ITP001 Axioms: ITP087_5.ax
%------------------------------------------------------------------------------
% File : ITP087_5 : TPTP v9.0.0. 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 : quote_2.ax [Gau20]
% : HL4087_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 117 ( 30 unt; 45 typ; 0 def)
% Number of atoms : 998 ( 104 equ)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 207 ( 4 ~; 6 |; 60 &)
% ( 8 <=>; 129 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 723 ( 723 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 50 ( 31 >; 19 *; 0 +; 0 <<)
% Number of predicates : 44 ( 43 usr; 20 prp; 0-2 aty)
% Number of functors : 42 ( 42 usr; 11 con; 0-5 aty)
% Number of variables : 256 ( 242 !; 14 ?; 256 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_ty_2Equote_2Eindex,type,
ty_2Equote_2Eindex: del ).
tff(tp_ty_2Equote_2Evarmap,type,
ty_2Equote_2Evarmap: del > del ).
tff(tp_c_2Equote_2EEmpty__vm,type,
c_2Equote_2EEmpty__vm: del > $i ).
tff(mem_c_2Equote_2EEmpty__vm,axiom,
! [A_27a: del] : mem(c_2Equote_2EEmpty__vm(A_27a),ty_2Equote_2Evarmap(A_27a)) ).
tff(stp_ty_2Equote_2Eindex,type,
tp__ty_2Equote_2Eindex: $tType ).
tff(stp_inj_ty_2Equote_2Eindex,type,
inj__ty_2Equote_2Eindex: tp__ty_2Equote_2Eindex > $i ).
tff(stp_surj_ty_2Equote_2Eindex,type,
surj__ty_2Equote_2Eindex: $i > tp__ty_2Equote_2Eindex ).
tff(stp_inj_surj_ty_2Equote_2Eindex,axiom,
! [X: tp__ty_2Equote_2Eindex] : ( surj__ty_2Equote_2Eindex(inj__ty_2Equote_2Eindex(X)) = X ) ).
tff(stp_inj_mem_ty_2Equote_2Eindex,axiom,
! [X: tp__ty_2Equote_2Eindex] : mem(inj__ty_2Equote_2Eindex(X),ty_2Equote_2Eindex) ).
tff(stp_iso_mem_ty_2Equote_2Eindex,axiom,
! [X: $i] :
( mem(X,ty_2Equote_2Eindex)
=> ( X = inj__ty_2Equote_2Eindex(surj__ty_2Equote_2Eindex(X)) ) ) ).
tff(tp_c_2Equote_2EEnd__idx,type,
c_2Equote_2EEnd__idx: $i ).
tff(mem_c_2Equote_2EEnd__idx,axiom,
mem(c_2Equote_2EEnd__idx,ty_2Equote_2Eindex) ).
tff(stp_fo_c_2Equote_2EEnd__idx,type,
fo__c_2Equote_2EEnd__idx: tp__ty_2Equote_2Eindex ).
tff(stp_eq_fo_c_2Equote_2EEnd__idx,axiom,
inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx) = c_2Equote_2EEnd__idx ).
tff(tp_c_2Equote_2ELeft__idx,type,
c_2Equote_2ELeft__idx: $i ).
tff(mem_c_2Equote_2ELeft__idx,axiom,
mem(c_2Equote_2ELeft__idx,arr(ty_2Equote_2Eindex,ty_2Equote_2Eindex)) ).
tff(stp_fo_c_2Equote_2ELeft__idx,type,
fo__c_2Equote_2ELeft__idx: tp__ty_2Equote_2Eindex > tp__ty_2Equote_2Eindex ).
tff(stp_eq_fo_c_2Equote_2ELeft__idx,axiom,
! [X0: tp__ty_2Equote_2Eindex] : ( inj__ty_2Equote_2Eindex(fo__c_2Equote_2ELeft__idx(X0)) = ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(X0)) ) ).
tff(tp_c_2Equote_2ENode__vm,type,
c_2Equote_2ENode__vm: del > $i ).
tff(mem_c_2Equote_2ENode__vm,axiom,
! [A_27a: del] : mem(c_2Equote_2ENode__vm(A_27a),arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),ty_2Equote_2Evarmap(A_27a))))) ).
tff(tp_c_2Equote_2ERight__idx,type,
c_2Equote_2ERight__idx: $i ).
tff(mem_c_2Equote_2ERight__idx,axiom,
mem(c_2Equote_2ERight__idx,arr(ty_2Equote_2Eindex,ty_2Equote_2Eindex)) ).
tff(stp_fo_c_2Equote_2ERight__idx,type,
fo__c_2Equote_2ERight__idx: tp__ty_2Equote_2Eindex > tp__ty_2Equote_2Eindex ).
tff(stp_eq_fo_c_2Equote_2ERight__idx,axiom,
! [X0: tp__ty_2Equote_2Eindex] : ( inj__ty_2Equote_2Eindex(fo__c_2Equote_2ERight__idx(X0)) = ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(X0)) ) ).
tff(tp_c_2Equote_2Eindex__CASE,type,
c_2Equote_2Eindex__CASE: del > $i ).
tff(mem_c_2Equote_2Eindex__CASE,axiom,
! [A_27a: del] : mem(c_2Equote_2Eindex__CASE(A_27a),arr(ty_2Equote_2Eindex,arr(arr(ty_2Equote_2Eindex,A_27a),arr(arr(ty_2Equote_2Eindex,A_27a),arr(A_27a,A_27a))))) ).
tff(tp_c_2Equote_2Eindex__compare,type,
c_2Equote_2Eindex__compare: $i ).
tff(mem_c_2Equote_2Eindex__compare,axiom,
mem(c_2Equote_2Eindex__compare,arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Eindex,ty_2EternaryComparisons_2Eordering))) ).
