),bool))) ).
tff(tp_c_2Efcp_2EFCP__EXISTS,type,
c_2Efcp_2EFCP__EXISTS: ( del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP__EXISTS,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2EFCP__EXISTS(A_27a,A_27b),arr(arr(A_27b,bool),arr(ty_2Efcp_2Ecart(A_27b,A_27a),bool))) ).
tff(tp_c_2Efcp_2EFCP__FOLD,type,
c_2Efcp_2EFCP__FOLD: ( del * del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP__FOLD,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efcp_2EFCP__FOLD(A_27a,A_27b,A_27c),arr(arr(A_27b,arr(A_27a,A_27b)),arr(A_27b,arr(ty_2Efcp_2Ecart(A_27a,A_27c),A_27b)))) ).
tff(tp_c_2Efcp_2EFCP__HD,type,
c_2Efcp_2EFCP__HD: ( del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP__HD,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2EFCP__HD(A_27a,A_27b),arr(ty_2Efcp_2Ecart(A_27a,A_27b),A_27a)) ).
tff(tp_c_2Efcp_2EFCP__MAP,type,
c_2Efcp_2EFCP__MAP: ( del * del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP__MAP,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efcp_2EFCP__MAP(A_27a,A_27b,A_27c),arr(arr(A_27a,A_27b),arr(ty_2Efcp_2Ecart(A_27a,A_27c),ty_2Efcp_2Ecart(A_27b,A_27c)))) ).
tff(tp_c_2Efcp_2EFCP__TL,type,
c_2Efcp_2EFCP__TL: ( del * del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP__TL,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efcp_2EFCP__TL(A_27a,A_27b,A_27c),arr(ty_2Efcp_2Ecart(A_27a,A_27c),ty_2Efcp_2Ecart(A_27a,A_27b))) ).
tff(tp_c_2Efcp_2EFCP__ZIP,type,
c_2Efcp_2EFCP__ZIP: ( del * del * del ) > $i ).
tff(mem_c_2Efcp_2EFCP__ZIP,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efcp_2EFCP__ZIP(A_27a,A_27b,A_27c),arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(ty_2Efcp_2Ecart(A_27c,A_27b),ty_2Efcp_2Ecart(ty_2Epair_2Eprod(A_27a,A_27c),A_27b)))) ).
tff(tp_c_2Efcp_2EHAS__SIZE,type,
c_2Efcp_2EHAS__SIZE: del > $i ).
tff(mem_c_2Efcp_2EHAS__SIZE,axiom,
! [A_27a: del] : mem(c_2Efcp_2EHAS__SIZE(A_27a),arr(arr(A_27a,bool),arr(ty_2Enum_2Enum,bool))) ).
tff(tp_c_2Efcp_2EL2V,type,
c_2Efcp_2EL2V: ( del * del ) > $i ).
tff(mem_c_2Efcp_2EL2V,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2EL2V(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27a),ty_2Efcp_2Ecart(A_27a,A_27b))) ).
tff(tp_c_2Efcp_2EV2L,type,
c_2Efcp_2EV2L: ( del * del ) > $i ).
tff(mem_c_2Efcp_2EV2L,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2EV2L(A_27a,A_27b),arr(ty_2Efcp_2Ecart(A_27a,A_27b),ty_2Elist_2Elist(A_27a))) ).
tff(tp_c_2Efcp_2Ebit0__CASE,type,
c_2Efcp_2Ebit0__CASE: ( del * del ) > $i ).
tff(mem_c_2Efcp_2Ebit0__CASE,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2Ebit0__CASE(A_27a,A_27b),arr(ty_2Efcp_2Ebit0(A_27a),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),A_27b)))) ).
tff(tp_c_2Efcp_2Ebit0__size,type,
c_2Efcp_2Ebit0__size: del > $i ).
tff(mem_c_2Efcp_2Ebit0__size,axiom,
! [A_27a: del] : mem(c_2Efcp_2Ebit0__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Efcp_2Ebit0(A_27a),ty_2Enum_2Enum))) ).
tff(tp_c_2Efcp_2Ebit1__CASE,type,
c_2Efcp_2Ebit1__CASE: ( del * del ) > $i ).
tff(mem_c_2Efcp_2Ebit1__CASE,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2Ebit1__CASE(A_27a,A_27b),arr(ty_2Efcp_2Ebit1(A_27a),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27b,A_27b))))) ).
tff(tp_c_2Efcp_2Ebit1__size,type,
c_2Efcp_2Ebit1__size: del > $i ).
tff(mem_c_2Efcp_2Ebit1__size,axiom,
! [A_27a: del] : mem(c_2Efcp_2Ebit1__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Efcp_2Ebit1(A_27a),ty_2Enum_2Enum))) ).
tff(tp_c_2Efcp_2Edest__cart,type,
c_2Efcp_2Edest__cart: ( del * del ) > $i ).
tff(mem_c_2Efcp_2Edest__cart,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2Edest__cart(A_27a,A_27b),arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(ty_2Efcp_2Efinite__image(A_27b),A_27a))) ).
tff(tp_c_2Efcp_2Edest__finite__image,type,
c_2Efcp_2Edest__finite__image: del > $i ).
tff(mem_c_2Efcp_2Edest__finite__image,axiom,
! [A_27a: del] : mem(c_2Efcp_2Edest__finite__image(A_27a),arr(ty_2Efcp_2Efinite__image(A_27a),A_27a)) ).
tff(tp_c_2Efcp_2Edimindex,type,
c_2Efcp_2Edimindex: del > $i ).
tff(mem_c_2Efcp_2Edimindex,axiom,
! [A_27a: del] : mem(c_2Efcp_2Edimindex(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ).
tff(tp_c_2Efcp_2Efcp__CASE,type,
c_2Efcp_2Efcp__CASE: ( del * del * del ) > $i ).
tff(mem_c_2Efcp_2Efcp__CASE,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : mem(c_2Efcp_2Efcp__CASE(A_27a,A_27b,A_27c),arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(arr(arr(ty_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),A_27c))) ).
tff(tp_c_2Efcp_2Efcp__index,type,
c_2Efcp_2Efcp__index: ( del * del ) > $i ).
tff(mem_c_2Efcp_2Efcp__index,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2Efcp__index(A_27a,A_27b),arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(ty_2Enum_2Enum,A_27a))) ).
tff(tp_c_2Efcp_2Efinite__index,type,
c_2Efcp_2Efinite__index: del > $i ).
tff(mem_c_2Efcp_2Efinite__index,axiom,
! [A_27a: del] : mem(c_2Efcp_2Efinite__index(A_27a),arr(ty_2Enum_2Enum,A_27a)) ).
tff(tp_c_2Efcp_2Emk__cart,type,
c_2Efcp_2Emk__cart: ( del * del ) > $i ).
tff(mem_c_2Efcp_2Emk__cart,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Efcp_2Emk__cart(A_27a,A_27b),arr(arr(ty_2Efcp_2Efinite__image(A_27b),A_27a),ty_2Efcp_2Ecart(A_27a,A_27b))) ).
tff(tp_c_2Efcp_2Emk__finite__image,type,
c_2Efcp_2Emk__finite__image: del > $i ).
tff(mem_c_2Efcp_2Emk__finite__image,axiom,
! [A_27a: del] : mem(c_2Efcp_2Emk__finite__image(A_27a),arr(A_27a,ty_2Efcp_2Efinite__image(A_27a))) ).
tff(ax_thm_2Efcp_2EHAS__SIZE__def,axiom,
! [A_27a: del,V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Efcp_2EHAS__SIZE(A_27a),V0s),inj__ty_2Enum_2Enum(V1n)))
<=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
& ( surj__ty_2Enum_2Enum(ap(c_2Epred__set_2ECARD(A_27a),V0s)) = V1n ) ) ) ) ).
