ITP001 Axioms: ITP097_7.ax
%------------------------------------------------------------------------------
% File : ITP097_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : comparison.ax [Gau19]
% : HL4097_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 254 ( 87 unt; 114 typ; 0 def)
% Number of atoms : 308 ( 224 equ)
% Maximal formula atoms : 27 ( 1 avg)
% Number of connectives : 174 ( 6 ~; 5 |; 65 &)
% ( 42 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 92 ( 54 >; 38 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 109 ( 109 usr; 19 con; 0-8 aty)
% Number of variables : 650 ( 522 !; 1 ?; 650 :)
% ( 127 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Estring_2Echar,type,
tyop_2Estring_2Echar: $tType ).
tff(tyop_2EternaryComparisons_2Eordering,type,
tyop_2EternaryComparisons_2Eordering: $tType ).
tff(tyop_2Etoto_2Etoto,type,
tyop_2Etoto_2Etoto: $tType > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Epair_2ECURRY_2E0,type,
c_2Epair_2ECURRY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))) ).
tff(c_2Epair_2ECURRY_2E1,type,
c_2Epair_2ECURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) ) ).
tff(c_2EternaryComparisons_2EEQUAL_2E0,type,
c_2EternaryComparisons_2EEQUAL_2E0: tyop_2EternaryComparisons_2Eordering ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).
tff(c_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).
tff(c_2EternaryComparisons_2EGREATER_2E0,type,
c_2EternaryComparisons_2EGREATER_2E0: tyop_2EternaryComparisons_2Eordering ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2EternaryComparisons_2ELESS_2E0,type,
c_2EternaryComparisons_2ELESS_2E0: tyop_2EternaryComparisons_2Eordering ).
tff(c_2Elist_2ELIST__REL_2E0,type,
c_2Elist_2ELIST__REL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Elist_2ELIST__REL_2E3,type,
c_2Elist_2ELIST__REL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2ELLEX_2E0,type,
c_2Elist_2ELLEX_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))) ).
tff(c_2Elist_2ELLEX_2E1,type,
c_2Elist_2ELLEX_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ) ).
tff(c_2Etoto_2EListOrd_2E0,type,
c_2Etoto_2EListOrd_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering))) ).
tff(c_2Etoto_2EListOrd_2E1,type,
c_2Etoto_2EListOrd_2E1:
!>[A_27a: $tType] : ( tyop_2Etoto_2Etoto(A_27a) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0:
!>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).
tff(c_2Estring_2EORD_2E0,type,
c_2Estring_2EORD_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum) ).
tff(c_2Estring_2EORD_2E1,type,
c_2Estring_2EORD_2E1: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).
tff(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).
tff(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).
tff(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Etoto_2ETO_2E0,type,
c_2Etoto_2ETO_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Etoto_2Etoto(A_27a)) ).
tff(c_2Etoto_2ETO_2E1,type,
c_2Etoto_2ETO_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) > tyop_2Etoto_2Etoto(A_27a) ) ).
tff(c_2Etoto_2ETO__inv_2E0,type,
c_2Etoto_2ETO__inv_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))) ).
tff(c_2Etoto_2ETO__inv_2E1,type,
c_2Etoto_2ETO__inv_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2Etoto_2ETO__of__LinearOrder_2E0,type,
c_2Etoto_2ETO__of__LinearOrder_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))) ).
tff(c_2Etoto_2ETO__of__LinearOrder_2E1,type,
c_2Etoto_2ETO__of__LinearOrder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2Etoto_2ETotOrd_2E0,type,
c_2Etoto_2ETotOrd_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool) ).
tff(c_2Etoto_2ETotOrd_2E1,type,
c_2Etoto_2ETotOrd_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2EUNCURRY_2E0,type,
c_2Epair_2EUNCURRY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).
tff(c_2Epair_2EUNCURRY_2E1,type,
c_2Epair_2EUNCURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Etoto_2Eapto_2E0,type,
c_2Etoto_2Eapto_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))) ).
tff(c_2Etoto_2Eapto_2E1,type,
c_2Etoto_2Eapto_2E1:
!>[A_27a: $tType] : ( tyop_2Etoto_2Etoto(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2EternaryComparisons_2Ebool__compare_2E0,type,
c_2EternaryComparisons_2Ebool__compare_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering)) ).
tff(c_2EternaryComparisons_2Ebool__compare_2E2,type,
c_2EternaryComparisons_2Ebool__compare_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2EternaryComparisons_2Eordering ).
tff(c_2Etoto_2EcharOrd_2E0,type,
c_2Etoto_2EcharOrd_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)) ).
tff(c_2EternaryComparisons_2Echar__compare_2E0,type,
c_2EternaryComparisons_2Echar__compare_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)) ).
tff(c_2EternaryComparisons_2Echar__compare_2E2,type,
c_2EternaryComparisons_2Echar__compare_2E2: ( tyop_2Estring_2Echar * tyop_2Estring_2Echar ) > tyop_2EternaryComparisons_2Eordering ).
tff(c_2Ecomparison_2Eequiv__inj_2E0,type,
c_2Ecomparison_2Eequiv__inj_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Ecomparison_2Eequiv__inj_2E3,type,
c_2Ecomparison_2Eequiv__inj_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecomparison_2Egood__cmp_2E0,type,
c_2Ecomparison_2Egood__cmp_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool) ).
tff(c_2Ecomparison_2Egood__cmp_2E1,type,
c_2Ecomparison_2Egood__cmp_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) > tyop_2Emin_2Ebool ) ).
tff(c_2EternaryComparisons_2Einvert__comparison_2E0,type,
c_2EternaryComparisons_2Einvert__comparison_2E0: tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering) ).
tff(c_2Erelation_2Eirreflexive_2E0,type,
c_2Erelation_2Eirreflexive_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Eirreflexive_2E1,type,
c_2Erelation_2Eirreflexive_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Etoto_2ElexTO_2E0,type,
c_2Etoto_2ElexTO_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)))) ).
