ITP001 Axioms: ITP089_5.ax
%------------------------------------------------------------------------------
% File : ITP089_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 : toto_2.ax [Gau20]
% : HL4089_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 258 ( 68 unt; 68 typ; 0 def)
% Number of atoms : 3126 ( 265 equ)
% Maximal formula atoms : 42 ( 12 avg)
% Number of connectives : 565 ( 18 ~; 7 |; 116 &)
% ( 33 <=>; 391 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2389 (2389 fml; 0 var)
% Number of types : 5 ( 4 usr)
% Number of type conns : 71 ( 44 >; 27 *; 0 +; 0 <<)
% Number of predicates : 82 ( 79 usr; 34 prp; 0-3 aty)
% Number of functors : 64 ( 64 usr; 20 con; 0-7 aty)
% Number of variables : 562 ( 551 !; 11 ?; 562 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_ty_2Etoto_2Enum__dt,type,
ty_2Etoto_2Enum__dt: del ).
tff(tp_ty_2Etoto_2Etoto,type,
ty_2Etoto_2Etoto: del > del ).
tff(tp_c_2Etoto_2EListOrd,type,
c_2Etoto_2EListOrd: del > $i ).
tff(mem_c_2Etoto_2EListOrd,axiom,
! [A_27a: del] : mem(c_2Etoto_2EListOrd(A_27a),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2EternaryComparisons_2Eordering)))) ).
tff(tp_c_2Etoto_2EStrongLinearOrder__of__TO,type,
c_2Etoto_2EStrongLinearOrder__of__TO: del > $i ).
tff(mem_c_2Etoto_2EStrongLinearOrder__of__TO,axiom,
! [A_27a: del] : mem(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),arr(arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)),arr(A_27a,arr(A_27a,bool)))) ).
tff(tp_c_2Etoto_2ETO,type,
c_2Etoto_2ETO: del > $i ).
tff(mem_c_2Etoto_2ETO,axiom,
! [A_27a: del] : mem(c_2Etoto_2ETO(A_27a),arr(arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)),ty_2Etoto_2Etoto(A_27a))) ).
tff(tp_c_2Etoto_2ETO__inv,type,
c_2Etoto_2ETO__inv: del > $i ).
tff(mem_c_2Etoto_2ETO__inv,axiom,
! [A_27a: del] : mem(c_2Etoto_2ETO__inv(A_27a),arr(arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)),arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))) ).
tff(tp_c_2Etoto_2ETO__of__LinearOrder,type,
c_2Etoto_2ETO__of__LinearOrder: del > $i ).
tff(mem_c_2Etoto_2ETO__of__LinearOrder,axiom,
! [A_27a: del] : mem(c_2Etoto_2ETO__of__LinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))) ).
tff(tp_c_2Etoto_2ETotOrd,type,
c_2Etoto_2ETotOrd: del > $i ).
tff(mem_c_2Etoto_2ETotOrd,axiom,
! [A_27a: del] : mem(c_2Etoto_2ETotOrd(A_27a),arr(arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)),bool)) ).
tff(tp_c_2Etoto_2EWeakLinearOrder__of__TO,type,
c_2Etoto_2EWeakLinearOrder__of__TO: del > $i ).
tff(mem_c_2Etoto_2EWeakLinearOrder__of__TO,axiom,
! [A_27a: del] : mem(c_2Etoto_2EWeakLinearOrder__of__TO(A_27a),arr(arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)),arr(A_27a,arr(A_27a,bool)))) ).
tff(tp_c_2Etoto_2Eapto,type,
c_2Etoto_2Eapto: del > $i ).
tff(mem_c_2Etoto_2Eapto,axiom,
! [A_27a: del] : mem(c_2Etoto_2Eapto(A_27a),arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))) ).
tff(stp_ty_2Etoto_2Enum__dt,type,
tp__ty_2Etoto_2Enum__dt: $tType ).
tff(stp_inj_ty_2Etoto_2Enum__dt,type,
inj__ty_2Etoto_2Enum__dt: tp__ty_2Etoto_2Enum__dt > $i ).
tff(stp_surj_ty_2Etoto_2Enum__dt,type,
surj__ty_2Etoto_2Enum__dt: $i > tp__ty_2Etoto_2Enum__dt ).
tff(stp_inj_surj_ty_2Etoto_2Enum__dt,axiom,
! [X: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2Etoto_2Enum__dt(inj__ty_2Etoto_2Enum__dt(X)) = X ) ).
tff(stp_inj_mem_ty_2Etoto_2Enum__dt,axiom,
! [X: tp__ty_2Etoto_2Enum__dt] : mem(inj__ty_2Etoto_2Enum__dt(X),ty_2Etoto_2Enum__dt) ).
tff(stp_iso_mem_ty_2Etoto_2Enum__dt,axiom,
! [X: $i] :
( mem(X,ty_2Etoto_2Enum__dt)
=> ( X = inj__ty_2Etoto_2Enum__dt(surj__ty_2Etoto_2Enum__dt(X)) ) ) ).
tff(tp_c_2Etoto_2Ebit1,type,
c_2Etoto_2Ebit1: $i ).
tff(mem_c_2Etoto_2Ebit1,axiom,
mem(c_2Etoto_2Ebit1,arr(ty_2Etoto_2Enum__dt,ty_2Etoto_2Enum__dt)) ).
tff(stp_fo_c_2Etoto_2Ebit1,type,
fo__c_2Etoto_2Ebit1: tp__ty_2Etoto_2Enum__dt > tp__ty_2Etoto_2Enum__dt ).
tff(stp_eq_fo_c_2Etoto_2Ebit1,axiom,
! [X0: tp__ty_2Etoto_2Enum__dt] : ( inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ebit1(X0)) = ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(X0)) ) ).
tff(tp_c_2Etoto_2Ebit2,type,
c_2Etoto_2Ebit2: $i ).
tff(mem_c_2Etoto_2Ebit2,axiom,
mem(c_2Etoto_2Ebit2,arr(ty_2Etoto_2Enum__dt,ty_2Etoto_2Enum__dt)) ).
tff(stp_fo_c_2Etoto_2Ebit2,type,
fo__c_2Etoto_2Ebit2: tp__ty_2Etoto_2Enum__dt > tp__ty_2Etoto_2Enum__dt ).
tff(stp_eq_fo_c_2Etoto_2Ebit2,axiom,
! [X0: tp__ty_2Etoto_2Enum__dt] : ( inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ebit2(X0)) = ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(X0)) ) ).
tff(tp_c_2Etoto_2EcharOrd,type,
c_2Etoto_2EcharOrd: $i ).
tff(mem_c_2Etoto_2EcharOrd,axiom,
mem(c_2Etoto_2EcharOrd,arr(ty_2Estring_2Echar,arr(ty_2Estring_2Echar,ty_2EternaryComparisons_2Eordering))) ).
tff(stp_fo_c_2Etoto_2EcharOrd,type,
fo__c_2Etoto_2EcharOrd: ( tp__ty_2Estring_2Echar * tp__ty_2Estring_2Echar ) > tp__ty_2EternaryComparisons_2Eordering ).
tff(stp_eq_fo_c_2Etoto_2EcharOrd,axiom,
! [X0: tp__ty_2Estring_2Echar,X1: tp__ty_2Estring_2Echar] : ( inj__ty_2EternaryComparisons_2Eordering(fo__c_2Etoto_2EcharOrd(X0,X1)) = ap(ap(c_2Etoto_2EcharOrd,inj__ty_2Estring_2Echar(X0)),inj__ty_2Estring_2Echar(X1)) ) ).
tff(stp_c_ty_2Etoto_2Etoto_ty_2Estring_2Echar,type,
tp__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar: $tType ).
tff(stp_inj_c_ty_2Etoto_2Etoto_ty_2Estring_2Echar,type,
inj__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar: tp__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar > $i ).
tff(stp_surj_c_ty_2Etoto_2Etoto_ty_2Estring_2Echar,type,
surj__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar: $i > tp__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar ).
tff(stp_inj_surj_c_ty_2Etoto_2Etoto_ty_2Estring_2Echar,axiom,
! [X: tp__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar] : ( surj__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar(inj__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar(X)) = X ) ).
tff(stp_inj_mem_c_ty_2Etoto_2Etoto_ty_2Estring_2Echar,axiom,
! [X: tp__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar] : mem(inj__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar(X),ty_2Etoto_2Etoto(ty_2Estring_2Echar)) ).
tff(stp_iso_mem_c_ty_2Etoto_2Etoto_ty_2Estring_2Echar,axiom,
! [X: $i] :
( mem(X,ty_2Etoto_2Etoto(ty_2Estring_2Echar))
=> ( X = inj__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar(surj__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar(X)) ) ) ).
tff(tp_c_2Etoto_2Echarto,type,
c_2Etoto_2Echarto: $i ).
tff(mem_c_2Etoto_2Echarto,axiom,
mem(c_2Etoto_2Echarto,ty_2Etoto_2Etoto(ty_2Estring_2Echar)) ).
tff(tp_c_2Etoto_2EimageOrd,type,
c_2Etoto_2EimageOrd: ( del * del ) > $i ).
tff(mem_c_2Etoto_2EimageOrd,axiom,
! [A_27a: del,A_27c: del] : mem(c_2Etoto_2EimageOrd(A_27a,A_27c),arr(arr(A_27a,A_27c),arr(arr(A_27c,arr(A_27c,ty_2EternaryComparisons_2Eordering)),arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering))))) ).
tff(tp_c_2Etoto_2ElexTO,type,
c_2Etoto_2ElexTO: ( del * del ) > $i ).
tff(mem_c_2Etoto_2ElexTO,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Etoto_2ElexTO(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)),arr(arr(A_27b,arr(A_27b,ty_2EternaryComparisons_2Eordering)),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2EternaryComparisons_2Eordering))))) ).
tff(tp_c_2Etoto_2Elextoto,type,
c_2Etoto_2Elextoto: ( del * del ) > $i ).
tff(mem_c_2Etoto_2Elextoto,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Etoto_2Elextoto(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Etoto_2Etoto(A_27b),ty_2Etoto_2Etoto(ty_2Epair_2Eprod(A_27a,A_27b))))) ).
tff(tp_c_2Etoto_2Elistorder,type,
c_2Etoto_2Elistorder: del > $i ).
tff(mem_c_2Etoto_2Elistorder,axiom,
! [A_27a: del] : mem(c_2Etoto_2Elistorder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool)))) ).
tff(tp_c_2Etoto_2Elistoto,type,
c_2Etoto_2Elistoto: del > $i ).
tff(mem_c_2Etoto_2Elistoto,axiom,
! [A_27a: del] : mem(c_2Etoto_2Elistoto(A_27a),arr(ty_2Etoto_2Etoto(A_27a),ty_2Etoto_2Etoto(ty_2Elist_2Elist(A_27a)))) ).