tff(lamtp_f1071,type,
f1071: del > $i ).
tff(lameq_f1071,axiom,
! [A_27a: del,V1x: $i] : ( ap(f1071(A_27a),V1x) = ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(A_27a),V1x),c_2Ebool_2EARB(A_27a))),ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))) ) ).
tff(ax_thm_2Efcp_2Efinite__image__TY__DEF,axiom,
! [A_27a: del] :
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Efcp_2Efinite__image(A_27a),A_27a))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(A_27a,ty_2Efcp_2Efinite__image(A_27a)),f1071(A_27a)),V0rep)) ) ).
tff(lamtp_f1072,type,
f1072: del > $i ).
tff(lameq_f1072,axiom,
! [A_27a: del,V2x: $i] : ( ap(f1072(A_27a),V2x) = ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(A_27a),V2x),c_2Ebool_2EARB(A_27a))),ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))) ) ).
tff(ax_thm_2Efcp_2Efinite__image__tybij,axiom,
! [A_27a: del] :
( ! [V0a: $i] :
( mem(V0a,ty_2Efcp_2Efinite__image(A_27a))
=> ( ap(c_2Efcp_2Emk__finite__image(A_27a),ap(c_2Efcp_2Edest__finite__image(A_27a),V0a)) = V0a ) )
& ! [V1r: $i] :
( mem(V1r,A_27a)
=> ( p(ap(f1072(A_27a),V1r))
<=> ( ap(c_2Efcp_2Edest__finite__image(A_27a),ap(c_2Efcp_2Emk__finite__image(A_27a),V1r)) = V1r ) ) ) ) ).
tff(ax_thm_2Efcp_2Edimindex__def,axiom,
! [A_27a: del] : ( surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))),ap(c_2Epred__set_2ECARD(A_27a),c_2Epred__set_2EUNIV(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) ) ).
tff(conj_thm_2Efcp_2ENOT__FINITE__IMP__dimindex__1,axiom,
! [A_27a: del] :
( ~ p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a)))
=> ( surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) ) ) ).
tff(conj_thm_2Efcp_2EDIMINDEX__GE__1,axiom,
! [A_27a: del] : p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ).
tff(lamtp_f1073,type,
f1073: ( del * $i * $i ) > $i ).
tff(lameq_f1073,axiom,
! [A_27a: del,V1x: $i] :
( mem(V1x,A_27a)
=> ! [V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2n: tp__ty_2Enum_2Enum] : ( ap(f1073(A_27a,V1x,V0f),inj__ty_2Enum_2Enum(V2n)) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V2n)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(ap(c_2Emin_2E_3D(A_27a),ap(V0f,inj__ty_2Enum_2Enum(V2n))),V1x)) ) ) ) ).
tff(lamtp_f1074,type,
f1074: ( del * $i ) > $i ).
tff(lameq_f1074,axiom,
! [A_27a: del,V0f: $i] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1x: $i] : ( ap(f1074(A_27a,V0f),V1x) = ap(c_2Ebool_2E_3F_21(ty_2Enum_2Enum),f1073(A_27a,V1x,V0f)) ) ) ).
tff(lamtp_f1075,type,
f1075: del > $i ).
tff(lameq_f1075,axiom,
! [A_27a: del,V0f: $i] : ( ap(f1075(A_27a),V0f) = ap(c_2Ebool_2E_21(A_27a),f1074(A_27a,V0f)) ) ).
tff(ax_thm_2Efcp_2Efinite__index__def,axiom,
! [A_27a: del] : ( c_2Efcp_2Efinite__index(A_27a) = ap(c_2Emin_2E_40(arr(ty_2Enum_2Enum,A_27a)),f1075(A_27a)) ) ).
tff(ax_thm_2Efcp_2Ecart__TY__DEF,axiom,
! [A_27a: del,A_27b: del] :
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(ty_2Efcp_2Efinite__image(A_27b),A_27a)))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(ty_2Efcp_2Efinite__image(A_27b),A_27a),ty_2Efcp_2Ecart(A_27a,A_27b)),k(arr(ty_2Efcp_2Efinite__image(A_27b),A_27a),c_2Ebool_2ET)),V0rep)) ) ).
tff(ax_thm_2Efcp_2Ecart__tybij,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0a: $i] :
( mem(V0a,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( ap(c_2Efcp_2Emk__cart(A_27a,A_27b),ap(c_2Efcp_2Edest__cart(A_27a,A_27b),V0a)) = V0a ) )
& ! [V1r: $i] :
( mem(V1r,arr(ty_2Efcp_2Efinite__image(A_27b),A_27a))
=> ( p(ap(k(arr(ty_2Efcp_2Efinite__image(A_27b),A_27a),c_2Ebool_2ET),V1r))
<=> ( ap(c_2Efcp_2Edest__cart(A_27a,A_27b),ap(c_2Efcp_2Emk__cart(A_27a,A_27b),V1r)) = V1r ) ) ) ) ).
tff(ax_thm_2Efcp_2Efcp__index,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1i: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0x),inj__ty_2Enum_2Enum(V1i)) = ap(ap(c_2Efcp_2Edest__cart(A_27a,A_27b),V0x),ap(c_2Efcp_2Efinite__index(ty_2Efcp_2Efinite__image(A_27b)),inj__ty_2Enum_2Enum(V1i))) ) ) ).
tff(conj_thm_2Efcp_2Efcp__Axiom,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(arr(ty_2Efcp_2Efinite__image(A_27b),A_27a),A_27c))
=> ? [V1g: $i] :
( mem(V1g,arr(ty_2Efcp_2Ecart(A_27a,A_27b),A_27c))
& ! [V2h: $i] :
( mem(V2h,arr(ty_2Efcp_2Efinite__image(A_27b),A_27a))
=> ( ap(V1g,ap(c_2Efcp_2Emk__cart(A_27a,A_27b),V2h)) = ap(V0f,V2h) ) ) ) ) ).
tff(conj_thm_2Efcp_2Efcp__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(ty_2Efcp_2Ecart(A_27a,A_27b),bool))
=> ( ! [V1f: $i] :
( mem(V1f,arr(ty_2Efcp_2Efinite__image(A_27b),A_27a))
=> p(ap(V0P,ap(c_2Efcp_2Emk__cart(A_27a,A_27b),V1f))) )
=> ! [V2a: $i] :
( mem(V2a,ty_2Efcp_2Ecart(A_27a,A_27b))
=> p(ap(V0P,V2a)) ) ) ) ).
tff(ax_thm_2Efcp_2Efcp__case__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0h: $i] :
( mem(V0h,arr(ty_2Efcp_2Efinite__image(A_27b),A_27a))
=> ! [V1f: $i] :
( mem(V1f,arr(arr(ty_2Efcp_2Efinite__image(A_27b),A_27a),A_27c))
=> ( ap(ap(c_2Efcp_2Efcp__CASE(A_27a,A_27b,A_27c),ap(c_2Efcp_2Emk__cart(A_27a,A_27b),V0h)),V1f) = ap(V1f,V0h) ) ) ) ).
tff(conj_thm_2Efcp_2ECART__EQ,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1y: $i] :
( mem(V1y,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( ( V0x = V1y )
<=> ! [V2i: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V2i)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0x),inj__ty_2Enum_2Enum(V2i)) = ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V1y),inj__ty_2Enum_2Enum(V2i)) ) ) ) ) ) ).
tff(lamtp_f1076,type,
f1076: ( del * del * $i * $i ) > $i ).
