ITP001 Axioms: ITP089_7.ax
%------------------------------------------------------------------------------
% File : ITP089_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 : toto.ax [Gau19]
% : HL4089_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 428 ( 159 unt; 177 typ; 0 def)
% Number of atoms : 522 ( 370 equ)
% Maximal formula atoms : 18 ( 1 avg)
% Number of connectives : 295 ( 24 ~; 12 |; 117 &)
% ( 47 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 141 ( 85 >; 56 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 171 ( 171 usr; 36 con; 0-6 aty)
% Number of variables : 955 ( 801 !; 14 ?; 955 :)
% ( 140 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: $tType > $tType ).
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_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_2Enum__dt,type,
tyop_2Etoto_2Enum__dt: $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_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
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_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0:
!>[A_27a: $tType] : tyop_2Eind__type_2Erecspace(A_27a) ).
tff(c_2Estring_2ECHR_2E0,type,
c_2Estring_2ECHR_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar) ).
tff(c_2Estring_2ECHR_2E1,type,
c_2Estring_2ECHR_2E1: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).
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_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eind__type_2ECONSTR_2E0,type,
c_2Eind__type_2ECONSTR_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))) ).
tff(c_2Eind__type_2ECONSTR_2E3,type,
c_2Eind__type_2ECONSTR_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)) ) > tyop_2Eind__type_2Erecspace(A_27a) ) ).
tff(c_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EDIV2_2E0,type,
c_2Earithmetic_2EDIV2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EDIV2_2E1,type,
c_2Earithmetic_2EDIV2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
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_2Eind__type_2EFCONS_2E0,type,
c_2Eind__type_2EFCONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))) ).
tff(c_2Eind__type_2EFCONS_2E2,type,
c_2Eind__type_2EFCONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) ).
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_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Ecombin_2EI_2E1,type,
c_2Ecombin_2EI_2E1:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
tff(c_2EternaryComparisons_2ELESS_2E0,type,
c_2EternaryComparisons_2ELESS_2E0: tyop_2EternaryComparisons_2Eordering ).
tff(c_2Epair_2ELEX_2E0,type,
c_2Epair_2ELEX_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(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)))) ).
tff(c_2Epair_2ELEX_2E2,type,
c_2Epair_2ELEX_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(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)) ) ).
tff(c_2Epair_2ELEX_2E4,type,
c_2Epair_2ELEX_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Epair_2Eprod(A_27a,A_27b) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ELinearOrder_2E0,type,
c_2Erelation_2ELinearOrder_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_2ELinearOrder_2E1,type,
c_2Erelation_2ELinearOrder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > 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_2Etoto_2EListOrd_2E3,type,
c_2Etoto_2EListOrd_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EODD_2E0,type,
c_2Earithmetic_2EODD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EODD_2E1,type,
c_2Earithmetic_2EODD_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2EONE__ONE_2E0,type,
c_2Ebool_2EONE__ONE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EONE__ONE_2E1,type,
c_2Ebool_2EONE__ONE_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Ebool ) ).
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_2Erelation_2ESTRORD_2E0,type,
c_2Erelation_2ESTRORD_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_2Emin_2Ebool))) ).
tff(c_2Erelation_2ESTRORD_2E1,type,
c_2Erelation_2ESTRORD_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_2Emin_2Ebool)) ) ).
tff(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Erelation_2EStrongLinearOrder_2E0,type,
c_2Erelation_2EStrongLinearOrder_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_2EStrongLinearOrder_2E1,type,
c_2Erelation_2EStrongLinearOrder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Etoto_2EStrongLinearOrder__of__TO_2E0,type,
c_2Etoto_2EStrongLinearOrder__of__TO_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_2Emin_2Ebool))) ).
tff(c_2Etoto_2EStrongLinearOrder__of__TO_2E1,type,
c_2Etoto_2EStrongLinearOrder__of__TO_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_2Emin_2Ebool)) ) ).
tff(c_2Etoto_2EStrongLinearOrder__of__TO_2E3,type,
c_2Etoto_2EStrongLinearOrder__of__TO_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EStrongOrder_2E0,type,
c_2Erelation_2EStrongOrder_2E0:
!>[A_27g: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EStrongOrder_2E1,type,
c_2Erelation_2EStrongOrder_2E1:
!>[A_27g: $tType] : ( tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
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__inv_2E3,type,
c_2Etoto_2ETO__inv_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) * A_27a * 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_2ETO__of__LinearOrder_2E3,type,
c_2Etoto_2ETO__of__LinearOrder_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
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_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_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_2EWF_2E1,type,
c_2Erelation_2EWF_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EWFREC_2E0,type,
c_2Erelation_2EWFREC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Erelation_2EWFREC_2E2,type,
c_2Erelation_2EWFREC_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Erelation_2EWeakLinearOrder_2E0,type,
c_2Erelation_2EWeakLinearOrder_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_2EWeakLinearOrder_2E1,type,
c_2Erelation_2EWeakLinearOrder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Etoto_2EWeakLinearOrder__of__TO_2E0,type,
c_2Etoto_2EWeakLinearOrder__of__TO_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_2Emin_2Ebool))) ).
tff(c_2Etoto_2EWeakLinearOrder__of__TO_2E1,type,
c_2Etoto_2EWeakLinearOrder__of__TO_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_2Emin_2Ebool)) ) ).
tff(c_2Etoto_2EWeakLinearOrder__of__TO_2E3,type,
c_2Etoto_2EWeakLinearOrder__of__TO_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
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_2Etoto_2Eapto_2E3,type,
c_2Etoto_2Eapto_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * A_27a ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2Etoto_2Ebit1_2E0,type,
c_2Etoto_2Ebit1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt) ).
tff(c_2Etoto_2Ebit1_2E1,type,
c_2Etoto_2Ebit1_2E1: tyop_2Etoto_2Enum__dt > tyop_2Etoto_2Enum__dt ).
tff(c_2Etoto_2Ebit2_2E0,type,
c_2Etoto_2Ebit2_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt) ).
tff(c_2Etoto_2Ebit2_2E1,type,
c_2Etoto_2Ebit2_2E1: tyop_2Etoto_2Enum__dt > tyop_2Etoto_2Enum__dt ).
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_2Etoto_2EcharOrd_2E2,type,
c_2Etoto_2EcharOrd_2E2: ( tyop_2Estring_2Echar * tyop_2Estring_2Echar ) > tyop_2EternaryComparisons_2Eordering ).
tff(c_2Estring_2Echar__lt_2E0,type,
c_2Estring_2Echar__lt_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)) ).
tff(c_2Etoto_2Echarto_2E0,type,
c_2Etoto_2Echarto_2E0: tyop_2Etoto_2Etoto(tyop_2Estring_2Echar) ).
tff(c_2Etoto_2EimageOrd_2E0,type,
c_2Etoto_2EimageOrd_2E0:
!>[A_27a: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)))) ).
tff(c_2Etoto_2EimageOrd_2E2,type,
c_2Etoto_2EimageOrd_2E2:
!>[A_27a: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)) ) ).
tff(c_2Etoto_2EimageOrd_2E4,type,
c_2Etoto_2EimageOrd_2E4:
!>[A_27a: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)) * A_27a * A_27a ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2Erelation_2Einv_2E0,type,
c_2Erelation_2Einv_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(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2Einv_2E1,type,
c_2Erelation_2Einv_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
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_2Etoto_2ElexTO_2E4,type,
c_2Etoto_2ElexTO_2E4:
!>[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_2Epair_2Eprod(A_27a,A_27b) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2Etoto_2Elextoto_2E0,type,
c_2Etoto_2Elextoto_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27b),tyop_2Etoto_2Etoto(tyop_2Epair_2Eprod(A_27a,A_27b)))) ).
tff(c_2Etoto_2Elextoto_2E2,type,
c_2Etoto_2Elextoto_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Etoto_2Etoto(A_27b) ) > tyop_2Etoto_2Etoto(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).
tff(c_2Etoto_2Elistorder_2E0,type,
c_2Etoto_2Elistorder_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_2Etoto_2Elistorder_2E1,type,
c_2Etoto_2Elistorder_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_2Elistorder_2E3,type,
c_2Etoto_2Elistorder_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Etoto_2Elistoto_2E0,type,
c_2Etoto_2Elistoto_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Etoto_2Elistoto_2E1,type,
c_2Etoto_2Elistoto_2E1:
!>[A_27a: $tType] : ( tyop_2Etoto_2Etoto(A_27a) > tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(A_27a)) ) ).
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_2Etoto_2EnumOrd_2E2,type,
c_2Etoto_2EnumOrd_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2EternaryComparisons_2Eordering ).
tff(c_2Etoto_2Enum__dtOrd_2E0,type,
c_2Etoto_2Enum__dtOrd_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2EternaryComparisons_2Eordering)) ).
tff(c_2Etoto_2Enum__dtOrd_2E2,type,
c_2Etoto_2Enum__dtOrd_2E2: ( tyop_2Etoto_2Enum__dt * tyop_2Etoto_2Enum__dt ) > tyop_2EternaryComparisons_2Eordering ).
tff(c_2Etoto_2Enum__dt__CASE_2E0,type,
c_2Etoto_2Enum__dt__CASE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),A_27a)))) ).
tff(c_2Etoto_2Enum__dt__CASE_2E4,type,
c_2Etoto_2Enum__dt__CASE_2E4:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Enum__dt * A_27a * tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a) * tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a) ) > A_27a ) ).
tff(c_2Etoto_2Enum__dt__size_2E0,type,
c_2Etoto_2Enum__dt__size_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Enum_2Enum) ).
tff(c_2Etoto_2Enum__dt__size_2E1,type,
c_2Etoto_2Enum__dt__size_2E1: tyop_2Etoto_2Enum__dt > tyop_2Enum_2Enum ).
tff(c_2Etoto_2Enum__to__dt_2E0,type,
c_2Etoto_2Enum__to__dt_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt) ).
tff(c_2Etoto_2Enum__to__dt_2E1,type,
c_2Etoto_2Enum__to__dt_2E1: tyop_2Enum_2Enum > tyop_2Etoto_2Enum__dt ).
tff(c_2Etoto_2Enumto_2E0,type,
c_2Etoto_2Enumto_2E0: tyop_2Etoto_2Etoto(tyop_2Enum_2Enum) ).