tff(tp_c_2Etoto_2EnumOrd,type,
c_2Etoto_2EnumOrd: $i ).
tff(mem_c_2Etoto_2EnumOrd,axiom,
mem(c_2Etoto_2EnumOrd,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2EternaryComparisons_2Eordering))) ).
tff(stp_fo_c_2Etoto_2EnumOrd,type,
fo__c_2Etoto_2EnumOrd: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__ty_2EternaryComparisons_2Eordering ).
tff(stp_eq_fo_c_2Etoto_2EnumOrd,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : ( inj__ty_2EternaryComparisons_2Eordering(fo__c_2Etoto_2EnumOrd(X0,X1)) = ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ) ).
tff(tp_c_2Etoto_2Enum__dtOrd,type,
c_2Etoto_2Enum__dtOrd: $i ).
tff(mem_c_2Etoto_2Enum__dtOrd,axiom,
mem(c_2Etoto_2Enum__dtOrd,arr(ty_2Etoto_2Enum__dt,arr(ty_2Etoto_2Enum__dt,ty_2EternaryComparisons_2Eordering))) ).
tff(stp_fo_c_2Etoto_2Enum__dtOrd,type,
fo__c_2Etoto_2Enum__dtOrd: ( tp__ty_2Etoto_2Enum__dt * tp__ty_2Etoto_2Enum__dt ) > tp__ty_2EternaryComparisons_2Eordering ).
tff(stp_eq_fo_c_2Etoto_2Enum__dtOrd,axiom,
! [X0: tp__ty_2Etoto_2Enum__dt,X1: tp__ty_2Etoto_2Enum__dt] : ( inj__ty_2EternaryComparisons_2Eordering(fo__c_2Etoto_2Enum__dtOrd(X0,X1)) = ap(ap(c_2Etoto_2Enum__dtOrd,inj__ty_2Etoto_2Enum__dt(X0)),inj__ty_2Etoto_2Enum__dt(X1)) ) ).
tff(tp_c_2Etoto_2Enum__dt__CASE,type,
c_2Etoto_2Enum__dt__CASE: del > $i ).
tff(mem_c_2Etoto_2Enum__dt__CASE,axiom,
! [A_27a: del] : mem(c_2Etoto_2Enum__dt__CASE(A_27a),arr(ty_2Etoto_2Enum__dt,arr(A_27a,arr(arr(ty_2Etoto_2Enum__dt,A_27a),arr(arr(ty_2Etoto_2Enum__dt,A_27a),A_27a))))) ).
tff(tp_c_2Etoto_2Enum__dt__size,type,
c_2Etoto_2Enum__dt__size: $i ).
tff(mem_c_2Etoto_2Enum__dt__size,axiom,
mem(c_2Etoto_2Enum__dt__size,arr(ty_2Etoto_2Enum__dt,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Etoto_2Enum__dt__size,type,
fo__c_2Etoto_2Enum__dt__size: tp__ty_2Etoto_2Enum__dt > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Etoto_2Enum__dt__size,axiom,
! [X0: tp__ty_2Etoto_2Enum__dt] : ( inj__ty_2Enum_2Enum(fo__c_2Etoto_2Enum__dt__size(X0)) = ap(c_2Etoto_2Enum__dt__size,inj__ty_2Etoto_2Enum__dt(X0)) ) ).
tff(tp_c_2Etoto_2Enum__to__dt,type,
c_2Etoto_2Enum__to__dt: $i ).
tff(mem_c_2Etoto_2Enum__to__dt,axiom,
mem(c_2Etoto_2Enum__to__dt,arr(ty_2Enum_2Enum,ty_2Etoto_2Enum__dt)) ).
tff(stp_fo_c_2Etoto_2Enum__to__dt,type,
fo__c_2Etoto_2Enum__to__dt: tp__ty_2Enum_2Enum > tp__ty_2Etoto_2Enum__dt ).
tff(stp_eq_fo_c_2Etoto_2Enum__to__dt,axiom,
! [X0: tp__ty_2Enum_2Enum] : ( inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Enum__to__dt(X0)) = ap(c_2Etoto_2Enum__to__dt,inj__ty_2Enum_2Enum(X0)) ) ).
tff(stp_c_ty_2Etoto_2Etoto_ty_2Enum_2Enum,type,
tp__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum: $tType ).
tff(stp_inj_c_ty_2Etoto_2Etoto_ty_2Enum_2Enum,type,
inj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum: tp__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum > $i ).
tff(stp_surj_c_ty_2Etoto_2Etoto_ty_2Enum_2Enum,type,
surj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum: $i > tp__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum ).
tff(stp_inj_surj_c_ty_2Etoto_2Etoto_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum] : ( surj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum(inj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum(X)) = X ) ).
tff(stp_inj_mem_c_ty_2Etoto_2Etoto_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum] : mem(inj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum(X),ty_2Etoto_2Etoto(ty_2Enum_2Enum)) ).
tff(stp_iso_mem_c_ty_2Etoto_2Etoto_ty_2Enum_2Enum,axiom,
! [X: $i] :
( mem(X,ty_2Etoto_2Etoto(ty_2Enum_2Enum))
=> ( X = inj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum(surj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum(X)) ) ) ).
tff(tp_c_2Etoto_2Enumto,type,
c_2Etoto_2Enumto: $i ).
tff(mem_c_2Etoto_2Enumto,axiom,
mem(c_2Etoto_2Enumto,ty_2Etoto_2Etoto(ty_2Enum_2Enum)) ).
tff(tp_c_2Etoto_2Eqk__numOrd,type,
c_2Etoto_2Eqk__numOrd: $i ).
tff(mem_c_2Etoto_2Eqk__numOrd,axiom,
mem(c_2Etoto_2Eqk__numOrd,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2EternaryComparisons_2Eordering))) ).
tff(stp_fo_c_2Etoto_2Eqk__numOrd,type,
fo__c_2Etoto_2Eqk__numOrd: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__ty_2EternaryComparisons_2Eordering ).
tff(stp_eq_fo_c_2Etoto_2Eqk__numOrd,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : ( inj__ty_2EternaryComparisons_2Eordering(fo__c_2Etoto_2Eqk__numOrd(X0,X1)) = ap(ap(c_2Etoto_2Eqk__numOrd,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ) ).
tff(tp_c_2Etoto_2Eqk__numto,type,
c_2Etoto_2Eqk__numto: $i ).
tff(mem_c_2Etoto_2Eqk__numto,axiom,
mem(c_2Etoto_2Eqk__numto,ty_2Etoto_2Etoto(ty_2Enum_2Enum)) ).
tff(stp_c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar,type,
tp__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar: $tType ).
tff(stp_inj_c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar,type,
inj__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar: tp__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar > $i ).
tff(stp_surj_c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar,type,
surj__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar: $i > tp__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar ).
tff(stp_inj_surj_c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar,axiom,
! [X: tp__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar] : ( surj__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar(inj__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar(X)) = X ) ).
tff(stp_inj_mem_c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar,axiom,
! [X: tp__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar] : mem(inj__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar(X),ty_2Etoto_2Etoto(ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
tff(stp_iso_mem_c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar,axiom,
! [X: $i] :
( mem(X,ty_2Etoto_2Etoto(ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ( X = inj__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar(surj__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar(X)) ) ) ).
tff(tp_c_2Etoto_2Estringto,type,
c_2Etoto_2Estringto: $i ).
tff(mem_c_2Etoto_2Estringto,axiom,
mem(c_2Etoto_2Estringto,ty_2Etoto_2Etoto(ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
tff(tp_c_2Etoto_2Etoto__inv,type,
c_2Etoto_2Etoto__inv: del > $i ).
tff(mem_c_2Etoto_2Etoto__inv,axiom,
! [A_27a: del] : mem(c_2Etoto_2Etoto__inv(A_27a),arr(ty_2Etoto_2Etoto(A_27a),ty_2Etoto_2Etoto(A_27a))) ).
tff(tp_c_2Etoto_2Etoto__of__LinearOrder,type,
c_2Etoto_2Etoto__of__LinearOrder: del > $i ).
tff(mem_c_2Etoto_2Etoto__of__LinearOrder,axiom,
! [A_27a: del] : mem(c_2Etoto_2Etoto__of__LinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),ty_2Etoto_2Etoto(A_27a))) ).
tff(tp_c_2Etoto_2Ezer,type,
c_2Etoto_2Ezer: $i ).
tff(mem_c_2Etoto_2Ezer,axiom,
mem(c_2Etoto_2Ezer,ty_2Etoto_2Enum__dt) ).
tff(stp_fo_c_2Etoto_2Ezer,type,
fo__c_2Etoto_2Ezer: tp__ty_2Etoto_2Enum__dt ).
tff(stp_eq_fo_c_2Etoto_2Ezer,axiom,
inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer) = c_2Etoto_2Ezer ).
tff(conj_thm_2Etoto_2EStrongLinearOrderExists,axiom,
! [A_27a: del] :
? [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
& p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0R)) ) ).
tff(ax_thm_2Etoto_2ETotOrd,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0c))
<=> ( ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
<=> ( V1x = V2y ) ) ) )
& ! [V3x: $i] :
( mem(V3x,A_27a)
=> ! [V4y: $i] :
( mem(V4y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V3x),V4y)) = fo__c_2EternaryComparisons_2EGREATER )
<=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V4y),V3x)) = fo__c_2EternaryComparisons_2ELESS ) ) ) )
& ! [V5x: $i] :
( mem(V5x,A_27a)
=> ! [V6y: $i] :
( mem(V6y,A_27a)
=> ! [V7z: $i] :
( mem(V7z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V5x),V6y)) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V6y),V7z)) = fo__c_2EternaryComparisons_2ELESS ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V5x),V7z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ).
tff(ax_thm_2Etoto_2ETO__of__LinearOrder,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0r),V1x),V2y)) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Ebool_2ECOND(ty_2EternaryComparisons_2Eordering),ap(ap(c_2Emin_2E_3D(A_27a),V1x),V2y)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EEQUAL)),ap(ap(ap(c_2Ebool_2ECOND(ty_2EternaryComparisons_2Eordering),ap(ap(V0r,V1x),V2y)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER)))) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etrichotomous__ALT,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R))
<=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( ~ p(ap(ap(V0R,V1x),V2y))
& ~ p(ap(ap(V0R,V2y),V1x)) )
=> ( V1x = V2y ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ETotOrd__TO__of__LO,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2ELinearOrder(A_27a),V0r))
=> p(ap(c_2Etoto_2ETotOrd(A_27a),ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0r))) ) ) ).