tff(lameq_f1076,axiom,
! [A_27b: del,A_27a: del,V0g: $i] :
( mem(V0g,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1f: $i] :
( mem(V1f,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V2i: tp__ty_2Enum_2Enum] : ( ap(f1076(A_27b,A_27a,V0g,V1f),inj__ty_2Enum_2Enum(V2i)) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V2i)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))),ap(ap(c_2Emin_2E_3D(A_27a),ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V1f),inj__ty_2Enum_2Enum(V2i))),ap(V0g,inj__ty_2Enum_2Enum(V2i)))) ) ) ) ).
tff(lamtp_f1077,type,
f1077: ( del * del * $i ) > $i ).
tff(lameq_f1077,axiom,
! [A_27a: del,A_27b: del,V0g: $i] :
( mem(V0g,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1f: $i] : ( ap(f1077(A_27a,A_27b,V0g),V1f) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f1076(A_27b,A_27a,V0g,V1f)) ) ) ).
tff(lamtp_f1078,type,
f1078: ( del * del ) > $i ).
tff(lameq_f1078,axiom,
! [A_27b: del,A_27a: del,V0g: $i] : ( ap(f1078(A_27b,A_27a),V0g) = ap(c_2Emin_2E_40(ty_2Efcp_2Ecart(A_27a,A_27b)),f1077(A_27a,A_27b,V0g)) ) ).
tff(ax_thm_2Efcp_2EFCP,axiom,
! [A_27a: del,A_27b: del] : ( c_2Efcp_2EFCP(A_27a,A_27b) = f1078(A_27b,A_27a) ) ).
tff(conj_thm_2Efcp_2EFCP__BETA,axiom,
! [A_27a: del,A_27b: del,V0g: $i] :
( mem(V0g,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1i: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1i)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),ap(c_2Efcp_2EFCP(A_27a,A_27b),V0g)),inj__ty_2Enum_2Enum(V1i)) = ap(V0g,inj__ty_2Enum_2Enum(V1i)) ) ) ) ).
tff(conj_thm_2Efcp_2EFCP__UNIQUE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1g: $i] :
( mem(V1g,arr(ty_2Enum_2Enum,A_27a))
=> ( ! [V2i: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V2i)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0f),inj__ty_2Enum_2Enum(V2i)) = ap(V1g,inj__ty_2Enum_2Enum(V2i)) ) )
<=> ( ap(c_2Efcp_2EFCP(A_27a,A_27b),V1g) = V0f ) ) ) ) ).
tff(lamtp_f1079,type,
f1079: ( del * del * $i ) > $i ).
tff(lameq_f1079,axiom,
! [A_27a: del,A_27b: del,V0g: $i] :
( mem(V0g,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1i: tp__ty_2Enum_2Enum] : ( ap(f1079(A_27a,A_27b,V0g),inj__ty_2Enum_2Enum(V1i)) = ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0g),inj__ty_2Enum_2Enum(V1i)) ) ) ).
tff(conj_thm_2Efcp_2EFCP__ETA,axiom,
! [A_27a: del,A_27b: del,V0g: $i] :
( mem(V0g,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( ap(c_2Efcp_2EFCP(A_27a,A_27b),f1079(A_27a,A_27b,V0g)) = V0g ) ) ).
tff(conj_thm_2Efcp_2Ecard__dimindex,axiom,
! [A_27a: del] :
( p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a)))
=> ( surj__ty_2Enum_2Enum(ap(c_2Epred__set_2ECARD(A_27a),c_2Epred__set_2EUNIV(A_27a))) = surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ) ).
tff(conj_thm_2Efcp_2Eindex__sum,axiom,
! [A_27a: del,A_27b: del] : ( surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(ty_2Esum_2Esum(A_27a,A_27b)),c_2Ebool_2Ethe__value(ty_2Esum_2Esum(A_27a,A_27b)))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))),ap(c_2Epred__set_2EFINITE(A_27b),c_2Epred__set_2EUNIV(A_27b)))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) ) ).
tff(conj_thm_2Efcp_2Efinite__sum,axiom,
! [A_27a: del,A_27b: del] :
( p(ap(c_2Epred__set_2EFINITE(ty_2Esum_2Esum(A_27a,A_27b)),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(A_27a,A_27b))))
<=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a)))
& p(ap(c_2Epred__set_2EFINITE(A_27b),c_2Epred__set_2EUNIV(A_27b))) ) ) ).
tff(lamtp_f1080,type,
f1080: del > $i ).
tff(lameq_f1080,axiom,
! [A_27a: del,V5a: $i] : ( ap(f1080(A_27a),V5a) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V5a),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))) ) ).
tff(lamtp_f1081,type,
f1081: ( del * $i ) > $i ).
tff(lameq_f1081,axiom,
! [A_27a: del,V3a0: $i] :
( mem(V3a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V4a: $i] : ( ap(f1081(A_27a,V3a0),V4a) = ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0),ap(f1080(A_27a),V4a)) ) ) ).
tff(lamtp_f1082,type,
f1082: del > $i ).
tff(lameq_f1082,axiom,
! [A_27a: del,V8a: $i] : ( ap(f1082(A_27a),V8a) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),V8a),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))) ) ).
tff(lamtp_f1083,type,
f1083: ( del * $i ) > $i ).
tff(lameq_f1083,axiom,
! [A_27a: del,V3a0: $i] :
( mem(V3a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V7a: $i] : ( ap(f1083(A_27a,V3a0),V7a) = ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0),ap(f1082(A_27a),V7a)) ) ) ).
tff(lamtp_f1084,type,
f1084: ( del * $i ) > $i ).
tff(lameq_f1084,axiom,
! [A_27a: del,V2_27bit0_27: $i] :
( mem(V2_27bit0_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0: $i] : ( ap(f1084(A_27a,V2_27bit0_27),V3a0) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(A_27a),f1081(A_27a,V3a0))),ap(c_2Ebool_2E_3F(A_27a),f1083(A_27a,V3a0)))),ap(V2_27bit0_27,V3a0)) ) ) ).
tff(lamtp_f1085,type,
f1085: ( del * $i ) > $i ).
tff(lameq_f1085,axiom,
! [A_27a: del,V1a0: $i] :
( mem(V1a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27bit0_27: $i] : ( ap(f1085(A_27a,V1a0),V2_27bit0_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(A_27a)),f1084(A_27a,V2_27bit0_27))),ap(V2_27bit0_27,V1a0)) ) ) ).
tff(lamtp_f1086,type,
f1086: del > $i ).
tff(lameq_f1086,axiom,
! [A_27a: del,V1a0: $i] : ( ap(f1086(A_27a),V1a0) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(A_27a),bool)),f1085(A_27a,V1a0)) ) ).
tff(ax_thm_2Efcp_2Ebit0__TY__DEF,axiom,
! [A_27a: del] :
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Efcp_2Ebit0(A_27a),ty_2Eind__type_2Erecspace(A_27a)))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(A_27a),ty_2Efcp_2Ebit0(A_27a)),f1086(A_27a)),V0rep)) ) ).
tff(ax_thm_2Efcp_2Ebit0__case__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0a: $i] :
( mem(V0a,A_27a)
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2f1: $i] :
( mem(V2f1,arr(A_27a,A_27b))
=> ( ap(ap(ap(c_2Efcp_2Ebit0__CASE(A_27a,A_27b),ap(c_2Efcp_2EBIT0A(A_27a),V0a)),V1f),V2f1) = ap(V1f,V0a) ) ) ) )
& ! [V3a: $i] :
( mem(V3a,A_27a)
=> ! [V4f: $i] :
( mem(V4f,arr(A_27a,A_27b))
=> ! [V5f1: $i] :
( mem(V5f1,arr(A_27a,A_27b))
=> ( ap(ap(ap(c_2Efcp_2Ebit0__CASE(A_27a,A_27b),ap(c_2Efcp_2EBIT0B(A_27a),V3a)),V4f),V5f1) = ap(V5f1,V3a) ) ) ) ) ) ).