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_2Etoto_2Eqk__numOrd_2E0,type,
c_2Etoto_2Eqk__numOrd_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)) ).
tff(c_2Etoto_2Eqk__numOrd_2E2,type,
c_2Etoto_2Eqk__numOrd_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2EternaryComparisons_2Eordering ).
tff(c_2Etoto_2Eqk__numto_2E0,type,
c_2Etoto_2Eqk__numto_2E0: tyop_2Etoto_2Etoto(tyop_2Enum_2Enum) ).
tff(c_2Etoto_2Estringto_2E0,type,
c_2Etoto_2Estringto_2E0: tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).
tff(c_2Etoto_2Etoto__inv_2E0,type,
c_2Etoto_2Etoto__inv_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Etoto_2Etoto(A_27a)) ).
tff(c_2Etoto_2Etoto__inv_2E1,type,
c_2Etoto_2Etoto__inv_2E1:
!>[A_27a: $tType] : ( tyop_2Etoto_2Etoto(A_27a) > tyop_2Etoto_2Etoto(A_27a) ) ).
tff(c_2Etoto_2Etoto__of__LinearOrder_2E0,type,
c_2Etoto_2Etoto__of__LinearOrder_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Etoto_2Etoto(A_27a)) ).
tff(c_2Etoto_2Etoto__of__LinearOrder_2E1,type,
c_2Etoto_2Etoto__of__LinearOrder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Etoto_2Etoto(A_27a) ) ).
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_2Erelation_2Etrichotomous_2E0,type,
c_2Erelation_2Etrichotomous_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_2Etrichotomous_2E1,type,
c_2Erelation_2Etrichotomous_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Etoto_2Ezer_2E0,type,
c_2Etoto_2Ezer_2E0: tyop_2Etoto_2Enum__dt ).
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(arityeq1_2Ec_2Ebool_2E_21_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_2Ebool)] : ( c_2Ebool_2E_21_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2E_2C_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,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(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Estring_2ECHR_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Estring_2ECHR_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,c_2Estring_2ECHR_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Etoto_2Enum__dt,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Etoto_2Enum__dt,X2_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Ebool_2ECOND_2E3(tyop_2Etoto_2Enum__dt,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt)),c_2Ebool_2ECOND_2E0(tyop_2Etoto_2Enum__dt),X0_2E0),X1_2E0),X2_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(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))] : ( c_2Eind__type_2ECONSTR_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))),c_2Eind__type_2ECONSTR_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EDIV2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Emin_2Ebool_29,axiom,
! [X0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))] : ( c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))),c_2Eind__type_2EFCONS_2E0(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2EFST_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Etoto_2Enum__dt,axiom,
! [X0_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Ecombin_2EI_2E1(tyop_2Etoto_2Enum__dt,X0_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt,c_2Ecombin_2EI_2E0(tyop_2Etoto_2Enum__dt),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2ELEX_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_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epair_2ELEX_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(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)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(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_2ELEX_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Epair_2ELEX_2E4_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_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X3_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2ELEX_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(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)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(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_2ELEX_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ELinearOrder_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_2ELinearOrder_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_2ELinearOrder_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(arityeq3_2Ec_2Etoto_2EListOrd_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Etoto_2EListOrd_2E3(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_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),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EODD_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EODD_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2Ebool_2EONE__ONE_2E1(A_27d,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E0(A_27d,A_27c),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_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2ESND_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ESTRORD_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_2ESTRORD_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_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_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_2EStrongLinearOrder_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_2EStrongLinearOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EStrongLinearOrder_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_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_2Erelation_2EStrongLinearOrder_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_2Ebool,c_2Erelation_2EStrongLinearOrder_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EStrongLinearOrder_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_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_2EStrongLinearOrder_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_2EStrongLinearOrder_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2EStrongLinearOrder__of__TO_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_2EStrongLinearOrder__of__TO_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_2Emin_2Ebool)),c_2Etoto_2EStrongLinearOrder__of__TO_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Etoto_2EStrongLinearOrder__of__TO_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Etoto_2EStrongLinearOrder__of__TO_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = 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)),c_2Etoto_2EStrongLinearOrder__of__TO_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2EStrongLinearOrder__of__TO_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_2EStrongLinearOrder__of__TO_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Etoto_2EStrongLinearOrder__of__TO_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongOrder_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_2EStrongOrder_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_2EStrongOrder_2E0(A_27a),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_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETO_2E1(tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),tyop_2Etoto_2Etoto(tyop_2Estring_2Echar),c_2Etoto_2ETO_2E0(tyop_2Estring_2Echar),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO_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_2ETO_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_2Etoto_2Etoto(tyop_2Elist_2Elist(A_27a)),c_2Etoto_2ETO_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETO_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),tyop_2Etoto_2Etoto(tyop_2Enum_2Enum),c_2Etoto_2ETO_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO_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_2Etoto_2ETO_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_2Etoto_2Etoto(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Etoto_2ETO_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),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(arityeq3_2Ec_2Etoto_2ETO__inv_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Etoto_2ETO__inv_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),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),X1_2E0),X2_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(arityeq3_2Ec_2Etoto_2ETO__of__LinearOrder_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Etoto_2ETO__of__LinearOrder_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),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),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO__of__LinearOrder_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Etoto_2ETO__of__LinearOrder_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO__of__LinearOrder_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool))] : ( c_2Etoto_2ETO__of__LinearOrder_2E1(tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E0(tyop_2Estring_2Echar),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_2ETO__of__LinearOrder_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Etoto_2ETO__of__LinearOrder_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETO__of__LinearOrder_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_2Etoto_2ETO__of__LinearOrder_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_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Etoto_2Etoto_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Etoto_2Etoto(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Etoto_2Etoto(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Etoto_2Enum__dt,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Etoto_2Enum__dt,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Etoto_2Enum__dt),X0_2E0),X1_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_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETotOrd_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E0(A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2EA_27d,axiom,
! [A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETotOrd_2E1(A_27d,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E0(A_27d),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETotOrd_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_2Etoto_2ETotOrd_2E0(tyop_2Estring_2Echar),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_2Etoto_2ETotOrd_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETotOrd_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_2Etoto_2ETotOrd_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2ETotOrd_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_2Etoto_2ETotOrd_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_2Etoto_2ETotOrd_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),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_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Etoto_2Enum__dt,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt)),c_2Erelation_2EWFREC_2E0(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWeakLinearOrder_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_2EWeakLinearOrder_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_2EWeakLinearOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2EWeakLinearOrder__of__TO_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_2EWeakLinearOrder__of__TO_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_2Emin_2Ebool)),c_2Etoto_2EWeakLinearOrder__of__TO_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Etoto_2EWeakLinearOrder__of__TO_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Etoto_2EWeakLinearOrder__of__TO_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = 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)),c_2Etoto_2EWeakLinearOrder__of__TO_2E0(A_27a),X0_2E0),X1_2E0),X2_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_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2Eapto_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Etoto_2Eapto_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Etoto_2Eapto_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Eapto_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27b)] : ( c_2Etoto_2Eapto_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Etoto_2Etoto(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(A_27b),X0_2E0) ) ).
tff(arityeq3_2Ec_2Etoto_2Eapto_2E3_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27b),X1_2E0: A_27b,X2_2E0: A_27b] : ( c_2Etoto_2Eapto_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Etoto_2Etoto(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Eapto_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Etoto_2Etoto(tyop_2Estring_2Echar)] : ( c_2Etoto_2Eapto_2E1(tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Etoto_2Etoto(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(tyop_2Estring_2Echar),X0_2E0) ) ).
tff(arityeq3_2Ec_2Etoto_2Eapto_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Etoto_2Eapto_2E3(tyop_2Elist_2Elist(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_2Etoto_2Etoto(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Eapto_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Etoto_2Etoto(tyop_2Enum_2Enum)] : ( c_2Etoto_2Eapto_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Etoto_2Etoto(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq3_2Ec_2Etoto_2Eapto_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Etoto_2Eapto_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0,X2_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_2Etoto_2Etoto(tyop_2Epair_2Eprod(A_27a,A_27b)),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_2Eapto_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Ebit1_2E1,axiom,
! [X0_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Ebit1_2E1(X0_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt,c_2Etoto_2Ebit1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Ebit2_2E1,axiom,
! [X0_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Ebit2_2E1(X0_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt,c_2Etoto_2Ebit2_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Etoto_2EcharOrd_2E2,axiom,
! [X0_2E0: tyop_2Estring_2Echar,X1_2E0: tyop_2Estring_2Echar] : ( c_2Etoto_2EcharOrd_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_2Etoto_2EcharOrd_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Etoto_2EimageOrd_2E4_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)),X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2Etoto_2EimageOrd_2E4(A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2EimageOrd_2E0(A_27a,A_27c),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Etoto_2EimageOrd_2E2_2Emono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2EimageOrd_2E2(A_27d,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2EimageOrd_2E0(A_27d,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27a,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_2Emin_2Ebool)),c_2Erelation_2Einv_2E0(A_27a,A_27a),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(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eirreflexive_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E0(A_27b),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(arityeq4_2Ec_2Etoto_2ElexTO_2E4_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_2Epair_2Eprod(A_27a,A_27b),X3_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Etoto_2ElexTO_2E4(A_27a,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_2Etoto_2ElexTO_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Etoto_2Elextoto_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Etoto_2Etoto(A_27b)] : ( c_2Etoto_2Elextoto_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Etoto_2Etoto(A_27b),tyop_2Etoto_2Etoto(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27b),tyop_2Etoto_2Etoto(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Etoto_2Elextoto_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Elistorder_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_2Elistorder_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_2Etoto_2Elistorder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Etoto_2Elistorder_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Etoto_2Elistorder_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),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_2Etoto_2Elistorder_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Elistoto_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2Elistoto_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(A_27a)),c_2Etoto_2Elistoto_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Elistoto_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Etoto_2Etoto(tyop_2Estring_2Echar)] : ( c_2Etoto_2Elistoto_2E1(tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Etoto_2Etoto(tyop_2Estring_2Echar),tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Etoto_2Elistoto_2E0(tyop_2Estring_2Echar),X0_2E0) ) ).
