ITP001 Axioms: ITP047_7.ax
%------------------------------------------------------------------------------
% File : ITP047_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 : fcp.ax [Gau19]
% : HL4047_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 362 ( 129 unt; 165 typ; 0 def)
% Number of atoms : 341 ( 249 equ)
% Maximal formula atoms : 10 ( 0 avg)
% Number of connectives : 154 ( 10 ~; 15 |; 36 &)
% ( 37 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 132 ( 82 >; 50 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 161 ( 161 usr; 18 con; 0-6 aty)
% Number of variables : 943 ( 735 !; 21 ?; 943 :)
% ( 187 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(tyop_2Efcp_2Ebit0,type,
tyop_2Efcp_2Ebit0: $tType > $tType ).
tff(tyop_2Efcp_2Ebit1,type,
tyop_2Efcp_2Ebit1: $tType > $tType ).
tff(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: ( $tType * $tType ) > $tType ).
tff(tyop_2Efcp_2Efinite__image,type,
tyop_2Efcp_2Efinite__image: $tType > $tType ).
tff(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: $tType > $tType ).
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: ( $tType * $tType ) > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Efcp_2E_3A_2B_2E0,type,
c_2Efcp_2E_3A_2B_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27b)))) ).
tff(c_2Efcp_2E_3A_2B_2E3,type,
c_2Efcp_2E_3A_2B_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Efcp_2Ecart(A_27a,A_27b) ) > tyop_2Efcp_2Ecart(A_27a,A_27b) ) ).
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_2Ebool_2E_3F_21_2E0,type,
c_2Ebool_2E_3F_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_21_2E1,type,
c_2Ebool_2E_3F_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2Efcp_2EBIT0A_2E0,type,
c_2Efcp_2EBIT0A_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)) ).
tff(c_2Efcp_2EBIT0A_2E1,type,
c_2Efcp_2EBIT0A_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Efcp_2Ebit0(A_27a) ) ).
tff(c_2Efcp_2EBIT0B_2E0,type,
c_2Efcp_2EBIT0B_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)) ).
tff(c_2Efcp_2EBIT0B_2E1,type,
c_2Efcp_2EBIT0B_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Efcp_2Ebit0(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_2Efcp_2EBIT1A_2E0,type,
c_2Efcp_2EBIT1A_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)) ).
tff(c_2Efcp_2EBIT1A_2E1,type,
c_2Efcp_2EBIT1A_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Efcp_2Ebit1(A_27a) ) ).
tff(c_2Efcp_2EBIT1B_2E0,type,
c_2Efcp_2EBIT1B_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)) ).
tff(c_2Efcp_2EBIT1B_2E1,type,
c_2Efcp_2EBIT1B_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Efcp_2Ebit1(A_27a) ) ).
tff(c_2Efcp_2EBIT1C_2E0,type,
c_2Efcp_2EBIT1C_2E0:
!>[A_27a: $tType] : tyop_2Efcp_2Ebit1(A_27a) ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0:
!>[A_27a: $tType] : tyop_2Eind__type_2Erecspace(A_27a) ).
tff(c_2Epred__set_2ECARD_2E0,type,
c_2Epred__set_2ECARD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2ECARD_2E1,type,
c_2Epred__set_2ECARD_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eind__type_2ECONSTR_2E0,type,
c_2Eind__type_2ECONSTR_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))) ).
tff(c_2Eind__type_2ECONSTR_2E3,type,
c_2Eind__type_2ECONSTR_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)) ) > tyop_2Eind__type_2Erecspace(A_27a) ) ).
tff(c_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_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_2Elist_2EEVERY_2E0,type,
c_2Elist_2EEVERY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EEVERY_2E2,type,
c_2Elist_2EEVERY_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EEXISTS_2E0,type,
c_2Elist_2EEXISTS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EEXISTS_2E2,type,
c_2Elist_2EEXISTS_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ecombin_2EFAIL_2E0,type,
c_2Ecombin_2EFAIL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EFAIL_2E2,type,
c_2Ecombin_2EFAIL_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > A_27a ) ).
tff(c_2Efcp_2EFCP_2E0,type,
c_2Efcp_2EFCP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b)) ).
tff(c_2Efcp_2EFCP_2E1,type,
c_2Efcp_2EFCP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) > tyop_2Efcp_2Ecart(A_27a,A_27b) ) ).
tff(c_2Efcp_2EFCP__CONCAT_2E0,type,
c_2Efcp_2EFCP__CONCAT_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)))) ).
tff(c_2Efcp_2EFCP__CONCAT_2E2,type,
c_2Efcp_2EFCP__CONCAT_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Efcp_2Ecart(A_27a,A_27b) * tyop_2Efcp_2Ecart(A_27a,A_27c) ) > tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)) ) ).
tff(c_2Efcp_2EFCP__CONS_2E0,type,
c_2Efcp_2EFCP__CONS_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27c))) ).
tff(c_2Efcp_2EFCP__CONS_2E2,type,
c_2Efcp_2EFCP__CONS_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27a * tyop_2Efcp_2Ecart(A_27a,A_27b) ) > tyop_2Efcp_2Ecart(A_27a,A_27c) ) ).
tff(c_2Efcp_2EFCP__EVERY_2E0,type,
c_2Efcp_2EFCP__EVERY_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Efcp_2EFCP__EVERY_2E2,type,
c_2Efcp_2EFCP__EVERY_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Efcp_2Ecart(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Efcp_2EFCP__EXISTS_2E0,type,
c_2Efcp_2EFCP__EXISTS_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Efcp_2EFCP__EXISTS_2E2,type,
c_2Efcp_2EFCP__EXISTS_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Efcp_2Ecart(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Efcp_2EFCP__FOLD_2E0,type,
c_2Efcp_2EFCP__FOLD_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),A_27b))) ).
tff(c_2Efcp_2EFCP__FOLD_2E3,type,
c_2Efcp_2EFCP__FOLD_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27b * tyop_2Efcp_2Ecart(A_27a,A_27c) ) > A_27b ) ).
tff(c_2Efcp_2EFCP__HD_2E0,type,
c_2Efcp_2EFCP__HD_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),A_27a) ).
tff(c_2Efcp_2EFCP__HD_2E1,type,
c_2Efcp_2EFCP__HD_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(A_27a,A_27b) > A_27a ) ).
tff(c_2Efcp_2EFCP__MAP_2E0,type,
c_2Efcp_2EFCP__MAP_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27b,A_27c))) ).
tff(c_2Efcp_2EFCP__MAP_2E2,type,
c_2Efcp_2EFCP__MAP_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Efcp_2Ecart(A_27a,A_27c) ) > tyop_2Efcp_2Ecart(A_27b,A_27c) ) ).
tff(c_2Efcp_2EFCP__TL_2E0,type,
c_2Efcp_2EFCP__TL_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,A_27b)) ).
tff(c_2Efcp_2EFCP__TL_2E1,type,
c_2Efcp_2EFCP__TL_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Efcp_2Ecart(A_27a,A_27c) > tyop_2Efcp_2Ecart(A_27a,A_27b) ) ).
tff(c_2Efcp_2EFCP__ZIP_2E0,type,
c_2Efcp_2EFCP__ZIP_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b))) ).
tff(c_2Efcp_2EFCP__ZIP_2E2,type,
c_2Efcp_2EFCP__ZIP_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Efcp_2Ecart(A_27a,A_27b) * tyop_2Efcp_2Ecart(A_27c,A_27b) ) > tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b) ) ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EFOLDL_2E0,type,
c_2Elist_2EFOLDL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDL_2E3,type,
c_2Elist_2EFOLDL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).