tff(ax_thm_2Efcp_2Ebit0__size__def,axiom,
! [A_27a: del] :
( ! [V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Efcp_2Ebit0__size(A_27a),V0f),ap(c_2Efcp_2EBIT0A(A_27a),V1a))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(V0f,V1a))) ) ) )
& ! [V2f: $i] :
( mem(V2f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V3a: $i] :
( mem(V3a,A_27a)
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Efcp_2Ebit0__size(A_27a),V2f),ap(c_2Efcp_2EBIT0B(A_27a),V3a))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(V2f,V3a))) ) ) ) ) ).
tff(conj_thm_2Efcp_2Edatatype__bit0,axiom,
! [A_27a: del,V0bit0: $i] :
( mem(V0bit0,arr(arr(A_27a,ty_2Efcp_2Ebit0(A_27a)),arr(arr(A_27a,ty_2Efcp_2Ebit0(A_27a)),bool)))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(V0bit0,c_2Efcp_2EBIT0A(A_27a)),c_2Efcp_2EBIT0B(A_27a)))) ) ).
tff(conj_thm_2Efcp_2Ebit0__11,axiom,
! [A_27a: del] :
( ! [V0a: $i] :
( mem(V0a,A_27a)
=> ! [V1a_27: $i] :
( mem(V1a_27,A_27a)
=> ( ( ap(c_2Efcp_2EBIT0A(A_27a),V0a) = ap(c_2Efcp_2EBIT0A(A_27a),V1a_27) )
<=> ( V0a = V1a_27 ) ) ) )
& ! [V2a: $i] :
( mem(V2a,A_27a)
=> ! [V3a_27: $i] :
( mem(V3a_27,A_27a)
=> ( ( ap(c_2Efcp_2EBIT0B(A_27a),V2a) = ap(c_2Efcp_2EBIT0B(A_27a),V3a_27) )
<=> ( V2a = V3a_27 ) ) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit0__distinct,axiom,
! [A_27a: del,V0a_27: $i] :
( mem(V0a_27,A_27a)
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ( ap(c_2Efcp_2EBIT0A(A_27a),V1a) != ap(c_2Efcp_2EBIT0B(A_27a),V0a_27) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit0__nchotomy,axiom,
! [A_27a: del,V0bb: $i] :
( mem(V0bb,ty_2Efcp_2Ebit0(A_27a))
=> ( ? [V1a: $i] :
( mem(V1a,A_27a)
& ( V0bb = ap(c_2Efcp_2EBIT0A(A_27a),V1a) ) )
| ? [V2a: $i] :
( mem(V2a,A_27a)
& ( V0bb = ap(c_2Efcp_2EBIT0B(A_27a),V2a) ) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit0__Axiom,axiom,
! [A_27a: del,A_27b: del,V0f0: $i] :
( mem(V0f0,arr(A_27a,A_27b))
=> ! [V1f1: $i] :
( mem(V1f1,arr(A_27a,A_27b))
=> ? [V2fn: $i] :
( mem(V2fn,arr(ty_2Efcp_2Ebit0(A_27a),A_27b))
& ! [V3a: $i] :
( mem(V3a,A_27a)
=> ( ap(V2fn,ap(c_2Efcp_2EBIT0A(A_27a),V3a)) = ap(V0f0,V3a) ) )
& ! [V4a: $i] :
( mem(V4a,A_27a)
=> ( ap(V2fn,ap(c_2Efcp_2EBIT0B(A_27a),V4a)) = ap(V1f1,V4a) ) ) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit0__induction,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Efcp_2Ebit0(A_27a),bool))
=> ( ( ! [V1a: $i] :
( mem(V1a,A_27a)
=> p(ap(V0P,ap(c_2Efcp_2EBIT0A(A_27a),V1a))) )
& ! [V2a: $i] :
( mem(V2a,A_27a)
=> p(ap(V0P,ap(c_2Efcp_2EBIT0B(A_27a),V2a))) ) )
=> ! [V3b: $i] :
( mem(V3b,ty_2Efcp_2Ebit0(A_27a))
=> p(ap(V0P,V3b)) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit0__case__cong,axiom,
! [A_27a: del,A_27b: del,V0f_27: $i] :
( mem(V0f_27,arr(A_27a,A_27b))
=> ! [V1f1_27: $i] :
( mem(V1f1_27,arr(A_27a,A_27b))
=> ! [V2M: $i] :
( mem(V2M,ty_2Efcp_2Ebit0(A_27a))
=> ! [V3M_27: $i] :
( mem(V3M_27,ty_2Efcp_2Ebit0(A_27a))
=> ! [V4f: $i] :
( mem(V4f,arr(A_27a,A_27b))
=> ! [V5f1: $i] :
( mem(V5f1,arr(A_27a,A_27b))
=> ( ( ( V2M = V3M_27 )
& ! [V6a: $i] :
( mem(V6a,A_27a)
=> ( ( V3M_27 = ap(c_2Efcp_2EBIT0A(A_27a),V6a) )
=> ( ap(V4f,V6a) = ap(V0f_27,V6a) ) ) )
& ! [V7a: $i] :
( mem(V7a,A_27a)
=> ( ( V3M_27 = ap(c_2Efcp_2EBIT0B(A_27a),V7a) )
=> ( ap(V5f1,V7a) = ap(V1f1_27,V7a) ) ) ) )
=> ( ap(ap(ap(c_2Efcp_2Ebit0__CASE(A_27a,A_27b),V2M),V4f),V5f1) = ap(ap(ap(c_2Efcp_2Ebit0__CASE(A_27a,A_27b),V3M_27),V0f_27),V1f1_27) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit0__case__eq,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,ty_2Efcp_2Ebit0(A_27a))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2f1: $i] :
( mem(V2f1,arr(A_27a,A_27b))
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ( ap(ap(ap(c_2Efcp_2Ebit0__CASE(A_27a,A_27b),V0x),V1f),V2f1) = V3v )
<=> ( ? [V4a: $i] :
( mem(V4a,A_27a)
& ( V0x = ap(c_2Efcp_2EBIT0A(A_27a),V4a) )
& ( ap(V1f,V4a) = V3v ) )
| ? [V5a: $i] :
( mem(V5a,A_27a)
& ( V0x = ap(c_2Efcp_2EBIT0B(A_27a),V5a) )
& ( ap(V2f1,V5a) = V3v ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efcp_2Eindex__bit0,axiom,
! [A_27a: del] : ( surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(ty_2Efcp_2Ebit0(A_27a)),c_2Ebool_2Ethe__value(ty_2Efcp_2Ebit0(A_27a)))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) ) ).
tff(conj_thm_2Efcp_2Efinite__bit0,axiom,
! [A_27a: del] :
( p(ap(c_2Epred__set_2EFINITE(ty_2Efcp_2Ebit0(A_27a)),c_2Epred__set_2EUNIV(ty_2Efcp_2Ebit0(A_27a))))
<=> p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))) ) ).
tff(lamtp_f1087,type,
f1087: ( del * $i ) > $i ).
tff(lameq_f1087,axiom,
! [A_27a: del,V2_27bit1_27: $i] :
( mem(V2_27bit1_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0: $i] : ( ap(f1087(A_27a,V2_27bit1_27),V3a0) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(A_27a),f1081(A_27a,V3a0))),ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(A_27a),f1083(A_27a,V3a0))),ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0),ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),c_2Ebool_2EARB(A_27a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))))),ap(V2_27bit1_27,V3a0)) ) ) ).
