ITP001 Axioms: ITP040_7.ax
%------------------------------------------------------------------------------
% File : ITP040_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 : indexedLists.ax [Gau19]
% : HL4040_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 229 ( 79 unt; 98 typ; 0 def)
% Number of atoms : 259 ( 150 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 131 ( 3 ~; 6 |; 49 &)
% ( 25 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 87 ( 47 >; 40 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 95 ( 95 usr; 16 con; 0-7 aty)
% Number of variables : 714 ( 599 !; 13 ?; 714 :)
% ( 102 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(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_2E1,type,
c_2Earithmetic_2E_2B_2E1: 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_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_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_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_2Elist_2EALL__DISTINCT_2E0,type,
c_2Elist_2EALL__DISTINCT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Elist_2EALL__DISTINCT_2E1,type,
c_2Elist_2EALL__DISTINCT_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(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_2Ecombin_2EC_2E0,type,
c_2Ecombin_2EC_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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ecombin_2EC_2E2,type,
c_2Ecombin_2EC_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * A_27b ) > tyop_2Emin_2Efun(A_27a,A_27c) ) ).
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_2Elist_2EEL_2E0,type,
c_2Elist_2EEL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)) ).
tff(c_2Elist_2EEL_2E2,type,
c_2Elist_2EEL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > A_27a ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Elist_2EFOLDR_2E0,type,
c_2Elist_2EFOLDR_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDR_2E3,type,
c_2Elist_2EFOLDR_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).
tff(c_2EindexedLists_2EFOLDRi_2E0,type,
c_2EindexedLists_2EFOLDRi_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))) ).
tff(c_2EindexedLists_2EFOLDRi_2E3,type,
c_2EindexedLists_2EFOLDRi_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))) * A_27a * tyop_2Elist_2Elist(A_27b) ) > A_27a ) ).
tff(c_2Elist_2EFRONT_2E0,type,
c_2Elist_2EFRONT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2EFRONT_2E1,type,
c_2Elist_2EFRONT_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2EGENLIST_2E0,type,
c_2Elist_2EGENLIST_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EGENLIST_2E2,type,
c_2Elist_2EGENLIST_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) * tyop_2Enum_2Enum ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2ELAST_2E0,type,
c_2Elist_2ELAST_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a) ).
tff(c_2Elist_2ELAST_2E1,type,
c_2Elist_2ELAST_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > A_27a ) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2EindexedLists_2ELIST__RELi_2E0,type,
c_2EindexedLists_2ELIST__RELi_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2EindexedLists_2ELIST__RELi_2E3,type,
c_2EindexedLists_2ELIST__RELi_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2EMAP_2E0,type,
c_2Elist_2EMAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).
tff(c_2Elist_2EMAP_2E2,type,
c_2Elist_2EMAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).
tff(c_2EindexedLists_2EMAP2i_2E0,type,
c_2EindexedLists_2EMAP2i_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2EindexedLists_2EMAP2i_2E3,type,
c_2EindexedLists_2EMAP2i_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))) * tyop_2Elist_2Elist(A_27b) * tyop_2Elist_2Elist(A_27c) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2EindexedLists_2EMAP2ia_2E0,type,
c_2EindexedLists_2EMAP2ia_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))))) ).
tff(c_2EindexedLists_2EMAP2ia_2E4,type,
c_2EindexedLists_2EMAP2ia_2E4:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))) * tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27b) * tyop_2Elist_2Elist(A_27c) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2EindexedLists_2EMAPi_2E0,type,
c_2EindexedLists_2EMAPi_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2EindexedLists_2EMAPi_2E2,type,
c_2EindexedLists_2EMAPi_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2EindexedLists_2EMAPi__ACC_2E0,type,
c_2EindexedLists_2EMAPi__ACC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))))) ).
tff(c_2EindexedLists_2EMAPi__ACC_2E4,type,
c_2EindexedLists_2EMAPi__ACC_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)) * tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Earithmetic_2EMIN_2E0,type,
c_2Earithmetic_2EMIN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EMIN_2E2,type,
c_2Earithmetic_2EMIN_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Elist_2EREVERSE_2E0,type,
c_2Elist_2EREVERSE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2EREVERSE_2E1,type,
c_2Elist_2EREVERSE_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ecombin_2ES_2E0,type,
c_2Ecombin_2ES_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_2Ecombin_2ES_2E2,type,
c_2Ecombin_2ES_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27c) ) ).
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_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: 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_2EindexedLists_2EdelN_2E0,type,
c_2EindexedLists_2EdelN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2EindexedLists_2EdelN_2E2,type,
c_2EindexedLists_2EdelN_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2EindexedLists_2Efindi_2E0,type,
c_2EindexedLists_2Efindi_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)) ).
tff(c_2EindexedLists_2Efindi_2E2,type,
c_2EindexedLists_2Efindi_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Enum_2Enum ) ).
tff(c_2EindexedLists_2EfupdLast_2E0,type,
c_2EindexedLists_2EfupdLast_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2EindexedLists_2EfupdLast_2E2,type,
c_2EindexedLists_2EfupdLast_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Ecombin_2Eo_2E1,type,
c_2Ecombin_2Eo_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27c,A_27b) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)) ) ).