tff(conj_thm_2Etoto_2ESPLIT__PAIRS,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V1y: $i] :
( mem(V1y,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( ( V0x = V1y )
<=> ( ( ap(c_2Epair_2EFST(A_27a,A_27b),V0x) = ap(c_2Epair_2EFST(A_27a,A_27b),V1y) )
& ( ap(c_2Epair_2ESND(A_27a,A_27b),V0x) = ap(c_2Epair_2ESND(A_27a,A_27b),V1y) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Eall__cpn__distinct,axiom,
( ( fo__c_2EternaryComparisons_2ELESS != fo__c_2EternaryComparisons_2EEQUAL )
& ( fo__c_2EternaryComparisons_2ELESS != fo__c_2EternaryComparisons_2EGREATER )
& ( fo__c_2EternaryComparisons_2EEQUAL != fo__c_2EternaryComparisons_2EGREATER )
& ( fo__c_2EternaryComparisons_2EEQUAL != fo__c_2EternaryComparisons_2ELESS )
& ( fo__c_2EternaryComparisons_2EGREATER != fo__c_2EternaryComparisons_2ELESS )
& ( fo__c_2EternaryComparisons_2EGREATER != fo__c_2EternaryComparisons_2EEQUAL ) ) ).
tff(conj_thm_2Etoto_2ETO__exists,axiom,
! [A_27a: del] :
? [V0x: $i] :
( mem(V0x,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
& p(ap(c_2Etoto_2ETotOrd(A_27a),V0x)) ) ).
tff(ax_thm_2Etoto_2Etoto__TY__DEF,axiom,
! [A_27a: del] :
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering))))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)),ty_2Etoto_2Etoto(A_27a)),c_2Etoto_2ETotOrd(A_27a)),V0rep)) ) ).
tff(ax_thm_2Etoto_2Eto__bij,axiom,
! [A_27a: del] :
( ! [V0a: $i] :
( mem(V0a,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2ETO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0a)) = V0a ) )
& ! [V1r: $i] :
( mem(V1r,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V1r))
<=> ( ap(c_2Etoto_2Eapto(A_27a),ap(c_2Etoto_2ETO(A_27a),V1r)) = V1r ) ) ) ) ).
tff(conj_thm_2Etoto_2ETO__apto__ID,axiom,
! [A_27a: del,V0a: $i] :
( mem(V0a,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2ETO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0a)) = V0a ) ) ).
tff(conj_thm_2Etoto_2ETO__apto__TO__ID,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0r))
<=> ( ap(c_2Etoto_2Eapto(A_27a),ap(c_2Etoto_2ETO(A_27a),V0r)) = V0r ) ) ) ).
tff(conj_thm_2Etoto_2ETO__11,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V1r_27: $i] :
( mem(V1r_27,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0r))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V1r_27))
=> ( ( ap(c_2Etoto_2ETO(A_27a),V0r) = ap(c_2Etoto_2ETO(A_27a),V1r_27) )
<=> ( V0r = V1r_27 ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Eonto__apto,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0r))
<=> ? [V1a: $i] :
( mem(V1a,ty_2Etoto_2Etoto(A_27a))
& ( V0r = ap(c_2Etoto_2Eapto(A_27a),V1a) ) ) ) ) ).
tff(conj_thm_2Etoto_2ETO__onto,axiom,
! [A_27a: del,V0a: $i] :
( mem(V0a,ty_2Etoto_2Etoto(A_27a))
=> ? [V1r: $i] :
( mem(V1r,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
& ( V0a = ap(c_2Etoto_2ETO(A_27a),V1r) )
& p(ap(c_2Etoto_2ETotOrd(A_27a),V1r)) ) ) ).
tff(conj_thm_2Etoto_2ETotOrd__apto,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> p(ap(c_2Etoto_2ETotOrd(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c))) ) ).
tff(conj_thm_2Etoto_2ETO__apto__TO__IMP,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0r))
=> ( ap(c_2Etoto_2Eapto(A_27a),ap(c_2Etoto_2ETO(A_27a),V0r)) = V0r ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__thm,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
<=> ( V1x = V2y ) ) ) )
& ! [V3x: $i] :
( mem(V3x,A_27a)
=> ! [V4y: $i] :
( mem(V4y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V3x),V4y)) = fo__c_2EternaryComparisons_2EGREATER )
<=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V4y),V3x)) = fo__c_2EternaryComparisons_2ELESS ) ) ) )
& ! [V5x: $i] :
( mem(V5x,A_27a)
=> ! [V6y: $i] :
( mem(V6y,A_27a)
=> ! [V7z: $i] :
( mem(V7z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V5x),V6y)) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V6y),V7z)) = fo__c_2EternaryComparisons_2ELESS ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V5x),V7z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ETO__equal__eq,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0c))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
<=> ( V1x = V2y ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__equal__eq,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
<=> ( V1x = V2y ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__equal__imp__eq,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
=> ( V1x = V2y ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ETO__refl,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0c))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V1x),V1x)) = fo__c_2EternaryComparisons_2EEQUAL ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__refl,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V1x)) = fo__c_2EternaryComparisons_2EEQUAL ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__equal__sym,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
<=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V1x)) = fo__c_2EternaryComparisons_2EEQUAL ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ETO__antisym,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0c))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V1x),V2y)) = fo__c_2EternaryComparisons_2EGREATER )
<=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V2y),V1x)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__antisym,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2EGREATER )
<=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V1x)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__not__less__refl,axiom,
! [A_27a: del,V0cmp: $i] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1h: $i] :
( mem(V1h,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V1h),V1h)) = fo__c_2EternaryComparisons_2ELESS )
<=> $false ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__swap__cases,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V1x)) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EEQUAL)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS))) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__glneq,axiom,
! [A_27a: del] :
( ! [V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2ELESS )
=> ( V1x != V2y ) ) ) ) )
& ! [V3c: $i] :
( mem(V3c,ty_2Etoto_2Etoto(A_27a))
=> ! [V4x: $i] :
( mem(V4x,A_27a)
=> ! [V5y: $i] :
( mem(V5y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V3c),V4x),V5y)) = fo__c_2EternaryComparisons_2EGREATER )
=> ( V4x != V5y ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__cpn__eqn,axiom,
! [A_27a: del] :
( ! [V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
=> ( V1x = V2y ) ) ) ) )
& ! [V3c: $i] :
( mem(V3c,ty_2Etoto_2Etoto(A_27a))
=> ! [V4x: $i] :
( mem(V4x,A_27a)
=> ! [V5y: $i] :
( mem(V5y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V3c),V4x),V5y)) = fo__c_2EternaryComparisons_2ELESS )
=> ( V4x != V5y ) ) ) ) )
& ! [V6c: $i] :
( mem(V6c,ty_2Etoto_2Etoto(A_27a))
=> ! [V7x: $i] :
( mem(V7x,A_27a)
=> ! [V8y: $i] :
( mem(V8y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V6c),V7x),V8y)) = fo__c_2EternaryComparisons_2EGREATER )
=> ( V7x != V8y ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ETO__cpn__eqn,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0c))
=> ( ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V1x),V2y)) = fo__c_2EternaryComparisons_2ELESS )
=> ( V1x != V2y ) ) ) )
& ! [V3x: $i] :
( mem(V3x,A_27a)
=> ! [V4y: $i] :
( mem(V4y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V3x),V4y)) = fo__c_2EternaryComparisons_2EGREATER )
=> ( V3x != V4y ) ) ) )
& ! [V5x: $i] :
( mem(V5x,A_27a)
=> ! [V6y: $i] :
( mem(V6y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V5x),V6y)) = fo__c_2EternaryComparisons_2EEQUAL )
=> ( V5x = V6y ) ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ENOT__EQ__LESS__IMP,axiom,
! [A_27a: del,V0cmp: $i] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V1x),V2y)) != fo__c_2EternaryComparisons_2ELESS )
=> ( ( V1x = V2y )
| ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V2y),V1x)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2EtotoEEtrans,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,A_27a)
=> ( ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V3z)) = fo__c_2EternaryComparisons_2EEQUAL ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V3z)) = fo__c_2EternaryComparisons_2EEQUAL ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V3z),V2y)) = fo__c_2EternaryComparisons_2EEQUAL ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V3z)) = fo__c_2EternaryComparisons_2EEQUAL ) ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2EtotoLLtrans,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V3z)) = fo__c_2EternaryComparisons_2ELESS ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V3z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2EtotoLGtrans,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V3z),V2y)) = fo__c_2EternaryComparisons_2EGREATER ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V3z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2EtotoGGtrans,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V1x)) = fo__c_2EternaryComparisons_2EGREATER )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V3z),V2y)) = fo__c_2EternaryComparisons_2EGREATER ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V3z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2EtotoGLtrans,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V1x)) = fo__c_2EternaryComparisons_2EGREATER )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V3z)) = fo__c_2EternaryComparisons_2ELESS ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V3z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2EtotoLEtrans,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V3z)) = fo__c_2EternaryComparisons_2EEQUAL ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V3z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2EtotoELtrans,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2EEQUAL )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V3z)) = fo__c_2EternaryComparisons_2ELESS ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V3z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__trans__less,axiom,
! [A_27a: del] :
( ! [V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ! [V3z: $i] :
( mem(V3z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V2y)) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2y),V3z)) = fo__c_2EternaryComparisons_2ELESS ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V1x),V3z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) )
& ! [V4c: $i] :
( mem(V4c,ty_2Etoto_2Etoto(A_27a))
=> ! [V5x: $i] :
( mem(V5x,A_27a)
=> ! [V6y: $i] :
( mem(V6y,A_27a)
=> ! [V7z: $i] :
( mem(V7z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4c),V5x),V6y)) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4c),V7z),V6y)) = fo__c_2EternaryComparisons_2EGREATER ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4c),V5x),V7z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) )
& ! [V8c: $i] :
( mem(V8c,ty_2Etoto_2Etoto(A_27a))
=> ! [V9x: $i] :
( mem(V9x,A_27a)
=> ! [V10y: $i] :
( mem(V10y,A_27a)
=> ! [V11z: $i] :
( mem(V11z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V8c),V10y),V9x)) = fo__c_2EternaryComparisons_2EGREATER )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V8c),V11z),V10y)) = fo__c_2EternaryComparisons_2EGREATER ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V8c),V9x),V11z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) )
& ! [V12c: $i] :
( mem(V12c,ty_2Etoto_2Etoto(A_27a))
=> ! [V13x: $i] :
( mem(V13x,A_27a)
=> ! [V14y: $i] :
( mem(V14y,A_27a)
=> ! [V15z: $i] :
( mem(V15z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V12c),V14y),V13x)) = fo__c_2EternaryComparisons_2EGREATER )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V12c),V14y),V15z)) = fo__c_2EternaryComparisons_2ELESS ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V12c),V13x),V15z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) )
& ! [V16c: $i] :
( mem(V16c,ty_2Etoto_2Etoto(A_27a))
=> ! [V17x: $i] :
( mem(V17x,A_27a)
=> ! [V18y: $i] :
( mem(V18y,A_27a)
=> ! [V19z: $i] :
( mem(V19z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V16c),V17x),V18y)) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V16c),V18y),V19z)) = fo__c_2EternaryComparisons_2EEQUAL ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V16c),V17x),V19z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) )
& ! [V20c: $i] :
( mem(V20c,ty_2Etoto_2Etoto(A_27a))
=> ! [V21x: $i] :
( mem(V21x,A_27a)
=> ! [V22y: $i] :
( mem(V22y,A_27a)
=> ! [V23z: $i] :
( mem(V23z,A_27a)
=> ( ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V20c),V21x),V22y)) = fo__c_2EternaryComparisons_2EEQUAL )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V20c),V22y),V23z)) = fo__c_2EternaryComparisons_2ELESS ) )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V20c),V21x),V23z)) = fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ).