tff(lamtp_f1088,type,
f1088: ( del * $i ) > $i ).
tff(lameq_f1088,axiom,
! [A_27a: del,V1a0: $i] :
( mem(V1a0,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27bit1_27: $i] : ( ap(f1088(A_27a,V1a0),V2_27bit1_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(A_27a)),f1087(A_27a,V2_27bit1_27))),ap(V2_27bit1_27,V1a0)) ) ) ).
tff(lamtp_f1089,type,
f1089: del > $i ).
tff(lameq_f1089,axiom,
! [A_27a: del,V1a0: $i] : ( ap(f1089(A_27a),V1a0) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(A_27a),bool)),f1088(A_27a,V1a0)) ) ).
tff(ax_thm_2Efcp_2Ebit1__TY__DEF,axiom,
! [A_27a: del] :
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Efcp_2Ebit1(A_27a),ty_2Eind__type_2Erecspace(A_27a)))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(A_27a),ty_2Efcp_2Ebit1(A_27a)),f1089(A_27a)),V0rep)) ) ).
tff(ax_thm_2Efcp_2Ebit1__case__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0a: $i] :
( mem(V0a,A_27a)
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2f1: $i] :
( mem(V2f1,arr(A_27a,A_27b))
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ( ap(ap(ap(ap(c_2Efcp_2Ebit1__CASE(A_27a,A_27b),ap(c_2Efcp_2EBIT1A(A_27a),V0a)),V1f),V2f1),V3v) = ap(V1f,V0a) ) ) ) ) )
& ! [V4a: $i] :
( mem(V4a,A_27a)
=> ! [V5f: $i] :
( mem(V5f,arr(A_27a,A_27b))
=> ! [V6f1: $i] :
( mem(V6f1,arr(A_27a,A_27b))
=> ! [V7v: $i] :
( mem(V7v,A_27b)
=> ( ap(ap(ap(ap(c_2Efcp_2Ebit1__CASE(A_27a,A_27b),ap(c_2Efcp_2EBIT1B(A_27a),V4a)),V5f),V6f1),V7v) = ap(V6f1,V4a) ) ) ) ) )
& ! [V8f: $i] :
( mem(V8f,arr(A_27a,A_27b))
=> ! [V9f1: $i] :
( mem(V9f1,arr(A_27a,A_27b))
=> ! [V10v: $i] :
( mem(V10v,A_27b)
=> ( ap(ap(ap(ap(c_2Efcp_2Ebit1__CASE(A_27a,A_27b),c_2Efcp_2EBIT1C(A_27a)),V8f),V9f1),V10v) = V10v ) ) ) ) ) ).
tff(ax_thm_2Efcp_2Ebit1__size__def,axiom,
! [A_27a: del] :
( ! [V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Efcp_2Ebit1__size(A_27a),V0f),ap(c_2Efcp_2EBIT1A(A_27a),V1a))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(V0f,V1a))) ) ) )
& ! [V2f: $i] :
( mem(V2f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V3a: $i] :
( mem(V3a,A_27a)
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Efcp_2Ebit1__size(A_27a),V2f),ap(c_2Efcp_2EBIT1B(A_27a),V3a))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(V2f,V3a))) ) ) )
& ! [V4f: $i] :
( mem(V4f,arr(A_27a,ty_2Enum_2Enum))
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Efcp_2Ebit1__size(A_27a),V4f),c_2Efcp_2EBIT1C(A_27a))) = fo__c_2Enum_2E0 ) ) ) ).
tff(conj_thm_2Efcp_2Edatatype__bit1,axiom,
! [A_27a: del,V0bit1: $i] :
( mem(V0bit1,arr(arr(A_27a,ty_2Efcp_2Ebit1(A_27a)),arr(arr(A_27a,ty_2Efcp_2Ebit1(A_27a)),arr(ty_2Efcp_2Ebit1(A_27a),bool))))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(V0bit1,c_2Efcp_2EBIT1A(A_27a)),c_2Efcp_2EBIT1B(A_27a)),c_2Efcp_2EBIT1C(A_27a)))) ) ).
tff(conj_thm_2Efcp_2Ebit1__11,axiom,
! [A_27a: del] :
( ! [V0a: $i] :
( mem(V0a,A_27a)
=> ! [V1a_27: $i] :
( mem(V1a_27,A_27a)
=> ( ( ap(c_2Efcp_2EBIT1A(A_27a),V0a) = ap(c_2Efcp_2EBIT1A(A_27a),V1a_27) )
<=> ( V0a = V1a_27 ) ) ) )
& ! [V2a: $i] :
( mem(V2a,A_27a)
=> ! [V3a_27: $i] :
( mem(V3a_27,A_27a)
=> ( ( ap(c_2Efcp_2EBIT1B(A_27a),V2a) = ap(c_2Efcp_2EBIT1B(A_27a),V3a_27) )
<=> ( V2a = V3a_27 ) ) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit1__distinct,axiom,
! [A_27a: del] :
( ! [V0a_27: $i] :
( mem(V0a_27,A_27a)
=> ! [V1a: $i] :
( mem(V1a,A_27a)
=> ( ap(c_2Efcp_2EBIT1A(A_27a),V1a) != ap(c_2Efcp_2EBIT1B(A_27a),V0a_27) ) ) )
& ! [V2a: $i] :
( mem(V2a,A_27a)
=> ( ap(c_2Efcp_2EBIT1A(A_27a),V2a) != c_2Efcp_2EBIT1C(A_27a) ) )
& ! [V3a: $i] :
( mem(V3a,A_27a)
=> ( ap(c_2Efcp_2EBIT1B(A_27a),V3a) != c_2Efcp_2EBIT1C(A_27a) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit1__nchotomy,axiom,
! [A_27a: del,V0bb: $i] :
( mem(V0bb,ty_2Efcp_2Ebit1(A_27a))
=> ( ? [V1a: $i] :
( mem(V1a,A_27a)
& ( V0bb = ap(c_2Efcp_2EBIT1A(A_27a),V1a) ) )
| ? [V2a: $i] :
( mem(V2a,A_27a)
& ( V0bb = ap(c_2Efcp_2EBIT1B(A_27a),V2a) ) )
| ( V0bb = c_2Efcp_2EBIT1C(A_27a) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit1__Axiom,axiom,
! [A_27a: del,A_27b: del,V0f0: $i] :
( mem(V0f0,arr(A_27a,A_27b))
=> ! [V1f1: $i] :
( mem(V1f1,arr(A_27a,A_27b))
=> ! [V2f2: $i] :
( mem(V2f2,A_27b)
=> ? [V3fn: $i] :
( mem(V3fn,arr(ty_2Efcp_2Ebit1(A_27a),A_27b))
& ! [V4a: $i] :
( mem(V4a,A_27a)
=> ( ap(V3fn,ap(c_2Efcp_2EBIT1A(A_27a),V4a)) = ap(V0f0,V4a) ) )
& ! [V5a: $i] :
( mem(V5a,A_27a)
=> ( ap(V3fn,ap(c_2Efcp_2EBIT1B(A_27a),V5a)) = ap(V1f1,V5a) ) )
& ( ap(V3fn,c_2Efcp_2EBIT1C(A_27a)) = V2f2 ) ) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit1__induction,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Efcp_2Ebit1(A_27a),bool))
=> ( ( ! [V1a: $i] :
( mem(V1a,A_27a)
=> p(ap(V0P,ap(c_2Efcp_2EBIT1A(A_27a),V1a))) )
& ! [V2a: $i] :
( mem(V2a,A_27a)
=> p(ap(V0P,ap(c_2Efcp_2EBIT1B(A_27a),V2a))) )
& p(ap(V0P,c_2Efcp_2EBIT1C(A_27a))) )
=> ! [V3b: $i] :
( mem(V3b,ty_2Efcp_2Ebit1(A_27a))
=> p(ap(V0P,V3b)) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit1__case__cong,axiom,
! [A_27a: del,A_27b: del,V0f_27: $i] :
( mem(V0f_27,arr(A_27a,A_27b))
=> ! [V1f1_27: $i] :
( mem(V1f1_27,arr(A_27a,A_27b))
=> ! [V2v_27: $i] :
( mem(V2v_27,A_27b)
=> ! [V3M: $i] :
( mem(V3M,ty_2Efcp_2Ebit1(A_27a))
=> ! [V4M_27: $i] :
( mem(V4M_27,ty_2Efcp_2Ebit1(A_27a))
=> ! [V5f: $i] :
( mem(V5f,arr(A_27a,A_27b))
=> ! [V6f1: $i] :
( mem(V6f1,arr(A_27a,A_27b))
=> ! [V7v: $i] :
( mem(V7v,A_27b)
=> ( ( ( V3M = V4M_27 )
& ! [V8a: $i] :
( mem(V8a,A_27a)