tff(stp_fo_c_2Equote_2Eindex__compare,type,
fo__c_2Equote_2Eindex__compare: ( tp__ty_2Equote_2Eindex * tp__ty_2Equote_2Eindex ) > tp__ty_2EternaryComparisons_2Eordering ).
tff(stp_eq_fo_c_2Equote_2Eindex__compare,axiom,
! [X0: tp__ty_2Equote_2Eindex,X1: tp__ty_2Equote_2Eindex] : ( inj__ty_2EternaryComparisons_2Eordering(fo__c_2Equote_2Eindex__compare(X0,X1)) = ap(ap(c_2Equote_2Eindex__compare,inj__ty_2Equote_2Eindex(X0)),inj__ty_2Equote_2Eindex(X1)) ) ).
tff(tp_c_2Equote_2Eindex__lt,type,
c_2Equote_2Eindex__lt: $i ).
tff(mem_c_2Equote_2Eindex__lt,axiom,
mem(c_2Equote_2Eindex__lt,arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Eindex,bool))) ).
tff(stp_fo_c_2Equote_2Eindex__lt,type,
fo__c_2Equote_2Eindex__lt: ( tp__ty_2Equote_2Eindex * tp__ty_2Equote_2Eindex ) > tp__o ).
tff(stp_eq_fo_c_2Equote_2Eindex__lt,axiom,
! [X0: tp__ty_2Equote_2Eindex,X1: tp__ty_2Equote_2Eindex] : ( inj__o(fo__c_2Equote_2Eindex__lt(X0,X1)) = ap(ap(c_2Equote_2Eindex__lt,inj__ty_2Equote_2Eindex(X0)),inj__ty_2Equote_2Eindex(X1)) ) ).
tff(tp_c_2Equote_2Eindex__size,type,
c_2Equote_2Eindex__size: $i ).
tff(mem_c_2Equote_2Eindex__size,axiom,
mem(c_2Equote_2Eindex__size,arr(ty_2Equote_2Eindex,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Equote_2Eindex__size,type,
fo__c_2Equote_2Eindex__size: tp__ty_2Equote_2Eindex > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Equote_2Eindex__size,axiom,
! [X0: tp__ty_2Equote_2Eindex] : ( inj__ty_2Enum_2Enum(fo__c_2Equote_2Eindex__size(X0)) = ap(c_2Equote_2Eindex__size,inj__ty_2Equote_2Eindex(X0)) ) ).
tff(tp_c_2Equote_2Evarmap__CASE,type,
c_2Equote_2Evarmap__CASE: ( del * del ) > $i ).
tff(mem_c_2Equote_2Evarmap__CASE,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Equote_2Evarmap__CASE(A_27a,A_27b),arr(ty_2Equote_2Evarmap(A_27a),arr(A_27b,arr(arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),A_27b))),A_27b)))) ).
tff(tp_c_2Equote_2Evarmap__find,type,
c_2Equote_2Evarmap__find: del > $i ).
tff(mem_c_2Equote_2Evarmap__find,axiom,
! [A_27a: del] : mem(c_2Equote_2Evarmap__find(A_27a),arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Evarmap(A_27a),A_27a))) ).
tff(tp_c_2Equote_2Evarmap__size,type,
c_2Equote_2Evarmap__size: del > $i ).
tff(mem_c_2Equote_2Evarmap__size,axiom,
! [A_27a: del] : mem(c_2Equote_2Evarmap__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Equote_2Evarmap(A_27a),ty_2Enum_2Enum))) ).
tff(stp_c_ty_2Eind__type_2Erecspace_o,type,
tp__c_ty_2Eind__type_2Erecspace_o: $tType ).
tff(stp_inj_c_ty_2Eind__type_2Erecspace_o,type,
inj__c_ty_2Eind__type_2Erecspace_o: tp__c_ty_2Eind__type_2Erecspace_o > $i ).
tff(stp_surj_c_ty_2Eind__type_2Erecspace_o,type,
surj__c_ty_2Eind__type_2Erecspace_o: $i > tp__c_ty_2Eind__type_2Erecspace_o ).
tff(stp_inj_surj_c_ty_2Eind__type_2Erecspace_o,axiom,
! [X: tp__c_ty_2Eind__type_2Erecspace_o] : ( surj__c_ty_2Eind__type_2Erecspace_o(inj__c_ty_2Eind__type_2Erecspace_o(X)) = X ) ).
tff(stp_inj_mem_c_ty_2Eind__type_2Erecspace_o,axiom,
! [X: tp__c_ty_2Eind__type_2Erecspace_o] : mem(inj__c_ty_2Eind__type_2Erecspace_o(X),ty_2Eind__type_2Erecspace(bool)) ).
tff(stp_iso_mem_c_ty_2Eind__type_2Erecspace_o,axiom,
! [X: $i] :
( mem(X,ty_2Eind__type_2Erecspace(bool))
=> ( X = inj__c_ty_2Eind__type_2Erecspace_o(surj__c_ty_2Eind__type_2Erecspace_o(X)) ) ) ).
tff(lamtp_f2118,type,
f2118: $i ).
tff(lameq_f2118,axiom,
! [V5a: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2118,inj__c_ty_2Eind__type_2Erecspace_o(V5a)) = ap(ap(ap(c_2Eind__type_2ECONSTR(bool),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Ebool_2EARB(bool)),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(bool)),inj__c_ty_2Eind__type_2Erecspace_o(V5a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(bool)))) ) ).
tff(lamtp_f2119,type,
f2119: ( tp__c_ty_2Eind__type_2Erecspace_o * $i ) > $i ).
tff(lameq_f2119,axiom,
! [V3a0: tp__c_ty_2Eind__type_2Erecspace_o,V2_27index_27: $i] :
( mem(V2_27index_27,arr(ty_2Eind__type_2Erecspace(bool),bool))
=> ! [V4a: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2119(V3a0,V2_27index_27),inj__c_ty_2Eind__type_2Erecspace_o(V4a)) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(bool)),inj__c_ty_2Eind__type_2Erecspace_o(V3a0)),ap(f2118,inj__c_ty_2Eind__type_2Erecspace_o(V4a)))),ap(V2_27index_27,inj__c_ty_2Eind__type_2Erecspace_o(V4a))) ) ) ).