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_2Efcp_2EHAS__SIZE_2E0,type,
c_2Efcp_2EHAS__SIZE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Efcp_2EHAS__SIZE_2E2,type,
c_2Efcp_2EHAS__SIZE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EHD_2E0,type,
c_2Elist_2EHD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a) ).
tff(c_2Elist_2EHD_2E1,type,
c_2Elist_2EHD_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > A_27a ) ).
tff(c_2Efcp_2EL2V_2E0,type,
c_2Efcp_2EL2V_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b)) ).
tff(c_2Efcp_2EL2V_2E1,type,
c_2Efcp_2EL2V_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Efcp_2Ecart(A_27a,A_27b) ) ).
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_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_2Elist_2ENULL_2E0,type,
c_2Elist_2ENULL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Elist_2ENULL_2E1,type,
c_2Elist_2ENULL_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).
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_2Eprim__rec_2EPRE_2E0,type,
c_2Eprim__rec_2EPRE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Eprim__rec_2EPRE_2E1,type,
c_2Eprim__rec_2EPRE_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
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_2Elist_2ETL_2E0,type,
c_2Elist_2ETL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2ETL_2E1,type,
c_2Elist_2ETL_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Efcp_2EV2L_2E0,type,
c_2Efcp_2EV2L_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Efcp_2EV2L_2E1,type,
c_2Efcp_2EV2L_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(A_27a,A_27b) > tyop_2Elist_2Elist(A_27a) ) ).
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_2Efcp_2Ebit0__CASE_2E0,type,
c_2Efcp_2Ebit0__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).
tff(c_2Efcp_2Ebit0__CASE_2E3,type,
c_2Efcp_2Ebit0__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ebit0(A_27a) * tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27b ) ).
tff(c_2Efcp_2Ebit0__size_2E0,type,
c_2Efcp_2Ebit0__size_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Enum_2Enum)) ).
tff(c_2Efcp_2Ebit0__size_2E2,type,
c_2Efcp_2Ebit0__size_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Efcp_2Ebit0(A_27a) ) > tyop_2Enum_2Enum ) ).
tff(c_2Efcp_2Ebit1__CASE_2E0,type,
c_2Efcp_2Ebit1__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)))) ).
tff(c_2Efcp_2Ebit1__CASE_2E4,type,
c_2Efcp_2Ebit1__CASE_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ebit1(A_27a) * tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,A_27b) * A_27b ) > A_27b ) ).
tff(c_2Efcp_2Ebit1__size_2E0,type,
c_2Efcp_2Ebit1__size_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Enum_2Enum)) ).
tff(c_2Efcp_2Ebit1__size_2E2,type,
c_2Efcp_2Ebit1__size_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Efcp_2Ebit1(A_27a) ) > tyop_2Enum_2Enum ) ).
tff(c_2Efcp_2Edest__cart_2E0,type,
c_2Efcp_2Edest__cart_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)) ).
tff(c_2Efcp_2Edest__cart_2E1,type,
c_2Efcp_2Edest__cart_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a) ) ).
tff(c_2Efcp_2Edest__cart_2E2,type,
c_2Efcp_2Edest__cart_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart(A_27a,A_27b) * tyop_2Efcp_2Efinite__image(A_27b) ) > A_27a ) ).
tff(c_2Efcp_2Edest__finite__image_2E0,type,
c_2Efcp_2Edest__finite__image_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a) ).
tff(c_2Efcp_2Edest__finite__image_2E1,type,
c_2Efcp_2Edest__finite__image_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Efinite__image(A_27a) > A_27a ) ).
tff(c_2Efcp_2Edimindex_2E0,type,
c_2Efcp_2Edimindex_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Efcp_2Edimindex_2E1,type,
c_2Efcp_2Edimindex_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Efcp_2Efcp__CASE_2E0,type,
c_2Efcp_2Efcp__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),A_27c)) ).
tff(c_2Efcp_2Efcp__CASE_2E2,type,
c_2Efcp_2Efcp__CASE_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Efcp_2Ecart(A_27a,A_27b) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c) ) > A_27c ) ).
tff(c_2Efcp_2Efcp__index_2E0,type,
c_2Efcp_2Efcp__index_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)) ).
tff(c_2Efcp_2Efcp__index_2E1,type,
c_2Efcp_2Efcp__index_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) ).
tff(c_2Efcp_2Efcp__index_2E2,type,
c_2Efcp_2Efcp__index_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart(A_27a,A_27b) * tyop_2Enum_2Enum ) > A_27a ) ).
tff(c_2Efcp_2Efinite__index_2E0,type,
c_2Efcp_2Efinite__index_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ).
tff(c_2Efcp_2Efinite__index_2E1,type,
c_2Efcp_2Efinite__index_2E1:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > A_27a ) ).
tff(c_2Efcp_2Emk__cart_2E0,type,
c_2Efcp_2Emk__cart_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b)) ).
tff(c_2Efcp_2Emk__cart_2E1,type,
c_2Efcp_2Emk__cart_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a) > tyop_2Efcp_2Ecart(A_27a,A_27b) ) ).
tff(c_2Efcp_2Emk__finite__image_2E0,type,
c_2Efcp_2Emk__finite__image_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Efinite__image(A_27a)) ).
tff(c_2Efcp_2Emk__finite__image_2E1,type,
c_2Efcp_2Emk__finite__image_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Efcp_2Efinite__image(A_27a) ) ).