tff(c_2Etoto_2ElexTO_2E2,type,
c_2Etoto_2ElexTO_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2EternaryComparisons_2Elist__compare_2E0,type,
c_2EternaryComparisons_2Elist__compare_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering))) ).
tff(c_2EternaryComparisons_2Elist__compare_2E1,type,
c_2EternaryComparisons_2Elist__compare_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2EternaryComparisons_2Elist__compare_2E3,type,
c_2EternaryComparisons_2Elist__compare_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2Etoto_2EnumOrd_2E0,type,
c_2Etoto_2EnumOrd_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)) ).
tff(c_2EternaryComparisons_2Enum__compare_2E0,type,
c_2EternaryComparisons_2Enum__compare_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)) ).
tff(c_2EternaryComparisons_2Enum__compare_2E2,type,
c_2EternaryComparisons_2Enum__compare_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2EternaryComparisons_2Eordering ).
tff(c_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Ecomparison_2Eoption__cmp2_2E0,type,
c_2Ecomparison_2Eoption__cmp2_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering))) ).
tff(c_2Ecomparison_2Eoption__cmp2_2E1,type,
c_2Ecomparison_2Eoption__cmp2_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) > tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2Ecomparison_2Eoption__cmp2_2E3,type,
c_2Ecomparison_2Eoption__cmp2_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) * tyop_2Eoption_2Eoption(A_27a) * tyop_2Eoption_2Eoption(A_27b) ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2EternaryComparisons_2Eoption__compare_2E0,type,
c_2EternaryComparisons_2Eoption__compare_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering))) ).
tff(c_2EternaryComparisons_2Eoption__compare_2E1,type,
c_2EternaryComparisons_2Eoption__compare_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) > tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2EternaryComparisons_2Eoption__compare_2E3,type,
c_2EternaryComparisons_2Eoption__compare_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) * tyop_2Eoption_2Eoption(A_27a) * tyop_2Eoption_2Eoption(A_27b) ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2EternaryComparisons_2Eordering__CASE_2E0,type,
c_2EternaryComparisons_2Eordering__CASE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))) ).
tff(c_2EternaryComparisons_2Eordering__CASE_2E4,type,
c_2EternaryComparisons_2Eordering__CASE_2E4:
!>[A_27a: $tType] : ( ( tyop_2EternaryComparisons_2Eordering * A_27a * A_27a * A_27a ) > A_27a ) ).
tff(c_2EternaryComparisons_2Epair__compare_2E0,type,
c_2EternaryComparisons_2Epair__compare_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering)))) ).
tff(c_2EternaryComparisons_2Epair__compare_2E2,type,
c_2EternaryComparisons_2Epair__compare_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) * tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2EternaryComparisons_2Epair__compare_2E4,type,
c_2EternaryComparisons_2Epair__compare_2E4:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) * tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)) * tyop_2Epair_2Eprod(A_27a,A_27c) * tyop_2Epair_2Eprod(A_27b,A_27d) ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2Ecomparison_2Eresp__equiv_2E0,type,
c_2Ecomparison_2Eresp__equiv_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool)) ).
tff(c_2Ecomparison_2Eresp__equiv_2E2,type,
c_2Ecomparison_2Eresp__equiv_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecomparison_2Eresp__equiv2_2E0,type,
c_2Ecomparison_2Eresp__equiv2_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Ecomparison_2Eresp__equiv2_2E3,type,
c_2Ecomparison_2Eresp__equiv2_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2EternaryComparisons_2Estring__compare_2E0,type,
c_2EternaryComparisons_2Estring__compare_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)) ).
tff(c_2EternaryComparisons_2Estring__compare_2E2,type,
c_2EternaryComparisons_2Estring__compare_2E2: ( tyop_2Elist_2Elist(tyop_2Estring_2Echar) * tyop_2Elist_2Elist(tyop_2Estring_2Echar) ) > tyop_2EternaryComparisons_2Eordering ).
tff(c_2Etoto_2Estringto_2E0,type,
c_2Etoto_2Estringto_2E0: tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).
tff(c_2Erelation_2Etransitive_2E0,type,
c_2Erelation_2Etransitive_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Etransitive_2E1,type,
c_2Erelation_2Etransitive_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27a,X1_2E0: A_27c] : ( c_2Epair_2E_2C_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Epair_2E_2C_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: A_27b,X1_2E0: A_27d] : ( c_2Epair_2E_2C_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d)),c_2Epair_2E_2C_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2EternaryComparisons_2Eordering,X2_2E0: tyop_2EternaryComparisons_2Eordering] : ( c_2Ebool_2ECOND_2E3(tyop_2EternaryComparisons_2Eordering,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering)),c_2Ebool_2ECOND_2E0(tyop_2EternaryComparisons_2Eordering),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering)] : ( c_2Epair_2ECURRY_2E1(A_27a,A_27a,tyop_2EternaryComparisons_2Eordering,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Epair_2ECURRY_2E0(A_27a,A_27a,tyop_2EternaryComparisons_2Eordering),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27c)] : ( c_2Epair_2EFST_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27d)] : ( c_2Epair_2EFST_2E1(A_27b,A_27d,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27d),A_27b,c_2Epair_2EFST_2E0(A_27b,A_27d),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELLEX_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Elist_2ELLEX_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2EListOrd_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2EListOrd_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2EListOrd_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estring_2EORD_2E1,axiom,
! [X0_2E0: tyop_2Estring_2Echar] : ( c_2Estring_2EORD_2E1(X0_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,c_2Estring_2EORD_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27c)] : ( c_2Epair_2ESND_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27c,c_2Epair_2ESND_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27d)] : ( c_2Epair_2ESND_2E1(A_27b,A_27d,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27d),A_27d,c_2Epair_2ESND_2E0(A_27b,A_27d),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Eoption_2ESOME_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETO_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Etoto_2Etoto(A_27a),c_2Etoto_2ETO_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO__inv_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETO__inv_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__inv_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO__inv_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETO__inv_2E1(tyop_2Eoption_2Eoption(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__inv_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO__of__LinearOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO__of__LinearOrder_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Etoto_2ETO__of__LinearOrder_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETotOrd_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETotOrd_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETotOrd_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2EternaryComparisons_2Eordering,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),c_2Epair_2EUNCURRY_2E0(A_27a,A_27a,tyop_2EternaryComparisons_2Eordering),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Etoto_2Eapto_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0: tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(tyop_2Estring_2Echar))] : ( c_2Etoto_2Eapto_2E1(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0) = app_2E2(tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0) ) ).