tff(arityeq2_2Ec_2Etoto_2EnumOrd_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Etoto_2EnumOrd_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_2Etoto_2EnumOrd_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Etoto_2Enum__dtOrd_2E2,axiom,
! [X0_2E0: tyop_2Etoto_2Enum__dt,X1_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dtOrd_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2EternaryComparisons_2Eordering),c_2Etoto_2Enum__dtOrd_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Etoto_2Enum__dt__CASE_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Enum__dt,X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),X3_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a)] : ( c_2Etoto_2Enum__dt__CASE_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),A_27a)),app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),A_27a))),c_2Etoto_2Enum__dt__CASE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Enum__dt__size_2E1,axiom,
! [X0_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dt__size_2E1(X0_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Enum_2Enum,c_2Etoto_2Enum__dt__size_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Enum__to__dt_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Etoto_2Enum__to__dt_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt,c_2Etoto_2Enum__to__dt_2E0,X0_2E0) ) ).
tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool,X3_2E0: tyop_2Emin_2Ebool] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2EternaryComparisons_2Eordering__CASE_2E0(tyop_2Emin_2Ebool),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_2Etoto_2Eqk__numOrd_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Etoto_2Eqk__numOrd_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_2Etoto_2Eqk__numOrd_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Etoto__inv_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2Etoto__inv_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Etoto_2Etoto(A_27a),c_2Etoto_2Etoto__inv_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etoto_2Etoto__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_2Etoto__of__LinearOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Etoto_2Etoto(A_27a),c_2Etoto_2Etoto__of__LinearOrder_2E0(A_27a),X0_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_2Etrichotomous_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_2Etrichotomous_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_2Etrichotomous_2E0(A_27a),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_2Etoto_2ETotOrd,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))
<=> ( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V1x_2E0),V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V1x_2E0 = V2y_2E0 ) )
& ! [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),V0c_2E0,V3x_2E0),V4y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
<=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V4y_2E0),V3x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V5x_2E0: A_27a,V6y_2E0: A_27a,V7z_2E0: A_27a] :
( ( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V5x_2E0),V6y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V6y_2E0),V7z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V5x_2E0),V7z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ) ).
tff(thm_2Etoto_2ETO__of__LinearOrder,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1x_2E0),V2y_2E0))
<=> ( V1x_2E0 = V2y_2E0 ) )
=> ! [V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] : ( c_2Etoto_2ETO__of__LinearOrder_2E3(A_27a,V0r_2E0,V1x_2E0,V2y_2E0) = c_2Ebool_2ECOND_2E3(tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1x_2E0),V2y_2E0),c_2EternaryComparisons_2EEQUAL_2E0,c_2Ebool_2ECOND_2E3(tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0,V1x_2E0),V2y_2E0),c_2EternaryComparisons_2ELESS_2E0,c_2EternaryComparisons_2EGREATER_2E0)) ) ) ).
tff(thm_2Etoto_2Etoto__TY__DEF,axiom,
! [A_27a: $tType] :
? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Etoto_2Etoto(A_27a),c_2Etoto_2ETotOrd_2E0(A_27a),V0rep_2E0)) ).
tff(thm_2Etoto_2Eto__bij,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2ETO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V1r_2E0))
<=> ( c_2Etoto_2Eapto_2E1(A_27a,c_2Etoto_2ETO_2E1(A_27a,V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Etoto_2EWeakLinearOrder__of__TO,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1x_2E0: A_27a,V2y_2E0: A_27a] : ( c_2Etoto_2EWeakLinearOrder__of__TO_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V1x_2E0),V2y_2E0),c_2Ebool_2ET_2E0,c_2Ebool_2ET_2E0,c_2Ebool_2EF_2E0) ) ).
tff(thm_2Etoto_2EStrongLinearOrder__of__TO,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1x_2E0: A_27a,V2y_2E0: A_27a] : ( c_2Etoto_2EStrongLinearOrder__of__TO_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V1x_2E0),V2y_2E0),c_2Ebool_2ET_2E0,c_2Ebool_2EF_2E0,c_2Ebool_2EF_2E0) ) ).
tff(thm_2Etoto_2Etoto__of__LinearOrder,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etoto_2Etoto__of__LinearOrder_2E1(A_27a,V0r_2E0) = c_2Etoto_2ETO_2E1(A_27a,c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,V0r_2E0)) ) ).
tff(thm_2Etoto_2ETO__inv,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1x_2E0: A_27a,V2y_2E0: A_27a] : ( c_2Etoto_2ETO__inv_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V2y_2E0),V1x_2E0) ) ).
tff(thm_2Etoto_2Etoto__inv,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2Etoto__inv_2E1(A_27a,V0c_2E0) = c_2Etoto_2ETO_2E1(A_27a,c_2Etoto_2ETO__inv_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0))) ) ).
tff(thm_2Etoto_2ElexTO,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))] : ( c_2Etoto_2ElexTO_2E2(A_27a,A_27b,V0R_2E0,V1V_2E0) = c_2Etoto_2ETO__of__LinearOrder_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2ELEX_2E2(A_27a,A_27b,c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27a,V0R_2E0),c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27b,V1V_2E0))) ) ).
tff(thm_2Etoto_2Elextoto,axiom,
! [A_27a: $tType,A_27b: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1v_2E0: tyop_2Etoto_2Etoto(A_27b)] : ( c_2Etoto_2Elextoto_2E2(A_27a,A_27b,V0c_2E0,V1v_2E0) = c_2Etoto_2ETO_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Etoto_2ElexTO_2E2(A_27a,A_27b,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0),c_2Etoto_2Eapto_2E1(A_27b,V1v_2E0))) ) ).
tff(thm_2Etoto_2EnumOrd,axiom,
c_2Etoto_2EnumOrd_2E0 = c_2Etoto_2ETO__of__LinearOrder_2E1(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E0) ).
tff(thm_2Etoto_2Enumto,axiom,
c_2Etoto_2Enumto_2E0 = c_2Etoto_2ETO_2E1(tyop_2Enum_2Enum,c_2Etoto_2EnumOrd_2E0) ).
tff(thm_2Etoto_2Enum__dt__TY__DEF,axiom,
! [F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V8n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),F3_2E0,V8n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Emin_2Ebool) )
=> ( ! [V6n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),F2_2E0,V6n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Emin_2Ebool) )
=> ( ! [V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),F1_2E0,V4n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Emin_2Ebool) )
=> ( ! [V1a0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V1a0_2E0))
<=> ! [V2_27num__dt_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V3a0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)] :
( ( ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Emin_2Ebool,c_2Enum_2E0_2E0,c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),F1_2E0) )
| ? [V5a_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)] :
( ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Emin_2Ebool,c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),V5a_2E0,F2_2E0)) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2_27num__dt_27_2E0,V5a_2E0)) )
| ? [V7a_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)] :
( ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Emin_2Ebool,c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0)),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),V7a_2E0,F3_2E0)) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2_27num__dt_27_2E0,V7a_2E0)) ) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2_27num__dt_27_2E0,V3a0_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2_27num__dt_27_2E0,V1a0_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Etoto_2Enum__dt,F0_2E0,V0rep_2E0)) ) ) ) ) ).
tff(thm_2Etoto_2Enum__dt__case__def,axiom,
! [A_27a: $tType] :
( ! [V0v_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),V2f1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a)] : ( c_2Etoto_2Enum__dt__CASE_2E4(A_27a,c_2Etoto_2Ezer_2E0,V0v_2E0,V1f_2E0,V2f1_2E0) = V0v_2E0 )
& ! [V3a_2E0: tyop_2Etoto_2Enum__dt,V4v_2E0: A_27a,V5f_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),V6f1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a)] : ( c_2Etoto_2Enum__dt__CASE_2E4(A_27a,c_2Etoto_2Ebit1_2E1(V3a_2E0),V4v_2E0,V5f_2E0,V6f1_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V5f_2E0,V3a_2E0) )
& ! [V7a_2E0: tyop_2Etoto_2Enum__dt,V8v_2E0: A_27a,V9f_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),V10f1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a)] : ( c_2Etoto_2Enum__dt__CASE_2E4(A_27a,c_2Etoto_2Ebit2_2E1(V7a_2E0),V8v_2E0,V9f_2E0,V10f1_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V10f1_2E0,V7a_2E0) ) ) ).
tff(thm_2Etoto_2Enum__dt__size__def,axiom,
( ( c_2Etoto_2Enum__dt__size_2E1(c_2Etoto_2Ezer_2E0) = c_2Enum_2E0_2E0 )
& ! [V0a_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dt__size_2E1(c_2Etoto_2Ebit1_2E1(V0a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Etoto_2Enum__dt__size_2E1(V0a_2E0)) )
& ! [V1a_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dt__size_2E1(c_2Etoto_2Ebit2_2E1(V1a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Etoto_2Enum__dt__size_2E1(V1a_2E0)) ) ) ).
tff(thm_2Etoto_2Enum__to__dt__primitive,axiom,
! [F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
( ! [V4a_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V4a_2E0))
<=> ( V4a_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V3num__to__dt_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt),V4a_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt),F1_2E0,V3num__to__dt_2E0),V4a_2E0) = c_2Ecombin_2EI_2E1(tyop_2Etoto_2Enum__dt,c_2Ebool_2ECOND_2E3(tyop_2Etoto_2Enum__dt,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V4a_2E0),c_2Etoto_2Ezer_2E0,c_2Ebool_2ECOND_2E3(tyop_2Etoto_2Enum__dt,c_2Earithmetic_2EODD_2E1(V4a_2E0),c_2Etoto_2Ebit1_2E1(app_2E2(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt,V3num__to__dt_2E0,c_2Earithmetic_2EDIV2_2E1(c_2Earithmetic_2E_2D_2E2(V4a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))),c_2Etoto_2Ebit2_2E1(app_2E2(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt,V3num__to__dt_2E0,c_2Earithmetic_2EDIV2_2E1(c_2Earithmetic_2E_2D_2E2(V4a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
<=> ( p(c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,V0R_2E0))
& ! [V1n_2E0: tyop_2Enum_2Enum] :
( ( ( V1n_2E0 != c_2Enum_2E0_2E0 )
& p(c_2Earithmetic_2EODD_2E1(V1n_2E0)) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0R_2E0,c_2Earithmetic_2EDIV2_2E1(c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),V1n_2E0)) )
& ! [V2n_2E0: tyop_2Enum_2Enum] :
( ( ( V2n_2E0 != c_2Enum_2E0_2E0 )
& ~ p(c_2Earithmetic_2EODD_2E1(V2n_2E0)) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0R_2E0,c_2Earithmetic_2EDIV2_2E1(c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),V2n_2E0)) ) ) )
=> ( c_2Etoto_2Enum__to__dt_2E0 = c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Etoto_2Enum__dt,c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ).