tff(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_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_2Earithmetic_2E_2B_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,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_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_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_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_2Earithmetic_2E_3C_3D_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_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EAPPEND_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EAPPEND_2E0(A_27b),X0_2E0),X1_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(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ecombin_2EC_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ecombin_2EC_2E0(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),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(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ECONS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ECONS_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E0(A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEL_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),c_2Elist_2EEL_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EEL_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),A_27c,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c),c_2Elist_2EEL_2E0(A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),c_2Elist_2EFOLDR_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2EindexedLists_2EFOLDRi_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),c_2EindexedLists_2EFOLDRi_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2EindexedLists_2EFOLDRi_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EindexedLists_2EFOLDRi_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),c_2EindexedLists_2EFOLDRi_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2EindexedLists_2EFOLDRi_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27b)),c_2EindexedLists_2EFOLDRi_2E0(A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFRONT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFRONT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),c_2Elist_2EGENLIST_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b)),c_2Elist_2EGENLIST_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELAST_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2ELAST_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ELENGTH_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27c),X0_2E0) ) ).
tff(arityeq3_2Ec_2EindexedLists_2ELIST__RELi_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2EindexedLists_2ELIST__RELi_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EindexedLists_2EMAP2i_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EindexedLists_2EMAP2i_2E3(A_27c,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2EindexedLists_2EMAP2i_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2EindexedLists_2EMAP2i_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X1_2E0: tyop_2Elist_2Elist(A_27b),X2_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2EindexedLists_2EMAP2i_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),c_2EindexedLists_2EMAP2i_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2EindexedLists_2EMAP2ia_2E4_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a),X3_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EindexedLists_2EMAP2ia_2E4(A_27c,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)))),c_2EindexedLists_2EMAP2ia_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2EindexedLists_2EMAP2ia_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27b),X3_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2EindexedLists_2EMAP2ia_2E4(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))),c_2EindexedLists_2EMAP2ia_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2EindexedLists_2EMAPi_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2EindexedLists_2EMAPi_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EindexedLists_2EMAPi_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EindexedLists_2EMAPi_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2EindexedLists_2EMAPi_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EindexedLists_2EMAPi_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2EindexedLists_2EMAPi_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),c_2EindexedLists_2EMAPi_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EindexedLists_2EMAPi_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2EindexedLists_2EMAPi_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),c_2EindexedLists_2EMAPi_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2EindexedLists_2EMAPi__ACC_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a),X3_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EindexedLists_2EMAPi__ACC_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)))),c_2EindexedLists_2EMAPi__ACC_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EMIN_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMIN_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_2EMIN_2E0,X0_2E0),X1_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_2Elist_2EREVERSE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Ecombin_2ES_2E2(tyop_2Enum_2Enum,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),c_2Ecombin_2ES_2E0(tyop_2Enum_2Enum,A_27a,A_27b),X0_2E0),X1_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(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(arityeq2_2Ec_2EindexedLists_2EdelN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EindexedLists_2EdelN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2EindexedLists_2EdelN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EindexedLists_2Efindi_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EindexedLists_2Efindi_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2EindexedLists_2Efindi_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EindexedLists_2EfupdLast_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EindexedLists_2EfupdLast_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2EindexedLists_2EfupdLast_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2Eo_2E1_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E1(A_27c,A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2Eo_2E1_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27b_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Ecombin_2Eo_2E1(A_27c,tyop_2Emin_2Efun(A_27b,A_27b),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E0(A_27c,tyop_2Emin_2Efun(A_27b,A_27b),A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Efun_28A_27b_2CA_27b_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2CA_27b_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Enum_2Enum),X0_2E0),X1_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_2EindexedLists_2EMAPi__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a))] : ( c_2EindexedLists_2EMAPi_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ENIL_2E0(A_27b)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V2h_2E0: A_27b,V3t_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EindexedLists_2EMAPi_2E2(A_27a,A_27b,V1f_2E0,c_2Elist_2ECONS_2E2(A_27b,V2h_2E0,V3t_2E0)) = c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27b,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0,c_2Enum_2E0_2E0),V2h_2E0),c_2EindexedLists_2EMAPi_2E2(A_27a,A_27b,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Enum_2Enum,V1f_2E0,c_2Enum_2ESUC_2E0),V3t_2E0)) ) ) ).
tff(thm_2EindexedLists_2EMAPi__ACC__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1i_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EindexedLists_2EMAPi__ACC_2E4(A_27a,A_27b,V0f_2E0,V1i_2E0,V2a_2E0,c_2Elist_2ENIL_2E0(A_27b)) = c_2Elist_2EREVERSE_2E1(A_27a,V2a_2E0) )
& ! [V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V4i_2E0: tyop_2Enum_2Enum,V5a_2E0: tyop_2Elist_2Elist(A_27a),V6h_2E0: A_27b,V7t_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EindexedLists_2EMAPi__ACC_2E4(A_27a,A_27b,V3f_2E0,V4i_2E0,V5a_2E0,c_2Elist_2ECONS_2E2(A_27b,V6h_2E0,V7t_2E0)) = c_2EindexedLists_2EMAPi__ACC_2E4(A_27a,A_27b,V3f_2E0,c_2Earithmetic_2E_2B_2E2(V4i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27b,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),V3f_2E0,V4i_2E0),V6h_2E0),V5a_2E0),V7t_2E0) ) ) ).