=> ( ( V4M_27 = ap(c_2Efcp_2EBIT1A(A_27a),V8a) )
=> ( ap(V5f,V8a) = ap(V0f_27,V8a) ) ) )
& ! [V9a: $i] :
( mem(V9a,A_27a)
=> ( ( V4M_27 = ap(c_2Efcp_2EBIT1B(A_27a),V9a) )
=> ( ap(V6f1,V9a) = ap(V1f1_27,V9a) ) ) )
& ( ( V4M_27 = c_2Efcp_2EBIT1C(A_27a) )
=> ( V7v = V2v_27 ) ) )
=> ( ap(ap(ap(ap(c_2Efcp_2Ebit1__CASE(A_27a,A_27b),V3M),V5f),V6f1),V7v) = ap(ap(ap(ap(c_2Efcp_2Ebit1__CASE(A_27a,A_27b),V4M_27),V0f_27),V1f1_27),V2v_27) ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efcp_2Ebit1__case__eq,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,ty_2Efcp_2Ebit1(A_27a))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2f1: $i] :
( mem(V2f1,arr(A_27a,A_27b))
=> ! [V3v: $i] :
( mem(V3v,A_27b)
=> ! [V4v_27: $i] :
( mem(V4v_27,A_27b)
=> ( ( ap(ap(ap(ap(c_2Efcp_2Ebit1__CASE(A_27a,A_27b),V0x),V1f),V2f1),V3v) = V4v_27 )
<=> ( ? [V5a: $i] :
( mem(V5a,A_27a)
& ( V0x = ap(c_2Efcp_2EBIT1A(A_27a),V5a) )
& ( ap(V1f,V5a) = V4v_27 ) )
| ? [V6a: $i] :
( mem(V6a,A_27a)
& ( V0x = ap(c_2Efcp_2EBIT1B(A_27a),V6a) )
& ( ap(V2f1,V6a) = V4v_27 ) )
| ( ( V0x = c_2Efcp_2EBIT1C(A_27a) )
& ( V3v = V4v_27 ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Efcp_2Eindex__bit1,axiom,
! [A_27a: del] : ( surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(ty_2Efcp_2Ebit1(A_27a)),c_2Ebool_2Ethe__value(ty_2Efcp_2Ebit1(A_27a)))) = surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) ) ).
tff(conj_thm_2Efcp_2Efinite__bit1,axiom,
! [A_27a: del] :
( p(ap(c_2Epred__set_2EFINITE(ty_2Efcp_2Ebit1(A_27a)),c_2Epred__set_2EUNIV(ty_2Efcp_2Ebit1(A_27a))))
<=> p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))) ) ).
tff(conj_thm_2Efcp_2Eindex__one,axiom,
surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(ty_2Eone_2Eone),c_2Ebool_2Ethe__value(ty_2Eone_2Eone))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) ).
tff(conj_thm_2Efcp_2Efinite__one,axiom,
p(ap(c_2Epred__set_2EFINITE(ty_2Eone_2Eone),c_2Epred__set_2EUNIV(ty_2Eone_2Eone))) ).
tff(lamtp_f1090,type,
f1090: ( del * del * $i * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f1090,axiom,
! [A_27a: del,A_27b: del,V1b: $i] :
( mem(V1b,A_27a)
=> ! [V0a: tp__ty_2Enum_2Enum,V2m: $i] :
( mem(V2m,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V3c: tp__ty_2Enum_2Enum] : ( ap(f1090(A_27a,A_27b,V1b,V0a,V2m),inj__ty_2Enum_2Enum(V3c)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0a)),inj__ty_2Enum_2Enum(V3c))),V1b),ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V2m),inj__ty_2Enum_2Enum(V3c))) ) ) ) ).
tff(lamtp_f1091,type,
f1091: ( del * del * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f1091,axiom,
! [A_27a: del,A_27b: del,V0a: tp__ty_2Enum_2Enum,V1b: $i] :
( mem(V1b,A_27a)
=> ! [V2m: $i] : ( ap(f1091(A_27a,A_27b,V0a,V1b),V2m) = ap(c_2Efcp_2EFCP(A_27a,A_27b),f1090(A_27a,A_27b,V1b,V0a,V2m)) ) ) ).
tff(ax_thm_2Efcp_2EFCP__UPDATE__def,axiom,
! [A_27a: del,A_27b: del,V0a: tp__ty_2Enum_2Enum,V1b: $i] :
( mem(V1b,A_27a)
=> ( ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V0a)),V1b) = f1091(A_27a,A_27b,V0a,V1b) ) ) ).
tff(conj_thm_2Efcp_2EFCP__UPDATE__COMMUTES,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum,V3c: $i] :
( mem(V3c,A_27a)
=> ! [V4d: $i] :
( mem(V4d,A_27a)
=> ( ( V1a != V2b )
=> ( ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V1a)),V3c),ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V2b)),V4d),V0m)) = ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V2b)),V4d),ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V1a)),V3c),V0m)) ) ) ) ) ) ).
tff(conj_thm_2Efcp_2EFCP__UPDATE__EQ,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1a: tp__ty_2Enum_2Enum,V2b: $i] :
( mem(V2b,A_27a)
=> ! [V3c: $i] :
( mem(V3c,A_27a)
=> ( ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V1a)),V3c),ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V1a)),V2b),V0m)) = ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V1a)),V3c),V0m) ) ) ) ) ).
tff(conj_thm_2Efcp_2EFCP__UPDATE__IMP__ID,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1a: tp__ty_2Enum_2Enum,V2v: $i] :
( mem(V2v,A_27a)
=> ( ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0m),inj__ty_2Enum_2Enum(V1a)) = V2v )
=> ( ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V1a)),V2v),V0m) = V0m ) ) ) ) ).
tff(conj_thm_2Efcp_2EAPPLY__FCP__UPDATE__ID,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1a: tp__ty_2Enum_2Enum] : ( ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V1a)),ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0m),inj__ty_2Enum_2Enum(V1a))),V0m) = V0m ) ) ).
tff(conj_thm_2Efcp_2EFCP__APPLY__UPDATE__THM,axiom,
! [A_27a: del,A_27b: del,V0index_20out_20of_20range: tp__o,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V2a: tp__ty_2Enum_2Enum,V3w: $i] :
( mem(V3w,A_27a)
=> ! [V4b: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V2a)),V3w),V1m)),inj__ty_2Enum_2Enum(V4b)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V4b)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))),ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2a)),inj__ty_2Enum_2Enum(V4b))),V3w),ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V1m),inj__ty_2Enum_2Enum(V4b)))),ap(ap(ap(ap(c_2Ecombin_2EFAIL(arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(ty_2Enum_2Enum,A_27a)),bool),c_2Efcp_2Efcp__index(A_27a,A_27b)),inj__o(V0index_20out_20of_20range)),ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V2a)),V3w),V1m)),inj__ty_2Enum_2Enum(V4b))) ) ) ) ).