tff(thm_2Etoto_2Eqk__numOrd__def,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Etoto_2Eqk__numOrd_2E2(V0m_2E0,V1n_2E0) = c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Enum__to__dt_2E1(V0m_2E0),c_2Etoto_2Enum__to__dt_2E1(V1n_2E0)) ) ).
tff(thm_2Etoto_2Eqk__numto,axiom,
c_2Etoto_2Eqk__numto_2E0 = c_2Etoto_2ETO_2E1(tyop_2Enum_2Enum,c_2Etoto_2Eqk__numOrd_2E0) ).
tff(thm_2Etoto_2EcharOrd,axiom,
! [V0a_2E0: tyop_2Estring_2Echar,V1b_2E0: tyop_2Estring_2Echar] : ( c_2Etoto_2EcharOrd_2E2(V0a_2E0,V1b_2E0) = c_2Etoto_2EnumOrd_2E2(c_2Estring_2EORD_2E1(V0a_2E0),c_2Estring_2EORD_2E1(V1b_2E0)) ) ).
tff(thm_2Etoto_2Echarto,axiom,
c_2Etoto_2Echarto_2E0 = c_2Etoto_2ETO_2E1(tyop_2Estring_2Echar,c_2Etoto_2EcharOrd_2E0) ).
tff(thm_2Etoto_2EListOrd,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2EListOrd_2E1(A_27a,V0c_2E0) = c_2Etoto_2ETO__of__LinearOrder_2E1(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Elistorder_2E1(A_27a,c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0)))) ) ).
tff(thm_2Etoto_2Elistoto,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2Elistoto_2E1(A_27a,V0c_2E0) = c_2Etoto_2ETO_2E1(tyop_2Elist_2Elist(A_27a),c_2Etoto_2EListOrd_2E1(A_27a,V0c_2E0)) ) ).
tff(thm_2Etoto_2Estringto,axiom,
c_2Etoto_2Estringto_2E0 = c_2Etoto_2Elistoto_2E1(tyop_2Estring_2Echar,c_2Etoto_2Echarto_2E0) ).
tff(thm_2Etoto_2EimageOrd,axiom,
! [A_27a: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1cp_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering)),V2a_2E0: A_27a,V3b_2E0: A_27a] : ( c_2Etoto_2EimageOrd_2E4(A_27a,A_27c,V0f_2E0,V1cp_2E0,V2a_2E0,V3b_2E0) = app_2E2(A_27c,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering),V1cp_2E0,app_2E2(A_27a,A_27c,V0f_2E0,V2a_2E0)),app_2E2(A_27a,A_27c,V0f_2E0,V3b_2E0)) ) ).
tff(thm_2Etoto_2EStrongLinearOrderExists,axiom,
! [A_27a: $tType] :
? [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0R_2E0)) ).
tff(thm_2Etoto_2Etrichotomous__ALT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Etrichotomous_2E1(A_27a,V0R_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
& ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V1x_2E0)) )
=> ( V1x_2E0 = V2y_2E0 ) ) ) ).
tff(thm_2Etoto_2ETotOrd__TO__of__LO,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2ELinearOrder_2E1(A_27a,V0r_2E0))
=> p(c_2Etoto_2ETotOrd_2E1(A_27a,c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,V0r_2E0))) ) ).
tff(thm_2Etoto_2ESPLIT__PAIRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V1q_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
( ( V0p_2E0 = V1q_2E0 )
<=> ( ( c_2Epair_2EFST_2E1(A_27a,A_27b,V0p_2E0) = c_2Epair_2EFST_2E1(A_27a,A_27b,V1q_2E0) )
& ( c_2Epair_2ESND_2E1(A_27a,A_27b,V0p_2E0) = c_2Epair_2ESND_2E1(A_27a,A_27b,V1q_2E0) ) ) ) ).
tff(thm_2Etoto_2Eall__cpn__distinct,axiom,
( ( c_2EternaryComparisons_2ELESS_2E0 != c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2EternaryComparisons_2ELESS_2E0 != c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2EternaryComparisons_2EEQUAL_2E0 != c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2EternaryComparisons_2EEQUAL_2E0 != c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2EternaryComparisons_2EGREATER_2E0 != c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2EternaryComparisons_2EGREATER_2E0 != c_2EternaryComparisons_2EEQUAL_2E0 ) ) ).
tff(thm_2Etoto_2ETO__exists,axiom,
! [A_27a: $tType] :
? [V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : p(c_2Etoto_2ETotOrd_2E1(A_27a,V0x_2E0)) ).
tff(thm_2Etoto_2ETO__apto__ID,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2ETO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0a_2E0)) = V0a_2E0 ) ).
tff(thm_2Etoto_2ETO__apto__TO__ID,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0r_2E0))
<=> ( c_2Etoto_2Eapto_2E1(A_27a,c_2Etoto_2ETO_2E1(A_27a,V0r_2E0)) = V0r_2E0 ) ) ).
tff(thm_2Etoto_2ETO__11,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V1r_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0r_2E0))
=> ( p(c_2Etoto_2ETotOrd_2E1(A_27a,V1r_27_2E0))
=> ( ( c_2Etoto_2ETO_2E1(A_27a,V0r_2E0) = c_2Etoto_2ETO_2E1(A_27a,V1r_27_2E0) )
<=> ( V0r_2E0 = V1r_27_2E0 ) ) ) ) ).
tff(thm_2Etoto_2Eonto__apto,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0r_2E0))
<=> ? [V1a_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( V0r_2E0 = c_2Etoto_2Eapto_2E1(A_27a,V1a_2E0) ) ) ).
tff(thm_2Etoto_2ETO__onto,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Etoto_2Etoto(A_27a)] :
? [V1r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( ( V0a_2E0 = c_2Etoto_2ETO_2E1(A_27a,V1r_2E0) )
& p(c_2Etoto_2ETotOrd_2E1(A_27a,V1r_2E0)) ) ).
tff(thm_2Etoto_2ETotOrd__apto,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(c_2Etoto_2ETotOrd_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0))) ).
tff(thm_2Etoto_2ETO__apto__TO__IMP,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0r_2E0))
=> ( c_2Etoto_2Eapto_2E1(A_27a,c_2Etoto_2ETO_2E1(A_27a,V0r_2E0)) = V0r_2E0 ) ) ).
tff(thm_2Etoto_2Etoto__thm,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V1x_2E0 = V2y_2E0 ) )
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V3x_2E0,V4y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V4y_2E0,V3x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V5x_2E0: A_27a,V6y_2E0: A_27a,V7z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V5x_2E0,V6y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V6y_2E0,V7z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V5x_2E0,V7z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ).
tff(thm_2Etoto_2ETO__equal__eq,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))
=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V1x_2E0),V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V1x_2E0 = V2y_2E0 ) ) ) ).
tff(thm_2Etoto_2Etoto__equal__eq,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V1x_2E0 = V2y_2E0 ) ) ).
tff(thm_2Etoto_2Etoto__equal__imp__eq,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( V1x_2E0 = V2y_2E0 ) ) ).
tff(thm_2Etoto_2ETO__refl,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))
=> ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V1x_2E0),V1x_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) ) ).
tff(thm_2Etoto_2Etoto__refl,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a] : ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V1x_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) ).
tff(thm_2Etoto_2Etoto__equal__sym,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V1x_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) ) ).
tff(thm_2Etoto_2ETO__antisym,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))
=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V1x_2E0),V2y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
<=> ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V2y_2E0),V1x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ).
tff(thm_2Etoto_2Etoto__antisym,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V1x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Etoto_2Etoto__not__less__refl,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1h_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1h_2E0,V1h_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
<=> p(c_2Ebool_2EF_2E0) ) ).
tff(thm_2Etoto_2Etoto__swap__cases,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] : ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V1x_2E0) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0),c_2EternaryComparisons_2EGREATER_2E0,c_2EternaryComparisons_2EEQUAL_2E0,c_2EternaryComparisons_2ELESS_2E0) ) ).
tff(thm_2Etoto_2Etoto__glneq,axiom,
! [A_27a: $tType] :
( ! [V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
=> ( V1x_2E0 != V2y_2E0 ) )
& ! [V3c_2E0: tyop_2Etoto_2Etoto(A_27a),V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V3c_2E0,V4x_2E0,V5y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
=> ( V4x_2E0 != V5y_2E0 ) ) ) ).
tff(thm_2Etoto_2Etoto__cpn__eqn,axiom,
! [A_27a: $tType] :
( ! [V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( V1x_2E0 = V2y_2E0 ) )
& ! [V3c_2E0: tyop_2Etoto_2Etoto(A_27a),V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V3c_2E0,V4x_2E0,V5y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
=> ( V4x_2E0 != V5y_2E0 ) )
& ! [V6c_2E0: tyop_2Etoto_2Etoto(A_27a),V7x_2E0: A_27a,V8y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V6c_2E0,V7x_2E0,V8y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
=> ( V7x_2E0 != V8y_2E0 ) ) ) ).