tff(thm_2EindexedLists_2EFOLDRi__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V1a_2E0: A_27a] : ( c_2EindexedLists_2EFOLDRi_2E3(A_27a,A_27b,V0f_2E0,V1a_2E0,c_2Elist_2ENIL_2E0(A_27b)) = V1a_2E0 )
& ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V3a_2E0: A_27a,V4h_2E0: A_27b,V5t_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2EindexedLists_2EFOLDRi_2E3(A_27a,A_27b,V2f_2E0,V3a_2E0,c_2Elist_2ECONS_2E2(A_27b,V4h_2E0,V5t_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0,c_2Enum_2E0_2E0),V4h_2E0),c_2EindexedLists_2EFOLDRi_2E3(A_27a,A_27b,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Enum_2Enum,V2f_2E0,c_2Enum_2ESUC_2E0),V3a_2E0,V5t_2E0)) ) ) ).
tff(thm_2EindexedLists_2Efindi__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a,V2h_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),V2h_2E0))
<=> ( V1x_2E0 = V2h_2E0 ) )
=> ( ! [V0x_2E0: A_27a] : ( c_2EindexedLists_2Efindi_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Enum_2E0_2E0 )
& ! [V1x_2E0: A_27a,V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EindexedLists_2Efindi_2E2(A_27a,V1x_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1x_2E0),V2h_2E0),c_2Enum_2E0_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2EindexedLists_2Efindi_2E2(A_27a,V1x_2E0,V3t_2E0))) ) ) ) ).
tff(thm_2EindexedLists_2EdelN__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V1i_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1i_2E0))
<=> ( V1i_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V0i_2E0: tyop_2Enum_2Enum] : ( c_2EindexedLists_2EdelN_2E2(A_27a,V0i_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1i_2E0: tyop_2Enum_2Enum,V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EindexedLists_2EdelN_2E2(A_27a,V1i_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1i_2E0),V3t_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,c_2EindexedLists_2EdelN_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V3t_2E0))) ) ) ) ).
tff(thm_2EindexedLists_2ELIST__RELi__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1x_27_2E0: tyop_2Elist_2Elist(A_27a),V2x_27_27_2E0: tyop_2Elist_2Elist(A_27b)] :
( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0))
<=> ! [V3LIST__RELi_27_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))] :
( ! [V4a0_2E0: tyop_2Elist_2Elist(A_27a),V5a1_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( ( ( V4a0_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
& ( V5a1_2E0 = c_2Elist_2ENIL_2E0(A_27b) ) )
| ? [V6h1_2E0: A_27a,V7h2_2E0: A_27b,V8l1_2E0: tyop_2Elist_2Elist(A_27a),V9l2_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( V4a0_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V8l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V6h1_2E0,c_2Elist_2ENIL_2E0(A_27a))) )
& ( V5a1_2E0 = c_2Elist_2EAPPEND_2E2(A_27b,V9l2_2E0,c_2Elist_2ECONS_2E2(A_27b,V7h2_2E0,c_2Elist_2ENIL_2E0(A_27b))) )
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0x_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V8l1_2E0)),V6h1_2E0),V7h2_2E0))
& p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V3LIST__RELi_27_2E0,V8l1_2E0),V9l2_2E0)) ) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V3LIST__RELi_27_2E0,V4a0_2E0),V5a1_2E0)) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V3LIST__RELi_27_2E0,V1x_27_2E0),V2x_27_27_2E0)) ) ) ).
tff(thm_2EindexedLists_2EMAPi__ACC__MAPi,axiom,
! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27b),V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V3a_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EindexedLists_2EMAPi__ACC_2E4(A_27a,A_27b,V2f_2E0,V0n_2E0,V3a_2E0,V1l_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V3a_2E0),c_2EindexedLists_2EMAPi_2E2(A_27a,A_27b,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Enum_2Enum,V2f_2E0,c_2Earithmetic_2E_2B_2E1(V0n_2E0)),V1l_2E0)) ) ).
tff(thm_2EindexedLists_2EMAPi__compute,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27b),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a))] : ( c_2EindexedLists_2EMAPi_2E2(A_27a,A_27b,V1f_2E0,V0l_2E0) = c_2EindexedLists_2EMAPi__ACC_2E4(A_27a,A_27b,V1f_2E0,c_2Enum_2E0_2E0,c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) ) ).
tff(thm_2EindexedLists_2ELT__SUC,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Enum_2ESUC_2E1(V1m_2E0)))
<=> ( ( V0n_2E0 = c_2Enum_2E0_2E0 )
| ? [V2n0_2E0: tyop_2Enum_2Enum] :
( ( V0n_2E0 = c_2Enum_2ESUC_2E1(V2n0_2E0) )
& p(c_2Eprim__rec_2E_3C_2E2(V2n0_2E0,V1m_2E0)) ) ) ) ).
tff(thm_2EindexedLists_2EMEM__MAPi,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V2l_2E0: tyop_2Elist_2Elist(A_27b)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2EindexedLists_2EMAPi_2E2(A_27a,A_27b,V1f_2E0,V2l_2E0))))
<=> ? [V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27b,V2l_2E0)))
& ( V0x_2E0 = app_2E2(A_27b,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0,V3n_2E0),c_2Elist_2EEL_2E2(A_27b,V3n_2E0,V2l_2E0)) ) ) ) ).