tff(c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0:
!>[A_27a: $tType] : tyop_2Ebool_2Eitself(A_27a) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_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_2A_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27a,X1_2E0: A_27c] : ( c_2Epair_2E_2C_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Epair_2E_2C_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_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(arityeq3_2Ec_2Efcp_2E_3A_2B_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a,X2_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27b))),c_2Efcp_2E_3A_2B_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Efcp_2E_3A_2B_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a,X2_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2E_3A_2B_2E3(A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,A_27c)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,A_27c))),c_2Efcp_2E_3A_2B_2E0(A_27a,A_27c),X0_2E0),X1_2E0),X2_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_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_21_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Efcp_2Ecart_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Emin_2E_40_2E0(tyop_2Efcp_2Ecart(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EBIT0A_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Efcp_2EBIT0A_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EBIT0B_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Efcp_2EBIT0B_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EBIT1A_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Efcp_2EBIT1A_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EBIT1B_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Efcp_2EBIT1B_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ebool_2ECOND_2E0(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(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2ECONSTR_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),c_2Eind__type_2ECONSTR_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(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_2EEVERY_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEXISTS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EEXISTS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efcp_2Ecart_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Ecombin_2EFAIL_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Ecombin_2EFAIL_2E0(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Efcp_2EFCP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Efcp_2EFCP_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EFCP_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Efcp_2EFCP_2E1(A_27a,tyop_2Esum_2Esum(A_27b,A_27c),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),c_2Efcp_2EFCP_2E0(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] : ( c_2Efcp_2EFCP_2E1(A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Efcp_2Ecart(A_27b,A_27c),c_2Efcp_2EFCP_2E0(A_27b,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Efcp_2EFCP_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),c_2Efcp_2EFCP_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2EFCP__CONCAT_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EFCP__CONCAT_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c))),c_2Efcp_2EFCP__CONCAT_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2EFCP__CONS_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__CONS_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27c)),c_2Efcp_2EFCP__CONS_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2EFCP__CONS_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__CONS_2E2(A_27a,A_27b,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),c_2Efcp_2EFCP__CONS_2E0(A_27a,A_27b,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2EFCP__EVERY_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__EVERY_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Efcp_2EFCP__EVERY_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2EFCP__EVERY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Efcp_2Ecart(A_27b,A_27a)] : ( c_2Efcp_2EFCP__EVERY_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool),c_2Efcp_2EFCP__EVERY_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2EFCP__EXISTS_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__EXISTS_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Efcp_2EFCP__EXISTS_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2EFCP__EXISTS_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Efcp_2Ecart(A_27b,A_27a)] : ( c_2Efcp_2EFCP__EXISTS_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool),c_2Efcp_2EFCP__EXISTS_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Efcp_2EFCP__FOLD_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(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EFCP__FOLD_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),A_27b)),c_2Efcp_2EFCP__FOLD_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EFCP__HD_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__HD_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),A_27a,c_2Efcp_2EFCP__HD_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2EFCP__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EFCP__MAP_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27b,A_27c)),c_2Efcp_2EFCP__MAP_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EFCP__TL_2E1_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__TL_2E1(A_27a,A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EFCP__TL_2E0(A_27a,A_27c,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EFCP__TL_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EFCP__TL_2E1(A_27a,A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP__TL_2E0(A_27a,A_27b,A_27c),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2EFCP__ZIP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0: tyop_2Efcp_2Ecart(A_27c,A_27b)] : ( c_2Efcp_2EFCP__ZIP_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)),c_2Efcp_2EFCP__ZIP_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit0(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Efcp_2Ebit0(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Efcp_2Ebit1_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit1(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Efcp_2Ebit1(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_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_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),c_2Elist_2EFOLDL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_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_2Efcp_2EHAS__SIZE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2EHAS__SIZE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Efcp_2EHAS__SIZE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EHD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2EHD_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EL2V_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Efcp_2EL2V_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EL2V_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EL2V_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Efcp_2EL2V_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EL2V_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EL2V_2E1_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Efcp_2EL2V_2E1(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Efcp_2EL2V_2E0(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EL2V_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Efcp_2EL2V_2E1(A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Efcp_2Ecart(A_27b,A_27c),c_2Efcp_2EL2V_2E0(A_27b,A_27c),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(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(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENULL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E0(A_27a),X0_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_2Eprim__rec_2EPRE_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2Etyop_2Efcp_2Efinite__image_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a)] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(A_27a,tyop_2Efcp_2Efinite__image(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(A_27a,tyop_2Efcp_2Efinite__image(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efcp_2Efinite__image_28A_27b_29_2CA_27a_29_20mono_2Etyop_2Efcp_2Ecart_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Efcp_2Ebit0_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Efcp_2Ebit0(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Efcp_2Ebit0(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Efcp_2Ebit1_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Efcp_2Ebit1(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Efcp_2Ebit1(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EV2L_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EV2L_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2EV2L_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EV2L_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E0(A_27a,A_27c),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(arityeq3_2Ec_2Efcp_2Ebit0__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ebit0(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efcp_2Ebit0__CASE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),c_2Efcp_2Ebit0__CASE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Ebit0__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Efcp_2Ebit0(A_27a)] : ( c_2Efcp_2Ebit0__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ebit0(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Enum_2Enum),c_2Efcp_2Ebit0__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Efcp_2Ebit1__CASE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ebit1(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0: A_27b] : ( c_2Efcp_2Ebit1__CASE_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Efcp_2Ebit1__CASE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Ebit1__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Efcp_2Ebit1(A_27a)] : ( c_2Efcp_2Ebit1__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ebit1(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Enum_2Enum),c_2Efcp_2Ebit1__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edest__cart_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2Edest__cart_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),c_2Efcp_2Edest__cart_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Edest__cart_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0: tyop_2Efcp_2Efinite__image(A_27b)] : ( c_2Efcp_2Edest__cart_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Efinite__image(A_27b),A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),c_2Efcp_2Edest__cart_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edest__finite__image_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Efinite__image(A_27a)] : ( c_2Efcp_2Edest__finite__image_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Efinite__image(A_27a),A_27a,c_2Efcp_2Edest__finite__image_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : ( c_2Efcp_2Edimindex_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27b)] : ( c_2Efcp_2Edimindex_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27b),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27c)] : ( c_2Efcp_2Edimindex_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27c),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(A_27a))] : ( c_2Efcp_2Edimindex_2E1(tyop_2Efcp_2Ebit0(A_27a),X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(A_27a)),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(tyop_2Efcp_2Ebit0(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Efcp_2Ebit1_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit1(A_27a))] : ( c_2Efcp_2Edimindex_2E1(tyop_2Efcp_2Ebit1(A_27a),X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit1(A_27a)),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(tyop_2Efcp_2Ebit1(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Ebool_2Eitself(tyop_2Eone_2Eone)] : ( c_2Efcp_2Edimindex_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(tyop_2Esum_2Esum(A_27a,A_27b))] : ( c_2Efcp_2Edimindex_2E1(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Efcp__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c)] : ( c_2Efcp_2Efcp__CASE_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),A_27c,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),A_27c),c_2Efcp_2Efcp__CASE_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Efcp__index_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2Efcp__index_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Efcp_2Efcp__index_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Efcp_2Efcp__index_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c),X1_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Efcp_2Efcp__index_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27b,A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,A_27b,app_2E2(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),c_2Efcp_2Efcp__index_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(A_27c,A_27b),X1_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,A_27c,app_2E2(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27c),c_2Efcp_2Efcp__index_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Efinite__index_2E1_2Emono_2Etyop_2Efcp_2Efinite__image_28A_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efinite__index_2E1(tyop_2Efcp_2Efinite__image(A_27b),X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Efinite__image(A_27b),c_2Efcp_2Efinite__index_2E0(tyop_2Efcp_2Efinite__image(A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Emk__cart_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)] : ( c_2Efcp_2Emk__cart_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2Emk__cart_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Emk__finite__image_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Efcp_2Emk__finite__image_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Efcp_2Efinite__image(A_27a),c_2Efcp_2Emk__finite__image_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Efcp_2EHAS__SIZE__def,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Efcp_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V1n_2E0))
<=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = V1n_2E0 ) ) ) ).
tff(thm_2Efcp_2Efinite__image__TY__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V1x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,F0_2E0,V1x_2E0))
<=> ( ( V1x_2E0 = c_2Ebool_2EARB_2E0(A_27a) )
| p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a))) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a)] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(A_27a,tyop_2Efcp_2Efinite__image(A_27a),F0_2E0,V0rep_2E0)) ) ).
tff(thm_2Efcp_2Efinite__image__tybij,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Efcp_2Efinite__image(A_27a)] : ( c_2Efcp_2Emk__finite__image_2E1(A_27a,c_2Efcp_2Edest__finite__image_2E1(A_27a,V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: A_27a] :
( ( ( V1r_2E0 = c_2Ebool_2EARB_2E0(A_27a) )
| p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a))) )
<=> ( c_2Efcp_2Edest__finite__image_2E1(A_27a,c_2Efcp_2Emk__finite__image_2E1(A_27a,V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Efcp_2Edimindex__def,axiom,
! [A_27a: $tType] : ( c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)),c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ).
tff(thm_2Efcp_2Efinite__index__def,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1x_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V0f_2E0),V1x_2E0),V2n_2E0))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
& ( app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,V2n_2E0) = V1x_2E0 ) ) )
=> ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool,F0_2E0,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(c_2Ebool_2E_3F_21_2E1(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V0f_2E0),V1x_2E0))) )
=> ( c_2Efcp_2Efinite__index_2E0(A_27a) = c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0) ) ) ) ).
tff(thm_2Efcp_2Ecart__TY__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Emin_2Ebool)] :
( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Emin_2Ebool,F0_2E0,V1f_2E0) = c_2Ebool_2ET_2E0 )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b),F0_2E0,V0rep_2E0)) ) ).