tff(thm_2Etoto_2ETO__cpn__eqn,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))
=> ( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V1x_2E0),V2y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
=> ( V1x_2E0 != V2y_2E0 ) )
& ! [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),V0c_2E0,V3x_2E0),V4y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
=> ( V3x_2E0 != V4y_2E0 ) )
& ! [V5x_2E0: A_27a,V6y_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0c_2E0,V5x_2E0),V6y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( V5x_2E0 = V6y_2E0 ) ) ) ) ).
tff(thm_2Etoto_2ENOT__EQ__LESS__IMP,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1x_2E0,V2y_2E0) != c_2EternaryComparisons_2ELESS_2E0 )
=> ( ( V1x_2E0 = V2y_2E0 )
| ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V2y_2E0,V1x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ).
tff(thm_2Etoto_2EtotoEEtrans,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V3z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V3z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
& ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V3z_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V3z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) ) ) ).
tff(thm_2Etoto_2EtotoLLtrans,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Etoto_2EtotoLGtrans,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V3z_2E0,V2y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Etoto_2EtotoGGtrans,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V1x_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V3z_2E0,V2y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Etoto_2EtotoGLtrans,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V1x_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Etoto_2EtotoLEtrans,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V3z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Etoto_2EtotoELtrans,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Etoto_2Etoto__trans__less,axiom,
! [A_27a: $tType] :
( ! [V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2y_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V1x_2E0,V3z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V4c_2E0: tyop_2Etoto_2Etoto(A_27a),V5x_2E0: A_27a,V6y_2E0: A_27a,V7z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V4c_2E0,V5x_2E0,V6y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V4c_2E0,V7z_2E0,V6y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V4c_2E0,V5x_2E0,V7z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V8c_2E0: tyop_2Etoto_2Etoto(A_27a),V9x_2E0: A_27a,V10y_2E0: A_27a,V11z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V8c_2E0,V10y_2E0,V9x_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V8c_2E0,V11z_2E0,V10y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V8c_2E0,V9x_2E0,V11z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V12c_2E0: tyop_2Etoto_2Etoto(A_27a),V13x_2E0: A_27a,V14y_2E0: A_27a,V15z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V12c_2E0,V14y_2E0,V13x_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V12c_2E0,V14y_2E0,V15z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V12c_2E0,V13x_2E0,V15z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V16c_2E0: tyop_2Etoto_2Etoto(A_27a),V17x_2E0: A_27a,V18y_2E0: A_27a,V19z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V16c_2E0,V17x_2E0,V18y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V16c_2E0,V18y_2E0,V19z_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V16c_2E0,V17x_2E0,V19z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V20c_2E0: tyop_2Etoto_2Etoto(A_27a),V21x_2E0: A_27a,V22y_2E0: A_27a,V23z_2E0: A_27a] :
( ( ( c_2Etoto_2Eapto_2E3(A_27a,V20c_2E0,V21x_2E0,V22y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V20c_2E0,V22y_2E0,V23z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V20c_2E0,V21x_2E0,V23z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ).
tff(thm_2Etoto_2EWeak__Weak__of,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(c_2Erelation_2EWeakLinearOrder_2E1(A_27a,c_2Etoto_2EWeakLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0)))) ).
tff(thm_2Etoto_2ESTRORD__SLO,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWeakLinearOrder_2E1(A_27a,V0R_2E0))
=> p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,c_2Erelation_2ESTRORD_2E1(A_27a,V0R_2E0))) ) ).
tff(thm_2Etoto_2EStrongof__toto__STRORD,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0)) = c_2Erelation_2ESTRORD_2E1(A_27a,c_2Etoto_2EWeakLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0))) ) ).
tff(thm_2Etoto_2EStrong__Strong__of,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0)))) ).
tff(thm_2Etoto_2EStrong__Strong__of__TO,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_2Erelation_2EStrongLinearOrder_2E1(A_27a,c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27a,V0c_2E0))) ) ).
tff(thm_2Etoto_2ETotOrd__TO__of__Weak,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWeakLinearOrder_2E1(A_27a,V0r_2E0))
=> p(c_2Etoto_2ETotOrd_2E1(A_27a,c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,V0r_2E0))) ) ).
tff(thm_2Etoto_2ETotOrd__TO__of__Strong,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0r_2E0))
=> p(c_2Etoto_2ETotOrd_2E1(A_27a,c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,V0r_2E0))) ) ).
tff(thm_2Etoto_2Etoto__Weak__thm,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2Etoto__of__LinearOrder_2E1(A_27a,c_2Etoto_2EWeakLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0))) = V0c_2E0 ) ).
tff(thm_2Etoto_2Etoto__Strong__thm,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2Etoto__of__LinearOrder_2E1(A_27a,c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0))) = V0c_2E0 ) ).
tff(thm_2Etoto_2EWeak__toto__thm,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EWeakLinearOrder_2E1(A_27a,V0r_2E0))
=> ( c_2Etoto_2EWeakLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,c_2Etoto_2Etoto__of__LinearOrder_2E1(A_27a,V0r_2E0))) = V0r_2E0 ) ) ).
tff(thm_2Etoto_2EStrong__toto__thm,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0r_2E0))
=> ( c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,c_2Etoto_2Etoto__of__LinearOrder_2E1(A_27a,V0r_2E0))) = V0r_2E0 ) ) ).
tff(thm_2Etoto_2ETotOrd__inv,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(A_27a,c_2Etoto_2ETO__inv_2E1(A_27a,V0c_2E0))) ) ).
tff(thm_2Etoto_2Einv__TO,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27a,V0r_2E0))
=> ( c_2Etoto_2Etoto__inv_2E1(A_27a,c_2Etoto_2ETO_2E1(A_27a,V0r_2E0)) = c_2Etoto_2ETO_2E1(A_27a,c_2Etoto_2ETO__inv_2E1(A_27a,V0r_2E0)) ) ) ).
tff(thm_2Etoto_2Eapto__inv,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2Eapto_2E1(A_27a,c_2Etoto_2Etoto__inv_2E1(A_27a,V0c_2E0)) = c_2Etoto_2ETO__inv_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0)) ) ).
tff(thm_2Etoto_2EWeak__toto__inv,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2EWeakLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,c_2Etoto_2Etoto__inv_2E1(A_27a,V0c_2E0))) = c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Etoto_2EWeakLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0))) ) ).
tff(thm_2Etoto_2EStrong__toto__inv,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,c_2Etoto_2Etoto__inv_2E1(A_27a,V0c_2E0))) = c_2Erelation_2Einv_2E1(A_27a,A_27a,c_2Etoto_2EStrongLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2Eapto_2E1(A_27a,V0c_2E0))) ) ).
tff(thm_2Etoto_2ETO__inv__TO__inv,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))] : ( c_2Etoto_2ETO__inv_2E1(A_27a,c_2Etoto_2ETO__inv_2E1(A_27a,V0c_2E0)) = V0c_2E0 ) ).
tff(thm_2Etoto_2Etoto__inv__toto__inv,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Etoto_2Etoto__inv_2E1(A_27a,c_2Etoto_2Etoto__inv_2E1(A_27a,V0c_2E0)) = V0c_2E0 ) ).
tff(thm_2Etoto_2ETO__inv__Ord,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0r_2E0)) = c_2Etoto_2ETO__inv_2E1(A_27a,c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,V0r_2E0)) ) ).
tff(thm_2Etoto_2ETO__of__less__rel,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0r_2E0))
=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2ETO__of__LinearOrder_2E3(A_27a,V0r_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0,V1x_2E0),V2y_2E0)) ) ) ).
tff(thm_2Etoto_2ETO__of__greater__ler,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0r_2E0))
=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Etoto_2ETO__of__LinearOrder_2E3(A_27a,V0r_2E0,V1x_2E0,V2y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0,V2y_2E0),V1x_2E0)) ) ) ).
tff(thm_2Etoto_2Etoto__equal__imp,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1phi_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2ELinearOrder_2E1(A_27a,V1phi_2E0))
& ( V0cmp_2E0 = c_2Etoto_2Etoto__of__LinearOrder_2E1(A_27a,V1phi_2E0) ) )
=> ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( ( V2x_2E0 = V3y_2E0 )
<=> p(c_2Ebool_2ET_2E0) )
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V2x_2E0,V3y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 ) ) ) ).
tff(thm_2Etoto_2Etoto__unequal__imp,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2x_2E0: A_27a,V3y_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_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0cmp_2E0),V2x_2E0),V3y_2E0))
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V2x_2E0,V3y_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2x_2E0: A_27a,V3y_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_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0cmp_2E0),V2x_2E0),V3y_2E0))
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V2x_2E0,V3y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 ) )
=> ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1phi_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2ELinearOrder_2E1(A_27a,V1phi_2E0))
& ( V0cmp_2E0 = c_2Etoto_2Etoto__of__LinearOrder_2E1(A_27a,V1phi_2E0) ) )
=> ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( ( V2x_2E0 = V3y_2E0 )
<=> p(c_2Ebool_2EF_2E0) )
=> p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1phi_2E0,V2x_2E0),V3y_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0cmp_2E0),V2x_2E0),V3y_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0cmp_2E0),V2x_2E0),V3y_2E0))) ) ) ) ) ).
tff(thm_2Etoto_2EStrongOrder__ALT,axiom,
! [A_27a: $tType,V0Z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongOrder_2E1(A_27a,V0Z_2E0))
<=> ( p(c_2Erelation_2Eirreflexive_2E1(A_27a,V0Z_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27a,V0Z_2E0)) ) ) ).
tff(thm_2Etoto_2ELEX__ALT,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1U_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2c_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V3d_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
( p(c_2Epair_2ELEX_2E4(A_27a,A_27b,V0R_2E0,V1U_2E0,V2c_2E0,V3d_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V2c_2E0)),c_2Epair_2EFST_2E1(A_27a,A_27b,V3d_2E0)))
| ( ( c_2Epair_2EFST_2E1(A_27a,A_27b,V2c_2E0) = c_2Epair_2EFST_2E1(A_27a,A_27b,V3d_2E0) )
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1U_2E0,c_2Epair_2ESND_2E1(A_27a,A_27b,V2c_2E0)),c_2Epair_2ESND_2E1(A_27a,A_27b,V3d_2E0))) ) ) ) ).