tff(arityeq2_2Ec_2EternaryComparisons_2Ebool__compare_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] : ( c_2EternaryComparisons_2Ebool__compare_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering),c_2EternaryComparisons_2Ebool__compare_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EternaryComparisons_2Echar__compare_2E2,axiom,
! [X0_2E0: tyop_2Estring_2Echar,X1_2E0: tyop_2Estring_2Echar] : ( c_2EternaryComparisons_2Echar__compare_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering),c_2EternaryComparisons_2Echar__compare_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ecomparison_2Eequiv__inj_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecomparison_2Eequiv__inj_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Ecomparison_2Eequiv__inj_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(tyop_2Estring_2Echar),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(tyop_2Eoption_2Eoption(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Egood__cmp_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eirreflexive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Etoto_2ElexTO_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ElexTO_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2ElexTO_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EternaryComparisons_2Elist__compare_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2EternaryComparisons_2Elist__compare_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EternaryComparisons_2Elist__compare_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EternaryComparisons_2Elist__compare_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2EternaryComparisons_2Elist__compare_2E1_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering))] : ( c_2EternaryComparisons_2Elist__compare_2E1(tyop_2Estring_2Echar,tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E0(tyop_2Estring_2Echar,tyop_2Estring_2Echar),X0_2E0) ) ).
tff(arityeq2_2Ec_2EternaryComparisons_2Enum__compare_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2EternaryComparisons_2Enum__compare_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering),c_2EternaryComparisons_2Enum__compare_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering)] : ( c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Ecombin_2Eo_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecomparison_2Eoption__cmp2_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Eoption__cmp2_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Ecomparison_2Eoption__cmp2_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ecomparison_2Eoption__cmp2_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Ecomparison_2Eoption__cmp2_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Ecomparison_2Eoption__cmp2_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ecomparison_2Eoption__cmp2_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Ecomparison_2Eoption__cmp2_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering)),c_2Ecomparison_2Eoption__cmp2_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2EternaryComparisons_2Eoption__compare_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2EternaryComparisons_2Eoption__compare_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Eoption__compare_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2EternaryComparisons_2Eoption__compare_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2EternaryComparisons_2Eoption__compare_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Eoption__compare_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2EternaryComparisons_2Eoption__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2EternaryComparisons_2Eoption__compare_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Eoption__compare_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: A_27a,X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2EternaryComparisons_2Eordering__CASE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: tyop_2EternaryComparisons_2Eordering,X2_2E0: tyop_2EternaryComparisons_2Eordering,X3_2E0: tyop_2EternaryComparisons_2Eordering] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering)),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Eordering__CASE_2E0(tyop_2EternaryComparisons_2Eordering),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2EternaryComparisons_2Epair__compare_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] : ( c_2EternaryComparisons_2Epair__compare_2E2(A_27a,A_27a,A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Epair__compare_2E0(A_27a,A_27a,A_27b,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2EternaryComparisons_2Epair__compare_2E4_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X2_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X3_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2EternaryComparisons_2Epair__compare_2E4(A_27a,A_27a,A_27b,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Epair__compare_2E0(A_27a,A_27a,A_27b,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2EternaryComparisons_2Epair__compare_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),X2_2E0: tyop_2Epair_2Eprod(A_27a,A_27c),X3_2E0: tyop_2Epair_2Eprod(A_27b,A_27d)] : ( c_2EternaryComparisons_2Epair__compare_2E4(A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Epair__compare_2E0(A_27a,A_27b,A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Ecomparison_2Eresp__equiv_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2Ecomparison_2Eresp__equiv_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool),c_2Ecomparison_2Eresp__equiv_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ecomparison_2Eresp__equiv2_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecomparison_2Eresp__equiv2_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Ecomparison_2Eresp__equiv2_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ecomparison_2Eresp__equiv2_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2Ecomparison_2Eresp__equiv2_2E3(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool)),c_2Ecomparison_2Eresp__equiv2_2E0(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2EternaryComparisons_2Estring__compare_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EternaryComparisons_2Estring__compare_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering),c_2EternaryComparisons_2Estring__compare_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Ecomparison_2Egood__cmp__def,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp_2E0))
<=> ( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V1x_2E0),V1x_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V2x_2E0),V3y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3y_2E0),V2x_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V4x_2E0),V5y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
<=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V5y_2E0),V4x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V6x_2E0: A_27a,V7y_2E0: A_27a,V8z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V6x_2E0),V7y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V7y_2E0),V8z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V6x_2E0),V8z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V9x_2E0: A_27a,V10y_2E0: A_27a,V11z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V9x_2E0),V10y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V10y_2E0),V11z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V9x_2E0),V11z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V12x_2E0: A_27a,V13y_2E0: A_27a,V14z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V12x_2E0),V13y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V13y_2E0),V14z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V12x_2E0),V14z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
& ! [V15x_2E0: A_27a,V16y_2E0: A_27a,V17z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V15x_2E0),V16y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V16y_2E0),V17z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V15x_2E0),V17z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ) ).