tff(thm_2Efcp_2Ecart__tybij,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0a_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2Emk__cart_2E1(A_27a,A_27b,c_2Efcp_2Edest__cart_2E1(A_27a,A_27b,V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)] :
( p(c_2Ebool_2ET_2E0)
<=> ( c_2Efcp_2Edest__cart_2E1(A_27a,A_27b,c_2Efcp_2Emk__cart_2E1(A_27a,A_27b,V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Efcp_2Efcp__index,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V0x_2E0,V1i_2E0) = c_2Efcp_2Edest__cart_2E2(A_27a,A_27b,V0x_2E0,c_2Efcp_2Efinite__index_2E1(tyop_2Efcp_2Efinite__image(A_27b),V1i_2E0)) ) ).
tff(thm_2Efcp_2Efcp__case__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0h_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),V1f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c)] : ( c_2Efcp_2Efcp__CASE_2E2(A_27a,A_27b,A_27c,c_2Efcp_2Emk__cart_2E1(A_27a,A_27b,V0h_2E0),V1f_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c,V1f_2E0,V0h_2E0) ) ).
tff(thm_2Efcp_2EFCP,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool))] :
( ! [V0x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] :
( p(app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V0x_2E0),V1f_2E0))
<=> ! [V2i_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2i_2E0,c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V1f_2E0,V2i_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V0x_2E0,V2i_2E0) ) ) )
=> ! [V0x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Efcp_2EFCP_2E1(A_27a,A_27b,V0x_2E0) = c_2Emin_2E_40_2E1(tyop_2Efcp_2Ecart(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V0x_2E0)) ) ) ).
tff(thm_2Efcp_2Ebit0__TY__DEF,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V7n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F2_2E0,V7n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V5n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F1_2E0,V5n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V1a0_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1a0_2E0))
<=> ! [V2_27bit0_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V3a0_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( ? [V4a_2E0: A_27a] : ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2E0_2E0,V4a_2E0,F1_2E0) )
| ? [V6a_2E0: A_27a] : ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),V6a_2E0,F2_2E0) ) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27bit0_27_2E0,V3a0_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27bit0_27_2E0,V1a0_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Efcp_2Ebit0(A_27a),F0_2E0,V0rep_2E0)) ) ) ) ).
tff(thm_2Efcp_2Ebit0__case__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0a_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efcp_2Ebit0__CASE_2E3(A_27a,A_27b,c_2Efcp_2EBIT0A_2E1(A_27a,V0a_2E0),V1f_2E0,V2f1_2E0) = app_2E2(A_27a,A_27b,V1f_2E0,V0a_2E0) )
& ! [V3a_2E0: A_27a,V4f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V5f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efcp_2Ebit0__CASE_2E3(A_27a,A_27b,c_2Efcp_2EBIT0B_2E1(A_27a,V3a_2E0),V4f_2E0,V5f1_2E0) = app_2E2(A_27a,A_27b,V5f1_2E0,V3a_2E0) ) ) ).
tff(thm_2Efcp_2Ebit0__size__def,axiom,
! [A_27a: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1a_2E0: A_27a] : ( c_2Efcp_2Ebit0__size_2E2(A_27a,V0f_2E0,c_2Efcp_2EBIT0A_2E1(A_27a,V1a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1a_2E0)) )
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3a_2E0: A_27a] : ( c_2Efcp_2Ebit0__size_2E2(A_27a,V2f_2E0,c_2Efcp_2EBIT0B_2E1(A_27a,V3a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(A_27a,tyop_2Enum_2Enum,V2f_2E0,V3a_2E0)) ) ) ).
tff(thm_2Efcp_2Ebit1__TY__DEF,axiom,
! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V8n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F3_2E0,V8n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V7n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F2_2E0,V7n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V5n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F1_2E0,V5n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V1a0_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1a0_2E0))
<=> ! [V2_27bit1_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V3a0_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( ? [V4a_2E0: A_27a] : ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2E0_2E0,V4a_2E0,F1_2E0) )
| ? [V6a_2E0: A_27a] : ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),V6a_2E0,F2_2E0) )
| ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0)),c_2Ebool_2EARB_2E0(A_27a),F3_2E0) ) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27bit1_27_2E0,V3a0_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27bit1_27_2E0,V1a0_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Efcp_2Ebit1(A_27a),F0_2E0,V0rep_2E0)) ) ) ) ) ).
tff(thm_2Efcp_2Ebit1__case__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0a_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3v_2E0: A_27b] : ( c_2Efcp_2Ebit1__CASE_2E4(A_27a,A_27b,c_2Efcp_2EBIT1A_2E1(A_27a,V0a_2E0),V1f_2E0,V2f1_2E0,V3v_2E0) = app_2E2(A_27a,A_27b,V1f_2E0,V0a_2E0) )
& ! [V4a_2E0: A_27a,V5f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V7v_2E0: A_27b] : ( c_2Efcp_2Ebit1__CASE_2E4(A_27a,A_27b,c_2Efcp_2EBIT1B_2E1(A_27a,V4a_2E0),V5f_2E0,V6f1_2E0,V7v_2E0) = app_2E2(A_27a,A_27b,V6f1_2E0,V4a_2E0) )
& ! [V8f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V9f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V10v_2E0: A_27b] : ( c_2Efcp_2Ebit1__CASE_2E4(A_27a,A_27b,c_2Efcp_2EBIT1C_2E0(A_27a),V8f_2E0,V9f1_2E0,V10v_2E0) = V10v_2E0 ) ) ).
tff(thm_2Efcp_2Ebit1__size__def,axiom,
! [A_27a: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1a_2E0: A_27a] : ( c_2Efcp_2Ebit1__size_2E2(A_27a,V0f_2E0,c_2Efcp_2EBIT1A_2E1(A_27a,V1a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1a_2E0)) )
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3a_2E0: A_27a] : ( c_2Efcp_2Ebit1__size_2E2(A_27a,V2f_2E0,c_2Efcp_2EBIT1B_2E1(A_27a,V3a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(A_27a,tyop_2Enum_2Enum,V2f_2E0,V3a_2E0)) )
& ! [V4f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Efcp_2Ebit1__size_2E2(A_27a,V4f_2E0,c_2Efcp_2EBIT1C_2E0(A_27a)) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Efcp_2EFCP__UPDATE__def,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))] :
( ! [V0a_2E0: tyop_2Enum_2Enum,V3c_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0a_2E0),V3c_2E0))
<=> ( V0a_2E0 = V3c_2E0 ) )
=> ( ! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: A_27a,V2x_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V3c_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0,V0a_2E0),V1b_2E0),V2x_2E0),V3c_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0a_2E0),V3c_2E0),V1b_2E0,c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V2x_2E0,V3c_2E0)) )
=> ! [V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: A_27a,V2x_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V0a_2E0,V1b_2E0,V2x_2E0) = c_2Efcp_2EFCP_2E1(A_27a,A_27b,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0,V0a_2E0),V1b_2E0),V2x_2E0)) ) ) ) ).
tff(thm_2Efcp_2EFCP__HD__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__HD_2E1(A_27a,A_27b,V0v_2E0) = c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V0v_2E0,c_2Enum_2E0_2E0) ) ).
tff(thm_2Efcp_2EFCP__TL__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))] :
( ! [V0v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c),V1i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0v_2E0),V1i_2E0) = c_2Efcp_2Efcp__index_2E2(A_27a,A_27c,V0v_2E0,c_2Enum_2ESUC_2E1(V1i_2E0)) )
=> ! [V0v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EFCP__TL_2E1(A_27a,A_27b,A_27c,V0v_2E0) = c_2Efcp_2EFCP_2E1(A_27a,A_27b,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0v_2E0)) ) ) ).