tff(thm_2Etoto_2ESLO__LEX,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1V_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2EStrongLinearOrder_2E1(A_27b,V1V_2E0)) )
=> p(c_2Erelation_2EStrongLinearOrder_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2ELEX_2E2(A_27a,A_27b,V0R_2E0,V1V_2E0))) ) ).
tff(thm_2Etoto_2ElexTO__thm,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)) )
=> ! [V2x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V3y_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Etoto_2ElexTO_2E4(A_27a,A_27b,V0R_2E0,V1V_2E0,V2x_2E0,V3y_2E0) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0R_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V2x_2E0)),c_2Epair_2EFST_2E1(A_27a,A_27b,V3y_2E0)),c_2EternaryComparisons_2ELESS_2E0,app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V1V_2E0,c_2Epair_2ESND_2E1(A_27a,A_27b,V2x_2E0)),c_2Epair_2ESND_2E1(A_27a,A_27b,V3y_2E0)),c_2EternaryComparisons_2EGREATER_2E0) ) ) ).
tff(thm_2Etoto_2ElexTO__ALT,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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))] :
( ! [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)),V2r_2E0: A_27a,V3u_2E0: A_27b,V4r_27_2E0: A_27a,V5u_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_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),F1_2E0,V0R_2E0),V1V_2E0),V2r_2E0),V3u_2E0),V4r_27_2E0),V5u_27_2E0))
<=> ( c_2Etoto_2ElexTO_2E4(A_27a,A_27b,V0R_2E0,V1V_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2r_2E0,V3u_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4r_27_2E0,V5u_27_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),V0R_2E0,V2r_2E0),V4r_27_2E0),c_2EternaryComparisons_2ELESS_2E0,app_2E2(A_27b,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),V1V_2E0,V3u_2E0),V5u_27_2E0),c_2EternaryComparisons_2EGREATER_2E0) ) )
=> ( ! [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)),V2r_2E0: A_27a,V3u_2E0: A_27b] : ( 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_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0),V1V_2E0),V2r_2E0),V3u_2E0) = c_2Ebool_2E_21_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),F1_2E0,V0R_2E0),V1V_2E0),V2r_2E0),V3u_2E0))) )
=> ! [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)) )
=> p(c_2Ebool_2E_21_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(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(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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0),V1V_2E0)))) ) ) ) ).
tff(thm_2Etoto_2ETO__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)) )
=> p(c_2Etoto_2ETotOrd_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Etoto_2ElexTO_2E2(A_27a,A_27b,V0R_2E0,V1V_2E0))) ) ).
tff(thm_2Etoto_2Epre__aplextoto,axiom,
! [A_27a: $tType,A_27b: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1v_2E0: tyop_2Etoto_2Etoto(A_27b),V2x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V3y_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Etoto_2Eapto_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Etoto_2Elextoto_2E2(A_27a,A_27b,V0c_2E0,V1v_2E0),V2x_2E0,V3y_2E0) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V2x_2E0),c_2Epair_2EFST_2E1(A_27a,A_27b,V3y_2E0)),c_2EternaryComparisons_2ELESS_2E0,c_2Etoto_2Eapto_2E3(A_27b,V1v_2E0,c_2Epair_2ESND_2E1(A_27a,A_27b,V2x_2E0),c_2Epair_2ESND_2E1(A_27a,A_27b,V3y_2E0)),c_2EternaryComparisons_2EGREATER_2E0) ) ).
tff(thm_2Etoto_2Eaplextoto,axiom,
! [A_27a: $tType,A_27b: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a),V1v_2E0: tyop_2Etoto_2Etoto(A_27b),V2x1_2E0: A_27a,V3x2_2E0: A_27b,V4y1_2E0: A_27a,V5y2_2E0: A_27b] : ( c_2Etoto_2Eapto_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Etoto_2Elextoto_2E2(A_27a,A_27b,V0c_2E0,V1v_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x1_2E0,V3x2_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4y1_2E0,V5y2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V2x1_2E0,V4y1_2E0),c_2EternaryComparisons_2ELESS_2E0,c_2Etoto_2Eapto_2E3(A_27b,V1v_2E0,V3x2_2E0,V5y2_2E0),c_2EternaryComparisons_2EGREATER_2E0) ) ).
tff(thm_2Etoto_2EStrongLinearOrder__LESS,axiom,
p(c_2Erelation_2EStrongLinearOrder_2E1(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E0)) ).
tff(thm_2Etoto_2ETO__numOrd,axiom,
p(c_2Etoto_2ETotOrd_2E1(tyop_2Enum_2Enum,c_2Etoto_2EnumOrd_2E0)) ).
tff(thm_2Etoto_2Eapnumto__thm,axiom,
c_2Etoto_2Eapto_2E1(tyop_2Enum_2Enum,c_2Etoto_2Enumto_2E0) = c_2Etoto_2EnumOrd_2E0 ).
tff(thm_2Etoto_2EnumeralOrd,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] :
( ( c_2Etoto_2EnumOrd_2E2(c_2Earithmetic_2EZERO_2E0,c_2Earithmetic_2EZERO_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2Etoto_2EnumOrd_2E2(c_2Earithmetic_2EZERO_2E0,c_2Earithmetic_2EBIT1_2E1(V1y_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2EnumOrd_2E2(c_2Earithmetic_2EZERO_2E0,c_2Earithmetic_2EBIT2_2E1(V1y_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2EnumOrd_2E2(c_2Earithmetic_2EBIT1_2E1(V0x_2E0),c_2Earithmetic_2EZERO_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2Etoto_2EnumOrd_2E2(c_2Earithmetic_2EBIT2_2E1(V0x_2E0),c_2Earithmetic_2EZERO_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2Etoto_2EnumOrd_2E2(c_2Earithmetic_2EBIT1_2E1(V0x_2E0),c_2Earithmetic_2EBIT1_2E1(V1y_2E0)) = c_2Etoto_2EnumOrd_2E2(V0x_2E0,V1y_2E0) )
& ( c_2Etoto_2EnumOrd_2E2(c_2Earithmetic_2EBIT2_2E1(V0x_2E0),c_2Earithmetic_2EBIT2_2E1(V1y_2E0)) = c_2Etoto_2EnumOrd_2E2(V0x_2E0,V1y_2E0) )
& ( c_2Etoto_2EnumOrd_2E2(c_2Earithmetic_2EBIT1_2E1(V0x_2E0),c_2Earithmetic_2EBIT2_2E1(V1y_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2EnumOrd_2E2(V0x_2E0,V1y_2E0),c_2EternaryComparisons_2ELESS_2E0,c_2EternaryComparisons_2ELESS_2E0,c_2EternaryComparisons_2EGREATER_2E0) )
& ( c_2Etoto_2EnumOrd_2E2(c_2Earithmetic_2EBIT2_2E1(V0x_2E0),c_2Earithmetic_2EBIT1_2E1(V1y_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2EnumOrd_2E2(V0x_2E0,V1y_2E0),c_2EternaryComparisons_2ELESS_2E0,c_2EternaryComparisons_2EGREATER_2E0,c_2EternaryComparisons_2EGREATER_2E0) ) ) ).
tff(thm_2Etoto_2Edatatype__num__dt,axiom,
! [V0num__dt_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Ebool)))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Etoto_2Enum__dt),tyop_2Emin_2Ebool)),V0num__dt_2E0,c_2Etoto_2Ezer_2E0),c_2Etoto_2Ebit1_2E0),c_2Etoto_2Ebit2_2E0))) ).
tff(thm_2Etoto_2Enum__dt__11,axiom,
( ! [V0a_2E0: tyop_2Etoto_2Enum__dt,V1a_27_2E0: tyop_2Etoto_2Enum__dt] :
( ( c_2Etoto_2Ebit1_2E1(V0a_2E0) = c_2Etoto_2Ebit1_2E1(V1a_27_2E0) )
<=> ( V0a_2E0 = V1a_27_2E0 ) )
& ! [V2a_2E0: tyop_2Etoto_2Enum__dt,V3a_27_2E0: tyop_2Etoto_2Enum__dt] :
( ( c_2Etoto_2Ebit2_2E1(V2a_2E0) = c_2Etoto_2Ebit2_2E1(V3a_27_2E0) )
<=> ( V2a_2E0 = V3a_27_2E0 ) ) ) ).
tff(thm_2Etoto_2Enum__dt__distinct,axiom,
( ! [V0a_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Ezer_2E0 != c_2Etoto_2Ebit1_2E1(V0a_2E0) )
& ! [V1a_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Ezer_2E0 != c_2Etoto_2Ebit2_2E1(V1a_2E0) )
& ! [V2a_27_2E0: tyop_2Etoto_2Enum__dt,V3a_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Ebit1_2E1(V3a_2E0) != c_2Etoto_2Ebit2_2E1(V2a_27_2E0) ) ) ).
tff(thm_2Etoto_2Enum__dt__nchotomy,axiom,
! [V0nn_2E0: tyop_2Etoto_2Enum__dt] :
( ( V0nn_2E0 = c_2Etoto_2Ezer_2E0 )
| ? [V1n_2E0: tyop_2Etoto_2Enum__dt] : ( V0nn_2E0 = c_2Etoto_2Ebit1_2E1(V1n_2E0) )
| ? [V2n_2E0: tyop_2Etoto_2Enum__dt] : ( V0nn_2E0 = c_2Etoto_2Ebit2_2E1(V2n_2E0) ) ) ).
tff(thm_2Etoto_2Enum__dt__Axiom,axiom,
! [A_27a: $tType,V0f0_2E0: A_27a,V1f1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(A_27a,A_27a)),V2f2_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(A_27a,A_27a))] :
? [V3fn_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a)] :
( ( app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V3fn_2E0,c_2Etoto_2Ezer_2E0) = V0f0_2E0 )
& ! [V4a_2E0: tyop_2Etoto_2Enum__dt] : ( app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V3fn_2E0,c_2Etoto_2Ebit1_2E1(V4a_2E0)) = app_2E2(A_27a,A_27a,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(A_27a,A_27a),V1f1_2E0,V4a_2E0),app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V3fn_2E0,V4a_2E0)) )
& ! [V5a_2E0: tyop_2Etoto_2Enum__dt] : ( app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V3fn_2E0,c_2Etoto_2Ebit2_2E1(V5a_2E0)) = app_2E2(A_27a,A_27a,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(A_27a,A_27a),V2f2_2E0,V5a_2E0),app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V3fn_2E0,V5a_2E0)) ) ) ).