tff(thm_2Ecomparison_2Eresp__equiv__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] :
( p(c_2Ecomparison_2Eresp__equiv_2E2(A_27a,A_27b,A_27c,V0cmp_2E0,V1f_2E0))
<=> ! [V2k1_2E0: A_27a,V3k2_2E0: A_27a,V4v_2E0: A_27b] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V2k1_2E0),V3k2_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V1f_2E0,V2k1_2E0),V4v_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V1f_2E0,V3k2_2E0),V4v_2E0) ) ) ) ).
tff(thm_2Ecomparison_2Eresp__equiv2__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Ecomparison_2Eresp__equiv2_2E3(A_27a,A_27b,V0cmp_2E0,V1cmp2_2E0,V2f_2E0))
<=> ! [V3k1_2E0: A_27a,V4k2_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3k1_2E0),V4k2_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V1cmp2_2E0,app_2E2(A_27a,A_27b,V2f_2E0,V3k1_2E0)),app_2E2(A_27a,A_27b,V2f_2E0,V4k2_2E0)) = c_2EternaryComparisons_2EEQUAL_2E0 ) ) ) ).
tff(thm_2Ecomparison_2Eequiv__inj__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Ecomparison_2Eequiv__inj_2E3(A_27a,A_27b,V0cmp_2E0,V1cmp2_2E0,V2f_2E0))
<=> ! [V3k1_2E0: A_27a,V4k2_2E0: A_27a] :
( ( app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V1cmp2_2E0,app_2E2(A_27a,A_27b,V2f_2E0,V3k1_2E0)),app_2E2(A_27a,A_27b,V2f_2E0,V4k2_2E0)) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3k1_2E0),V4k2_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) ) ) ).
tff(thm_2Ecomparison_2Egood__cmp__thm,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp_2E0))
<=> ( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V1x_2E0),V1x_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ! [V2x_2E0: A_27a,V3y_2E0: A_27a,V4z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V2x_2E0),V3y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
<=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3y_2E0),V2x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V2x_2E0),V3y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3y_2E0),V4z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V2x_2E0),V4z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V2x_2E0),V3y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3y_2E0),V4z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V2x_2E0),V4z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ) ) ).
tff(thm_2Ecomparison_2Ecmp__thms,axiom,
! [A_27a: $tType] :
( ( c_2EternaryComparisons_2ELESS_2E0 != c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2EternaryComparisons_2ELESS_2E0 != c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2EternaryComparisons_2EEQUAL_2E0 != c_2EternaryComparisons_2EGREATER_2E0 )
& ! [V0v0_2E0: A_27a,V1v1_2E0: A_27a,V2v2_2E0: A_27a] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(A_27a,c_2EternaryComparisons_2ELESS_2E0,V0v0_2E0,V1v1_2E0,V2v2_2E0) = V0v0_2E0 )
& ! [V3v0_2E0: A_27a,V4v1_2E0: A_27a,V5v2_2E0: A_27a] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(A_27a,c_2EternaryComparisons_2EEQUAL_2E0,V3v0_2E0,V4v1_2E0,V5v2_2E0) = V4v1_2E0 )
& ! [V6v0_2E0: A_27a,V7v1_2E0: A_27a,V8v2_2E0: A_27a] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(A_27a,c_2EternaryComparisons_2EGREATER_2E0,V6v0_2E0,V7v1_2E0,V8v2_2E0) = V8v2_2E0 )
& ! [V9a_2E0: tyop_2EternaryComparisons_2Eordering] :
( ( V9a_2E0 = c_2EternaryComparisons_2ELESS_2E0 )
| ( V9a_2E0 = c_2EternaryComparisons_2EEQUAL_2E0 )
| ( V9a_2E0 = c_2EternaryComparisons_2EGREATER_2E0 ) )
& ! [V10cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V10cmp_2E0))
<=> ( ! [V11x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V11x_2E0),V11x_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ! [V12x_2E0: A_27a,V13y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V12x_2E0),V13y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V13y_2E0),V12x_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
& ! [V14x_2E0: A_27a,V15y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V14x_2E0),V15y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
<=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V15y_2E0),V14x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V16x_2E0: A_27a,V17y_2E0: A_27a,V18z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V16x_2E0),V17y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V17y_2E0),V18z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V16x_2E0),V18z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V19x_2E0: A_27a,V20y_2E0: A_27a,V21z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V19x_2E0),V20y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V20y_2E0),V21z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V19x_2E0),V21z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V22x_2E0: A_27a,V23y_2E0: A_27a,V24z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V22x_2E0),V23y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V23y_2E0),V24z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V22x_2E0),V24z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
& ! [V25x_2E0: A_27a,V26y_2E0: A_27a,V27z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V25x_2E0),V26y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V26y_2E0),V27z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V10cmp_2E0,V25x_2E0),V27z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ) ) ).
tff(thm_2Ecomparison_2Eoption__cmp__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0v3_2E0: A_27a,V1v2_2E0: A_27b,V2v1_2E0: A_27a,V3v0_2E0: A_27b,V4c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] :
( ( c_2EternaryComparisons_2Eoption__compare_2E3(A_27a,A_27b,V4c_2E0,c_2Eoption_2ENONE_2E0(A_27a),c_2Eoption_2ENONE_2E0(A_27b)) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2EternaryComparisons_2Eoption__compare_2E3(A_27a,A_27b,V4c_2E0,c_2Eoption_2ENONE_2E0(A_27a),c_2Eoption_2ESOME_2E1(A_27b,V3v0_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2EternaryComparisons_2Eoption__compare_2E3(A_27a,A_27b,V4c_2E0,c_2Eoption_2ESOME_2E1(A_27a,V0v3_2E0),c_2Eoption_2ENONE_2E0(A_27b)) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2EternaryComparisons_2Eoption__compare_2E3(A_27a,A_27b,V4c_2E0,c_2Eoption_2ESOME_2E1(A_27a,V2v1_2E0),c_2Eoption_2ESOME_2E1(A_27b,V1v2_2E0)) = app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V4c_2E0,V2v1_2E0),V1v2_2E0) ) ) ).