tff(lamtp_f2120,type,
f2120: $i ).
tff(lameq_f2120,axiom,
! [V8a: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2120,inj__c_ty_2Eind__type_2Erecspace_o(V8a)) = ap(ap(ap(c_2Eind__type_2ECONSTR(bool),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),c_2Ebool_2EARB(bool)),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(bool)),inj__c_ty_2Eind__type_2Erecspace_o(V8a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(bool)))) ) ).
tff(lamtp_f2121,type,
f2121: ( tp__c_ty_2Eind__type_2Erecspace_o * $i ) > $i ).
tff(lameq_f2121,axiom,
! [V3a0: tp__c_ty_2Eind__type_2Erecspace_o,V2_27index_27: $i] :
( mem(V2_27index_27,arr(ty_2Eind__type_2Erecspace(bool),bool))
=> ! [V7a: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2121(V3a0,V2_27index_27),inj__c_ty_2Eind__type_2Erecspace_o(V7a)) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(bool)),inj__c_ty_2Eind__type_2Erecspace_o(V3a0)),ap(f2120,inj__c_ty_2Eind__type_2Erecspace_o(V7a)))),ap(V2_27index_27,inj__c_ty_2Eind__type_2Erecspace_o(V7a))) ) ) ).
tff(lamtp_f2122,type,
f2122: $i > $i ).
tff(lameq_f2122,axiom,
! [V2_27index_27: $i] :
( mem(V2_27index_27,arr(ty_2Eind__type_2Erecspace(bool),bool))
=> ! [V3a0: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2122(V2_27index_27),inj__c_ty_2Eind__type_2Erecspace_o(V3a0)) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(bool)),f2119(V3a0,V2_27index_27))),ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(bool)),f2121(V3a0,V2_27index_27))),ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(bool)),inj__c_ty_2Eind__type_2Erecspace_o(V3a0)),ap(ap(ap(c_2Eind__type_2ECONSTR(bool),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),c_2Ebool_2EARB(bool)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(bool))))))),ap(V2_27index_27,inj__c_ty_2Eind__type_2Erecspace_o(V3a0))) ) ) ).
tff(lamtp_f2123,type,
f2123: tp__c_ty_2Eind__type_2Erecspace_o > $i ).
tff(lameq_f2123,axiom,
! [V1a0: tp__c_ty_2Eind__type_2Erecspace_o,V2_27index_27: $i] : ( ap(f2123(V1a0),V2_27index_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(bool)),f2122(V2_27index_27))),ap(V2_27index_27,inj__c_ty_2Eind__type_2Erecspace_o(V1a0))) ) ).
tff(lamtp_f2124,type,
f2124: $i ).
tff(lameq_f2124,axiom,
! [V1a0: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2124,inj__c_ty_2Eind__type_2Erecspace_o(V1a0)) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(bool),bool)),f2123(V1a0)) ) ).
tff(ax_thm_2Equote_2Eindex__TY__DEF,axiom,
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Equote_2Eindex,ty_2Eind__type_2Erecspace(bool)))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(bool),ty_2Equote_2Eindex),f2124),V0rep)) ) ).
tff(ax_thm_2Equote_2Eindex__case__def,axiom,
! [A_27a: del] :
( ! [V0a: tp__ty_2Equote_2Eindex,V1f: $i] :
( mem(V1f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V2f1: $i] :
( mem(V2f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V3v: $i] :
( mem(V3v,A_27a)
=> ( ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V0a))),V1f),V2f1),V3v) = ap(V1f,inj__ty_2Equote_2Eindex(V0a)) ) ) ) )
& ! [V4a: tp__ty_2Equote_2Eindex,V5f: $i] :
( mem(V5f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V6f1: $i] :
( mem(V6f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V7v: $i] :
( mem(V7v,A_27a)
=> ( ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V4a))),V5f),V6f1),V7v) = ap(V6f1,inj__ty_2Equote_2Eindex(V4a)) ) ) ) )
& ! [V8f: $i] :
( mem(V8f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V9f1: $i] :
( mem(V9f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V10v: $i] :
( mem(V10v,A_27a)
=> ( ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)),V8f),V9f1),V10v) = V10v ) ) ) ) ) ).
tff(ax_thm_2Equote_2Eindex__size__def,axiom,
( ! [V0a: tp__ty_2Equote_2Eindex] : ( surj__ty_2Enum_2Enum(ap(c_2Equote_2Eindex__size,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V0a)))) = 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(c_2Equote_2Eindex__size,inj__ty_2Equote_2Eindex(V0a)))) )
& ! [V1a: tp__ty_2Equote_2Eindex] : ( surj__ty_2Enum_2Enum(ap(c_2Equote_2Eindex__size,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(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(c_2Equote_2Eindex__size,inj__ty_2Equote_2Eindex(V1a)))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Equote_2Eindex__size,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx))) = fo__c_2Enum_2E0 ) ) ).
tff(conj_thm_2Equote_2Edatatype__index,axiom,
! [V0index: $i] :
( mem(V0index,arr(arr(ty_2Equote_2Eindex,ty_2Equote_2Eindex),arr(arr(ty_2Equote_2Eindex,ty_2Equote_2Eindex),arr(ty_2Equote_2Eindex,bool))))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(V0index,c_2Equote_2ELeft__idx),c_2Equote_2ERight__idx),inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)))) ) ).