tff(thm_2Etoto_2Enum__dt__induction,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,V0P_2E0,c_2Etoto_2Ezer_2E0))
& ! [V1n_2E0: tyop_2Etoto_2Enum__dt] :
( p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,V0P_2E0,V1n_2E0))
=> p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,V0P_2E0,c_2Etoto_2Ebit1_2E1(V1n_2E0))) )
& ! [V2n_2E0: tyop_2Etoto_2Enum__dt] :
( p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,V0P_2E0,V2n_2E0))
=> p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,V0P_2E0,c_2Etoto_2Ebit2_2E1(V2n_2E0))) ) )
=> ! [V3n_2E0: tyop_2Etoto_2Enum__dt] : p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,V0P_2E0,V3n_2E0)) ) ).
tff(thm_2Etoto_2Enum__dt__case__cong,axiom,
! [A_27a: $tType,V0v_27_2E0: A_27a,V1f1_27_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),V2f_27_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),V3M_2E0: tyop_2Etoto_2Enum__dt,V4M_27_2E0: tyop_2Etoto_2Enum__dt,V5v_2E0: A_27a,V6f_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),V7f1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a)] :
( ( ( V3M_2E0 = V4M_27_2E0 )
& ( ( V4M_27_2E0 = c_2Etoto_2Ezer_2E0 )
=> ( V5v_2E0 = V0v_27_2E0 ) )
& ! [V8a_2E0: tyop_2Etoto_2Enum__dt] :
( ( V4M_27_2E0 = c_2Etoto_2Ebit1_2E1(V8a_2E0) )
=> ( app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V6f_2E0,V8a_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V2f_27_2E0,V8a_2E0) ) )
& ! [V9a_2E0: tyop_2Etoto_2Enum__dt] :
( ( V4M_27_2E0 = c_2Etoto_2Ebit2_2E1(V9a_2E0) )
=> ( app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V7f1_2E0,V9a_2E0) = app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V1f1_27_2E0,V9a_2E0) ) ) )
=> ( c_2Etoto_2Enum__dt__CASE_2E4(A_27a,V3M_2E0,V5v_2E0,V6f_2E0,V7f1_2E0) = c_2Etoto_2Enum__dt__CASE_2E4(A_27a,V4M_27_2E0,V0v_27_2E0,V2f_27_2E0,V1f1_27_2E0) ) ) ).
tff(thm_2Etoto_2Enum__dt__case__eq,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Etoto_2Enum__dt,V1v_27_2E0: A_27a,V2v_2E0: A_27a,V3f1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a),V4f_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,A_27a)] :
( ( c_2Etoto_2Enum__dt__CASE_2E4(A_27a,V0x_2E0,V2v_2E0,V4f_2E0,V3f1_2E0) = V1v_27_2E0 )
<=> ( ( ( V0x_2E0 = c_2Etoto_2Ezer_2E0 )
& ( V2v_2E0 = V1v_27_2E0 ) )
| ? [V5n_2E0: tyop_2Etoto_2Enum__dt] :
( ( V0x_2E0 = c_2Etoto_2Ebit1_2E1(V5n_2E0) )
& ( app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V4f_2E0,V5n_2E0) = V1v_27_2E0 ) )
| ? [V6n_2E0: tyop_2Etoto_2Enum__dt] :
( ( V0x_2E0 = c_2Etoto_2Ebit2_2E1(V6n_2E0) )
& ( app_2E2(tyop_2Etoto_2Enum__dt,A_27a,V3f1_2E0,V6n_2E0) = V1v_27_2E0 ) ) ) ) ).
tff(thm_2Etoto_2Enum__dtOrd__ind,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool))] :
( ( p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,c_2Etoto_2Ezer_2E0),c_2Etoto_2Ezer_2E0))
& ! [V1x_2E0: tyop_2Etoto_2Enum__dt] : p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,c_2Etoto_2Ezer_2E0),c_2Etoto_2Ebit1_2E1(V1x_2E0)))
& ! [V2x_2E0: tyop_2Etoto_2Enum__dt] : p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,c_2Etoto_2Ezer_2E0),c_2Etoto_2Ebit2_2E1(V2x_2E0)))
& ! [V3x_2E0: tyop_2Etoto_2Enum__dt] : p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,c_2Etoto_2Ebit1_2E1(V3x_2E0)),c_2Etoto_2Ezer_2E0))
& ! [V4x_2E0: tyop_2Etoto_2Enum__dt] : p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,c_2Etoto_2Ebit2_2E1(V4x_2E0)),c_2Etoto_2Ezer_2E0))
& ! [V5x_2E0: tyop_2Etoto_2Enum__dt,V6y_2E0: tyop_2Etoto_2Enum__dt] : p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,c_2Etoto_2Ebit1_2E1(V5x_2E0)),c_2Etoto_2Ebit2_2E1(V6y_2E0)))
& ! [V7x_2E0: tyop_2Etoto_2Enum__dt,V8y_2E0: tyop_2Etoto_2Enum__dt] : p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,c_2Etoto_2Ebit2_2E1(V7x_2E0)),c_2Etoto_2Ebit1_2E1(V8y_2E0)))
& ! [V9x_2E0: tyop_2Etoto_2Enum__dt,V10y_2E0: tyop_2Etoto_2Enum__dt] :
( p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,V9x_2E0),V10y_2E0))
=> p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,c_2Etoto_2Ebit1_2E1(V9x_2E0)),c_2Etoto_2Ebit1_2E1(V10y_2E0))) )
& ! [V11x_2E0: tyop_2Etoto_2Enum__dt,V12y_2E0: tyop_2Etoto_2Enum__dt] :
( p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,V11x_2E0),V12y_2E0))
=> p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,c_2Etoto_2Ebit2_2E1(V11x_2E0)),c_2Etoto_2Ebit2_2E1(V12y_2E0))) ) )
=> ! [V13v_2E0: tyop_2Etoto_2Enum__dt,V14v1_2E0: tyop_2Etoto_2Enum__dt] : p(app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Efun(tyop_2Etoto_2Enum__dt,tyop_2Emin_2Ebool),V0P_2E0,V13v_2E0),V14v1_2E0)) ) ).
tff(thm_2Etoto_2Enum__dtOrd,axiom,
( ( c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Ezer_2E0,c_2Etoto_2Ezer_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ! [V0x_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Ezer_2E0,c_2Etoto_2Ebit1_2E1(V0x_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ! [V1x_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Ezer_2E0,c_2Etoto_2Ebit2_2E1(V1x_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ! [V2x_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Ebit1_2E1(V2x_2E0),c_2Etoto_2Ezer_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ! [V3x_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Ebit2_2E1(V3x_2E0),c_2Etoto_2Ezer_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ! [V4y_2E0: tyop_2Etoto_2Enum__dt,V5x_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Ebit1_2E1(V5x_2E0),c_2Etoto_2Ebit2_2E1(V4y_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ! [V6y_2E0: tyop_2Etoto_2Enum__dt,V7x_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Ebit2_2E1(V7x_2E0),c_2Etoto_2Ebit1_2E1(V6y_2E0)) = c_2EternaryComparisons_2EGREATER_2E0 )
& ! [V8y_2E0: tyop_2Etoto_2Enum__dt,V9x_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Ebit1_2E1(V9x_2E0),c_2Etoto_2Ebit1_2E1(V8y_2E0)) = c_2Etoto_2Enum__dtOrd_2E2(V9x_2E0,V8y_2E0) )
& ! [V10y_2E0: tyop_2Etoto_2Enum__dt,V11x_2E0: tyop_2Etoto_2Enum__dt] : ( c_2Etoto_2Enum__dtOrd_2E2(c_2Etoto_2Ebit2_2E1(V11x_2E0),c_2Etoto_2Ebit2_2E1(V10y_2E0)) = c_2Etoto_2Enum__dtOrd_2E2(V11x_2E0,V10y_2E0) ) ) ).
tff(thm_2Etoto_2ETO__qk__numOrd,axiom,
p(c_2Etoto_2ETotOrd_2E1(tyop_2Enum_2Enum,c_2Etoto_2Eqk__numOrd_2E0)) ).
tff(thm_2Etoto_2Eqk__numeralOrd,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] :
( ( c_2Etoto_2Eqk__numOrd_2E2(c_2Earithmetic_2EZERO_2E0,c_2Earithmetic_2EZERO_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ( c_2Etoto_2Eqk__numOrd_2E2(c_2Earithmetic_2EZERO_2E0,c_2Earithmetic_2EBIT1_2E1(V1y_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eqk__numOrd_2E2(c_2Earithmetic_2EZERO_2E0,c_2Earithmetic_2EBIT2_2E1(V1y_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eqk__numOrd_2E2(c_2Earithmetic_2EBIT1_2E1(V0x_2E0),c_2Earithmetic_2EZERO_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2Etoto_2Eqk__numOrd_2E2(c_2Earithmetic_2EBIT2_2E1(V0x_2E0),c_2Earithmetic_2EZERO_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ( c_2Etoto_2Eqk__numOrd_2E2(c_2Earithmetic_2EBIT1_2E1(V0x_2E0),c_2Earithmetic_2EBIT1_2E1(V1y_2E0)) = c_2Etoto_2Eqk__numOrd_2E2(V0x_2E0,V1y_2E0) )
& ( c_2Etoto_2Eqk__numOrd_2E2(c_2Earithmetic_2EBIT2_2E1(V0x_2E0),c_2Earithmetic_2EBIT2_2E1(V1y_2E0)) = c_2Etoto_2Eqk__numOrd_2E2(V0x_2E0,V1y_2E0) )
& ( c_2Etoto_2Eqk__numOrd_2E2(c_2Earithmetic_2EBIT1_2E1(V0x_2E0),c_2Earithmetic_2EBIT2_2E1(V1y_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eqk__numOrd_2E2(c_2Earithmetic_2EBIT2_2E1(V0x_2E0),c_2Earithmetic_2EBIT1_2E1(V1y_2E0)) = c_2EternaryComparisons_2EGREATER_2E0 ) ) ).