tff(ax_thm_2Efcp_2EFCP__HD__def,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( mem(V0v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( ap(c_2Efcp_2EFCP__HD(A_27a,A_27b),V0v) = ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0v),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) ) ) ).
tff(lamtp_f1092,type,
f1092: ( del * del * $i ) > $i ).
tff(lameq_f1092,axiom,
! [A_27a: del,A_27c: del,V0v: $i] :
( mem(V0v,ty_2Efcp_2Ecart(A_27a,A_27c))
=> ! [V1i: tp__ty_2Enum_2Enum] : ( ap(f1092(A_27a,A_27c,V0v),inj__ty_2Enum_2Enum(V1i)) = ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27c),V0v),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1i))) ) ) ).
tff(ax_thm_2Efcp_2EFCP__TL__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( mem(V0v,ty_2Efcp_2Ecart(A_27a,A_27c))
=> ( ap(c_2Efcp_2EFCP__TL(A_27a,A_27b,A_27c),V0v) = ap(c_2Efcp_2EFCP(A_27a,A_27b),f1092(A_27a,A_27c,V0v)) ) ) ).
tff(lamtp_f1093,type,
f1093: ( del * del * $i ) > $i ).
tff(lameq_f1093,axiom,
! [A_27a: del,A_27b: del,V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V2i: tp__ty_2Enum_2Enum] : ( ap(f1093(A_27a,A_27b,V1v),inj__ty_2Enum_2Enum(V2i)) = ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V1v),ap(c_2Eprim__rec_2EPRE,inj__ty_2Enum_2Enum(V2i))) ) ) ).
tff(ax_thm_2Efcp_2EFCP__CONS__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0h: $i] :
( mem(V0h,A_27a)
=> ! [V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( ap(ap(c_2Efcp_2EFCP__CONS(A_27a,A_27b,A_27c),V0h),V1v) = ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27c),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V0h),ap(c_2Efcp_2EFCP(A_27a,A_27c),f1093(A_27a,A_27b,V1v))) ) ) ) ).
tff(lamtp_f1094,type,
f1094: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1094,axiom,
! [A_27a: del,A_27c: del,A_27b: del,V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27a,A_27c))
=> ! [V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V2i: tp__ty_2Enum_2Enum] : ( ap(f1094(A_27a,A_27c,A_27b,V1v,V0f),inj__ty_2Enum_2Enum(V2i)) = ap(V0f,ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27c),V1v),inj__ty_2Enum_2Enum(V2i))) ) ) ) ).
tff(ax_thm_2Efcp_2EFCP__MAP__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27a,A_27c))
=> ( ap(ap(c_2Efcp_2EFCP__MAP(A_27a,A_27b,A_27c),V0f),V1v) = ap(c_2Efcp_2EFCP(A_27b,A_27c),f1094(A_27a,A_27c,A_27b,V1v,V0f)) ) ) ) ).
tff(ax_thm_2Efcp_2EFCP__EXISTS__def,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27b,bool))
=> ! [V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27b,A_27a))
=> ( p(ap(ap(c_2Efcp_2EFCP__EXISTS(A_27a,A_27b),V0P),V1v))
<=> ? [V2i: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V2i)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
& p(ap(V0P,ap(ap(c_2Efcp_2Efcp__index(A_27b,A_27a),V1v),inj__ty_2Enum_2Enum(V2i)))) ) ) ) ) ).
tff(ax_thm_2Efcp_2EFCP__EVERY__def,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27b,bool))
=> ! [V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27b,A_27a))
=> ( p(ap(ap(c_2Efcp_2EFCP__EVERY(A_27a,A_27b),V0P),V1v))
<=> ! [V2i: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),inj__ty_2Enum_2Enum(V2i)))
| p(ap(V0P,ap(ap(c_2Efcp_2Efcp__index(A_27b,A_27a),V1v),inj__ty_2Enum_2Enum(V2i)))) ) ) ) ) ).
tff(lamtp_f1095,type,
f1095: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1095,axiom,
! [A_27a: del,A_27c: del,A_27b: del,V1b: $i] :
( mem(V1b,ty_2Efcp_2Ecart(A_27a,A_27c))
=> ! [V0a: $i] :
( mem(V0a,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V2i: tp__ty_2Enum_2Enum] : ( ap(f1095(A_27a,A_27c,A_27b,V1b,V0a),inj__ty_2Enum_2Enum(V2i)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V2i)),ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c)))),ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27c),V1b),inj__ty_2Enum_2Enum(V2i))),ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0a),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2i)),ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c))))) ) ) ) ).
tff(ax_thm_2Efcp_2EFCP__CONCAT__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0a: $i] :
( mem(V0a,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1b: $i] :
( mem(V1b,ty_2Efcp_2Ecart(A_27a,A_27c))
=> ( ap(ap(c_2Efcp_2EFCP__CONCAT(A_27a,A_27b,A_27c),V0a),V1b) = ap(c_2Efcp_2EFCP(A_27a,ty_2Esum_2Esum(A_27b,A_27c)),f1095(A_27a,A_27c,A_27b,V1b,V0a)) ) ) ) ).
tff(lamtp_f1096,type,
f1096: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f1096,axiom,
! [A_27c: del,A_27b: del,A_27a: del,V0a: $i] :
( mem(V0a,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1b: $i] :
( mem(V1b,ty_2Efcp_2Ecart(A_27c,A_27b))
=> ! [V2i: tp__ty_2Enum_2Enum] : ( ap(f1096(A_27c,A_27b,A_27a,V0a,V1b),inj__ty_2Enum_2Enum(V2i)) = ap(ap(c_2Epair_2E_2C(A_27a,A_27c),ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0a),inj__ty_2Enum_2Enum(V2i))),ap(ap(c_2Efcp_2Efcp__index(A_27c,A_27b),V1b),inj__ty_2Enum_2Enum(V2i))) ) ) ) ).
tff(ax_thm_2Efcp_2EFCP__ZIP__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0a: $i] :
( mem(V0a,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1b: $i] :
( mem(V1b,ty_2Efcp_2Ecart(A_27c,A_27b))
=> ( ap(ap(c_2Efcp_2EFCP__ZIP(A_27a,A_27b,A_27c),V0a),V1b) = ap(c_2Efcp_2EFCP(ty_2Epair_2Eprod(A_27a,A_27c),A_27b),f1096(A_27c,A_27b,A_27a,V0a,V1b)) ) ) ) ).
tff(ax_thm_2Efcp_2EV2L__def,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( mem(V0v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( ap(c_2Efcp_2EV2L(A_27a,A_27b),V0v) = ap(ap(c_2Elist_2EGENLIST(A_27a),ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0v)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))) ) ) ).
tff(lamtp_f1097,type,
f1097: ( del * $i ) > $i ).
tff(lameq_f1097,axiom,
! [A_27a: del,V0L: $i] :
( mem(V0L,ty_2Elist_2Elist(A_27a))
=> ! [V1i: tp__ty_2Enum_2Enum] : ( ap(f1097(A_27a,V0L),inj__ty_2Enum_2Enum(V1i)) = ap(ap(c_2Elist_2EEL(A_27a),inj__ty_2Enum_2Enum(V1i)),V0L) ) ) ).
tff(ax_thm_2Efcp_2EL2V__def,axiom,
! [A_27a: del,A_27b: del,V0L: $i] :
( mem(V0L,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Efcp_2EL2V(A_27a,A_27b),V0L) = ap(c_2Efcp_2EFCP(A_27a,A_27b),f1097(A_27a,V0L)) ) ) ).