tff(thm_2Efcp_2EFCP__CONS__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))] :
( ! [V1v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V2i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V1v_2E0),V2i_2E0) = c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V1v_2E0,c_2Eprim__rec_2EPRE_2E1(V2i_2E0)) )
=> ! [V0h_2E0: A_27a,V1v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__CONS_2E2(A_27a,A_27b,A_27c,V0h_2E0,V1v_2E0) = c_2Efcp_2E_3A_2B_2E3(A_27a,A_27c,c_2Enum_2E0_2E0,V0h_2E0,c_2Efcp_2EFCP_2E1(A_27a,A_27c,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V1v_2E0))) ) ) ).
tff(thm_2Efcp_2EFCP__MAP__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c),V2i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27b,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),F0_2E0,V0f_2E0),V1v_2E0),V2i_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,c_2Efcp_2Efcp__index_2E2(A_27a,A_27c,V1v_2E0,V2i_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EFCP__MAP_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1v_2E0) = c_2Efcp_2EFCP_2E1(A_27b,A_27c,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),F0_2E0,V0f_2E0),V1v_2E0)) ) ) ).
tff(thm_2Efcp_2EFCP__EXISTS__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1v_2E0: tyop_2Efcp_2Ecart(A_27b,A_27a)] :
( p(c_2Efcp_2EFCP__EXISTS_2E2(A_27a,A_27b,V0P_2E0,V1v_2E0))
<=> ? [V2i_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2i_2E0,c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,V0P_2E0,c_2Efcp_2Efcp__index_2E2(A_27b,A_27a,V1v_2E0,V2i_2E0))) ) ) ).
tff(thm_2Efcp_2EFCP__EVERY__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1v_2E0: tyop_2Efcp_2Ecart(A_27b,A_27a)] :
( p(c_2Efcp_2EFCP__EVERY_2E2(A_27a,A_27b,V0P_2E0,V1v_2E0))
<=> ! [V2i_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V2i_2E0))
| p(app_2E2(A_27b,tyop_2Emin_2Ebool,V0P_2E0,c_2Efcp_2Efcp__index_2E2(A_27b,A_27a,V1v_2E0,V2i_2E0))) ) ) ).
tff(thm_2Efcp_2EFCP__CONCAT__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))] :
( ! [V1b_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c),V0a_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V2i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0,V1b_2E0),V0a_2E0),V2i_2E0) = c_2Ebool_2ECOND_2E3(A_27a,c_2Eprim__rec_2E_3C_2E2(V2i_2E0,c_2Efcp_2Edimindex_2E1(A_27c,c_2Ebool_2Ethe__value_2E0(A_27c))),c_2Efcp_2Efcp__index_2E2(A_27a,A_27c,V1b_2E0,V2i_2E0),c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V0a_2E0,c_2Earithmetic_2E_2D_2E2(V2i_2E0,c_2Efcp_2Edimindex_2E1(A_27c,c_2Ebool_2Ethe__value_2E0(A_27c))))) )
=> ! [V0a_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1b_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EFCP__CONCAT_2E2(A_27a,A_27b,A_27c,V0a_2E0,V1b_2E0) = c_2Efcp_2EFCP_2E1(A_27a,tyop_2Esum_2Esum(A_27b,A_27c),app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0,V1b_2E0),V0a_2E0)) ) ) ).
tff(thm_2Efcp_2EFCP__ZIP__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c))))] :
( ! [V0a_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1b_2E0: tyop_2Efcp_2Ecart(A_27c,A_27b),V2i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c))),F0_2E0,V0a_2E0),V1b_2E0),V2i_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27c,c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V0a_2E0,V2i_2E0),c_2Efcp_2Efcp__index_2E2(A_27c,A_27b,V1b_2E0,V2i_2E0)) )
=> ! [V0a_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1b_2E0: tyop_2Efcp_2Ecart(A_27c,A_27b)] : ( c_2Efcp_2EFCP__ZIP_2E2(A_27a,A_27b,A_27c,V0a_2E0,V1b_2E0) = c_2Efcp_2EFCP_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,app_2E2(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c))),F0_2E0,V0a_2E0),V1b_2E0)) ) ) ).
tff(thm_2Efcp_2EV2L__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EV2L_2E1(A_27a,A_27b,V0v_2E0) = c_2Elist_2EGENLIST_2E2(A_27a,c_2Efcp_2Efcp__index_2E1(A_27a,A_27b,V0v_2E0),c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))) ) ).
tff(thm_2Efcp_2EL2V__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))] :
( ! [V0L_2E0: tyop_2Elist_2Elist(A_27a),V1i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0L_2E0),V1i_2E0) = c_2Elist_2EEL_2E2(A_27a,V1i_2E0,V0L_2E0) )
=> ! [V0L_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Efcp_2EL2V_2E1(A_27a,A_27b,V0L_2E0) = c_2Efcp_2EFCP_2E1(A_27a,A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0L_2E0)) ) ) ).
tff(thm_2Efcp_2EFCP__FOLD__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V1i_2E0: A_27b,V2v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EFCP__FOLD_2E3(A_27a,A_27b,A_27c,V0f_2E0,V1i_2E0,V2v_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,A_27b,V0f_2E0,V1i_2E0,c_2Efcp_2EV2L_2E1(A_27a,A_27c,V2v_2E0)) ) ).
tff(thm_2Efcp_2ENOT__FINITE__IMP__dimindex__1,axiom,
! [A_27a: $tType] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> ( c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Efcp_2EDIMINDEX__GE__1,axiom,
! [A_27a: $tType] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ).
tff(thm_2Efcp_2Efcp__Axiom,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c)] :
? [V1g_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),A_27c)] :
! [V2h_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)] : ( app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),A_27c,V1g_2E0,c_2Efcp_2Emk__cart_2E1(A_27a,A_27b,V2h_2E0)) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c,V0f_2E0,V2h_2E0) ) ).
tff(thm_2Efcp_2Efcp__ind,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)] : p(app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Efcp_2Emk__cart_2E1(A_27a,A_27b,V1f_2E0)))
=> ! [V2a_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : p(app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V2a_2E0)) ) ).
tff(thm_2Efcp_2ECART__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1y_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] :
( ( V0x_2E0 = V1y_2E0 )
<=> ! [V2i_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2i_2E0,c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V0x_2E0,V2i_2E0) = c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V1y_2E0,V2i_2E0) ) ) ) ).
tff(thm_2Efcp_2EFCP__BETA,axiom,
! [A_27a: $tType,A_27b: $tType,V0g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1i_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V1i_2E0,c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,c_2Efcp_2EFCP_2E1(A_27a,A_27b,V0g_2E0),V1i_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V0g_2E0,V1i_2E0) ) ) ).
tff(thm_2Efcp_2EFCP__UNIQUE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
( ! [V2i_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2i_2E0,c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V0f_2E0,V2i_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V1g_2E0,V2i_2E0) ) )
<=> ( c_2Efcp_2EFCP_2E1(A_27a,A_27b,V1g_2E0) = V0f_2E0 ) ) ).
tff(thm_2Efcp_2EFCP__ETA,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))] :
( ! [V0g_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0g_2E0),V1i_2E0) = c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V0g_2E0,V1i_2E0) )
=> ! [V0g_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP_2E1(A_27a,A_27b,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0g_2E0)) = V0g_2E0 ) ) ).
tff(thm_2Efcp_2Ecard__dimindex,axiom,
! [A_27a: $tType] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) ) ) ).