tff(ax_thm_2Etoto_2EWeakLinearOrder__of__TO,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( p(ap(ap(ap(c_2Etoto_2EWeakLinearOrder__of__TO(A_27a),V0c),V1x),V2y))
<=> p(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(bool),ap(ap(V0c,V1x),V2y)),inj__o(fo__c_2Ebool_2ET)),inj__o(fo__c_2Ebool_2ET)),inj__o(fo__c_2Ebool_2EF))) ) ) ) ) ).
tff(ax_thm_2Etoto_2EStrongLinearOrder__of__TO,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( p(ap(ap(ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),V0c),V1x),V2y))
<=> p(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(bool),ap(ap(V0c,V1x),V2y)),inj__o(fo__c_2Ebool_2ET)),inj__o(fo__c_2Ebool_2EF)),inj__o(fo__c_2Ebool_2EF))) ) ) ) ) ).
tff(ax_thm_2Etoto_2Etoto__of__LinearOrder,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ( ap(c_2Etoto_2Etoto__of__LinearOrder(A_27a),V0r) = ap(c_2Etoto_2ETO(A_27a),ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0r)) ) ) ).
tff(conj_thm_2Etoto_2EWeak__Weak__of,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),ap(c_2Etoto_2EWeakLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c)))) ) ).
tff(conj_thm_2Etoto_2ESTRORD__SLO,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),V0R))
=> p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),ap(c_2Erelation_2ESTRORD(A_27a),V0R))) ) ) ).
tff(conj_thm_2Etoto_2EStrongof__toto__STRORD,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c)) = ap(c_2Erelation_2ESTRORD(A_27a),ap(c_2Etoto_2EWeakLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c))) ) ) ).
tff(conj_thm_2Etoto_2EStrong__Strong__of,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c)))) ) ).
tff(conj_thm_2Etoto_2EStrong__Strong__of__TO,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0c))
=> p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),V0c))) ) ) ).
tff(conj_thm_2Etoto_2ETotOrd__TO__of__Weak,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),V0r))
=> p(ap(c_2Etoto_2ETotOrd(A_27a),ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0r))) ) ) ).
tff(conj_thm_2Etoto_2ETotOrd__TO__of__Strong,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0r))
=> p(ap(c_2Etoto_2ETotOrd(A_27a),ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0r))) ) ) ).
tff(conj_thm_2Etoto_2Etoto__Weak__thm,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2Etoto__of__LinearOrder(A_27a),ap(c_2Etoto_2EWeakLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c))) = V0c ) ) ).
tff(conj_thm_2Etoto_2Etoto__Strong__thm,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2Etoto__of__LinearOrder(A_27a),ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c))) = V0c ) ) ).
tff(conj_thm_2Etoto_2EWeak__toto__thm,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),V0r))
=> ( ap(c_2Etoto_2EWeakLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),ap(c_2Etoto_2Etoto__of__LinearOrder(A_27a),V0r))) = V0r ) ) ) ).
tff(conj_thm_2Etoto_2EStrong__toto__thm,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0r))
=> ( ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),ap(c_2Etoto_2Etoto__of__LinearOrder(A_27a),V0r))) = V0r ) ) ) ).
tff(ax_thm_2Etoto_2ETO__inv,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2ETO__inv(A_27a),V0c),V1x),V2y)) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(V0c,V2y),V1x)) ) ) ) ) ).
tff(conj_thm_2Etoto_2ETotOrd__inv,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0c))
=> p(ap(c_2Etoto_2ETotOrd(A_27a),ap(c_2Etoto_2ETO__inv(A_27a),V0c))) ) ) ).
tff(ax_thm_2Etoto_2Etoto__inv,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2Etoto__inv(A_27a),V0c) = ap(c_2Etoto_2ETO(A_27a),ap(c_2Etoto_2ETO__inv(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c))) ) ) ).
tff(conj_thm_2Etoto_2Einv__TO,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0r))
=> ( ap(c_2Etoto_2Etoto__inv(A_27a),ap(c_2Etoto_2ETO(A_27a),V0r)) = ap(c_2Etoto_2ETO(A_27a),ap(c_2Etoto_2ETO__inv(A_27a),V0r)) ) ) ) ).
tff(conj_thm_2Etoto_2Eapto__inv,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2Eapto(A_27a),ap(c_2Etoto_2Etoto__inv(A_27a),V0c)) = ap(c_2Etoto_2ETO__inv(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c)) ) ) ).
tff(conj_thm_2Etoto_2EWeak__toto__inv,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2EWeakLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),ap(c_2Etoto_2Etoto__inv(A_27a),V0c))) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Etoto_2EWeakLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c))) ) ) ).
tff(conj_thm_2Etoto_2EStrong__toto__inv,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),ap(c_2Etoto_2Etoto__inv(A_27a),V0c))) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c))) ) ) ).
tff(conj_thm_2Etoto_2ETO__inv__TO__inv,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ( ap(c_2Etoto_2ETO__inv(A_27a),ap(c_2Etoto_2ETO__inv(A_27a),V0c)) = V0c ) ) ).
tff(conj_thm_2Etoto_2Etoto__inv__toto__inv,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2Etoto__inv(A_27a),ap(c_2Etoto_2Etoto__inv(A_27a),V0c)) = V0c ) ) ).
tff(conj_thm_2Etoto_2ETO__inv__Ord,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ( ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0r)) = ap(c_2Etoto_2ETO__inv(A_27a),ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0r)) ) ) ).
tff(conj_thm_2Etoto_2ETO__of__less__rel,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0r))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0r),V1x),V2y)) = fo__c_2EternaryComparisons_2ELESS )
<=> p(ap(ap(V0r,V1x),V2y)) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ETO__of__greater__ler,axiom,
! [A_27a: del,V0r: $i] :
( mem(V0r,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0r))
=> ! [V1x: $i] :
( mem(V1x,A_27a)
=> ! [V2y: $i] :
( mem(V2y,A_27a)
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0r),V1x),V2y)) = fo__c_2EternaryComparisons_2EGREATER )
<=> p(ap(ap(V0r,V2y),V1x)) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__equal__imp,axiom,
! [A_27a: del,V0cmp: $i] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1phi: $i] :
( mem(V1phi,arr(A_27a,arr(A_27a,bool)))
=> ( ( p(ap(c_2Erelation_2ELinearOrder(A_27a),V1phi))
& ( V0cmp = ap(c_2Etoto_2Etoto__of__LinearOrder(A_27a),V1phi) ) )
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27a)
=> ( ( ( V2x = V3y )
<=> $true )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V2x),V3y)) = fo__c_2EternaryComparisons_2EEQUAL ) ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Etoto__unequal__imp,axiom,
! [A_27a: del,V0cmp: $i] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1phi: $i] :
( mem(V1phi,arr(A_27a,arr(A_27a,bool)))
=> ( ( p(ap(c_2Erelation_2ELinearOrder(A_27a),V1phi))
& ( V0cmp = ap(c_2Etoto_2Etoto__of__LinearOrder(A_27a),V1phi) ) )
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V3y: $i] :
( mem(V3y,A_27a)
=> ( ( ( V2x = V3y )
<=> $false )
=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(V1phi,V2x),V3y)),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V2x),V3y)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V2x),V3y)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER)))) ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2EStrongOrder__ALT,axiom,
! [A_27a: del,V0Z: $i] :
( mem(V0Z,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EStrongOrder(A_27a),V0Z))
<=> ( p(ap(c_2Erelation_2Eirreflexive(A_27a),V0Z))
& p(ap(c_2Erelation_2Etransitive(A_27a),V0Z)) ) ) ) ).
tff(conj_thm_2Etoto_2ELEX__ALT,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1U: $i] :
( mem(V1U,arr(A_27b,arr(A_27b,bool)))
=> ! [V2c: $i] :
( mem(V2c,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V3d: $i] :
( mem(V3d,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R),V1U),V2c),V3d))
<=> ( p(ap(ap(V0R,ap(c_2Epair_2EFST(A_27a,A_27b),V2c)),ap(c_2Epair_2EFST(A_27a,A_27b),V3d)))
| ( ( ap(c_2Epair_2EFST(A_27a,A_27b),V2c) = ap(c_2Epair_2EFST(A_27a,A_27b),V3d) )
& p(ap(ap(V1U,ap(c_2Epair_2ESND(A_27a,A_27b),V2c)),ap(c_2Epair_2ESND(A_27a,A_27b),V3d))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ESLO__LEX,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,bool)))
=> ( ( p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0R))
& p(ap(c_2Erelation_2EStrongLinearOrder(A_27b),V1V)) )
=> p(ap(c_2Erelation_2EStrongLinearOrder(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R),V1V))) ) ) ) ).
tff(ax_thm_2Etoto_2ElexTO,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,ty_2EternaryComparisons_2Eordering)))
=> ( ap(ap(c_2Etoto_2ElexTO(A_27a,A_27b),V0R),V1V) = ap(c_2Etoto_2ETO__of__LinearOrder(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),V0R)),ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27b),V1V))) ) ) ) ).
tff(ax_thm_2Etoto_2Elextoto,axiom,
! [A_27a: del,A_27b: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1v: $i] :
( mem(V1v,ty_2Etoto_2Etoto(A_27b))
=> ( ap(ap(c_2Etoto_2Elextoto(A_27a,A_27b),V0c),V1v) = ap(c_2Etoto_2ETO(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Etoto_2ElexTO(A_27a,A_27b),ap(c_2Etoto_2Eapto(A_27a),V0c)),ap(c_2Etoto_2Eapto(A_27b),V1v))) ) ) ) ).