tff(ax_thm_2Efcp_2EFCP__FOLD__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27b,arr(A_27a,A_27b)))
=> ! [V1i: $i] :
( mem(V1i,A_27b)
=> ! [V2v: $i] :
( mem(V2v,ty_2Efcp_2Ecart(A_27a,A_27c))
=> ( ap(ap(ap(c_2Efcp_2EFCP__FOLD(A_27a,A_27b,A_27c),V0f),V1i),V2v) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V0f),V1i),ap(c_2Efcp_2EV2L(A_27a,A_27c),V2v)) ) ) ) ) ).
tff(conj_thm_2Efcp_2ELENGTH__V2L,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( mem(V0v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( surj__ty_2Enum_2Enum(ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Efcp_2EV2L(A_27a,A_27b),V0v))) = surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))) ) ) ).
tff(conj_thm_2Efcp_2EEL__V2L,axiom,
! [A_27a: del,A_27b: del,V0i: tp__ty_2Enum_2Enum,V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0i)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ( ap(ap(c_2Elist_2EEL(A_27a),inj__ty_2Enum_2Enum(V0i)),ap(c_2Efcp_2EV2L(A_27a,A_27b),V1v)) = ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V1v),inj__ty_2Enum_2Enum(V0i)) ) ) ) ).
tff(conj_thm_2Efcp_2EFCP__MAP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27a,A_27c))
=> ( ap(ap(c_2Efcp_2EFCP__MAP(A_27a,A_27b,A_27c),V0f),V1v) = ap(c_2Efcp_2EL2V(A_27b,A_27c),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(c_2Efcp_2EV2L(A_27a,A_27c),V1v))) ) ) ) ).
tff(conj_thm_2Efcp_2EFCP__TL,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( mem(V0v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
& ( surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) ) )
=> ( ap(c_2Efcp_2EFCP__TL(A_27a,A_27c,A_27b),V0v) = ap(c_2Efcp_2EL2V(A_27a,A_27c),ap(c_2Elist_2ETL(A_27a),ap(c_2Efcp_2EV2L(A_27a,A_27b),V0v))) ) ) ) ).
tff(conj_thm_2Efcp_2EFCP__EXISTS,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( p(ap(ap(c_2Efcp_2EFCP__EXISTS(A_27b,A_27a),V0P),V1v))
<=> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),ap(c_2Efcp_2EV2L(A_27a,A_27b),V1v))) ) ) ) ).
tff(conj_thm_2Efcp_2EFCP__EVERY,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( p(ap(ap(c_2Efcp_2EFCP__EVERY(A_27b,A_27a),V0P),V1v))
<=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(c_2Efcp_2EV2L(A_27a,A_27b),V1v))) ) ) ) ).
tff(conj_thm_2Efcp_2EFCP__HD,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( mem(V0v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( ap(c_2Efcp_2EFCP__HD(A_27a,A_27b),V0v) = ap(c_2Elist_2EHD(A_27a),ap(c_2Efcp_2EV2L(A_27a,A_27b),V0v)) ) ) ).
tff(conj_thm_2Efcp_2EFCP__CONS,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( mem(V0a,A_27a)
=> ! [V1v: $i] :
( mem(V1v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( ap(ap(c_2Efcp_2EFCP__CONS(A_27a,A_27b,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),V0a),V1v) = ap(c_2Efcp_2EL2V(A_27a,ty_2Esum_2Esum(A_27b,ty_2Eone_2Eone)),ap(ap(c_2Elist_2ECONS(A_27a),V0a),ap(c_2Efcp_2EV2L(A_27a,A_27b),V1v))) ) ) ) ).
tff(conj_thm_2Efcp_2EV2L__L2V,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,ty_2Elist_2Elist(A_27a))
=> ( ( surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))) = surj__ty_2Enum_2Enum(ap(c_2Elist_2ELENGTH(A_27a),V0x)) )
=> ( ap(c_2Efcp_2EV2L(A_27a,A_27b),ap(c_2Efcp_2EL2V(A_27a,A_27b),V0x)) = V0x ) ) ) ).
tff(conj_thm_2Efcp_2ENULL__V2L,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( mem(V0v,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ~ p(ap(c_2Elist_2ENULL(A_27a),ap(c_2Efcp_2EV2L(A_27a,A_27b),V0v))) ) ).
tff(conj_thm_2Efcp_2EREAD__TL,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0i: tp__ty_2Enum_2Enum,V1a: $i] :
( mem(V1a,ty_2Efcp_2Ecart(A_27a,A_27c))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0i)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),ap(c_2Efcp_2EFCP__TL(A_27a,A_27b,A_27c),V1a)),inj__ty_2Enum_2Enum(V0i)) = ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27c),V1a),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0i))) ) ) ) ).
tff(conj_thm_2Efcp_2EREAD__L2V,axiom,
! [A_27a: del,A_27b: del,V0i: tp__ty_2Enum_2Enum,V1a: $i] :
( mem(V1a,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0i)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),ap(c_2Efcp_2EL2V(A_27a,A_27b),V1a)),inj__ty_2Enum_2Enum(V0i)) = ap(ap(c_2Elist_2EEL(A_27a),inj__ty_2Enum_2Enum(V0i)),V1a) ) ) ) ).
tff(conj_thm_2Efcp_2Eindex__comp,axiom,
! [A_27a: del,A_27b: del,V0FCP_20out_20of_20bounds: tp__o,V1f: $i] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2n: tp__ty_2Enum_2Enum] : ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),ap(c_2Efcp_2EFCP(A_27a,A_27b),V1f)),inj__ty_2Enum_2Enum(V2n)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V2n)),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))),ap(V1f,inj__ty_2Enum_2Enum(V2n))),ap(ap(ap(ap(c_2Ecombin_2EFAIL(arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(ty_2Enum_2Enum,A_27a)),bool),c_2Efcp_2Efcp__index(A_27a,A_27b)),inj__o(V0FCP_20out_20of_20bounds)),ap(c_2Efcp_2EFCP(A_27a,A_27b),V1f)),inj__ty_2Enum_2Enum(V2n))) ) ) ).
tff(lamtp_f1098,type,
f1098: ( del * $i * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f1098,axiom,
! [A_27a: del,V1y: $i] :
( mem(V1y,A_27a)
=> ! [V0x: tp__ty_2Enum_2Enum,V4f: $i] :
( mem(V4f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V5c: tp__ty_2Enum_2Enum] : ( ap(f1098(A_27a,V1y,V0x,V4f),inj__ty_2Enum_2Enum(V5c)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0x)),inj__ty_2Enum_2Enum(V5c))),V1y),ap(V4f,inj__ty_2Enum_2Enum(V5c))) ) ) ) ).
tff(conj_thm_2Efcp_2Efcp__subst__comp,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0x: tp__ty_2Enum_2Enum,V1y: $i] :
( mem(V1y,A_27a)
=> ! [V2a: $i] :
( mem(V2a,A_27c)
=> ! [V3b: $i] :
( mem(V3b,A_27d)
=> ! [V4f: $i] :
( mem(V4f,arr(ty_2Enum_2Enum,A_27a))
=> ( ap(ap(ap(c_2Efcp_2E_3A_2B(A_27a,A_27b),inj__ty_2Enum_2Enum(V0x)),V1y),ap(c_2Efcp_2EFCP(A_27a,A_27b),V4f)) = ap(c_2Efcp_2EFCP(A_27a,A_27b),f1098(A_27a,V1y,V0x,V4f)) ) ) ) ) ) ).
%------------------------------------------------------------------------------