tff(thm_2Efcp_2Eindex__sum,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Ebool] :
( ( p(F0_2E0)
<=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EUNIV_2E0(A_27b))) ) )
=> ( c_2Efcp_2Edimindex_2E1(tyop_2Esum_2Esum(A_27a,A_27b),c_2Ebool_2Ethe__value_2E0(tyop_2Esum_2Esum(A_27a,A_27b))) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,F0_2E0,c_2Earithmetic_2E_2B_2E2(c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Efcp_2Efinite__sum,axiom,
! [A_27a: $tType,A_27b: $tType] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Esum_2Esum(A_27a,A_27b),c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(A_27a,A_27b))))
<=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EUNIV_2E0(A_27b))) ) ) ).
tff(thm_2Efcp_2Edatatype__bit0,axiom,
! [A_27a: $tType,V0bit0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),tyop_2Emin_2Ebool))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),tyop_2Emin_2Ebool),V0bit0_2E0,c_2Efcp_2EBIT0A_2E0(A_27a)),c_2Efcp_2EBIT0B_2E0(A_27a)))) ).
tff(thm_2Efcp_2Ebit0__11,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: A_27a,V1a_27_2E0: A_27a] :
( ( c_2Efcp_2EBIT0A_2E1(A_27a,V0a_2E0) = c_2Efcp_2EBIT0A_2E1(A_27a,V1a_27_2E0) )
<=> ( V0a_2E0 = V1a_27_2E0 ) )
& ! [V2a_2E0: A_27a,V3a_27_2E0: A_27a] :
( ( c_2Efcp_2EBIT0B_2E1(A_27a,V2a_2E0) = c_2Efcp_2EBIT0B_2E1(A_27a,V3a_27_2E0) )
<=> ( V2a_2E0 = V3a_27_2E0 ) ) ) ).
tff(thm_2Efcp_2Ebit0__distinct,axiom,
! [A_27a: $tType,V0a_27_2E0: A_27a,V1a_2E0: A_27a] : ( c_2Efcp_2EBIT0A_2E1(A_27a,V1a_2E0) != c_2Efcp_2EBIT0B_2E1(A_27a,V0a_27_2E0) ) ).
tff(thm_2Efcp_2Ebit0__nchotomy,axiom,
! [A_27a: $tType,V0bb_2E0: tyop_2Efcp_2Ebit0(A_27a)] :
( ? [V1a_2E0: A_27a] : ( V0bb_2E0 = c_2Efcp_2EBIT0A_2E1(A_27a,V1a_2E0) )
| ? [V2a_2E0: A_27a] : ( V0bb_2E0 = c_2Efcp_2EBIT0B_2E1(A_27a,V2a_2E0) ) ) ).
tff(thm_2Efcp_2Ebit0__Axiom,axiom,
! [A_27a: $tType,A_27b: $tType,V0f0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
? [V2fn_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),A_27b)] :
( ! [V3a_2E0: A_27a] : ( app_2E2(tyop_2Efcp_2Ebit0(A_27a),A_27b,V2fn_2E0,c_2Efcp_2EBIT0A_2E1(A_27a,V3a_2E0)) = app_2E2(A_27a,A_27b,V0f0_2E0,V3a_2E0) )
& ! [V4a_2E0: A_27a] : ( app_2E2(tyop_2Efcp_2Ebit0(A_27a),A_27b,V2fn_2E0,c_2Efcp_2EBIT0B_2E1(A_27a,V4a_2E0)) = app_2E2(A_27a,A_27b,V1f1_2E0,V4a_2E0) ) ) ).
tff(thm_2Efcp_2Ebit0__induction,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool)] :
( ( ! [V1a_2E0: A_27a] : p(app_2E2(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Efcp_2EBIT0A_2E1(A_27a,V1a_2E0)))
& ! [V2a_2E0: A_27a] : p(app_2E2(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Efcp_2EBIT0B_2E1(A_27a,V2a_2E0))) )
=> ! [V3b_2E0: tyop_2Efcp_2Ebit0(A_27a)] : p(app_2E2(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3b_2E0)) ) ).
tff(thm_2Efcp_2Ebit0__case__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_27_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2M_2E0: tyop_2Efcp_2Ebit0(A_27a),V3M_27_2E0: tyop_2Efcp_2Ebit0(A_27a),V4f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V5f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( ( V2M_2E0 = V3M_27_2E0 )
& ! [V6a_2E0: A_27a] :
( ( V3M_27_2E0 = c_2Efcp_2EBIT0A_2E1(A_27a,V6a_2E0) )
=> ( app_2E2(A_27a,A_27b,V4f_2E0,V6a_2E0) = app_2E2(A_27a,A_27b,V1f_27_2E0,V6a_2E0) ) )
& ! [V7a_2E0: A_27a] :
( ( V3M_27_2E0 = c_2Efcp_2EBIT0B_2E1(A_27a,V7a_2E0) )
=> ( app_2E2(A_27a,A_27b,V5f1_2E0,V7a_2E0) = app_2E2(A_27a,A_27b,V0f1_27_2E0,V7a_2E0) ) ) )
=> ( c_2Efcp_2Ebit0__CASE_2E3(A_27a,A_27b,V2M_2E0,V4f_2E0,V5f1_2E0) = c_2Efcp_2Ebit0__CASE_2E3(A_27a,A_27b,V3M_27_2E0,V1f_27_2E0,V0f1_27_2E0) ) ) ).
tff(thm_2Efcp_2Ebit0__case__eq,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Efcp_2Ebit0(A_27a),V1v_2E0: A_27b,V2f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( c_2Efcp_2Ebit0__CASE_2E3(A_27a,A_27b,V0x_2E0,V3f_2E0,V2f1_2E0) = V1v_2E0 )
<=> ( ? [V4a_2E0: A_27a] :
( ( V0x_2E0 = c_2Efcp_2EBIT0A_2E1(A_27a,V4a_2E0) )
& ( app_2E2(A_27a,A_27b,V3f_2E0,V4a_2E0) = V1v_2E0 ) )
| ? [V5a_2E0: A_27a] :
( ( V0x_2E0 = c_2Efcp_2EBIT0B_2E1(A_27a,V5a_2E0) )
& ( app_2E2(A_27a,A_27b,V2f1_2E0,V5a_2E0) = V1v_2E0 ) ) ) ) ).
tff(thm_2Efcp_2Eindex__bit0,axiom,
! [A_27a: $tType] : ( c_2Efcp_2Edimindex_2E1(tyop_2Efcp_2Ebit0(A_27a),c_2Ebool_2Ethe__value_2E0(tyop_2Efcp_2Ebit0(A_27a))) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ).
tff(thm_2Efcp_2Efinite__bit0,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit0(A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Efcp_2Ebit0(A_27a))) = c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)) ) ).
tff(thm_2Efcp_2Edatatype__bit1,axiom,
! [A_27a: $tType,V0bit1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool)))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool)),V0bit1_2E0,c_2Efcp_2EBIT1A_2E0(A_27a)),c_2Efcp_2EBIT1B_2E0(A_27a)),c_2Efcp_2EBIT1C_2E0(A_27a)))) ).
tff(thm_2Efcp_2Ebit1__11,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: A_27a,V1a_27_2E0: A_27a] :
( ( c_2Efcp_2EBIT1A_2E1(A_27a,V0a_2E0) = c_2Efcp_2EBIT1A_2E1(A_27a,V1a_27_2E0) )
<=> ( V0a_2E0 = V1a_27_2E0 ) )
& ! [V2a_2E0: A_27a,V3a_27_2E0: A_27a] :
( ( c_2Efcp_2EBIT1B_2E1(A_27a,V2a_2E0) = c_2Efcp_2EBIT1B_2E1(A_27a,V3a_27_2E0) )
<=> ( V2a_2E0 = V3a_27_2E0 ) ) ) ).