tff(thm_2Ecomparison_2Eoption__cmp2__ind,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)))] :
( ( ! [V1c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] : p(app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),V0P_2E0,V1c_2E0),c_2Eoption_2ENONE_2E0(A_27a)),c_2Eoption_2ENONE_2E0(A_27b)))
& ! [V2c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3v0_2E0: A_27b] : p(app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),V0P_2E0,V2c_2E0),c_2Eoption_2ENONE_2E0(A_27a)),c_2Eoption_2ESOME_2E1(A_27b,V3v0_2E0)))
& ! [V4c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V5v3_2E0: A_27a] : p(app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),V0P_2E0,V4c_2E0),c_2Eoption_2ESOME_2E1(A_27a,V5v3_2E0)),c_2Eoption_2ENONE_2E0(A_27b)))
& ! [V6c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V7v1_2E0: A_27a,V8v2_2E0: A_27b] : p(app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),V0P_2E0,V6c_2E0),c_2Eoption_2ESOME_2E1(A_27a,V7v1_2E0)),c_2Eoption_2ESOME_2E1(A_27b,V8v2_2E0))) )
=> ! [V9v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V10v1_2E0: tyop_2Eoption_2Eoption(A_27a),V11v2_2E0: tyop_2Eoption_2Eoption(A_27b)] : p(app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),V0P_2E0,V9v_2E0),V10v1_2E0),V11v2_2E0)) ) ).
tff(thm_2Ecomparison_2Eoption__cmp2__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_27_2E0: A_27b,V2x_2E0: A_27a,V3cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] :
( ( c_2Ecomparison_2Eoption__cmp2_2E3(A_27a,A_27b,V3cmp_2E0,c_2Eoption_2ENONE_2E0(A_27a),c_2Eoption_2ENONE_2E0(A_27b)) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2Ecomparison_2Eoption__cmp2_2E3(A_27a,A_27b,V3cmp_2E0,c_2Eoption_2ENONE_2E0(A_27a),c_2Eoption_2ESOME_2E1(A_27b,V1x_27_2E0)) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2Ecomparison_2Eoption__cmp2_2E3(A_27a,A_27b,V3cmp_2E0,c_2Eoption_2ESOME_2E1(A_27a,V2x_2E0),c_2Eoption_2ENONE_2E0(A_27b)) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Ecomparison_2Eoption__cmp2_2E3(A_27a,A_27b,V3cmp_2E0,c_2Eoption_2ESOME_2E1(A_27a,V2x_2E0),c_2Eoption_2ESOME_2E1(A_27b,V0y_2E0)) = app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V3cmp_2E0,V2x_2E0),V0y_2E0) ) ) ).
tff(thm_2Ecomparison_2Epair__cmp__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0y_2E0: tyop_2Epair_2Eprod(A_27b,A_27d),V1x_2E0: tyop_2Epair_2Eprod(A_27a,A_27c),V2c2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V3c1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] : ( c_2EternaryComparisons_2Epair__compare_2E4(A_27a,A_27b,A_27c,A_27d,V3c1_2E0,V2c2_2E0,V1x_2E0,V0y_2E0) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V3c1_2E0,c_2Epair_2EFST_2E1(A_27a,A_27c,V1x_2E0)),c_2Epair_2EFST_2E1(A_27b,A_27d,V0y_2E0)),c_2EternaryComparisons_2ELESS_2E0,app_2E2(A_27d,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering),V2c2_2E0,c_2Epair_2ESND_2E1(A_27a,A_27c,V1x_2E0)),c_2Epair_2ESND_2E1(A_27b,A_27d,V0y_2E0)),c_2EternaryComparisons_2EGREATER_2E0) ) ).
tff(thm_2Ecomparison_2Ebool__cmp__def,axiom,
( ( c_2EternaryComparisons_2Ebool__compare_2E2(c_2Ebool_2ET_2E0,c_2Ebool_2ET_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2EternaryComparisons_2Ebool__compare_2E2(c_2Ebool_2EF_2E0,c_2Ebool_2EF_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2EternaryComparisons_2Ebool__compare_2E2(c_2Ebool_2ET_2E0,c_2Ebool_2EF_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2EternaryComparisons_2Ebool__compare_2E2(c_2Ebool_2EF_2E0,c_2Ebool_2ET_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Ecomparison_2Enum__cmp__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ! [V0n1_2E0: tyop_2Enum_2Enum,V1n2_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0n1_2E0),V1n2_2E0))
<=> ( V0n1_2E0 = V1n2_2E0 ) )
=> ! [V0n1_2E0: tyop_2Enum_2Enum,V1n2_2E0: tyop_2Enum_2Enum] : ( c_2EternaryComparisons_2Enum__compare_2E2(V0n1_2E0,V1n2_2E0) = c_2Ebool_2ECOND_2E3(tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0n1_2E0),V1n2_2E0),c_2EternaryComparisons_2EEQUAL_2E0,c_2Ebool_2ECOND_2E3(tyop_2EternaryComparisons_2Eordering,c_2Eprim__rec_2E_3C_2E2(V0n1_2E0,V1n2_2E0),c_2EternaryComparisons_2ELESS_2E0,c_2EternaryComparisons_2EGREATER_2E0)) ) ) ).
tff(thm_2Ecomparison_2Echar__cmp__def,axiom,
! [V0c1_2E0: tyop_2Estring_2Echar,V1c2_2E0: tyop_2Estring_2Echar] : ( c_2EternaryComparisons_2Echar__compare_2E2(V0c1_2E0,V1c2_2E0) = c_2EternaryComparisons_2Enum__compare_2E2(c_2Estring_2EORD_2E1(V0c1_2E0),c_2Estring_2EORD_2E1(V1c2_2E0)) ) ).
tff(thm_2Ecomparison_2Estring__cmp__def,axiom,
c_2EternaryComparisons_2Estring__compare_2E0 = c_2EternaryComparisons_2Elist__compare_2E1(tyop_2Estring_2Echar,tyop_2Estring_2Echar,c_2EternaryComparisons_2Echar__compare_2E0) ).