tff(conj_thm_2Equote_2Eindex__11,axiom,
( ! [V0a: tp__ty_2Equote_2Eindex,V1a_27: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Equote_2Eindex(ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V0a))) = surj__ty_2Equote_2Eindex(ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V1a_27))) )
<=> ( V0a = V1a_27 ) )
& ! [V2a: tp__ty_2Equote_2Eindex,V3a_27: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Equote_2Eindex(ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V2a))) = surj__ty_2Equote_2Eindex(ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V3a_27))) )
<=> ( V2a = V3a_27 ) ) ) ).
tff(conj_thm_2Equote_2Eindex__distinct,axiom,
( ! [V0a_27: tp__ty_2Equote_2Eindex,V1a: tp__ty_2Equote_2Eindex] : ( surj__ty_2Equote_2Eindex(ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V1a))) != surj__ty_2Equote_2Eindex(ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V0a_27))) )
& ! [V2a: tp__ty_2Equote_2Eindex] : ( surj__ty_2Equote_2Eindex(ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V2a))) != fo__c_2Equote_2EEnd__idx )
& ! [V3a: tp__ty_2Equote_2Eindex] : ( surj__ty_2Equote_2Eindex(ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V3a))) != fo__c_2Equote_2EEnd__idx ) ) ).
tff(conj_thm_2Equote_2Eindex__nchotomy,axiom,
! [V0ii: tp__ty_2Equote_2Eindex] :
( ? [V1i: tp__ty_2Equote_2Eindex] : ( V0ii = surj__ty_2Equote_2Eindex(ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V1i))) )
| ? [V2i: tp__ty_2Equote_2Eindex] : ( V0ii = surj__ty_2Equote_2Eindex(ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V2i))) )
| ( V0ii = fo__c_2Equote_2EEnd__idx ) ) ).
tff(conj_thm_2Equote_2Eindex__Axiom,axiom,
! [A_27a: del,V0f0: $i] :
( mem(V0f0,arr(ty_2Equote_2Eindex,arr(A_27a,A_27a)))
=> ! [V1f1: $i] :
( mem(V1f1,arr(ty_2Equote_2Eindex,arr(A_27a,A_27a)))
=> ! [V2f2: $i] :
( mem(V2f2,A_27a)
=> ? [V3fn: $i] :
( mem(V3fn,arr(ty_2Equote_2Eindex,A_27a))
& ! [V4a: tp__ty_2Equote_2Eindex] : ( ap(V3fn,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V4a))) = ap(ap(V0f0,inj__ty_2Equote_2Eindex(V4a)),ap(V3fn,inj__ty_2Equote_2Eindex(V4a))) )
& ! [V5a: tp__ty_2Equote_2Eindex] : ( ap(V3fn,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V5a))) = ap(ap(V1f1,inj__ty_2Equote_2Eindex(V5a)),ap(V3fn,inj__ty_2Equote_2Eindex(V5a))) )
& ( ap(V3fn,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)) = V2f2 ) ) ) ) ) ).
tff(conj_thm_2Equote_2Eindex__induction,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Equote_2Eindex,bool))
=> ( ( ! [V1i: tp__ty_2Equote_2Eindex] :
( p(ap(V0P,inj__ty_2Equote_2Eindex(V1i)))
=> p(ap(V0P,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V1i)))) )
& ! [V2i: tp__ty_2Equote_2Eindex] :
( p(ap(V0P,inj__ty_2Equote_2Eindex(V2i)))
=> p(ap(V0P,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V2i)))) )
& p(ap(V0P,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx))) )
=> ! [V3i: tp__ty_2Equote_2Eindex] : p(ap(V0P,inj__ty_2Equote_2Eindex(V3i))) ) ) ).
tff(conj_thm_2Equote_2Eindex__case__cong,axiom,
! [A_27a: del,V0f_27: $i] :
( mem(V0f_27,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V1f1_27: $i] :
( mem(V1f1_27,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V2v_27: $i] :
( mem(V2v_27,A_27a)
=> ! [V3M: tp__ty_2Equote_2Eindex,V4M_27: tp__ty_2Equote_2Eindex,V5f: $i] :
( mem(V5f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V6f1: $i] :
( mem(V6f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V7v: $i] :
( mem(V7v,A_27a)
=> ( ( ( V3M = V4M_27 )
& ! [V8a: tp__ty_2Equote_2Eindex] :
( ( V4M_27 = surj__ty_2Equote_2Eindex(ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V8a))) )
=> ( ap(V5f,inj__ty_2Equote_2Eindex(V8a)) = ap(V0f_27,inj__ty_2Equote_2Eindex(V8a)) ) )
& ! [V9a: tp__ty_2Equote_2Eindex] :
( ( V4M_27 = surj__ty_2Equote_2Eindex(ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V9a))) )
=> ( ap(V6f1,inj__ty_2Equote_2Eindex(V9a)) = ap(V1f1_27,inj__ty_2Equote_2Eindex(V9a)) ) )
& ( ( V4M_27 = fo__c_2Equote_2EEnd__idx )
=> ( V7v = V2v_27 ) ) )
=> ( ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),inj__ty_2Equote_2Eindex(V3M)),V5f),V6f1),V7v) = ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),inj__ty_2Equote_2Eindex(V4M_27)),V0f_27),V1f1_27),V2v_27) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equote_2Eindex__case__eq,axiom,
! [A_27a: del,V0x: tp__ty_2Equote_2Eindex,V1f: $i] :
( mem(V1f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V2f1: $i] :
( mem(V2f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V3v: $i] :
( mem(V3v,A_27a)
=> ! [V4v_27: $i] :
( mem(V4v_27,A_27a)
=> ( ( ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),inj__ty_2Equote_2Eindex(V0x)),V1f),V2f1),V3v) = V4v_27 )
<=> ( ? [V5i: tp__ty_2Equote_2Eindex] :
( ( V0x = surj__ty_2Equote_2Eindex(ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V5i))) )
& ( ap(V1f,inj__ty_2Equote_2Eindex(V5i)) = V4v_27 ) )
| ? [V6i: tp__ty_2Equote_2Eindex] :
( ( V0x = surj__ty_2Equote_2Eindex(ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V6i))) )
& ( ap(V2f1,inj__ty_2Equote_2Eindex(V6i)) = V4v_27 ) )
| ( ( V0x = fo__c_2Equote_2EEnd__idx )
& ( V3v = V4v_27 ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equote_2Eindex__compare__ind,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Eindex,bool)))
=> ( ( p(ap(ap(V0P,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)),inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)))
& ! [V1v10: tp__ty_2Equote_2Eindex] : p(ap(ap(V0P,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)),ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V1v10))))
& ! [V2v11: tp__ty_2Equote_2Eindex] : p(ap(ap(V0P,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)),ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V2v11))))