tff(thm_2Efcp_2Ebit1__distinct,axiom,
! [A_27a: $tType] :
( ! [V0a_27_2E0: A_27a,V1a_2E0: A_27a] : ( c_2Efcp_2EBIT1A_2E1(A_27a,V1a_2E0) != c_2Efcp_2EBIT1B_2E1(A_27a,V0a_27_2E0) )
& ! [V2a_2E0: A_27a] : ( c_2Efcp_2EBIT1A_2E1(A_27a,V2a_2E0) != c_2Efcp_2EBIT1C_2E0(A_27a) )
& ! [V3a_2E0: A_27a] : ( c_2Efcp_2EBIT1B_2E1(A_27a,V3a_2E0) != c_2Efcp_2EBIT1C_2E0(A_27a) ) ) ).
tff(thm_2Efcp_2Ebit1__nchotomy,axiom,
! [A_27a: $tType,V0bb_2E0: tyop_2Efcp_2Ebit1(A_27a)] :
( ? [V1a_2E0: A_27a] : ( V0bb_2E0 = c_2Efcp_2EBIT1A_2E1(A_27a,V1a_2E0) )
| ? [V2a_2E0: A_27a] : ( V0bb_2E0 = c_2Efcp_2EBIT1B_2E1(A_27a,V2a_2E0) )
| ( V0bb_2E0 = c_2Efcp_2EBIT1C_2E0(A_27a) ) ) ).
tff(thm_2Efcp_2Ebit1__Axiom,axiom,
! [A_27a: $tType,A_27b: $tType,V0f0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2f2_2E0: A_27b] :
? [V3fn_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),A_27b)] :
( ! [V4a_2E0: A_27a] : ( app_2E2(tyop_2Efcp_2Ebit1(A_27a),A_27b,V3fn_2E0,c_2Efcp_2EBIT1A_2E1(A_27a,V4a_2E0)) = app_2E2(A_27a,A_27b,V0f0_2E0,V4a_2E0) )
& ! [V5a_2E0: A_27a] : ( app_2E2(tyop_2Efcp_2Ebit1(A_27a),A_27b,V3fn_2E0,c_2Efcp_2EBIT1B_2E1(A_27a,V5a_2E0)) = app_2E2(A_27a,A_27b,V1f1_2E0,V5a_2E0) )
& ( app_2E2(tyop_2Efcp_2Ebit1(A_27a),A_27b,V3fn_2E0,c_2Efcp_2EBIT1C_2E0(A_27a)) = V2f2_2E0 ) ) ).
tff(thm_2Efcp_2Ebit1__induction,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool)] :
( ( ! [V1a_2E0: A_27a] : p(app_2E2(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Efcp_2EBIT1A_2E1(A_27a,V1a_2E0)))
& ! [V2a_2E0: A_27a] : p(app_2E2(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Efcp_2EBIT1B_2E1(A_27a,V2a_2E0)))
& p(app_2E2(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Efcp_2EBIT1C_2E0(A_27a))) )
=> ! [V3b_2E0: tyop_2Efcp_2Ebit1(A_27a)] : p(app_2E2(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3b_2E0)) ) ).
tff(thm_2Efcp_2Ebit1__case__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_27_2E0: A_27b,V1f1_27_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2f_27_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3M_2E0: tyop_2Efcp_2Ebit1(A_27a),V4M_27_2E0: tyop_2Efcp_2Ebit1(A_27a),V5f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V7v_2E0: A_27b] :
( ( ( V3M_2E0 = V4M_27_2E0 )
& ! [V8a_2E0: A_27a] :
( ( V4M_27_2E0 = c_2Efcp_2EBIT1A_2E1(A_27a,V8a_2E0) )
=> ( app_2E2(A_27a,A_27b,V5f_2E0,V8a_2E0) = app_2E2(A_27a,A_27b,V2f_27_2E0,V8a_2E0) ) )
& ! [V9a_2E0: A_27a] :
( ( V4M_27_2E0 = c_2Efcp_2EBIT1B_2E1(A_27a,V9a_2E0) )
=> ( app_2E2(A_27a,A_27b,V6f1_2E0,V9a_2E0) = app_2E2(A_27a,A_27b,V1f1_27_2E0,V9a_2E0) ) )
& ( ( V4M_27_2E0 = c_2Efcp_2EBIT1C_2E0(A_27a) )
=> ( V7v_2E0 = V0v_27_2E0 ) ) )
=> ( c_2Efcp_2Ebit1__CASE_2E4(A_27a,A_27b,V3M_2E0,V5f_2E0,V6f1_2E0,V7v_2E0) = c_2Efcp_2Ebit1__CASE_2E4(A_27a,A_27b,V4M_27_2E0,V2f_27_2E0,V1f1_27_2E0,V0v_27_2E0) ) ) ).
tff(thm_2Efcp_2Ebit1__case__eq,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Efcp_2Ebit1(A_27a),V1v_27_2E0: A_27b,V2v_2E0: A_27b,V3f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( c_2Efcp_2Ebit1__CASE_2E4(A_27a,A_27b,V0x_2E0,V4f_2E0,V3f1_2E0,V2v_2E0) = V1v_27_2E0 )
<=> ( ? [V5a_2E0: A_27a] :
( ( V0x_2E0 = c_2Efcp_2EBIT1A_2E1(A_27a,V5a_2E0) )
& ( app_2E2(A_27a,A_27b,V4f_2E0,V5a_2E0) = V1v_27_2E0 ) )
| ? [V6a_2E0: A_27a] :
( ( V0x_2E0 = c_2Efcp_2EBIT1B_2E1(A_27a,V6a_2E0) )
& ( app_2E2(A_27a,A_27b,V3f1_2E0,V6a_2E0) = V1v_27_2E0 ) )
| ( ( V0x_2E0 = c_2Efcp_2EBIT1C_2E0(A_27a) )
& ( V2v_2E0 = V1v_27_2E0 ) ) ) ) ).
tff(thm_2Efcp_2Eindex__bit1,axiom,
! [A_27a: $tType] : ( c_2Efcp_2Edimindex_2E1(tyop_2Efcp_2Ebit1(A_27a),c_2Ebool_2Ethe__value_2E0(tyop_2Efcp_2Ebit1(A_27a))) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ).
tff(thm_2Efcp_2Efinite__bit1,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit1(A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Efcp_2Ebit1(A_27a))) = c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)) ) ).
tff(thm_2Efcp_2Eindex__one,axiom,
c_2Efcp_2Edimindex_2E1(tyop_2Eone_2Eone,c_2Ebool_2Ethe__value_2E0(tyop_2Eone_2Eone)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ).
tff(thm_2Efcp_2Efinite__one,axiom,
p(c_2Epred__set_2EFINITE_2E1(tyop_2Eone_2Eone,c_2Epred__set_2EUNIV_2E0(tyop_2Eone_2Eone))) ).
tff(thm_2Efcp_2EFCP__UPDATE__COMMUTES,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: tyop_2Enum_2Enum,V3c_2E0: A_27a,V4d_2E0: A_27a] :
( ( V1a_2E0 != V2b_2E0 )
=> ( c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,V0m_2E0)) = c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0m_2E0)) ) ) ).
tff(thm_2Efcp_2EFCP__UPDATE__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: A_27a,V3c_2E0: A_27a] : ( c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V1a_2E0,V2b_2E0,V0m_2E0)) = c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0m_2E0) ) ).