tff(thm_2Ecomparison_2ETotOrder__imp__good__cmp,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0cmp_2E0))
=> p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp_2E0)) ) ).
tff(thm_2Ecomparison_2ETO__inv__invert,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0c_2E0))
=> ( c_2Etoto_2ETO__inv_2E1(A_27a,V0c_2E0) = c_2Epair_2ECURRY_2E1(A_27a,A_27a,tyop_2EternaryComparisons_2Eordering,c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Einvert__comparison_2E0,c_2Epair_2EUNCURRY_2E1(A_27a,A_27a,tyop_2EternaryComparisons_2Eordering,V0c_2E0))) ) ) ).
tff(thm_2Ecomparison_2Eoption__cmp2__TO__inv,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2Ecomparison_2Eoption__cmp2_2E1(A_27a,A_27a,V0c_2E0) = c_2Etoto_2ETO__inv_2E1(tyop_2Eoption_2Eoption(A_27a),c_2EternaryComparisons_2Eoption__compare_2E1(A_27a,A_27a,c_2Etoto_2ETO__inv_2E1(A_27a,V0c_2E0))) ) ).
tff(thm_2Ecomparison_2Elist__cmp__ListOrd,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0c_2E0))
=> ( c_2EternaryComparisons_2Elist__compare_2E1(A_27a,A_27a,V0c_2E0) = c_2Etoto_2EListOrd_2E1(A_27a,c_2Etoto_2ETO_2E1(A_27a,V0c_2E0)) ) ) ).
tff(thm_2Ecomparison_2ETotOrd__list__cmp,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0c_2E0))
=> p(c_2Etoto_2ETotOrd_2E1(tyop_2Elist_2Elist(A_27a),c_2EternaryComparisons_2Elist__compare_2E1(A_27a,A_27a,V0c_2E0))) ) ).
tff(thm_2Ecomparison_2Epair__cmp__lexTO,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1V_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] :
( ( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0R_2E0))
& p(c_2Etoto_2ETotOrd_2E1(A_27b,V1V_2E0)) )
=> ( c_2EternaryComparisons_2Epair__compare_2E2(A_27a,A_27a,A_27b,A_27b,V0R_2E0,V1V_2E0) = c_2Etoto_2ElexTO_2E2(A_27a,A_27b,V0R_2E0,V1V_2E0) ) ) ).
tff(thm_2Ecomparison_2Enum__cmp__numOrd,axiom,
c_2EternaryComparisons_2Enum__compare_2E0 = c_2Etoto_2EnumOrd_2E0 ).
tff(thm_2Ecomparison_2Echar__cmp__charOrd,axiom,
c_2EternaryComparisons_2Echar__compare_2E0 = c_2Etoto_2EcharOrd_2E0 ).
tff(thm_2Ecomparison_2Estring__cmp__stringto,axiom,
c_2EternaryComparisons_2Estring__compare_2E0 = c_2Etoto_2Eapto_2E1(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Etoto_2Estringto_2E0) ).
tff(thm_2Ecomparison_2Eoption__cmp__good,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp_2E0))
=> p(c_2Ecomparison_2Egood__cmp_2E1(tyop_2Eoption_2Eoption(A_27a),c_2EternaryComparisons_2Eoption__compare_2E1(A_27a,A_27a,V0cmp_2E0))) ) ).
tff(thm_2Ecomparison_2Eoption__cmp2__good,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp_2E0))
=> p(c_2Ecomparison_2Egood__cmp_2E1(tyop_2Eoption_2Eoption(A_27a),c_2Ecomparison_2Eoption__cmp2_2E1(A_27a,A_27a,V0cmp_2E0))) ) ).
tff(thm_2Ecomparison_2Elist__cmp__good,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp_2E0))
=> p(c_2Ecomparison_2Egood__cmp_2E1(tyop_2Elist_2Elist(A_27a),c_2EternaryComparisons_2Elist__compare_2E1(A_27a,A_27a,V0cmp_2E0))) ) ).
tff(thm_2Ecomparison_2Epair__cmp__good,axiom,
! [A_27a: $tType,A_27b: $tType,V0cmp1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering))] :
( ( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp1_2E0))
& p(c_2Ecomparison_2Egood__cmp_2E1(A_27b,V1cmp2_2E0)) )
=> p(c_2Ecomparison_2Egood__cmp_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2EternaryComparisons_2Epair__compare_2E2(A_27a,A_27a,A_27b,A_27b,V0cmp1_2E0,V1cmp2_2E0))) ) ).
tff(thm_2Ecomparison_2Ebool__cmp__good,axiom,
p(c_2Ecomparison_2Egood__cmp_2E1(tyop_2Emin_2Ebool,c_2EternaryComparisons_2Ebool__compare_2E0)) ).
tff(thm_2Ecomparison_2Enum__cmp__good,axiom,
p(c_2Ecomparison_2Egood__cmp_2E1(tyop_2Enum_2Enum,c_2EternaryComparisons_2Enum__compare_2E0)) ).
tff(thm_2Ecomparison_2Echar__cmp__good,axiom,
p(c_2Ecomparison_2Egood__cmp_2E1(tyop_2Estring_2Echar,c_2EternaryComparisons_2Echar__compare_2E0)) ).
tff(thm_2Ecomparison_2Estring__cmp__good,axiom,
p(c_2Ecomparison_2Egood__cmp_2E1(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EternaryComparisons_2Estring__compare_2E0)) ).
tff(thm_2Ecomparison_2Elist__cmp__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3cmp_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4l1_27_2E0: tyop_2Elist_2Elist(A_27a),V5l2_27_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( ( V1l1_2E0 = V4l1_27_2E0 )
& ( V2l2_2E0 = V5l2_27_2E0 )
& ! [V6x_2E0: A_27a,V7x_27_2E0: A_27b] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V4l1_27_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27b,V7x_27_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,V5l2_27_2E0))) )
=> ( app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V6x_2E0),V7x_27_2E0) = app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V3cmp_27_2E0,V6x_2E0),V7x_27_2E0) ) ) )
=> ( c_2EternaryComparisons_2Elist__compare_2E3(A_27a,A_27b,V0cmp_2E0,V1l1_2E0,V2l2_2E0) = c_2EternaryComparisons_2Elist__compare_2E3(A_27a,A_27b,V3cmp_27_2E0,V4l1_27_2E0,V5l2_27_2E0) ) ) ).