tff(thm_2Etoto_2Eap__qk__numto__thm,axiom,
c_2Etoto_2Eapto_2E1(tyop_2Enum_2Enum,c_2Etoto_2Eqk__numto_2E0) = c_2Etoto_2Eqk__numOrd_2E0 ).
tff(thm_2Etoto_2ETO__charOrd,axiom,
p(c_2Etoto_2ETotOrd_2E1(tyop_2Estring_2Echar,c_2Etoto_2EcharOrd_2E0)) ).
tff(thm_2Etoto_2Eapcharto__thm,axiom,
c_2Etoto_2Eapto_2E1(tyop_2Estring_2Echar,c_2Etoto_2Echarto_2E0) = c_2Etoto_2EcharOrd_2E0 ).
tff(thm_2Etoto_2EcharOrd__lt__lem,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( ( c_2Etoto_2EnumOrd_2E2(V0a_2E0,V1b_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
=> ( ( c_2Eprim__rec_2E_3C_2E2(V1b_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))) = c_2Ebool_2ET_2E0 )
=> ( c_2Etoto_2EcharOrd_2E2(c_2Estring_2ECHR_2E1(V0a_2E0),c_2Estring_2ECHR_2E1(V1b_2E0)) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ).
tff(thm_2Etoto_2EcharOrd__gt__lem,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( ( c_2Etoto_2EnumOrd_2E2(V0a_2E0,V1b_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
=> ( ( c_2Eprim__rec_2E_3C_2E2(V0a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))) = c_2Ebool_2ET_2E0 )
=> ( c_2Etoto_2EcharOrd_2E2(c_2Estring_2ECHR_2E1(V0a_2E0),c_2Estring_2ECHR_2E1(V1b_2E0)) = c_2EternaryComparisons_2EGREATER_2E0 ) ) ) ).
tff(thm_2Etoto_2EcharOrd__eq__lem,axiom,
! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( ( c_2Etoto_2EnumOrd_2E2(V0a_2E0,V1b_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> ( c_2Etoto_2EcharOrd_2E2(c_2Estring_2ECHR_2E1(V0a_2E0),c_2Estring_2ECHR_2E1(V1b_2E0)) = c_2EternaryComparisons_2EEQUAL_2E0 ) ) ).
tff(thm_2Etoto_2EcharOrd__thm,axiom,
c_2Etoto_2EcharOrd_2E0 = c_2Etoto_2ETO__of__LinearOrder_2E1(tyop_2Estring_2Echar,c_2Estring_2Echar__lt_2E0) ).
tff(thm_2Etoto_2Elistorder__ind,axiom,
! [A_27a: $tType,V0P_2E0: 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)))] :
( ( ! [V1V_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),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)),V0P_2E0,V1V_2E0),V2l_2E0),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V3V_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4s_2E0: A_27a,V5m_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),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)),V0P_2E0,V3V_2E0),c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ECONS_2E2(A_27a,V4s_2E0,V5m_2E0)))
& ! [V6V_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V7r_2E0: A_27a,V8l_2E0: tyop_2Elist_2Elist(A_27a),V9s_2E0: A_27a,V10m_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),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)),V0P_2E0,V6V_2E0),V8l_2E0),V10m_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),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)),V0P_2E0,V6V_2E0),c_2Elist_2ECONS_2E2(A_27a,V7r_2E0,V8l_2E0)),c_2Elist_2ECONS_2E2(A_27a,V9s_2E0,V10m_2E0))) ) )
=> ! [V11v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V12v1_2E0: tyop_2Elist_2Elist(A_27a),V13v2_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),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)),V0P_2E0,V11v_2E0),V12v1_2E0),V13v2_2E0)) ) ).
tff(thm_2Etoto_2Elistorder,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1V_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etoto_2Elistorder_2E3(A_27a,V1V_2E0,V0l_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2EF_2E0 )
& ! [V2s_2E0: A_27a,V3m_2E0: tyop_2Elist_2Elist(A_27a),V4V_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etoto_2Elistorder_2E3(A_27a,V4V_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V2s_2E0,V3m_2E0)) = c_2Ebool_2ET_2E0 )
& ! [V5s_2E0: A_27a,V6r_2E0: A_27a,V7m_2E0: tyop_2Elist_2Elist(A_27a),V8l_2E0: tyop_2Elist_2Elist(A_27a),V9V_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Etoto_2Elistorder_2E3(A_27a,V9V_2E0,c_2Elist_2ECONS_2E2(A_27a,V6r_2E0,V8l_2E0),c_2Elist_2ECONS_2E2(A_27a,V5s_2E0,V7m_2E0)))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V9V_2E0,V6r_2E0),V5s_2E0))
| ( ( V6r_2E0 = V5s_2E0 )
& p(c_2Etoto_2Elistorder_2E3(A_27a,V9V_2E0,V8l_2E0,V7m_2E0)) ) ) ) ) ).
tff(thm_2Etoto_2ESLO__listorder,axiom,
! [A_27a: $tType,V0V_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2EStrongLinearOrder_2E1(A_27a,V0V_2E0))
=> p(c_2Erelation_2EStrongLinearOrder_2E1(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Elistorder_2E1(A_27a,V0V_2E0))) ) ).
tff(thm_2Etoto_2ETO__ListOrd,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(c_2Etoto_2ETotOrd_2E1(tyop_2Elist_2Elist(A_27a),c_2Etoto_2EListOrd_2E1(A_27a,V0c_2E0))) ).
tff(thm_2Etoto_2EListOrd__THM,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] :
( ( c_2Etoto_2EListOrd_2E3(A_27a,V0c_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a)) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ! [V1b_2E0: A_27a,V2y_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Etoto_2EListOrd_2E3(A_27a,V0c_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V1b_2E0,V2y_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ! [V3a_2E0: A_27a,V4x_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Etoto_2EListOrd_2E3(A_27a,V0c_2E0,c_2Elist_2ECONS_2E2(A_27a,V3a_2E0,V4x_2E0),c_2Elist_2ENIL_2E0(A_27a)) = c_2EternaryComparisons_2EGREATER_2E0 )
& ! [V5a_2E0: A_27a,V6x_2E0: tyop_2Elist_2Elist(A_27a),V7b_2E0: A_27a,V8y_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Etoto_2EListOrd_2E3(A_27a,V0c_2E0,c_2Elist_2ECONS_2E2(A_27a,V5a_2E0,V6x_2E0),c_2Elist_2ECONS_2E2(A_27a,V7b_2E0,V8y_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V5a_2E0,V7b_2E0),c_2EternaryComparisons_2ELESS_2E0,c_2Etoto_2EListOrd_2E3(A_27a,V0c_2E0,V6x_2E0,V8y_2E0),c_2EternaryComparisons_2EGREATER_2E0) ) ) ).
tff(thm_2Etoto_2Eaplistoto,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Etoto_2Etoto(A_27a)] :
( ( c_2Etoto_2Eapto_2E3(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Elistoto_2E1(A_27a,V0c_2E0),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a)) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ! [V1b_2E0: A_27a,V2y_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Etoto_2Eapto_2E3(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Elistoto_2E1(A_27a,V0c_2E0),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V1b_2E0,V2y_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ! [V3a_2E0: A_27a,V4x_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Etoto_2Eapto_2E3(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Elistoto_2E1(A_27a,V0c_2E0),c_2Elist_2ECONS_2E2(A_27a,V3a_2E0,V4x_2E0),c_2Elist_2ENIL_2E0(A_27a)) = c_2EternaryComparisons_2EGREATER_2E0 )
& ! [V5a_2E0: A_27a,V6x_2E0: tyop_2Elist_2Elist(A_27a),V7b_2E0: A_27a,V8y_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Etoto_2Eapto_2E3(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Elistoto_2E1(A_27a,V0c_2E0),c_2Elist_2ECONS_2E2(A_27a,V5a_2E0,V6x_2E0),c_2Elist_2ECONS_2E2(A_27a,V7b_2E0,V8y_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2EternaryComparisons_2Eordering,c_2Etoto_2Eapto_2E3(A_27a,V0c_2E0,V5a_2E0,V7b_2E0),c_2EternaryComparisons_2ELESS_2E0,c_2Etoto_2Eapto_2E3(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Elistoto_2E1(A_27a,V0c_2E0),V6x_2E0,V8y_2E0),c_2EternaryComparisons_2EGREATER_2E0) ) ) ).
tff(thm_2Etoto_2ETO__injection,axiom,
! [A_27c: $tType,A_27d: $tType,V0cp_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2EternaryComparisons_2Eordering))] :
( p(c_2Etoto_2ETotOrd_2E1(A_27c,V0cp_2E0))
=> ! [V1f_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] :
( p(c_2Ebool_2EONE__ONE_2E1(A_27d,A_27c,V1f_2E0))
=> p(c_2Etoto_2ETotOrd_2E1(A_27d,c_2Etoto_2EimageOrd_2E2(A_27d,A_27c,V1f_2E0,V0cp_2E0))) ) ) ).
tff(thm_2Etoto_2EStrongLinearOrder__of__TO__TO__of__LinearOrder,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_2EStrongLinearOrder__of__TO_2E1(A_27a,c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,V0R_2E0)) = V0R_2E0 ) ) ).
tff(thm_2Etoto_2ETO__of__LinearOrder__LEX,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1V_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Eirreflexive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Eirreflexive_2E1(A_27b,V1V_2E0)) )
=> ( c_2Etoto_2ETO__of__LinearOrder_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2ELEX_2E2(A_27a,A_27b,V0R_2E0,V1V_2E0)) = c_2Etoto_2ElexTO_2E2(A_27a,A_27b,c_2Etoto_2ETO__of__LinearOrder_2E1(A_27a,V0R_2E0),c_2Etoto_2ETO__of__LinearOrder_2E1(A_27b,V1V_2E0)) ) ) ).
%------------------------------------------------------------------------------