tff(thm_2EindexedLists_2EMAPi__CONG,axiom,
! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2f1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V3f2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b))] :
( ( ( V0l1_2E0 = V1l2_2E0 )
& ! [V4x_2E0: A_27a,V5n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0)))
=> ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0,V5n_2E0),V4x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0,V5n_2E0),V4x_2E0) ) ) )
=> ( c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,V2f1_2E0,V0l1_2E0) = c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,V3f2_2E0,V1l2_2E0) ) ) ).
tff(thm_2EindexedLists_2EMAPi__CONG_27,axiom,
! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2f2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V3f1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b))] :
( ( V1l1_2E0 = V0l2_2E0 )
=> ( ! [V4x_2E0: A_27a,V5n_2E0: tyop_2Enum_2Enum] :
( ( V4x_2E0 = c_2Elist_2EEL_2E2(A_27a,V5n_2E0,V0l2_2E0) )
=> ( p(c_2Eprim__rec_2E_3C_2E2(V5n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0)))
=> ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b),V3f1_2E0,V5n_2E0),V4x_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b),V2f2_2E0,V5n_2E0),V4x_2E0) ) ) )
=> ( c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,V3f1_2E0,V1l1_2E0) = c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,V2f2_2E0,V0l2_2E0) ) ) ) ).
tff(thm_2EindexedLists_2ELENGTH__MAPi,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27b,c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,V0f_2E0,V1l_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0) ) ).
tff(thm_2EindexedLists_2EMAP__MAPi,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),V2l_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2EindexedLists_2EMAPi_2E2(A_27a,A_27c,V1g_2E0,V2l_2E0)) = c_2EindexedLists_2EMAPi_2E2(A_27b,A_27c,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E1(A_27c,A_27b,A_27a,V0f_2E0),V1g_2E0),V2l_2E0) ) ).
tff(thm_2EindexedLists_2EEL__MAPi,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Elist_2EEL_2E2(A_27b,V1n_2E0,c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,V0f_2E0,V2l_2E0)) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,V1n_2E0),c_2Elist_2EEL_2E2(A_27a,V1n_2E0,V2l_2E0)) ) ) ).
tff(thm_2EindexedLists_2EMAPi__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,V2f_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27b,c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,V2f_2E0,V0l1_2E0),c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Enum_2Enum,V2f_2E0,c_2Earithmetic_2E_2B_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0))),V1l2_2E0)) ) ).
tff(thm_2EindexedLists_2EMAPi__GENLIST,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2EindexedLists_2EMAPi_2E2(A_27b,A_27a,V1f_2E0,V0l_2E0) = c_2Elist_2EGENLIST_2E2(A_27b,c_2Ecombin_2ES_2E2(tyop_2Enum_2Enum,A_27a,A_27b,V1f_2E0,c_2Ecombin_2EC_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2EEL_2E0(A_27a),V0l_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)) ) ).
tff(thm_2EindexedLists_2EGENLIST__CONG,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
( ! [V3m_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V3m_2E0,V0n_2E0))
=> ( app_2E2(tyop_2Enum_2Enum,A_27a,V2f1_2E0,V3m_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V1f2_2E0,V3m_2E0) ) )
=> ( c_2Elist_2EGENLIST_2E2(A_27a,V2f1_2E0,V0n_2E0) = c_2Elist_2EGENLIST_2E2(A_27a,V1f2_2E0,V0n_2E0) ) ) ).
tff(thm_2EindexedLists_2EFOLDR__MAPi,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),V2a_2E0: A_27b,V3l_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V2a_2E0,c_2EindexedLists_2EMAPi_2E2(A_27a,A_27c,V1g_2E0,V3l_2E0)) = c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27c,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E1(A_27c,tyop_2Emin_2Efun(A_27b,A_27b),A_27a,V0f_2E0),V1g_2E0),V2a_2E0,V3l_2E0) ) ).
tff(thm_2EindexedLists_2EFOLDRi__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2a_2E0: A_27b,V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)))] : ( c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27a,V3f_2E0,V2a_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0)) = c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27a,V3f_2E0,c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27a,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Enum_2Enum,V3f_2E0,c_2Earithmetic_2E_2B_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0))),V2a_2E0,V0l2_2E0),V1l1_2E0) ) ).
tff(thm_2EindexedLists_2EFOLDRi__CONG,axiom,
! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2f2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V3f1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V4a2_2E0: A_27b,V5a1_2E0: A_27b] :
( ( V1l1_2E0 = V0l2_2E0 )
=> ( ! [V6n_2E0: tyop_2Enum_2Enum,V7e_2E0: A_27a,V8a_2E0: A_27b] :
( p(c_2Eprim__rec_2E_3C_2E2(V6n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0)))
=> ( p(c_2Ebool_2EIN_2E2(A_27a,V7e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l2_2E0)))
=> ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3f1_2E0,V6n_2E0),V7e_2E0),V8a_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f2_2E0,V6n_2E0),V7e_2E0),V8a_2E0) ) ) )
=> ( ( V5a1_2E0 = V4a2_2E0 )
=> ( c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27a,V3f1_2E0,V5a1_2E0,V1l1_2E0) = c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27a,V2f2_2E0,V4a2_2E0,V0l2_2E0) ) ) ) ) ).