tff(thm_2Ecomparison_2Eoption__cmp__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1v1_2E0: tyop_2Eoption_2Eoption(A_27a),V2v2_2E0: tyop_2Eoption_2Eoption(A_27b),V3cmp_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4v1_27_2E0: tyop_2Eoption_2Eoption(A_27a),V5v2_27_2E0: tyop_2Eoption_2Eoption(A_27b)] :
( ( ( V1v1_2E0 = V4v1_27_2E0 )
& ( V2v2_2E0 = V5v2_27_2E0 )
& ! [V6x_2E0: A_27a,V7x_27_2E0: A_27b] :
( ( ( V4v1_27_2E0 = c_2Eoption_2ESOME_2E1(A_27a,V6x_2E0) )
& ( V5v2_27_2E0 = c_2Eoption_2ESOME_2E1(A_27b,V7x_27_2E0) ) )
=> ( app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V6x_2E0),V7x_27_2E0) = app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V3cmp_27_2E0,V6x_2E0),V7x_27_2E0) ) ) )
=> ( c_2EternaryComparisons_2Eoption__compare_2E3(A_27a,A_27b,V0cmp_2E0,V1v1_2E0,V2v2_2E0) = c_2EternaryComparisons_2Eoption__compare_2E3(A_27a,A_27b,V3cmp_27_2E0,V4v1_27_2E0,V5v2_27_2E0) ) ) ).
tff(thm_2Ecomparison_2Eoption__cmp2__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1v1_2E0: tyop_2Eoption_2Eoption(A_27a),V2v2_2E0: tyop_2Eoption_2Eoption(A_27b),V3cmp_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4v1_27_2E0: tyop_2Eoption_2Eoption(A_27a),V5v2_27_2E0: tyop_2Eoption_2Eoption(A_27b)] :
( ( ( V1v1_2E0 = V4v1_27_2E0 )
& ( V2v2_2E0 = V5v2_27_2E0 )
& ! [V6x_2E0: A_27a,V7x_27_2E0: A_27b] :
( ( ( V4v1_27_2E0 = c_2Eoption_2ESOME_2E1(A_27a,V6x_2E0) )
& ( V5v2_27_2E0 = c_2Eoption_2ESOME_2E1(A_27b,V7x_27_2E0) ) )
=> ( app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V6x_2E0),V7x_27_2E0) = app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V3cmp_27_2E0,V6x_2E0),V7x_27_2E0) ) ) )
=> ( c_2Ecomparison_2Eoption__cmp2_2E3(A_27a,A_27b,V0cmp_2E0,V1v1_2E0,V2v2_2E0) = c_2Ecomparison_2Eoption__cmp2_2E3(A_27a,A_27b,V3cmp_27_2E0,V4v1_27_2E0,V5v2_27_2E0) ) ) ).
tff(thm_2Ecomparison_2Epair__cmp__cong,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0cmp1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V2v1_2E0: tyop_2Epair_2Eprod(A_27a,A_27c),V3v2_2E0: tyop_2Epair_2Eprod(A_27b,A_27d),V4cmp1_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V5cmp2_27_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V6v1_27_2E0: tyop_2Epair_2Eprod(A_27a,A_27c),V7v2_27_2E0: tyop_2Epair_2Eprod(A_27b,A_27d)] :
( ( ( V2v1_2E0 = V6v1_27_2E0 )
& ( V3v2_2E0 = V7v2_27_2E0 )
& ! [V8a_2E0: A_27a,V9b_2E0: A_27c,V10c_2E0: A_27b,V11d_2E0: A_27d] :
( ( ( V6v1_27_2E0 = c_2Epair_2E_2C_2E2(A_27a,A_27c,V8a_2E0,V9b_2E0) )
& ( V7v2_27_2E0 = c_2Epair_2E_2C_2E2(A_27b,A_27d,V10c_2E0,V11d_2E0) ) )
=> ( app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V0cmp1_2E0,V8a_2E0),V10c_2E0) = app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V4cmp1_27_2E0,V8a_2E0),V10c_2E0) ) )
& ! [V12a_2E0: A_27a,V13b_2E0: A_27c,V14c_2E0: A_27b,V15d_2E0: A_27d] :
( ( ( V6v1_27_2E0 = c_2Epair_2E_2C_2E2(A_27a,A_27c,V12a_2E0,V13b_2E0) )
& ( V7v2_27_2E0 = c_2Epair_2E_2C_2E2(A_27b,A_27d,V14c_2E0,V15d_2E0) ) )
=> ( app_2E2(A_27d,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering),V1cmp2_2E0,V13b_2E0),V15d_2E0) = app_2E2(A_27d,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering),V5cmp2_27_2E0,V13b_2E0),V15d_2E0) ) ) )
=> ( c_2EternaryComparisons_2Epair__compare_2E4(A_27a,A_27b,A_27c,A_27d,V0cmp1_2E0,V1cmp2_2E0,V2v1_2E0,V3v2_2E0) = c_2EternaryComparisons_2Epair__compare_2E4(A_27a,A_27b,A_27c,A_27d,V4cmp1_27_2E0,V5cmp2_27_2E0,V6v1_27_2E0,V7v2_27_2E0) ) ) ).
tff(thm_2Ecomparison_2Egood__cmp__trans,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
( ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1k_2E0: A_27a,V3k_27_2E0: A_27a,V4v_27_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F1_2E0,V0cmp_2E0),V1k_2E0),V3k_27_2E0),V4v_27_2E0))
<=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V1k_2E0),V3k_27_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1k_2E0: A_27a,V2v_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0cmp_2E0),V1k_2E0),V2v_2E0) = c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F1_2E0,V0cmp_2E0),V1k_2E0)) )
=> ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp_2E0))
=> p(c_2Erelation_2Etransitive_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0cmp_2E0)))) ) ) ) ).