tff(conj_thm_2Etoto_2ElexTO__thm,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,ty_2EternaryComparisons_2Eordering)))
=> ( ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0R))
& p(ap(c_2Etoto_2ETotOrd(A_27b),V1V)) )
=> ! [V2x: $i] :
( mem(V2x,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V3y: $i] :
( mem(V3y,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2Etoto_2ElexTO(A_27a,A_27b),V0R),V1V),V2x),V3y)) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2EternaryComparisons_2Eordering),ap(ap(V0R,ap(c_2Epair_2EFST(A_27a,A_27b),V2x)),ap(c_2Epair_2EFST(A_27a,A_27b),V3y))),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),ap(ap(V1V,ap(c_2Epair_2ESND(A_27a,A_27b),V2x)),ap(c_2Epair_2ESND(A_27a,A_27b),V3y))),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER))) ) ) ) ) ) ) ).
tff(lamtp_f2259,type,
f2259: ( del * del * $i * $i * $i * $i * $i ) > $i ).
tff(lameq_f2259,axiom,
! [A_27a: del,A_27b: del,V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,ty_2EternaryComparisons_2Eordering)))
=> ! [V3u: $i] :
( mem(V3u,A_27b)
=> ! [V2r: $i] :
( mem(V2r,A_27a)
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V4r_27: $i] :
( mem(V4r_27,A_27a)
=> ! [V5u_27: $i] : ( ap(f2259(A_27a,A_27b,V1V,V3u,V2r,V0R,V4r_27),V5u_27) = ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(ap(c_2Etoto_2ElexTO(A_27a,A_27b),V0R),V1V),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2r),V3u)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4r_27),V5u_27))),ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2EternaryComparisons_2Eordering),ap(ap(V0R,V2r),V4r_27)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),ap(ap(V1V,V3u),V5u_27)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER))) ) ) ) ) ) ) ).
tff(lamtp_f2260,type,
f2260: ( del * del * $i * $i * $i * $i ) > $i ).
tff(lameq_f2260,axiom,
! [A_27b: del,A_27a: del,V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,ty_2EternaryComparisons_2Eordering)))
=> ! [V3u: $i] :
( mem(V3u,A_27b)
=> ! [V2r: $i] :
( mem(V2r,A_27a)
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V4r_27: $i] : ( ap(f2260(A_27b,A_27a,V1V,V3u,V2r,V0R),V4r_27) = f2259(A_27a,A_27b,V1V,V3u,V2r,V0R,V4r_27) ) ) ) ) ) ).
tff(lamtp_f2261,type,
f2261: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f2261,axiom,
! [A_27a: del,A_27b: del,V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,ty_2EternaryComparisons_2Eordering)))
=> ! [V2r: $i] :
( mem(V2r,A_27a)
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V3u: $i] : ( ap(f2261(A_27a,A_27b,V1V,V2r,V0R),V3u) = ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f2260(A_27b,A_27a,V1V,V3u,V2r,V0R))) ) ) ) ) ).
tff(lamtp_f2262,type,
f2262: ( del * del * $i * $i ) > $i ).
tff(lameq_f2262,axiom,
! [A_27b: del,A_27a: del,V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,ty_2EternaryComparisons_2Eordering)))
=> ! [V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V2r: $i] : ( ap(f2262(A_27b,A_27a,V1V,V0R),V2r) = f2261(A_27a,A_27b,V1V,V2r,V0R) ) ) ) ).
tff(conj_thm_2Etoto_2ElexTO__ALT,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,ty_2EternaryComparisons_2Eordering)))
=> ( ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0R))
& p(ap(c_2Etoto_2ETotOrd(A_27b),V1V)) )
=> p(ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f2262(A_27b,A_27a,V1V,V0R)))) ) ) ) ).
tff(conj_thm_2Etoto_2ETO__lexTO,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,ty_2EternaryComparisons_2Eordering)))
=> ! [V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,ty_2EternaryComparisons_2Eordering)))
=> ( ( p(ap(c_2Etoto_2ETotOrd(A_27a),V0R))
& p(ap(c_2Etoto_2ETotOrd(A_27b),V1V)) )
=> p(ap(c_2Etoto_2ETotOrd(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Etoto_2ElexTO(A_27a,A_27b),V0R),V1V))) ) ) ) ).
tff(conj_thm_2Etoto_2Epre__aplextoto,axiom,
! [A_27a: del,A_27b: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1v: $i] :
( mem(V1v,ty_2Etoto_2Etoto(A_27b))
=> ! [V2x: $i] :
( mem(V2x,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V3y: $i] :
( mem(V3y,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Etoto_2Elextoto(A_27a,A_27b),V0c),V1v)),V2x),V3y)) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),ap(c_2Epair_2EFST(A_27a,A_27b),V2x)),ap(c_2Epair_2EFST(A_27a,A_27b),V3y))),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),ap(ap(ap(c_2Etoto_2Eapto(A_27b),V1v),ap(c_2Epair_2ESND(A_27a,A_27b),V2x)),ap(c_2Epair_2ESND(A_27a,A_27b),V3y))),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER))) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Eaplextoto,axiom,
! [A_27a: del,A_27b: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ! [V1v: $i] :
( mem(V1v,ty_2Etoto_2Etoto(A_27b))
=> ! [V2x1: $i] :
( mem(V2x1,A_27a)
=> ! [V3x2: $i] :
( mem(V3x2,A_27b)
=> ! [V4y1: $i] :
( mem(V4y1,A_27a)
=> ! [V5y2: $i] :
( mem(V5y2,A_27b)
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Etoto_2Elextoto(A_27a,A_27b),V0c),V1v)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x1),V3x2)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4y1),V5y2))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V2x1),V4y1)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),ap(ap(ap(c_2Etoto_2Eapto(A_27b),V1v),V3x2),V5y2)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER))) ) ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2EStrongLinearOrder__LESS,axiom,
p(ap(c_2Erelation_2EStrongLinearOrder(ty_2Enum_2Enum),c_2Eprim__rec_2E_3C)) ).
tff(ax_thm_2Etoto_2EnumOrd,axiom,
c_2Etoto_2EnumOrd = ap(c_2Etoto_2ETO__of__LinearOrder(ty_2Enum_2Enum),c_2Eprim__rec_2E_3C) ).
tff(conj_thm_2Etoto_2ETO__numOrd,axiom,
p(ap(c_2Etoto_2ETotOrd(ty_2Enum_2Enum),c_2Etoto_2EnumOrd)) ).
tff(ax_thm_2Etoto_2Enumto,axiom,
surj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum(c_2Etoto_2Enumto) = surj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum(ap(c_2Etoto_2ETO(ty_2Enum_2Enum),c_2Etoto_2EnumOrd)) ).
tff(conj_thm_2Etoto_2Eapnumto__thm,axiom,
ap(c_2Etoto_2Eapto(ty_2Enum_2Enum),c_2Etoto_2Enumto) = c_2Etoto_2EnumOrd ).
tff(conj_thm_2Etoto_2EnumeralOrd,axiom,
! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2EternaryComparisons_2EEQUAL )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1y)))) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1y)))) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0x))),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2EternaryComparisons_2EGREATER )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0x))),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2EternaryComparisons_2EGREATER )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0x))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1y)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(V0x)),inj__ty_2Enum_2Enum(V1y))) )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0x))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1y)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(V0x)),inj__ty_2Enum_2Enum(V1y))) )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0x))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1y)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2EternaryComparisons_2Eordering),ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(V0x)),inj__ty_2Enum_2Enum(V1y))),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER))) )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0x))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1y)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2EternaryComparisons_2Eordering),ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(V0x)),inj__ty_2Enum_2Enum(V1y))),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER))) ) ) ).
tff(lamtp_f2263,type,
f2263: $i ).
tff(lameq_f2263,axiom,
! [V6a: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2263,inj__c_ty_2Eind__type_2Erecspace_o(V6a)) = 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(V6a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(bool)))) ) ).
tff(lamtp_f2264,type,
f2264: ( tp__c_ty_2Eind__type_2Erecspace_o * $i ) > $i ).
tff(lameq_f2264,axiom,
! [V3a0: tp__c_ty_2Eind__type_2Erecspace_o,V2_27num__dt_27: $i] :
( mem(V2_27num__dt_27,arr(ty_2Eind__type_2Erecspace(bool),bool))
=> ! [V5a: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2264(V3a0,V2_27num__dt_27),inj__c_ty_2Eind__type_2Erecspace_o(V5a)) = 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(f2263,inj__c_ty_2Eind__type_2Erecspace_o(V5a)))),ap(V2_27num__dt_27,inj__c_ty_2Eind__type_2Erecspace_o(V5a))) ) ) ).
tff(lamtp_f2265,type,
f2265: $i ).
tff(lameq_f2265,axiom,
! [V9a: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2265,inj__c_ty_2Eind__type_2Erecspace_o(V9a)) = 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)),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(bool)),inj__c_ty_2Eind__type_2Erecspace_o(V9a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(bool)))) ) ).
tff(lamtp_f2266,type,
f2266: ( tp__c_ty_2Eind__type_2Erecspace_o * $i ) > $i ).
tff(lameq_f2266,axiom,
! [V3a0: tp__c_ty_2Eind__type_2Erecspace_o,V2_27num__dt_27: $i] :
( mem(V2_27num__dt_27,arr(ty_2Eind__type_2Erecspace(bool),bool))
=> ! [V8a: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2266(V3a0,V2_27num__dt_27),inj__c_ty_2Eind__type_2Erecspace_o(V8a)) = 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(f2265,inj__c_ty_2Eind__type_2Erecspace_o(V8a)))),ap(V2_27num__dt_27,inj__c_ty_2Eind__type_2Erecspace_o(V8a))) ) ) ).
tff(lamtp_f2267,type,
f2267: $i > $i ).
tff(lameq_f2267,axiom,
! [V2_27num__dt_27: $i] :
( mem(V2_27num__dt_27,arr(ty_2Eind__type_2Erecspace(bool),bool))
=> ! [V3a0: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2267(V2_27num__dt_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(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),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),c_2Ebool_2EARB(bool)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(bool))))),ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(bool)),f2264(V3a0,V2_27num__dt_27))),ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(bool)),f2266(V3a0,V2_27num__dt_27))))),ap(V2_27num__dt_27,inj__c_ty_2Eind__type_2Erecspace_o(V3a0))) ) ) ).
tff(lamtp_f2268,type,
f2268: tp__c_ty_2Eind__type_2Erecspace_o > $i ).
tff(lameq_f2268,axiom,
! [V1a0: tp__c_ty_2Eind__type_2Erecspace_o,V2_27num__dt_27: $i] : ( ap(f2268(V1a0),V2_27num__dt_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(bool)),f2267(V2_27num__dt_27))),ap(V2_27num__dt_27,inj__c_ty_2Eind__type_2Erecspace_o(V1a0))) ) ).
tff(lamtp_f2269,type,
f2269: $i ).
tff(lameq_f2269,axiom,
! [V1a0: tp__c_ty_2Eind__type_2Erecspace_o] : ( ap(f2269,inj__c_ty_2Eind__type_2Erecspace_o(V1a0)) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(bool),bool)),f2268(V1a0)) ) ).