& ! [V3v2: tp__ty_2Equote_2Eindex] : p(ap(ap(V0P,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V3v2))),inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)))
& ! [V4v3: tp__ty_2Equote_2Eindex] : p(ap(ap(V0P,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V4v3))),inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)))
& ! [V5n_27: tp__ty_2Equote_2Eindex,V6m_27: tp__ty_2Equote_2Eindex] :
( p(ap(ap(V0P,inj__ty_2Equote_2Eindex(V5n_27)),inj__ty_2Equote_2Eindex(V6m_27)))
=> p(ap(ap(V0P,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V5n_27))),ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V6m_27)))) )
& ! [V7n_27: tp__ty_2Equote_2Eindex,V8m_27: tp__ty_2Equote_2Eindex] : p(ap(ap(V0P,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V7n_27))),ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V8m_27))))
& ! [V9n_27: tp__ty_2Equote_2Eindex,V10m_27: tp__ty_2Equote_2Eindex] :
( p(ap(ap(V0P,inj__ty_2Equote_2Eindex(V9n_27)),inj__ty_2Equote_2Eindex(V10m_27)))
=> p(ap(ap(V0P,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V9n_27))),ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V10m_27)))) )
& ! [V11n_27: tp__ty_2Equote_2Eindex,V12m_27: tp__ty_2Equote_2Eindex] : p(ap(ap(V0P,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V11n_27))),ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V12m_27)))) )
=> ! [V13v: tp__ty_2Equote_2Eindex,V14v1: tp__ty_2Equote_2Eindex] : p(ap(ap(V0P,inj__ty_2Equote_2Eindex(V13v)),inj__ty_2Equote_2Eindex(V14v1))) ) ) ).
tff(conj_thm_2Equote_2Eindex__compare__def,axiom,
( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)),inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx))) = fo__c_2EternaryComparisons_2EEQUAL )
& ! [V0v10: tp__ty_2Equote_2Eindex] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)),ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V0v10)))) = fo__c_2EternaryComparisons_2ELESS )
& ! [V1v11: tp__ty_2Equote_2Eindex] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)),ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V1v11)))) = fo__c_2EternaryComparisons_2ELESS )
& ! [V2v2: tp__ty_2Equote_2Eindex] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V2v2))),inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx))) = fo__c_2EternaryComparisons_2EGREATER )
& ! [V3v3: tp__ty_2Equote_2Eindex] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V3v3))),inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx))) = fo__c_2EternaryComparisons_2EGREATER )
& ! [V4n_27: tp__ty_2Equote_2Eindex,V5m_27: tp__ty_2Equote_2Eindex] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V4n_27))),ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V5m_27)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,inj__ty_2Equote_2Eindex(V4n_27)),inj__ty_2Equote_2Eindex(V5m_27))) )
& ! [V6n_27: tp__ty_2Equote_2Eindex,V7m_27: tp__ty_2Equote_2Eindex] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V6n_27))),ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V7m_27)))) = fo__c_2EternaryComparisons_2ELESS )
& ! [V8n_27: tp__ty_2Equote_2Eindex,V9m_27: tp__ty_2Equote_2Eindex] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V8n_27))),ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V9m_27)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,inj__ty_2Equote_2Eindex(V8n_27)),inj__ty_2Equote_2Eindex(V9m_27))) )
& ! [V10n_27: tp__ty_2Equote_2Eindex,V11m_27: tp__ty_2Equote_2Eindex] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V10n_27))),ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V11m_27)))) = fo__c_2EternaryComparisons_2EGREATER ) ) ).
tff(conj_thm_2Equote_2Ecompare__index__equal,axiom,
! [V0i1: tp__ty_2Equote_2Eindex,V1i2: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,inj__ty_2Equote_2Eindex(V0i1)),inj__ty_2Equote_2Eindex(V1i2))) = fo__c_2EternaryComparisons_2EEQUAL )
<=> ( V0i1 = V1i2 ) ) ).
tff(stp_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,type,
tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex: $tType ).
tff(stp_inj_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,type,
inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex > $i ).
tff(stp_surj_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,type,
surj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex: $i > tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex ).
tff(stp_inj_surj_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,axiom,
! [X: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] : ( surj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex(inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex(X)) = X ) ).
tff(stp_inj_mem_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,axiom,
! [X: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] : mem(inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex(X),ty_2Elist_2Elist(ty_2Equote_2Eindex)) ).
tff(stp_iso_mem_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,axiom,
! [X: $i] :
( mem(X,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ( X = inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex(surj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex(X)) ) ) ).
tff(conj_thm_2Equote_2Ecompare__list__index,axiom,
! [V0l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V1l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex(V0l1)),inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex(V1l2))) = fo__c_2EternaryComparisons_2EEQUAL )
<=> ( V0l1 = V1l2 ) ) ).
tff(ax_thm_2Equote_2Eindex__lt__def,axiom,
! [V0i1: tp__ty_2Equote_2Eindex,V1i2: tp__ty_2Equote_2Eindex] :
( p(ap(ap(c_2Equote_2Eindex__lt,inj__ty_2Equote_2Eindex(V0i1)),inj__ty_2Equote_2Eindex(V1i2)))
<=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Equote_2Eindex__compare,inj__ty_2Equote_2Eindex(V0i1)),inj__ty_2Equote_2Eindex(V1i2))) = fo__c_2EternaryComparisons_2ELESS ) ) ).