tff(thm_2EindexedLists_2EFOLDRi__CONG_27,axiom,
! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2f2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V3f1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V4a2_2E0: A_27b,V5a1_2E0: A_27b] :
( ( ( V1l1_2E0 = V0l2_2E0 )
& ! [V6n_2E0: tyop_2Enum_2Enum,V7a_2E0: A_27b] :
( p(c_2Eprim__rec_2E_3C_2E2(V6n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0)))
=> ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3f1_2E0,V6n_2E0),c_2Elist_2EEL_2E2(A_27a,V6n_2E0,V0l2_2E0)),V7a_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f2_2E0,V6n_2E0),c_2Elist_2EEL_2E2(A_27a,V6n_2E0,V0l2_2E0)),V7a_2E0) ) )
& ( V5a1_2E0 = V4a2_2E0 ) )
=> ( c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27a,V3f1_2E0,V5a1_2E0,V1l1_2E0) = c_2EindexedLists_2EFOLDRi_2E3(A_27b,A_27a,V2f2_2E0,V4a2_2E0,V0l2_2E0) ) ) ).
tff(thm_2EindexedLists_2EMEM__findi,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
=> p(c_2Eprim__rec_2E_3C_2E2(c_2EindexedLists_2Efindi_2E2(A_27a,V0x_2E0,V1l_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0))) ) ).
tff(thm_2EindexedLists_2Efindi__EL,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
& p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0l_2E0)) )
=> ( c_2EindexedLists_2Efindi_2E2(A_27a,c_2Elist_2EEL_2E2(A_27a,V1n_2E0,V0l_2E0),V0l_2E0) = V1n_2E0 ) ) ).
tff(thm_2EindexedLists_2EEL__findi,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0)))
=> ( c_2Elist_2EEL_2E2(A_27a,c_2EindexedLists_2Efindi_2E2(A_27a,V1x_2E0,V0l_2E0),V0l_2E0) = V1x_2E0 ) ) ).
tff(thm_2EindexedLists_2EdelN__shortens,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1i_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V1i_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
=> ( c_2Elist_2ELENGTH_2E1(A_27a,c_2EindexedLists_2EdelN_2E2(A_27a,V1i_2E0,V0l_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2EindexedLists_2EEL__delN__BEFORE,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V1i_2E0,V2j_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V2j_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0))) )
=> ( c_2Elist_2EEL_2E2(A_27a,V1i_2E0,c_2EindexedLists_2EdelN_2E2(A_27a,V2j_2E0,V0l_2E0)) = c_2Elist_2EEL_2E2(A_27a,V1i_2E0,V0l_2E0) ) ) ).
tff(thm_2EindexedLists_2EEL__delN__AFTER,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V2j_2E0,V1i_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2E_2B_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0))) )
=> ( c_2Elist_2EEL_2E2(A_27a,V1i_2E0,c_2EindexedLists_2EdelN_2E2(A_27a,V2j_2E0,V0l_2E0)) = c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0l_2E0) ) ) ).
tff(thm_2EindexedLists_2EfupdLast__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] :
( ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V1f_2E0),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V3h_2E0: A_27a] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V2f_2E0),c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,c_2Elist_2ENIL_2E0(A_27a))))
& ! [V4f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V5h_2E0: A_27a,V6v4_2E0: A_27a,V7v5_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V4f_2E0),c_2Elist_2ECONS_2E2(A_27a,V6v4_2E0,V7v5_2E0)))
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V4f_2E0),c_2Elist_2ECONS_2E2(A_27a,V5h_2E0,c_2Elist_2ECONS_2E2(A_27a,V6v4_2E0,V7v5_2E0)))) ) )
=> ! [V8v_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V9v1_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V8v_2E0),V9v1_2E0)) ) ).
tff(thm_2EindexedLists_2EfupdLast__def,axiom,
! [A_27a: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2EindexedLists_2EfupdLast_2E2(A_27a,V0f_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1h_2E0: A_27a,V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2EindexedLists_2EfupdLast_2E2(A_27a,V2f_2E0,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,c_2Elist_2ENIL_2E0(A_27a))) = c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27a,A_27a,V2f_2E0,V1h_2E0),c_2Elist_2ENIL_2E0(A_27a)) )
& ! [V3v5_2E0: tyop_2Elist_2Elist(A_27a),V4v4_2E0: A_27a,V5h_2E0: A_27a,V6f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2EindexedLists_2EfupdLast_2E2(A_27a,V6f_2E0,c_2Elist_2ECONS_2E2(A_27a,V5h_2E0,c_2Elist_2ECONS_2E2(A_27a,V4v4_2E0,V3v5_2E0))) = c_2Elist_2ECONS_2E2(A_27a,V5h_2E0,c_2EindexedLists_2EfupdLast_2E2(A_27a,V6f_2E0,c_2Elist_2ECONS_2E2(A_27a,V4v4_2E0,V3v5_2E0))) ) ) ).
tff(thm_2EindexedLists_2EfupdLast__EQ__NIL,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( ( ( c_2EindexedLists_2EfupdLast_2E2(A_27a,V1f_2E0,V0x_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
<=> ( V0x_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
& ( ( c_2Elist_2ENIL_2E0(A_27a) = c_2EindexedLists_2EfupdLast_2E2(A_27a,V1f_2E0,V0x_2E0) )
<=> ( V0x_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).