tff(ax_thm_2Etoto_2Enum__dt__TY__DEF,axiom,
? [V0rep: $i] :
( mem(V0rep,arr(ty_2Etoto_2Enum__dt,ty_2Eind__type_2Erecspace(bool)))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(bool),ty_2Etoto_2Enum__dt),f2269),V0rep)) ) ).
tff(ax_thm_2Etoto_2Enum__dt__case__def,axiom,
! [A_27a: del] :
( ! [V0v: $i] :
( mem(V0v,A_27a)
=> ! [V1f: $i] :
( mem(V1f,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ! [V2f1: $i] :
( mem(V2f1,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ( ap(ap(ap(ap(c_2Etoto_2Enum__dt__CASE(A_27a),inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)),V0v),V1f),V2f1) = V0v ) ) ) )
& ! [V3a: tp__ty_2Etoto_2Enum__dt,V4v: $i] :
( mem(V4v,A_27a)
=> ! [V5f: $i] :
( mem(V5f,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ! [V6f1: $i] :
( mem(V6f1,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ( ap(ap(ap(ap(c_2Etoto_2Enum__dt__CASE(A_27a),ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V3a))),V4v),V5f),V6f1) = ap(V5f,inj__ty_2Etoto_2Enum__dt(V3a)) ) ) ) )
& ! [V7a: tp__ty_2Etoto_2Enum__dt,V8v: $i] :
( mem(V8v,A_27a)
=> ! [V9f: $i] :
( mem(V9f,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ! [V10f1: $i] :
( mem(V10f1,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ( ap(ap(ap(ap(c_2Etoto_2Enum__dt__CASE(A_27a),ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V7a))),V8v),V9f),V10f1) = ap(V10f1,inj__ty_2Etoto_2Enum__dt(V7a)) ) ) ) ) ) ).
tff(ax_thm_2Etoto_2Enum__dt__size__def,axiom,
( ( surj__ty_2Enum_2Enum(ap(c_2Etoto_2Enum__dt__size,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer))) = fo__c_2Enum_2E0 )
& ! [V0a: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2Enum_2Enum(ap(c_2Etoto_2Enum__dt__size,ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(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_2Etoto_2Enum__dt__size,inj__ty_2Etoto_2Enum__dt(V0a)))) )
& ! [V1a: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2Enum_2Enum(ap(c_2Etoto_2Enum__dt__size,ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(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_2Etoto_2Enum__dt__size,inj__ty_2Etoto_2Enum__dt(V1a)))) ) ) ).
tff(conj_thm_2Etoto_2Edatatype__num__dt,axiom,
! [V0num__dt: $i] :
( mem(V0num__dt,arr(ty_2Etoto_2Enum__dt,arr(arr(ty_2Etoto_2Enum__dt,ty_2Etoto_2Enum__dt),arr(arr(ty_2Etoto_2Enum__dt,ty_2Etoto_2Enum__dt),bool))))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(V0num__dt,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)),c_2Etoto_2Ebit1),c_2Etoto_2Ebit2))) ) ).
tff(conj_thm_2Etoto_2Enum__dt__11,axiom,
( ! [V0a: tp__ty_2Etoto_2Enum__dt,V1a_27: tp__ty_2Etoto_2Enum__dt] :
( ( surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V0a))) = surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V1a_27))) )
<=> ( V0a = V1a_27 ) )
& ! [V2a: tp__ty_2Etoto_2Enum__dt,V3a_27: tp__ty_2Etoto_2Enum__dt] :
( ( surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V2a))) = surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V3a_27))) )
<=> ( V2a = V3a_27 ) ) ) ).
tff(conj_thm_2Etoto_2Enum__dt__distinct,axiom,
( ! [V0a: tp__ty_2Etoto_2Enum__dt] : ( fo__c_2Etoto_2Ezer != surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V0a))) )
& ! [V1a: tp__ty_2Etoto_2Enum__dt] : ( fo__c_2Etoto_2Ezer != surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V1a))) )
& ! [V2a_27: tp__ty_2Etoto_2Enum__dt,V3a: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V3a))) != surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V2a_27))) ) ) ).
tff(conj_thm_2Etoto_2Enum__dt__nchotomy,axiom,
! [V0nn: tp__ty_2Etoto_2Enum__dt] :
( ( V0nn = fo__c_2Etoto_2Ezer )
| ? [V1n: tp__ty_2Etoto_2Enum__dt] : ( V0nn = surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V1n))) )
| ? [V2n: tp__ty_2Etoto_2Enum__dt] : ( V0nn = surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V2n))) ) ) ).
tff(conj_thm_2Etoto_2Enum__dt__Axiom,axiom,
! [A_27a: del,V0f0: $i] :
( mem(V0f0,A_27a)
=> ! [V1f1: $i] :
( mem(V1f1,arr(ty_2Etoto_2Enum__dt,arr(A_27a,A_27a)))
=> ! [V2f2: $i] :
( mem(V2f2,arr(ty_2Etoto_2Enum__dt,arr(A_27a,A_27a)))
=> ? [V3fn: $i] :
( mem(V3fn,arr(ty_2Etoto_2Enum__dt,A_27a))
& ( ap(V3fn,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)) = V0f0 )
& ! [V4a: tp__ty_2Etoto_2Enum__dt] : ( ap(V3fn,ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V4a))) = ap(ap(V1f1,inj__ty_2Etoto_2Enum__dt(V4a)),ap(V3fn,inj__ty_2Etoto_2Enum__dt(V4a))) )
& ! [V5a: tp__ty_2Etoto_2Enum__dt] : ( ap(V3fn,ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V5a))) = ap(ap(V2f2,inj__ty_2Etoto_2Enum__dt(V5a)),ap(V3fn,inj__ty_2Etoto_2Enum__dt(V5a))) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Enum__dt__induction,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Etoto_2Enum__dt,bool))
=> ( ( p(ap(V0P,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)))
& ! [V1n: tp__ty_2Etoto_2Enum__dt] :
( p(ap(V0P,inj__ty_2Etoto_2Enum__dt(V1n)))
=> p(ap(V0P,ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V1n)))) )
& ! [V2n: tp__ty_2Etoto_2Enum__dt] :
( p(ap(V0P,inj__ty_2Etoto_2Enum__dt(V2n)))
=> p(ap(V0P,ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V2n)))) ) )
=> ! [V3n: tp__ty_2Etoto_2Enum__dt] : p(ap(V0P,inj__ty_2Etoto_2Enum__dt(V3n))) ) ) ).
tff(conj_thm_2Etoto_2Enum__dt__case__cong,axiom,
! [A_27a: del,V0v_27: $i] :
( mem(V0v_27,A_27a)
=> ! [V1f_27: $i] :
( mem(V1f_27,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ! [V2f1_27: $i] :
( mem(V2f1_27,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ! [V3M: tp__ty_2Etoto_2Enum__dt,V4M_27: tp__ty_2Etoto_2Enum__dt,V5v: $i] :
( mem(V5v,A_27a)
=> ! [V6f: $i] :
( mem(V6f,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ! [V7f1: $i] :
( mem(V7f1,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ( ( ( V3M = V4M_27 )
& ( ( V4M_27 = fo__c_2Etoto_2Ezer )
=> ( V5v = V0v_27 ) )
& ! [V8a: tp__ty_2Etoto_2Enum__dt] :
( ( V4M_27 = surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V8a))) )
=> ( ap(V6f,inj__ty_2Etoto_2Enum__dt(V8a)) = ap(V1f_27,inj__ty_2Etoto_2Enum__dt(V8a)) ) )
& ! [V9a: tp__ty_2Etoto_2Enum__dt] :
( ( V4M_27 = surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V9a))) )
=> ( ap(V7f1,inj__ty_2Etoto_2Enum__dt(V9a)) = ap(V2f1_27,inj__ty_2Etoto_2Enum__dt(V9a)) ) ) )
=> ( ap(ap(ap(ap(c_2Etoto_2Enum__dt__CASE(A_27a),inj__ty_2Etoto_2Enum__dt(V3M)),V5v),V6f),V7f1) = ap(ap(ap(ap(c_2Etoto_2Enum__dt__CASE(A_27a),inj__ty_2Etoto_2Enum__dt(V4M_27)),V0v_27),V1f_27),V2f1_27) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Enum__dt__case__eq,axiom,
! [A_27a: del,V0x: tp__ty_2Etoto_2Enum__dt,V1v: $i] :
( mem(V1v,A_27a)
=> ! [V2f: $i] :
( mem(V2f,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ! [V3f1: $i] :
( mem(V3f1,arr(ty_2Etoto_2Enum__dt,A_27a))
=> ! [V4v_27: $i] :
( mem(V4v_27,A_27a)
=> ( ( ap(ap(ap(ap(c_2Etoto_2Enum__dt__CASE(A_27a),inj__ty_2Etoto_2Enum__dt(V0x)),V1v),V2f),V3f1) = V4v_27 )
<=> ( ( ( V0x = fo__c_2Etoto_2Ezer )
& ( V1v = V4v_27 ) )
| ? [V5n: tp__ty_2Etoto_2Enum__dt] :
( ( V0x = surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V5n))) )
& ( ap(V2f,inj__ty_2Etoto_2Enum__dt(V5n)) = V4v_27 ) )
| ? [V6n: tp__ty_2Etoto_2Enum__dt] :
( ( V0x = surj__ty_2Etoto_2Enum__dt(ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V6n))) )
& ( ap(V3f1,inj__ty_2Etoto_2Enum__dt(V6n)) = V4v_27 ) ) ) ) ) ) ) ) ).
tff(lamtp_f2270,type,
f2270: $i > $i ).
tff(lameq_f2270,axiom,
! [V0R: $i] :
( mem(V0R,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ! [V1n: tp__ty_2Enum_2Enum] : ( ap(f2270(V0R),inj__ty_2Enum_2Enum(V1n)) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(V1n)))),ap(ap(V0R,ap(c_2Earithmetic_2EDIV2,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),inj__ty_2Enum_2Enum(V1n))) ) ) ).
tff(lamtp_f2271,type,
f2271: $i > $i ).
tff(lameq_f2271,axiom,
! [V0R: $i] :
( mem(V0R,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ! [V2n: tp__ty_2Enum_2Enum] : ( ap(f2271(V0R),inj__ty_2Enum_2Enum(V2n)) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ebool_2E_7E,ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(V2n))))),ap(ap(V0R,ap(c_2Earithmetic_2EDIV2,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),inj__ty_2Enum_2Enum(V2n))) ) ) ).
tff(lamtp_f2272,type,
f2272: $i ).
tff(lameq_f2272,axiom,
! [V0R: $i] : ( ap(f2272,V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Enum_2Enum),V0R)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f2270(V0R))),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f2271(V0R)))) ) ).
tff(lamtp_f2273,type,
f2273: $i > $i ).