tff(lamtp_f2125,type,
f2125: ( del * $i * $i ) > $i ).
tff(lameq_f2125,axiom,
! [A_27a: del,V9a1: $i] :
( mem(V9a1,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V8a0: $i] :
( mem(V8a0,A_27a)
=> ! [V10a2: $i] : ( ap(f2125(A_27a,V9a1,V8a0),V10a2) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),V8a0),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(A_27a)),V9a1),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(A_27a)),V10a2),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))) ) ) ) ).
tff(lamtp_f2126,type,
f2126: ( del * $i ) > $i ).
tff(lameq_f2126,axiom,
! [A_27a: del,V8a0: $i] :
( mem(V8a0,A_27a)
=> ! [V9a1: $i] : ( ap(f2126(A_27a,V8a0),V9a1) = f2125(A_27a,V9a1,V8a0) ) ) ).
tff(lamtp_f2127,type,
f2127: del > $i ).
tff(lameq_f2127,axiom,
! [A_27a: del,V8a0: $i] : ( ap(f2127(A_27a),V8a0) = f2126(A_27a,V8a0) ) ).
tff(lamtp_f2128,type,
f2128: ( del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2128,axiom,
! [A_27a: del,V5a0: $i] :
( mem(V5a0,A_27a)
=> ! [V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V6a1: $i] :
( mem(V6a1,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27varmap_27: $i] :
( mem(V2_27varmap_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V7a2: $i] : ( ap(f2128(A_27a,V5a0,V3a0_27,V6a1,V2_27varmap_27),V7a2) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(ap(f2127(A_27a),V5a0),V6a1),V7a2))),ap(ap(c_2Ebool_2E_2F_5C,ap(V2_27varmap_27,V6a1)),ap(V2_27varmap_27,V7a2))) ) ) ) ) ) ).
tff(lamtp_f2129,type,
f2129: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2129,axiom,
! [A_27a: del,V2_27varmap_27: $i] :
( mem(V2_27varmap_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V5a0: $i] :
( mem(V5a0,A_27a)
=> ! [V6a1: $i] : ( ap(f2129(A_27a,V2_27varmap_27,V3a0_27,V5a0),V6a1) = ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f2128(A_27a,V5a0,V3a0_27,V6a1,V2_27varmap_27)) ) ) ) ) ).
tff(lamtp_f2130,type,
f2130: ( del * $i * $i ) > $i ).
tff(lameq_f2130,axiom,
! [A_27a: del,V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27varmap_27: $i] :
( mem(V2_27varmap_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V5a0: $i] : ( ap(f2130(A_27a,V3a0_27,V2_27varmap_27),V5a0) = ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f2129(A_27a,V2_27varmap_27,V3a0_27,V5a0)) ) ) ) ).
tff(lamtp_f2131,type,
f2131: ( del * $i ) > $i ).
tff(lameq_f2131,axiom,
! [A_27a: del,V2_27varmap_27: $i] :
( mem(V2_27varmap_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0_27: $i] : ( ap(f2131(A_27a,V2_27varmap_27),V3a0_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Ebool_2EARB(A_27a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))),ap(c_2Ebool_2E_3F(A_27a),f2130(A_27a,V3a0_27,V2_27varmap_27)))),ap(V2_27varmap_27,V3a0_27)) ) ) ).
tff(lamtp_f2132,type,
f2132: ( del * $i ) > $i ).
tff(lameq_f2132,axiom,
! [A_27a: del,V1a0_27: $i] :
( mem(V1a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27varmap_27: $i] : ( ap(f2132(A_27a,V1a0_27),V2_27varmap_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(A_27a)),f2131(A_27a,V2_27varmap_27))),ap(V2_27varmap_27,V1a0_27)) ) ) ).
tff(lamtp_f2133,type,
f2133: del > $i ).
tff(lameq_f2133,axiom,
! [A_27a: del,V1a0_27: $i] : ( ap(f2133(A_27a),V1a0_27) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(A_27a),bool)),f2132(A_27a,V1a0_27)) ) ).
tff(ax_thm_2Equote_2Evarmap__TY__DEF,axiom,
! [A_27a: del] :
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Equote_2Evarmap(A_27a),ty_2Eind__type_2Erecspace(A_27a)))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(A_27a),ty_2Equote_2Evarmap(A_27a)),f2133(A_27a)),V0rep)) ) ).
tff(ax_thm_2Equote_2Evarmap__case__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0v: $i] :
( mem(V0v,A_27b)
=> ! [V1f: $i] :
( mem(V1f,arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),A_27b))))
=> ( ap(ap(ap(c_2Equote_2Evarmap__CASE(A_27a,A_27b),c_2Equote_2EEmpty__vm(A_27a)),V0v),V1f) = V0v ) ) )
& ! [V2a0: $i] :
( mem(V2a0,A_27a)
=> ! [V3a1: $i] :
( mem(V3a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V4a2: $i] :
( mem(V4a2,ty_2Equote_2Evarmap(A_27a))
=> ! [V5v: $i] :
( mem(V5v,A_27b)
=> ! [V6f: $i] :
( mem(V6f,arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),A_27b))))
=> ( ap(ap(ap(c_2Equote_2Evarmap__CASE(A_27a,A_27b),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V2a0),V3a1),V4a2)),V5v),V6f) = ap(ap(ap(V6f,V2a0),V3a1),V4a2) ) ) ) ) ) ) ) ).
