ITP001 Axioms: ITP022_7.ax
%------------------------------------------------------------------------------
% File : ITP022_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 : ind_type.ax [Gau19]
% : HL4022_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 194 ( 56 unt; 92 typ; 0 def)
% Number of atoms : 192 ( 119 equ)
% Maximal formula atoms : 7 ( 0 avg)
% Number of connectives : 95 ( 5 ~; 5 |; 25 &)
% ( 32 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 75 ( 44 >; 31 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 89 ( 89 usr; 22 con; 0-5 aty)
% Number of variables : 413 ( 345 !; 13 ?; 413 :)
% ( 55 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_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_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_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0:
!>[A_27a: $tType] : tyop_2Eind__type_2Erecspace(A_27a) ).
tff(c_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_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_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Eind__type_2EFCONS_2E0,type,
c_2Eind__type_2EFCONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))) ).
tff(c_2Eind__type_2EFCONS_2E3,type,
c_2Eind__type_2EFCONS_2E3:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) * tyop_2Enum_2Enum ) > A_27a ) ).
tff(c_2Eind__type_2EFNIL_2E0,type,
c_2Eind__type_2EFNIL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ).
tff(c_2Eind__type_2EFNIL_2E1,type,
c_2Eind__type_2EFNIL_2E1:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > A_27a ) ).
tff(c_2Eind__type_2EINJA_2E0,type,
c_2Eind__type_2EINJA_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Eind__type_2EINJA_2E1,type,
c_2Eind__type_2EINJA_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Eind__type_2EINJA_2E3,type,
c_2Eind__type_2EINJA_2E3:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Enum_2Enum * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eind__type_2EINJF_2E0,type,
c_2Eind__type_2EINJF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Eind__type_2EINJF_2E1,type,
c_2Eind__type_2EINJF_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Eind__type_2EINJF_2E2,type,
c_2Eind__type_2EINJF_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) * tyop_2Enum_2Enum ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eind__type_2EINJN_2E0,type,
c_2Eind__type_2EINJN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Eind__type_2EINJN_2E1,type,
c_2Eind__type_2EINJN_2E1:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Eind__type_2EINJN_2E3,type,
c_2Eind__type_2EINJN_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Enum_2Enum * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eind__type_2EINJP_2E0,type,
c_2Eind__type_2EINJP_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Eind__type_2EINJP_2E2,type,
c_2Eind__type_2EINJP_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Eind__type_2EINJP_2E4,type,
c_2Eind__type_2EINJP_2E4:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Enum_2Enum * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eind__type_2EISO_2E0,type,
c_2Eind__type_2EISO_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Eind__type_2EISO_2E2,type,
c_2Eind__type_2EISO_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27b,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_2Eind__type_2ENUMFST_2E0,type,
c_2Eind__type_2ENUMFST_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Eind__type_2ENUMFST_2E1,type,
c_2Eind__type_2ENUMFST_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2ENUMLEFT_2E0,type,
c_2Eind__type_2ENUMLEFT_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Eind__type_2ENUMLEFT_2E1,type,
c_2Eind__type_2ENUMLEFT_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
tff(c_2Eind__type_2ENUMPAIR_2E0,type,
c_2Eind__type_2ENUMPAIR_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eind__type_2ENUMPAIR_2E2,type,
c_2Eind__type_2ENUMPAIR_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2ENUMRIGHT_2E0,type,
c_2Eind__type_2ENUMRIGHT_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Eind__type_2ENUMRIGHT_2E1,type,
c_2Eind__type_2ENUMRIGHT_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2ENUMSND_2E0,type,
c_2Eind__type_2ENUMSND_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Eind__type_2ENUMSND_2E1,type,
c_2Eind__type_2ENUMSND_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2ENUMSUM_2E0,type,
c_2Eind__type_2ENUMSUM_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eind__type_2ENUMSUM_2E2,type,
c_2Eind__type_2ENUMSUM_2E2: ( tyop_2Emin_2Ebool * 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_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_2Eind__type_2EZBOT_2E0,type,
c_2Eind__type_2EZBOT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Eind__type_2EZCONSTR_2E0,type,
c_2Eind__type_2EZCONSTR_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))) ).