tff(thm_2EindexedLists_2EfupdLast__FRONT__LAST,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V0l_2E0))
<=> ( V0l_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2EindexedLists_2EfupdLast_2E2(A_27a,V1f_2E0,V0l_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,F0_2E0,V0l_2E0),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EFRONT_2E1(A_27a,V0l_2E0),c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27a,A_27a,V1f_2E0,c_2Elist_2ELAST_2E1(A_27a,V0l_2E0)),c_2Elist_2ENIL_2E0(A_27a)))) ) ) ).
tff(thm_2EindexedLists_2ELIST__RELi__rules,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0R_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27b)))
& ! [V1h1_2E0: A_27a,V2h2_2E0: A_27b,V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4l2_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V3l1_2E0)),V1h1_2E0),V2h2_2E0))
& p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0R_2E0,V3l1_2E0,V4l2_2E0)) )
=> p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0R_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V1h1_2E0,c_2Elist_2ENIL_2E0(A_27a))),c_2Elist_2EAPPEND_2E2(A_27b,V4l2_2E0,c_2Elist_2ECONS_2E2(A_27b,V2h2_2E0,c_2Elist_2ENIL_2E0(A_27b))))) ) ) ).
tff(thm_2EindexedLists_2ELIST__RELi__ind,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1LIST__RELi_27_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))] :
( ( p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__RELi_27_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27b)))
& ! [V2h1_2E0: A_27a,V3h2_2E0: A_27b,V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V4l1_2E0)),V2h1_2E0),V3h2_2E0))
& p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__RELi_27_2E0,V4l1_2E0),V5l2_2E0)) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__RELi_27_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V4l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h1_2E0,c_2Elist_2ENIL_2E0(A_27a)))),c_2Elist_2EAPPEND_2E2(A_27b,V5l2_2E0,c_2Elist_2ECONS_2E2(A_27b,V3h2_2E0,c_2Elist_2ENIL_2E0(A_27b))))) ) )
=> ! [V6a0_2E0: tyop_2Elist_2Elist(A_27a),V7a1_2E0: tyop_2Elist_2Elist(A_27b)] :
( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0R_2E0,V6a0_2E0,V7a1_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__RELi_27_2E0,V6a0_2E0),V7a1_2E0)) ) ) ).
tff(thm_2EindexedLists_2ELIST__RELi__strongind,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1LIST__RELi_27_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))] :
( ( p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__RELi_27_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27b)))
& ! [V2h1_2E0: A_27a,V3h2_2E0: A_27b,V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V4l1_2E0)),V2h1_2E0),V3h2_2E0))
& p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0R_2E0,V4l1_2E0,V5l2_2E0))
& p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__RELi_27_2E0,V4l1_2E0),V5l2_2E0)) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__RELi_27_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V4l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h1_2E0,c_2Elist_2ENIL_2E0(A_27a)))),c_2Elist_2EAPPEND_2E2(A_27b,V5l2_2E0,c_2Elist_2ECONS_2E2(A_27b,V3h2_2E0,c_2Elist_2ENIL_2E0(A_27b))))) ) )
=> ! [V6a0_2E0: tyop_2Elist_2Elist(A_27a),V7a1_2E0: tyop_2Elist_2Elist(A_27b)] :
( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0R_2E0,V6a0_2E0,V7a1_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),V1LIST__RELi_27_2E0,V6a0_2E0),V7a1_2E0)) ) ) ).
tff(thm_2EindexedLists_2ELIST__RELi__cases,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1a0_2E0: tyop_2Elist_2Elist(A_27a),V2a1_2E0: tyop_2Elist_2Elist(A_27b)] :
( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0R_2E0,V1a0_2E0,V2a1_2E0))
<=> ( ( ( V1a0_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
& ( V2a1_2E0 = c_2Elist_2ENIL_2E0(A_27b) ) )
| ? [V3h1_2E0: A_27a,V4h2_2E0: A_27b,V5l1_2E0: tyop_2Elist_2Elist(A_27a),V6l2_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( V1a0_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V5l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h1_2E0,c_2Elist_2ENIL_2E0(A_27a))) )
& ( V2a1_2E0 = c_2Elist_2EAPPEND_2E2(A_27b,V6l2_2E0,c_2Elist_2ECONS_2E2(A_27b,V4h2_2E0,c_2Elist_2ENIL_2E0(A_27b))) )
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V5l1_2E0)),V3h1_2E0),V4h2_2E0))
& p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0R_2E0,V5l1_2E0,V6l2_2E0)) ) ) ) ).
tff(thm_2EindexedLists_2ELIST__RELi__LENGTH,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b)] :
( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V0R_2E0,V1l1_2E0,V2l2_2E0))
=> ( c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V2l2_2E0) ) ) ).
tff(thm_2EindexedLists_2ELIST__RELi__EL__EQN,axiom,
! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V2R_2E0,V1l1_2E0,V0l2_2E0))
<=> ( ( c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V0l2_2E0) )
& ! [V3i_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0,V3i_2E0),c_2Elist_2EEL_2E2(A_27a,V3i_2E0,V1l1_2E0)),c_2Elist_2EEL_2E2(A_27b,V3i_2E0,V0l2_2E0))) ) ) ) ).