tff(ax_thm_2Equote_2Evarmap__size__def,axiom,
! [A_27a: del] :
( ! [V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Equote_2Evarmap__size(A_27a),V0f),c_2Equote_2EEmpty__vm(A_27a))) = fo__c_2Enum_2E0 ) )
& ! [V1f: $i] :
( mem(V1f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2a0: $i] :
( mem(V2a0,A_27a)
=> ! [V3a1: $i] :
( mem(V3a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V4a2: $i] :
( mem(V4a2,ty_2Equote_2Evarmap(A_27a))
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2Equote_2Evarmap__size(A_27a),V1f),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V2a0),V3a1),V4a2))) = 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(ap(c_2Earithmetic_2E_2B,ap(V1f,V2a0)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Equote_2Evarmap__size(A_27a),V1f),V3a1)),ap(ap(c_2Equote_2Evarmap__size(A_27a),V1f),V4a2))))) ) ) ) ) ) ) ).
tff(conj_thm_2Equote_2Edatatype__varmap,axiom,
! [A_27a: del,V0varmap: $i] :
( mem(V0varmap,arr(ty_2Equote_2Evarmap(A_27a),arr(arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),ty_2Equote_2Evarmap(A_27a)))),bool)))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(V0varmap,c_2Equote_2EEmpty__vm(A_27a)),c_2Equote_2ENode__vm(A_27a)))) ) ).
tff(conj_thm_2Equote_2Evarmap__11,axiom,
! [A_27a: del,V0a0: $i] :
( mem(V0a0,A_27a)
=> ! [V1a1: $i] :
( mem(V1a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V2a2: $i] :
( mem(V2a2,ty_2Equote_2Evarmap(A_27a))
=> ! [V3a0_27: $i] :
( mem(V3a0_27,A_27a)
=> ! [V4a1_27: $i] :
( mem(V4a1_27,ty_2Equote_2Evarmap(A_27a))
=> ! [V5a2_27: $i] :
( mem(V5a2_27,ty_2Equote_2Evarmap(A_27a))
=> ( ( ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V0a0),V1a1),V2a2) = ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V3a0_27),V4a1_27),V5a2_27) )
<=> ( ( V0a0 = V3a0_27 )
& ( V1a1 = V4a1_27 )
& ( V2a2 = V5a2_27 ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equote_2Evarmap__distinct,axiom,
! [A_27a: del,V0a2: $i] :
( mem(V0a2,ty_2Equote_2Evarmap(A_27a))
=> ! [V1a1: $i] :
( mem(V1a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V2a0: $i] :
( mem(V2a0,A_27a)
=> ( c_2Equote_2EEmpty__vm(A_27a) != ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V2a0),V1a1),V0a2) ) ) ) ) ).
tff(conj_thm_2Equote_2Evarmap__nchotomy,axiom,
! [A_27a: del,V0vv: $i] :
( mem(V0vv,ty_2Equote_2Evarmap(A_27a))
=> ( ( V0vv = c_2Equote_2EEmpty__vm(A_27a) )
| ? [V1a: $i] :
( mem(V1a,A_27a)
& ? [V2v: $i] :
( mem(V2v,ty_2Equote_2Evarmap(A_27a))
& ? [V3v0: $i] :
( mem(V3v0,ty_2Equote_2Evarmap(A_27a))
& ( V0vv = ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V1a),V2v),V3v0) ) ) ) ) ) ) ).
tff(conj_thm_2Equote_2Evarmap__Axiom,axiom,
! [A_27a: del,A_27b: del,V0f0: $i] :
( mem(V0f0,A_27b)
=> ! [V1f1: $i] :
( mem(V1f1,arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),arr(A_27b,arr(A_27b,A_27b))))))
=> ? [V2fn: $i] :
( mem(V2fn,arr(ty_2Equote_2Evarmap(A_27a),A_27b))
& ( ap(V2fn,c_2Equote_2EEmpty__vm(A_27a)) = V0f0 )
& ! [V3a0: $i] :
( mem(V3a0,A_27a)
=> ! [V4a1: $i] :
( mem(V4a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V5a2: $i] :
( mem(V5a2,ty_2Equote_2Evarmap(A_27a))
=> ( ap(V2fn,ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V3a0),V4a1),V5a2)) = ap(ap(ap(ap(ap(V1f1,V3a0),V4a1),V5a2),ap(V2fn,V4a1)),ap(V2fn,V5a2)) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equote_2Evarmap__induction,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Equote_2Evarmap(A_27a),bool))
=> ( ( p(ap(V0P,c_2Equote_2EEmpty__vm(A_27a)))
& ! [V1v: $i] :
( mem(V1v,ty_2Equote_2Evarmap(A_27a))
=> ! [V2v0: $i] :
( mem(V2v0,ty_2Equote_2Evarmap(A_27a))
=> ( ( p(ap(V0P,V1v))
& p(ap(V0P,V2v0)) )
=> ! [V3a: $i] :
( mem(V3a,A_27a)
=> p(ap(V0P,ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V3a),V1v),V2v0))) ) ) ) ) )
=> ! [V4v: $i] :
( mem(V4v,ty_2Equote_2Evarmap(A_27a))
=> p(ap(V0P,V4v)) ) ) ) ).