tff(lameq_f2273,axiom,
! [V3num__to__dt: $i] :
( mem(V3num__to__dt,arr(ty_2Enum_2Enum,ty_2Etoto_2Enum__dt))
=> ! [V4a: tp__ty_2Enum_2Enum] : ( ap(f2273(V3num__to__dt),inj__ty_2Enum_2Enum(V4a)) = ap(c_2Ecombin_2EI(ty_2Etoto_2Enum__dt),ap(ap(ap(c_2Ebool_2ECOND(ty_2Etoto_2Enum__dt),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V4a)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Etoto_2Enum__dt),ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(V4a))),ap(c_2Etoto_2Ebit1,ap(V3num__to__dt,ap(c_2Earithmetic_2EDIV2,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V4a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))),ap(c_2Etoto_2Ebit2,ap(V3num__to__dt,ap(c_2Earithmetic_2EDIV2,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V4a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))) ) ) ).
tff(lamtp_f2274,type,
f2274: $i ).
tff(lameq_f2274,axiom,
! [V3num__to__dt: $i] : ( ap(f2274,V3num__to__dt) = f2273(V3num__to__dt) ) ).
tff(ax_thm_2Etoto_2Enum__to__dt__primitive,axiom,
c_2Etoto_2Enum__to__dt = ap(ap(c_2Erelation_2EWFREC(ty_2Enum_2Enum,ty_2Etoto_2Enum__dt),ap(c_2Emin_2E_40(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))),f2272)),f2274) ).
tff(conj_thm_2Etoto_2Enum__dtOrd__ind,axiom,
! [V0P: $i] :
( mem(V0P,arr(ty_2Etoto_2Enum__dt,arr(ty_2Etoto_2Enum__dt,bool)))
=> ( ( p(ap(ap(V0P,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)),inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)))
& ! [V1x: tp__ty_2Etoto_2Enum__dt] : p(ap(ap(V0P,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)),ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V1x))))
& ! [V2x: tp__ty_2Etoto_2Enum__dt] : p(ap(ap(V0P,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)),ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V2x))))
& ! [V3x: tp__ty_2Etoto_2Enum__dt] : p(ap(ap(V0P,ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V3x))),inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)))
& ! [V4x: tp__ty_2Etoto_2Enum__dt] : p(ap(ap(V0P,ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V4x))),inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)))
& ! [V5x: tp__ty_2Etoto_2Enum__dt,V6y: tp__ty_2Etoto_2Enum__dt] : p(ap(ap(V0P,ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V5x))),ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V6y))))
& ! [V7x: tp__ty_2Etoto_2Enum__dt,V8y: tp__ty_2Etoto_2Enum__dt] : p(ap(ap(V0P,ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V7x))),ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V8y))))
& ! [V9x: tp__ty_2Etoto_2Enum__dt,V10y: tp__ty_2Etoto_2Enum__dt] :
( p(ap(ap(V0P,inj__ty_2Etoto_2Enum__dt(V9x)),inj__ty_2Etoto_2Enum__dt(V10y)))
=> p(ap(ap(V0P,ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V9x))),ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V10y)))) )
& ! [V11x: tp__ty_2Etoto_2Enum__dt,V12y: tp__ty_2Etoto_2Enum__dt] :
( p(ap(ap(V0P,inj__ty_2Etoto_2Enum__dt(V11x)),inj__ty_2Etoto_2Enum__dt(V12y)))
=> p(ap(ap(V0P,ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V11x))),ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V12y)))) ) )
=> ! [V13v: tp__ty_2Etoto_2Enum__dt,V14v1: tp__ty_2Etoto_2Enum__dt] : p(ap(ap(V0P,inj__ty_2Etoto_2Enum__dt(V13v)),inj__ty_2Etoto_2Enum__dt(V14v1))) ) ) ).
tff(conj_thm_2Etoto_2Enum__dtOrd,axiom,
( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)),inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer))) = fo__c_2EternaryComparisons_2EEQUAL )
& ! [V0x: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)),ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V0x)))) = fo__c_2EternaryComparisons_2ELESS )
& ! [V1x: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer)),ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V1x)))) = fo__c_2EternaryComparisons_2ELESS )
& ! [V2x: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V2x))),inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer))) = fo__c_2EternaryComparisons_2EGREATER )
& ! [V3x: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V3x))),inj__ty_2Etoto_2Enum__dt(fo__c_2Etoto_2Ezer))) = fo__c_2EternaryComparisons_2EGREATER )
& ! [V4y: tp__ty_2Etoto_2Enum__dt,V5x: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V5x))),ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V4y)))) = fo__c_2EternaryComparisons_2ELESS )
& ! [V6y: tp__ty_2Etoto_2Enum__dt,V7x: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V7x))),ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V6y)))) = fo__c_2EternaryComparisons_2EGREATER )
& ! [V8y: tp__ty_2Etoto_2Enum__dt,V9x: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V9x))),ap(c_2Etoto_2Ebit1,inj__ty_2Etoto_2Enum__dt(V8y)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,inj__ty_2Etoto_2Enum__dt(V9x)),inj__ty_2Etoto_2Enum__dt(V8y))) )
& ! [V10y: tp__ty_2Etoto_2Enum__dt,V11x: tp__ty_2Etoto_2Enum__dt] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V11x))),ap(c_2Etoto_2Ebit2,inj__ty_2Etoto_2Enum__dt(V10y)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,inj__ty_2Etoto_2Enum__dt(V11x)),inj__ty_2Etoto_2Enum__dt(V10y))) ) ) ).
tff(ax_thm_2Etoto_2Eqk__numOrd__def,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Enum__dtOrd,ap(c_2Etoto_2Enum__to__dt,inj__ty_2Enum_2Enum(V0m))),ap(c_2Etoto_2Enum__to__dt,inj__ty_2Enum_2Enum(V1n)))) ) ).
tff(conj_thm_2Etoto_2ETO__qk__numOrd,axiom,
p(ap(c_2Etoto_2ETotOrd(ty_2Enum_2Enum),c_2Etoto_2Eqk__numOrd)) ).
tff(conj_thm_2Etoto_2Eqk__numeralOrd,axiom,
! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2EternaryComparisons_2EEQUAL )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1y)))) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1y)))) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0x))),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2EternaryComparisons_2EGREATER )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0x))),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2EternaryComparisons_2EGREATER )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0x))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1y)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,inj__ty_2Enum_2Enum(V0x)),inj__ty_2Enum_2Enum(V1y))) )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0x))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1y)))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,inj__ty_2Enum_2Enum(V0x)),inj__ty_2Enum_2Enum(V1y))) )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0x))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1y)))) = fo__c_2EternaryComparisons_2ELESS )
& ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2Eqk__numOrd,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0x))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1y)))) = fo__c_2EternaryComparisons_2EGREATER ) ) ).
tff(ax_thm_2Etoto_2Eqk__numto,axiom,
surj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum(c_2Etoto_2Eqk__numto) = surj__c_ty_2Etoto_2Etoto_ty_2Enum_2Enum(ap(c_2Etoto_2ETO(ty_2Enum_2Enum),c_2Etoto_2Eqk__numOrd)) ).
tff(conj_thm_2Etoto_2Eap__qk__numto__thm,axiom,
ap(c_2Etoto_2Eapto(ty_2Enum_2Enum),c_2Etoto_2Eqk__numto) = c_2Etoto_2Eqk__numOrd ).
tff(ax_thm_2Etoto_2EcharOrd,axiom,
! [V0a: tp__ty_2Estring_2Echar,V1b: tp__ty_2Estring_2Echar] : ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EcharOrd,inj__ty_2Estring_2Echar(V0a)),inj__ty_2Estring_2Echar(V1b))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,ap(c_2Estring_2EORD,inj__ty_2Estring_2Echar(V0a))),ap(c_2Estring_2EORD,inj__ty_2Estring_2Echar(V1b)))) ) ).
tff(ax_thm_2Etoto_2Echarto,axiom,
surj__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar(c_2Etoto_2Echarto) = surj__c_ty_2Etoto_2Etoto_ty_2Estring_2Echar(ap(c_2Etoto_2ETO(ty_2Estring_2Echar),c_2Etoto_2EcharOrd)) ).
tff(conj_thm_2Etoto_2ETO__charOrd,axiom,
p(ap(c_2Etoto_2ETotOrd(ty_2Estring_2Echar),c_2Etoto_2EcharOrd)) ).
tff(conj_thm_2Etoto_2Eapcharto__thm,axiom,
ap(c_2Etoto_2Eapto(ty_2Estring_2Echar),c_2Etoto_2Echarto) = c_2Etoto_2EcharOrd ).
tff(conj_thm_2Etoto_2EcharOrd__lt__lem,axiom,
! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(V0a)),inj__ty_2Enum_2Enum(V1b))) = fo__c_2EternaryComparisons_2ELESS )
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1b)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))))
<=> $true )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EcharOrd,ap(c_2Estring_2ECHR,inj__ty_2Enum_2Enum(V0a))),ap(c_2Estring_2ECHR,inj__ty_2Enum_2Enum(V1b)))) = fo__c_2EternaryComparisons_2ELESS ) ) ) ).
tff(conj_thm_2Etoto_2EcharOrd__gt__lem,axiom,
! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(V0a)),inj__ty_2Enum_2Enum(V1b))) = fo__c_2EternaryComparisons_2EGREATER )
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))))
<=> $true )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EcharOrd,ap(c_2Estring_2ECHR,inj__ty_2Enum_2Enum(V0a))),ap(c_2Estring_2ECHR,inj__ty_2Enum_2Enum(V1b)))) = fo__c_2EternaryComparisons_2EGREATER ) ) ) ).
tff(conj_thm_2Etoto_2EcharOrd__eq__lem,axiom,
! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EnumOrd,inj__ty_2Enum_2Enum(V0a)),inj__ty_2Enum_2Enum(V1b))) = fo__c_2EternaryComparisons_2EEQUAL )
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(c_2Etoto_2EcharOrd,ap(c_2Estring_2ECHR,inj__ty_2Enum_2Enum(V0a))),ap(c_2Estring_2ECHR,inj__ty_2Enum_2Enum(V1b)))) = fo__c_2EternaryComparisons_2EEQUAL ) ) ).
tff(conj_thm_2Etoto_2EcharOrd__thm,axiom,
c_2Etoto_2EcharOrd = ap(c_2Etoto_2ETO__of__LinearOrder(ty_2Estring_2Echar),c_2Estring_2Echar__lt) ).