tff(thm_2Ecomparison_2Egood__cmp__Less__trans,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1k_2E0: A_27a,V2k_27_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0cmp_2E0),V1k_2E0),V2k_27_2E0))
<=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V1k_2E0),V2k_27_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp_2E0))
=> p(c_2Erelation_2Etransitive_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0cmp_2E0))) ) ) ).
tff(thm_2Ecomparison_2Egood__cmp__Less__irrefl__trans,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V3k_2E0: A_27a,V4k_27_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0cmp_2E0),V3k_2E0),V4k_27_2E0))
<=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3k_2E0),V4k_27_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1k_2E0: A_27a,V2k_27_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0cmp_2E0),V1k_2E0),V2k_27_2E0))
<=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V1k_2E0),V2k_27_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(A_27a,V0cmp_2E0))
=> ( p(c_2Erelation_2Eirreflexive_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0cmp_2E0)))
& p(c_2Erelation_2Etransitive_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0cmp_2E0))) ) ) ) ) ).
tff(thm_2Ecomparison_2Ebool__cmp__antisym,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Emin_2Ebool] :
( ( c_2EternaryComparisons_2Ebool__compare_2E2(V0x_2E0,V1y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Ecomparison_2Enum__cmp__antisym,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] :
( ( c_2EternaryComparisons_2Enum__compare_2E2(V0x_2E0,V1y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Ecomparison_2Echar__cmp__antisym,axiom,
! [V0x_2E0: tyop_2Estring_2Echar,V1y_2E0: tyop_2Estring_2Echar] :
( ( c_2EternaryComparisons_2Echar__compare_2E2(V0x_2E0,V1y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Ecomparison_2Elist__cmp__antisym,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1x_2E0: tyop_2Elist_2Elist(A_27a),V2y_2E0: tyop_2Elist_2Elist(A_27a)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3x_2E0),V4y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V3x_2E0 = V4y_2E0 ) )
=> ( ( c_2EternaryComparisons_2Elist__compare_2E3(A_27a,A_27a,V0cmp_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V1x_2E0 = V2y_2E0 ) ) ) ).
tff(thm_2Ecomparison_2Estring__cmp__antisym,axiom,
! [V0x_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1y_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
( ( c_2EternaryComparisons_2Estring__compare_2E2(V0x_2E0,V1y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Ecomparison_2Epair__cmp__antisym,axiom,
! [A_27a: $tType,A_27b: $tType,V0cmp1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V2x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V3y_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
( ( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp1_2E0,V4x_2E0),V5y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V4x_2E0 = V5y_2E0 ) )
& ! [V6x_2E0: A_27b,V7y_2E0: A_27b] :
( ( app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V1cmp2_2E0,V6x_2E0),V7y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V6x_2E0 = V7y_2E0 ) ) )
=> ( ( c_2EternaryComparisons_2Epair__compare_2E4(A_27a,A_27a,A_27b,A_27b,V0cmp1_2E0,V1cmp2_2E0,V2x_2E0,V3y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V2x_2E0 = V3y_2E0 ) ) ) ).
tff(thm_2Ecomparison_2Eoption__cmp__antisym,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1x_2E0: tyop_2Eoption_2Eoption(A_27a),V2y_2E0: tyop_2Eoption_2Eoption(A_27a)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3x_2E0),V4y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V3x_2E0 = V4y_2E0 ) )
=> ( ( c_2EternaryComparisons_2Eoption__compare_2E3(A_27a,A_27a,V0cmp_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V1x_2E0 = V2y_2E0 ) ) ) ).
tff(thm_2Ecomparison_2Eoption__cmp2__antisym,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1x_2E0: tyop_2Eoption_2Eoption(A_27a),V2y_2E0: tyop_2Eoption_2Eoption(A_27a)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3x_2E0),V4y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V3x_2E0 = V4y_2E0 ) )
=> ( ( c_2Ecomparison_2Eoption__cmp2_2E3(A_27a,A_27a,V0cmp_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V1x_2E0 = V2y_2E0 ) ) ) ).
tff(thm_2Ecomparison_2Eantisym__resp__equiv,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V2x_2E0),V3y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( V2x_2E0 = V3y_2E0 ) )
=> ( p(c_2Ecomparison_2Eresp__equiv_2E2(A_27a,A_27b,A_27c,V0cmp_2E0,V1f_2E0))
& ! [V4cmp2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Ecomparison_2Egood__cmp_2E1(tyop_2Emin_2Efun(A_27b,A_27c),V4cmp2_2E0))
=> p(c_2Ecomparison_2Eresp__equiv2_2E3(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0cmp_2E0,V4cmp2_2E0,V1f_2E0)) ) ) ) ).
tff(thm_2Ecomparison_2Elist__cmp__equal__list__rel,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
( ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3x_2E0: A_27a,V4y_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0cmp_2E0),V3x_2E0),V4y_2E0))
<=> ( app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V0cmp_2E0,V3x_2E0),V4y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ! [V0cmp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( c_2EternaryComparisons_2Elist__compare_2E3(A_27a,A_27b,V0cmp_2E0,V1l1_2E0,V2l2_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0cmp_2E0),V1l1_2E0,V2l2_2E0)) ) ) ).
tff(thm_2Ecomparison_2ETO__of__LinearOrder__LLEX,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Eirreflexive_2E1(A_27a,V0R_2E0))
=> ( c_2Etoto_2ETO__of__LinearOrder_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELLEX_2E1(A_27a,V0R_2E0)) = c_2EternaryComparisons_2Elist__compare_2E1(A_27a,A_27a,c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,V0R_2E0)) ) ) ).
%------------------------------------------------------------------------------