tff(conj_thm_2Equote_2Evarmap__case__cong,axiom,
! [A_27a: del,A_27b: del,V0v_27: $i] :
( mem(V0v_27,A_27b)
=> ! [V1f_27: $i] :
( mem(V1f_27,arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),A_27b))))
=> ! [V2M: $i] :
( mem(V2M,ty_2Equote_2Evarmap(A_27a))
=> ! [V3M_27: $i] :
( mem(V3M_27,ty_2Equote_2Evarmap(A_27a))
=> ! [V4v: $i] :
( mem(V4v,A_27b)
=> ! [V5f: $i] :
( mem(V5f,arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),A_27b))))
=> ( ( ( V2M = V3M_27 )
& ( ( V3M_27 = c_2Equote_2EEmpty__vm(A_27a) )
=> ( V4v = V0v_27 ) )
& ! [V6a0: $i] :
( mem(V6a0,A_27a)
=> ! [V7a1: $i] :
( mem(V7a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V8a2: $i] :
( mem(V8a2,ty_2Equote_2Evarmap(A_27a))
=> ( ( V3M_27 = ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V6a0),V7a1),V8a2) )
=> ( ap(ap(ap(V5f,V6a0),V7a1),V8a2) = ap(ap(ap(V1f_27,V6a0),V7a1),V8a2) ) ) ) ) ) )
=> ( ap(ap(ap(c_2Equote_2Evarmap__CASE(A_27a,A_27b),V2M),V4v),V5f) = ap(ap(ap(c_2Equote_2Evarmap__CASE(A_27a,A_27b),V3M_27),V0v_27),V1f_27) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equote_2Evarmap__case__eq,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,ty_2Equote_2Evarmap(A_27a))
=> ! [V1v: $i] :
( mem(V1v,A_27b)
=> ! [V2f: $i] :
( mem(V2f,arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),A_27b))))
=> ! [V3v_27: $i] :
( mem(V3v_27,A_27b)
=> ( ( ap(ap(ap(c_2Equote_2Evarmap__CASE(A_27a,A_27b),V0x),V1v),V2f) = V3v_27 )
<=> ( ( ( V0x = c_2Equote_2EEmpty__vm(A_27a) )
& ( V1v = V3v_27 ) )
| ? [V4a: $i] :
( mem(V4a,A_27a)
& ? [V5v_27_27: $i] :
( mem(V5v_27_27,ty_2Equote_2Evarmap(A_27a))
& ? [V6v0: $i] :
( mem(V6v0,ty_2Equote_2Evarmap(A_27a))
& ( V0x = ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V4a),V5v_27_27),V6v0) )
& ( ap(ap(ap(V2f,V4a),V5v_27_27),V6v0) = V3v_27 ) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Equote_2Evarmap__find__ind,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Evarmap(A_27a),bool)))
=> ( ( ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2v1: $i] :
( mem(V2v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V3v2: $i] :
( mem(V3v2,ty_2Equote_2Evarmap(A_27a))
=> p(ap(ap(V0P,inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V1x),V2v1),V3v2))) ) ) )
& ! [V4i1: tp__ty_2Equote_2Eindex,V5x: $i] :
( mem(V5x,A_27a)
=> ! [V6v1: $i] :
( mem(V6v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V7v2: $i] :
( mem(V7v2,ty_2Equote_2Evarmap(A_27a))
=> ( p(ap(ap(V0P,inj__ty_2Equote_2Eindex(V4i1)),V7v2))
=> p(ap(ap(V0P,ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V4i1))),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V5x),V6v1),V7v2))) ) ) ) )
& ! [V8i1: tp__ty_2Equote_2Eindex,V9x: $i] :
( mem(V9x,A_27a)
=> ! [V10v1: $i] :
( mem(V10v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V11v2: $i] :
( mem(V11v2,ty_2Equote_2Evarmap(A_27a))
=> ( p(ap(ap(V0P,inj__ty_2Equote_2Eindex(V8i1)),V10v1))
=> p(ap(ap(V0P,ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V8i1))),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V9x),V10v1),V11v2))) ) ) ) )
& ! [V12i: tp__ty_2Equote_2Eindex] : p(ap(ap(V0P,inj__ty_2Equote_2Eindex(V12i)),c_2Equote_2EEmpty__vm(A_27a))) )
=> ! [V13v: tp__ty_2Equote_2Eindex,V14v1: $i] :
( mem(V14v1,ty_2Equote_2Evarmap(A_27a))
=> p(ap(ap(V0P,inj__ty_2Equote_2Eindex(V13v)),V14v1)) ) ) ) ).
tff(conj_thm_2Equote_2Evarmap__find__def,axiom,
! [A_27a: del] :
( ! [V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1v2: $i] :
( mem(V1v2,ty_2Equote_2Evarmap(A_27a))
=> ! [V2v1: $i] :
( mem(V2v1,ty_2Equote_2Evarmap(A_27a))
=> ( ap(ap(c_2Equote_2Evarmap__find(A_27a),inj__ty_2Equote_2Eindex(fo__c_2Equote_2EEnd__idx)),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V0x),V2v1),V1v2)) = V0x ) ) ) )
& ! [V3x: $i] :
( mem(V3x,A_27a)
=> ! [V4v2: $i] :
( mem(V4v2,ty_2Equote_2Evarmap(A_27a))
=> ! [V5v1: $i] :
( mem(V5v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V6i1: tp__ty_2Equote_2Eindex] : ( ap(ap(c_2Equote_2Evarmap__find(A_27a),ap(c_2Equote_2ERight__idx,inj__ty_2Equote_2Eindex(V6i1))),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V3x),V5v1),V4v2)) = ap(ap(c_2Equote_2Evarmap__find(A_27a),inj__ty_2Equote_2Eindex(V6i1)),V4v2) ) ) ) )
& ! [V7x: $i] :
( mem(V7x,A_27a)
=> ! [V8v2: $i] :
( mem(V8v2,ty_2Equote_2Evarmap(A_27a))
=> ! [V9v1: $i] :
( mem(V9v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V10i1: tp__ty_2Equote_2Eindex] : ( ap(ap(c_2Equote_2Evarmap__find(A_27a),ap(c_2Equote_2ELeft__idx,inj__ty_2Equote_2Eindex(V10i1))),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V7x),V9v1),V8v2)) = ap(ap(c_2Equote_2Evarmap__find(A_27a),inj__ty_2Equote_2Eindex(V10i1)),V9v1) ) ) ) )
& ! [V11i: tp__ty_2Equote_2Eindex] : ( ap(ap(c_2Equote_2Evarmap__find(A_27a),inj__ty_2Equote_2Eindex(V11i)),c_2Equote_2EEmpty__vm(A_27a)) = ap(c_2Emin_2E_40(A_27a),k(A_27a,c_2Ebool_2ET)) ) ) ).
%------------------------------------------------------------------------------