tff(thm_2EindexedLists_2ELIST__RELi__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27b),V1t_2E0: tyop_2Elist_2Elist(A_27a),V2l_2E0: tyop_2Elist_2Elist(A_27b),V3h_2E0: A_27a,V4R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
( ( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2ENIL_2E0(A_27a),V0x_2E0))
<=> ( V0x_2E0 = c_2Elist_2ENIL_2E0(A_27b) ) )
& ( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V1t_2E0),V2l_2E0))
<=> ? [V5h_27_2E0: A_27b,V6t_27_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( V2l_2E0 = c_2Elist_2ECONS_2E2(A_27b,V5h_27_2E0,V6t_27_2E0) )
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0,c_2Enum_2E0_2E0),V3h_2E0),V5h_27_2E0))
& p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Enum_2Enum,V4R_2E0,c_2Enum_2ESUC_2E0),V1t_2E0,V6t_27_2E0)) ) ) ) ).
tff(thm_2EindexedLists_2ELIST__RELi__APPEND__I,axiom,
! [A_27a: $tType,A_27b: $tType,V0m2_2E0: tyop_2Elist_2Elist(A_27b),V1m1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
( ( p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V4R_2E0,V3l1_2E0,V2l2_2E0))
& p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Enum_2Enum,V4R_2E0,c_2Earithmetic_2E_2B_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V3l1_2E0))),V1m1_2E0,V0m2_2E0)) )
=> p(c_2EindexedLists_2ELIST__RELi_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,V1m1_2E0),c_2Elist_2EAPPEND_2E2(A_27b,V2l2_2E0,V0m2_2E0))) ) ).
tff(thm_2EindexedLists_2EMAP2i__ind,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))] :
( ( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V2v0_2E0: tyop_2Elist_2Elist(A_27c)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V1f_2E0),c_2Elist_2ENIL_2E0(A_27b)),V2v0_2E0))
& ! [V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V4v5_2E0: A_27b,V5v6_2E0: tyop_2Elist_2Elist(A_27b)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V3f_2E0),c_2Elist_2ECONS_2E2(A_27b,V4v5_2E0,V5v6_2E0)),c_2Elist_2ENIL_2E0(A_27c)))
& ! [V6f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V7h1_2E0: A_27b,V8t1_2E0: tyop_2Elist_2Elist(A_27b),V9h2_2E0: A_27c,V10t2_2E0: tyop_2Elist_2Elist(A_27c)] :
( p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Enum_2Enum,V6f_2E0,c_2Enum_2ESUC_2E0)),V8t1_2E0),V10t2_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V6f_2E0),c_2Elist_2ECONS_2E2(A_27b,V7h1_2E0,V8t1_2E0)),c_2Elist_2ECONS_2E2(A_27c,V9h2_2E0,V10t2_2E0))) ) )
=> ! [V11v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V12v1_2E0: tyop_2Elist_2Elist(A_27b),V13v2_2E0: tyop_2Elist_2Elist(A_27c)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V11v_2E0),V12v1_2E0),V13v2_2E0)) ) ).
tff(thm_2EindexedLists_2EMAP2i__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
( ! [V0v0_2E0: tyop_2Elist_2Elist(A_27c),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))] : ( c_2EindexedLists_2EMAP2i_2E3(A_27a,A_27b,A_27c,V1f_2E0,c_2Elist_2ENIL_2E0(A_27b),V0v0_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V2v6_2E0: tyop_2Elist_2Elist(A_27b),V3v5_2E0: A_27b,V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))] : ( c_2EindexedLists_2EMAP2i_2E3(A_27a,A_27b,A_27c,V4f_2E0,c_2Elist_2ECONS_2E2(A_27b,V3v5_2E0,V2v6_2E0),c_2Elist_2ENIL_2E0(A_27c)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V5t2_2E0: tyop_2Elist_2Elist(A_27c),V6t1_2E0: tyop_2Elist_2Elist(A_27b),V7h2_2E0: A_27c,V8h1_2E0: A_27b,V9f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))] : ( c_2EindexedLists_2EMAP2i_2E3(A_27a,A_27b,A_27c,V9f_2E0,c_2Elist_2ECONS_2E2(A_27b,V8h1_2E0,V6t1_2E0),c_2Elist_2ECONS_2E2(A_27c,V7h2_2E0,V5t2_2E0)) = c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V9f_2E0,c_2Enum_2E0_2E0),V8h1_2E0),V7h2_2E0),c_2EindexedLists_2EMAP2i_2E3(A_27a,A_27b,A_27c,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Enum_2Enum,V9f_2E0,c_2Enum_2ESUC_2E0),V6t1_2E0,V5t2_2E0)) ) ) ).
tff(thm_2EindexedLists_2EMAP2i__NIL2,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27b),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))] : ( c_2EindexedLists_2EMAP2i_2E3(A_27a,A_27b,A_27c,V1f_2E0,V0l1_2E0,c_2Elist_2ENIL_2E0(A_27c)) = c_2Elist_2ENIL_2E0(A_27a) ) ).