tff(thm_2Efcp_2EFCP__UPDATE__IMP__ID,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1a_2E0: tyop_2Enum_2Enum,V2v_2E0: A_27a] :
( ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V0m_2E0,V1a_2E0) = V2v_2E0 )
=> ( c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V1a_2E0,V2v_2E0,V0m_2E0) = V0m_2E0 ) ) ).
tff(thm_2Efcp_2EAPPLY__FCP__UPDATE__ID,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V1a_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V1a_2E0,c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V0m_2E0,V1a_2E0),V0m_2E0) = V0m_2E0 ) ).
tff(thm_2Efcp_2EFCP__APPLY__UPDATE__THM,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ! [V2a_2E0: tyop_2Enum_2Enum,V4b_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V4b_2E0))
<=> ( V2a_2E0 = V4b_2E0 ) )
=> ! [V0index_20out_20of_20range_2E0: tyop_2Emin_2Ebool,V1m_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b),V2a_2E0: tyop_2Enum_2Enum,V3w_2E0: A_27a,V4b_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V2a_2E0,V3w_2E0,V1m_2E0),V4b_2E0) = c_2Ebool_2ECOND_2E3(A_27a,c_2Eprim__rec_2E_3C_2E2(V4b_2E0,c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))),c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V4b_2E0),V3w_2E0,c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V1m_2E0,V4b_2E0)),app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EFAIL_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,c_2Efcp_2Efcp__index_2E0(A_27a,A_27b),V0index_20out_20of_20range_2E0),c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V2a_2E0,V3w_2E0,V1m_2E0)),V4b_2E0)) ) ) ).
tff(thm_2Efcp_2ELENGTH__V2L,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Efcp_2EV2L_2E1(A_27a,A_27b,V0v_2E0)) = c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)) ) ).
tff(thm_2Efcp_2EEL__V2L,axiom,
! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0i_2E0,c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( c_2Elist_2EEL_2E2(A_27a,V0i_2E0,c_2Efcp_2EV2L_2E1(A_27a,A_27b,V1v_2E0)) = c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,V1v_2E0,V0i_2E0) ) ) ).
tff(thm_2Efcp_2EFCP__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] : ( c_2Efcp_2EFCP__MAP_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1v_2E0) = c_2Efcp_2EL2V_2E1(A_27b,A_27c,c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Efcp_2EV2L_2E1(A_27a,A_27c,V1v_2E0))) ) ).
tff(thm_2Efcp_2EFCP__TL,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] :
( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
& ( c_2Efcp_2Edimindex_2E1(A_27c,c_2Ebool_2Ethe__value_2E0(A_27c)) = c_2Earithmetic_2E_2D_2E2(c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) )
=> ( c_2Efcp_2EFCP__TL_2E1(A_27a,A_27c,A_27b,V0v_2E0) = c_2Efcp_2EL2V_2E1(A_27a,A_27c,c_2Elist_2ETL_2E1(A_27a,c_2Efcp_2EV2L_2E1(A_27a,A_27b,V0v_2E0))) ) ) ).
tff(thm_2Efcp_2EFCP__EXISTS,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__EXISTS_2E2(A_27b,A_27a,V0P_2E0,V1v_2E0) = c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,c_2Efcp_2EV2L_2E1(A_27a,A_27b,V1v_2E0)) ) ).
tff(thm_2Efcp_2EFCP__EVERY,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__EVERY_2E2(A_27b,A_27a,V0P_2E0,V1v_2E0) = c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Efcp_2EV2L_2E1(A_27a,A_27b,V1v_2E0)) ) ).
tff(thm_2Efcp_2EFCP__HD,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__HD_2E1(A_27a,A_27b,V0v_2E0) = c_2Elist_2EHD_2E1(A_27a,c_2Efcp_2EV2L_2E1(A_27a,A_27b,V0v_2E0)) ) ).
tff(thm_2Efcp_2EFCP__CONS,axiom,
! [A_27a: $tType,A_27b: $tType,V0a_2E0: A_27a,V1v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ( c_2Efcp_2EFCP__CONS_2E2(A_27a,A_27b,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V0a_2E0,V1v_2E0) = c_2Efcp_2EL2V_2E1(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Elist_2ECONS_2E2(A_27a,V0a_2E0,c_2Efcp_2EV2L_2E1(A_27a,A_27b,V1v_2E0))) ) ).
tff(thm_2Efcp_2EV2L__L2V,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)) = c_2Elist_2ELENGTH_2E1(A_27a,V0x_2E0) )
=> ( c_2Efcp_2EV2L_2E1(A_27a,A_27b,c_2Efcp_2EL2V_2E1(A_27a,A_27b,V0x_2E0)) = V0x_2E0 ) ) ).
tff(thm_2Efcp_2ENULL__V2L,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: tyop_2Efcp_2Ecart(A_27a,A_27b)] : ~ p(c_2Elist_2ENULL_2E1(A_27a,c_2Efcp_2EV2L_2E1(A_27a,A_27b,V0v_2E0))) ).
tff(thm_2Efcp_2EREAD__TL,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0i_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Efcp_2Ecart(A_27a,A_27c)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0i_2E0,c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,c_2Efcp_2EFCP__TL_2E1(A_27a,A_27b,A_27c,V1a_2E0),V0i_2E0) = c_2Efcp_2Efcp__index_2E2(A_27a,A_27c,V1a_2E0,c_2Enum_2ESUC_2E1(V0i_2E0)) ) ) ).
tff(thm_2Efcp_2EREAD__L2V,axiom,
! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0i_2E0,c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,c_2Efcp_2EL2V_2E1(A_27a,A_27b,V1a_2E0),V0i_2E0) = c_2Elist_2EEL_2E2(A_27a,V0i_2E0,V1a_2E0) ) ) ).
tff(thm_2Efcp_2Eindex__comp,axiom,
! [A_27a: $tType,A_27b: $tType,V0FCP_20out_20of_20bounds_2E0: tyop_2Emin_2Ebool,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(A_27a,A_27b,c_2Efcp_2EFCP_2E1(A_27a,A_27b,V1f_2E0),V2n_2E0) = c_2Ebool_2ECOND_2E3(A_27a,c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))),app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V2n_2E0),app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EFAIL_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,c_2Efcp_2Efcp__index_2E0(A_27a,A_27b),V0FCP_20out_20of_20bounds_2E0),c_2Efcp_2EFCP_2E1(A_27a,A_27b,V1f_2E0)),V2n_2E0)) ) ).
tff(thm_2Efcp_2Efcp__subst__comp,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))] :
( ! [V1x_2E0: tyop_2Enum_2Enum,V5c_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V1x_2E0),V5c_2E0))
<=> ( V1x_2E0 = V5c_2E0 ) )
=> ( ! [V1x_2E0: tyop_2Enum_2Enum,V0y_2E0: A_27a,V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5c_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0,V1x_2E0),V0y_2E0),V4f_2E0),V5c_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V1x_2E0),V5c_2E0),V0y_2E0,app_2E2(tyop_2Enum_2Enum,A_27a,V4f_2E0,V5c_2E0)) )
=> ! [V0y_2E0: A_27a,V1x_2E0: tyop_2Enum_2Enum,V2a_2E0: A_27c,V3b_2E0: A_27d,V4f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Efcp_2E_3A_2B_2E3(A_27a,A_27b,V1x_2E0,V0y_2E0,c_2Efcp_2EFCP_2E1(A_27a,A_27b,V4f_2E0)) = c_2Efcp_2EFCP_2E1(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0,V1x_2E0),V0y_2E0),V4f_2E0)) ) ) ) ).
%------------------------------------------------------------------------------