tff(conj_thm_2Etoto_2Elistorder__ind,axiom,
! [A_27a: del,V0P: $i] :
( mem(V0P,arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool))))
=> ( ( ! [V1V: $i] :
( mem(V1V,arr(A_27a,arr(A_27a,bool)))
=> ! [V2l: $i] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(ap(V0P,V1V),V2l),c_2Elist_2ENIL(A_27a))) ) )
& ! [V3V: $i] :
( mem(V3V,arr(A_27a,arr(A_27a,bool)))
=> ! [V4s: $i] :
( mem(V4s,A_27a)
=> ! [V5m: $i] :
( mem(V5m,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(ap(V0P,V3V),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V4s),V5m))) ) ) )
& ! [V6V: $i] :
( mem(V6V,arr(A_27a,arr(A_27a,bool)))
=> ! [V7r: $i] :
( mem(V7r,A_27a)
=> ! [V8l: $i] :
( mem(V8l,ty_2Elist_2Elist(A_27a))
=> ! [V9s: $i] :
( mem(V9s,A_27a)
=> ! [V10m: $i] :
( mem(V10m,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(ap(V0P,V6V),V8l),V10m))
=> p(ap(ap(ap(V0P,V6V),ap(ap(c_2Elist_2ECONS(A_27a),V7r),V8l)),ap(ap(c_2Elist_2ECONS(A_27a),V9s),V10m))) ) ) ) ) ) ) )
=> ! [V11v: $i] :
( mem(V11v,arr(A_27a,arr(A_27a,bool)))
=> ! [V12v1: $i] :
( mem(V12v1,ty_2Elist_2Elist(A_27a))
=> ! [V13v2: $i] :
( mem(V13v2,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(ap(V0P,V11v),V12v1),V13v2)) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2Elistorder,axiom,
! [A_27a: del] :
( ! [V0l: $i] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1V: $i] :
( mem(V1V,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(ap(ap(c_2Etoto_2Elistorder(A_27a),V1V),V0l),c_2Elist_2ENIL(A_27a)))
<=> $false ) ) )
& ! [V2s: $i] :
( mem(V2s,A_27a)
=> ! [V3m: $i] :
( mem(V3m,ty_2Elist_2Elist(A_27a))
=> ! [V4V: $i] :
( mem(V4V,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(ap(ap(c_2Etoto_2Elistorder(A_27a),V4V),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V2s),V3m)))
<=> $true ) ) ) )
& ! [V5s: $i] :
( mem(V5s,A_27a)
=> ! [V6r: $i] :
( mem(V6r,A_27a)
=> ! [V7m: $i] :
( mem(V7m,ty_2Elist_2Elist(A_27a))
=> ! [V8l: $i] :
( mem(V8l,ty_2Elist_2Elist(A_27a))
=> ! [V9V: $i] :
( mem(V9V,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(ap(ap(c_2Etoto_2Elistorder(A_27a),V9V),ap(ap(c_2Elist_2ECONS(A_27a),V6r),V8l)),ap(ap(c_2Elist_2ECONS(A_27a),V5s),V7m)))
<=> ( p(ap(ap(V9V,V6r),V5s))
| ( ( V6r = V5s )
& p(ap(ap(ap(c_2Etoto_2Elistorder(A_27a),V9V),V8l),V7m)) ) ) ) ) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ESLO__listorder,axiom,
! [A_27a: del,V0V: $i] :
( mem(V0V,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0V))
=> p(ap(c_2Erelation_2EStrongLinearOrder(ty_2Elist_2Elist(A_27a)),ap(c_2Etoto_2Elistorder(A_27a),V0V))) ) ) ).
tff(ax_thm_2Etoto_2EListOrd,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2EListOrd(A_27a),V0c) = ap(c_2Etoto_2ETO__of__LinearOrder(ty_2Elist_2Elist(A_27a)),ap(c_2Etoto_2Elistorder(A_27a),ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),ap(c_2Etoto_2Eapto(A_27a),V0c)))) ) ) ).
tff(conj_thm_2Etoto_2ETO__ListOrd,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> p(ap(c_2Etoto_2ETotOrd(ty_2Elist_2Elist(A_27a)),ap(c_2Etoto_2EListOrd(A_27a),V0c))) ) ).
tff(conj_thm_2Etoto_2EListOrd__THM,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2EListOrd(A_27a),V0c),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a))) = fo__c_2EternaryComparisons_2EEQUAL )
& ! [V1b: $i] :
( mem(V1b,A_27a)
=> ! [V2y: $i] :
( mem(V2y,ty_2Elist_2Elist(A_27a))
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2EListOrd(A_27a),V0c),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V1b),V2y))) = fo__c_2EternaryComparisons_2ELESS ) ) )
& ! [V3a: $i] :
( mem(V3a,A_27a)
=> ! [V4x: $i] :
( mem(V4x,ty_2Elist_2Elist(A_27a))
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2EListOrd(A_27a),V0c),ap(ap(c_2Elist_2ECONS(A_27a),V3a),V4x)),c_2Elist_2ENIL(A_27a))) = fo__c_2EternaryComparisons_2EGREATER ) ) )
& ! [V5a: $i] :
( mem(V5a,A_27a)
=> ! [V6x: $i] :
( mem(V6x,ty_2Elist_2Elist(A_27a))
=> ! [V7b: $i] :
( mem(V7b,A_27a)
=> ! [V8y: $i] :
( mem(V8y,ty_2Elist_2Elist(A_27a))
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2EListOrd(A_27a),V0c),ap(ap(c_2Elist_2ECONS(A_27a),V5a),V6x)),ap(ap(c_2Elist_2ECONS(A_27a),V7b),V8y))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V5a),V7b)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),ap(ap(ap(c_2Etoto_2EListOrd(A_27a),V0c),V6x),V8y)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER))) ) ) ) ) ) ) ) ).
tff(ax_thm_2Etoto_2Elistoto,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ap(c_2Etoto_2Elistoto(A_27a),V0c) = ap(c_2Etoto_2ETO(ty_2Elist_2Elist(A_27a)),ap(c_2Etoto_2EListOrd(A_27a),V0c)) ) ) ).
tff(conj_thm_2Etoto_2Eaplistoto,axiom,
! [A_27a: del,V0c: $i] :
( mem(V0c,ty_2Etoto_2Etoto(A_27a))
=> ( ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(ty_2Elist_2Elist(A_27a)),ap(c_2Etoto_2Elistoto(A_27a),V0c)),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a))) = fo__c_2EternaryComparisons_2EEQUAL )
& ! [V1b: $i] :
( mem(V1b,A_27a)
=> ! [V2y: $i] :
( mem(V2y,ty_2Elist_2Elist(A_27a))
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(ty_2Elist_2Elist(A_27a)),ap(c_2Etoto_2Elistoto(A_27a),V0c)),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V1b),V2y))) = fo__c_2EternaryComparisons_2ELESS ) ) )
& ! [V3a: $i] :
( mem(V3a,A_27a)
=> ! [V4x: $i] :
( mem(V4x,ty_2Elist_2Elist(A_27a))
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(ty_2Elist_2Elist(A_27a)),ap(c_2Etoto_2Elistoto(A_27a),V0c)),ap(ap(c_2Elist_2ECONS(A_27a),V3a),V4x)),c_2Elist_2ENIL(A_27a))) = fo__c_2EternaryComparisons_2EGREATER ) ) )
& ! [V5a: $i] :
( mem(V5a,A_27a)
=> ! [V6x: $i] :
( mem(V6x,ty_2Elist_2Elist(A_27a))
=> ! [V7b: $i] :
( mem(V7b,A_27a)
=> ! [V8y: $i] :
( mem(V8y,ty_2Elist_2Elist(A_27a))
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(c_2Etoto_2Eapto(ty_2Elist_2Elist(A_27a)),ap(c_2Etoto_2Elistoto(A_27a),V0c)),ap(ap(c_2Elist_2ECONS(A_27a),V5a),V6x)),ap(ap(c_2Elist_2ECONS(A_27a),V7b),V8y))) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0c),V5a),V7b)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2ELESS)),ap(ap(ap(c_2Etoto_2Eapto(ty_2Elist_2Elist(A_27a)),ap(c_2Etoto_2Elistoto(A_27a),V0c)),V6x),V8y)),inj__ty_2EternaryComparisons_2Eordering(fo__c_2EternaryComparisons_2EGREATER))) ) ) ) ) ) ) ) ).
tff(ax_thm_2Etoto_2Estringto,axiom,
surj__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar(c_2Etoto_2Estringto) = surj__c_ty_2Etoto_2Etoto_c_ty_2Elist_2Elist_ty_2Estring_2Echar(ap(c_2Etoto_2Elistoto(ty_2Estring_2Echar),c_2Etoto_2Echarto)) ).
tff(ax_thm_2Etoto_2EimageOrd,axiom,
! [A_27a: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27c))
=> ! [V1cp: $i] :
( mem(V1cp,arr(A_27c,arr(A_27c,ty_2EternaryComparisons_2Eordering)))
=> ! [V2a: $i] :
( mem(V2a,A_27a)
=> ! [V3b: $i] :
( mem(V3b,A_27a)
=> ( surj__ty_2EternaryComparisons_2Eordering(ap(ap(ap(ap(c_2Etoto_2EimageOrd(A_27a,A_27c),V0f),V1cp),V2a),V3b)) = surj__ty_2EternaryComparisons_2Eordering(ap(ap(V1cp,ap(V0f,V2a)),ap(V0f,V3b))) ) ) ) ) ) ).
tff(conj_thm_2Etoto_2ETO__injection,axiom,
! [A_27c: del,A_27d: del,V0cp: $i] :
( mem(V0cp,arr(A_27c,arr(A_27c,ty_2EternaryComparisons_2Eordering)))
=> ( p(ap(c_2Etoto_2ETotOrd(A_27c),V0cp))
=> ! [V1f: $i] :
( mem(V1f,arr(A_27d,A_27c))
=> ( p(ap(c_2Ebool_2EONE__ONE(A_27d,A_27c),V1f))
=> p(ap(c_2Etoto_2ETotOrd(A_27d),ap(ap(c_2Etoto_2EimageOrd(A_27d,A_27c),V1f),V0cp))) ) ) ) ) ).
tff(conj_thm_2Etoto_2EStrongLinearOrder__of__TO__TO__of__LinearOrder,axiom,
! [A_27a: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R))
=> ( ap(c_2Etoto_2EStrongLinearOrder__of__TO(A_27a),ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0R)) = V0R ) ) ) ).
tff(conj_thm_2Etoto_2ETO__of__LinearOrder__LEX,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1V: $i] :
( mem(V1V,arr(A_27b,arr(A_27b,bool)))
=> ( ( p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R))
& p(ap(c_2Erelation_2Eirreflexive(A_27b),V1V)) )
=> ( ap(c_2Etoto_2ETO__of__LinearOrder(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R),V1V)) = ap(ap(c_2Etoto_2ElexTO(A_27a,A_27b),ap(c_2Etoto_2ETO__of__LinearOrder(A_27a),V0R)),ap(c_2Etoto_2ETO__of__LinearOrder(A_27b),V1V)) ) ) ) ) ).
%------------------------------------------------------------------------------