tff(thm_2EindexedLists_2ELENGTH__MAP2i,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27c,c_2EindexedLists_2EMAP2i_2E3(A_27c,A_27a,A_27b,V0f_2E0,V1l1_2E0,V2l2_2E0)) = c_2Earithmetic_2EMIN_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0),c_2Elist_2ELENGTH_2E1(A_27b,V2l2_2E0)) ) ).
tff(thm_2EindexedLists_2EEL__MAP2i,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
& p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27b,V2l2_2E0))) )
=> ( c_2Elist_2EEL_2E2(A_27c,V3n_2E0,c_2EindexedLists_2EMAP2i_2E3(A_27c,A_27a,A_27b,V0f_2E0,V1l1_2E0,V2l2_2E0)) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0,V3n_2E0),c_2Elist_2EEL_2E2(A_27a,V3n_2E0,V1l1_2E0)),c_2Elist_2EEL_2E2(A_27b,V3n_2E0,V2l2_2E0)) ) ) ).
tff(thm_2EindexedLists_2EMAP2ia__ind,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))))] :
( ( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V2i_2E0: tyop_2Enum_2Enum,V3v0_2E0: tyop_2Elist_2Elist(A_27c)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V1f_2E0),V2i_2E0),c_2Elist_2ENIL_2E0(A_27b)),V3v0_2E0))
& ! [V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V5i_2E0: tyop_2Enum_2Enum,V6v7_2E0: A_27b,V7v8_2E0: tyop_2Elist_2Elist(A_27b)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V4f_2E0),V5i_2E0),c_2Elist_2ECONS_2E2(A_27b,V6v7_2E0,V7v8_2E0)),c_2Elist_2ENIL_2E0(A_27c)))
& ! [V8f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V9i_2E0: tyop_2Enum_2Enum,V10h1_2E0: A_27b,V11t1_2E0: tyop_2Elist_2Elist(A_27b),V12h2_2E0: A_27c,V13t2_2E0: tyop_2Elist_2Elist(A_27c)] :
( p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V8f_2E0),c_2Earithmetic_2E_2B_2E2(V9i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V11t1_2E0),V13t2_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V8f_2E0),V9i_2E0),c_2Elist_2ECONS_2E2(A_27b,V10h1_2E0,V11t1_2E0)),c_2Elist_2ECONS_2E2(A_27c,V12h2_2E0,V13t2_2E0))) ) )
=> ! [V14v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V15v1_2E0: tyop_2Enum_2Enum,V16v2_2E0: tyop_2Elist_2Elist(A_27b),V17v3_2E0: tyop_2Elist_2Elist(A_27c)] : p(app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0,V14v_2E0),V15v1_2E0),V16v2_2E0),V17v3_2E0)) ) ).
tff(thm_2EindexedLists_2EMAP2ia__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
( ! [V0v0_2E0: tyop_2Elist_2Elist(A_27c),V1i_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))] : ( c_2EindexedLists_2EMAP2ia_2E4(A_27a,A_27b,A_27c,V2f_2E0,V1i_2E0,c_2Elist_2ENIL_2E0(A_27b),V0v0_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V3v8_2E0: tyop_2Elist_2Elist(A_27b),V4v7_2E0: A_27b,V5i_2E0: tyop_2Enum_2Enum,V6f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))] : ( c_2EindexedLists_2EMAP2ia_2E4(A_27a,A_27b,A_27c,V6f_2E0,V5i_2E0,c_2Elist_2ECONS_2E2(A_27b,V4v7_2E0,V3v8_2E0),c_2Elist_2ENIL_2E0(A_27c)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V7t2_2E0: tyop_2Elist_2Elist(A_27c),V8t1_2E0: tyop_2Elist_2Elist(A_27b),V9i_2E0: tyop_2Enum_2Enum,V10h2_2E0: A_27c,V11h1_2E0: A_27b,V12f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))] : ( c_2EindexedLists_2EMAP2ia_2E4(A_27a,A_27b,A_27c,V12f_2E0,V9i_2E0,c_2Elist_2ECONS_2E2(A_27b,V11h1_2E0,V8t1_2E0),c_2Elist_2ECONS_2E2(A_27c,V10h2_2E0,V7t2_2E0)) = c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V12f_2E0,V9i_2E0),V11h1_2E0),V10h2_2E0),c_2EindexedLists_2EMAP2ia_2E4(A_27a,A_27b,A_27c,V12f_2E0,c_2Earithmetic_2E_2B_2E2(V9i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V8t1_2E0,V7t2_2E0)) ) ) ).
tff(thm_2EindexedLists_2EMAP2ia__NIL2,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27b),V1i_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))] : ( c_2EindexedLists_2EMAP2ia_2E4(A_27a,A_27b,A_27c,V2f_2E0,V1i_2E0,V0l1_2E0,c_2Elist_2ENIL_2E0(A_27c)) = c_2Elist_2ENIL_2E0(A_27a) ) ).
tff(thm_2EindexedLists_2EMAP2i__compute,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))] : ( c_2EindexedLists_2EMAP2i_2E3(A_27c,A_27a,A_27b,V2f_2E0,V1l1_2E0,V0l2_2E0) = c_2EindexedLists_2EMAP2ia_2E4(A_27c,A_27a,A_27b,V2f_2E0,c_2Enum_2E0_2E0,V1l1_2E0,V0l2_2E0) ) ).
%------------------------------------------------------------------------------