tff(c_2Eind__type_2EZCONSTR_2E3,type,
c_2Eind__type_2EZCONSTR_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Eind__type_2EZRECSPACE_2E0,type,
c_2Eind__type_2EZRECSPACE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Eind__type_2EZRECSPACE_2E1,type,
c_2Eind__type_2EZRECSPACE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
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_2Eind__type_2Edest__rec_2E0,type,
c_2Eind__type_2Edest__rec_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Eind__type_2Edest__rec_2E1,type,
c_2Eind__type_2Edest__rec_2E1:
!>[A_27a: $tType] : ( tyop_2Eind__type_2Erecspace(A_27a) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Eind__type_2Emk__rec_2E0,type,
c_2Eind__type_2Emk__rec_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(A_27a)) ).
tff(c_2Eind__type_2Emk__rec_2E1,type,
c_2Eind__type_2Emk__rec_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Eind__type_2Erecspace(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_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(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_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_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(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(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_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_2EEXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2EFCONS_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2EFCONS_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = 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)),c_2Eind__type_2EFCONS_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2EFNIL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2EFNIL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,c_2Eind__type_2EFNIL_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2EINJA_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Eind__type_2EINJA_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2EINJA_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Enum_2Enum,X2_2E0: A_27a] : ( c_2Eind__type_2EINJA_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2EINJF_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Eind__type_2EINJF_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EINJF_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2EINJF_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2EINJN_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2EINJN_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2EINJN_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: A_27a] : ( c_2Eind__type_2EINJN_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EINJP_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Eind__type_2EINJP_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJP_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Eind__type_2EINJP_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Enum_2Enum,X3_2E0: A_27a] : ( c_2Eind__type_2EINJP_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJP_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2Eind__type_2EISO_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eind__type_2EISO_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EISO_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_2Emin_2Efun(A_27b,A_27a)] : ( c_2Eind__type_2EISO_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),c_2Eind__type_2EISO_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Eind__type_2EISO_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool),c_2Eind__type_2EISO_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] : ( c_2Eind__type_2EISO_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool),c_2Eind__type_2EISO_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2Eind__type_2EISO_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Eind__type_2EISO_2E0(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2ENUMFST_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2ENUMFST_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2ENUMLEFT_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2ENUMLEFT_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Eind__type_2ENUMLEFT_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2ENUMPAIR_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2ENUMPAIR_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_2Eind__type_2ENUMPAIR_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2ENUMRIGHT_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2ENUMRIGHT_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2ENUMSND_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2ENUMSND_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2ENUMSUM_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2ENUMSUM_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eind__type_2Erecspace_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2EZCONSTR_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Eind__type_2EZCONSTR_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Eind__type_2EZCONSTR_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2EZRECSPACE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Eind__type_2EZRECSPACE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Eind__type_2Edest__rec_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eind__type_2Erecspace(A_27a)] : ( c_2Eind__type_2Edest__rec_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eind__type_2Emk__rec_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Eind__type_2Emk__rec_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_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_2Eind__type_2ENUMPAIR,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2ENUMPAIR_2E2(V0x_2E0,V1y_2E0) = c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V0x_2E0),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1y_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ).
tff(thm_2Eind__type_2ENUMPAIR__DEST,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] :
( ( c_2Eind__type_2ENUMFST_2E1(c_2Eind__type_2ENUMPAIR_2E2(V0x_2E0,V1y_2E0)) = V0x_2E0 )
& ( c_2Eind__type_2ENUMSND_2E1(c_2Eind__type_2ENUMPAIR_2E2(V0x_2E0,V1y_2E0)) = V1y_2E0 ) ) ).
tff(thm_2Eind__type_2ENUMSUM,axiom,
! [V0b_2E0: tyop_2Emin_2Ebool,V1x_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2ENUMSUM_2E2(V0b_2E0,V1x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,V0b_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1x_2E0)),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1x_2E0)) ) ).
tff(thm_2Eind__type_2ENUMSUM__DEST,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Enum_2Enum] :
( ( c_2Eind__type_2ENUMLEFT_2E1(c_2Eind__type_2ENUMSUM_2E2(V0x_2E0,V1y_2E0)) = V0x_2E0 )
& ( c_2Eind__type_2ENUMRIGHT_2E1(c_2Eind__type_2ENUMSUM_2E2(V0x_2E0,V1y_2E0)) = V1y_2E0 ) ) ).
tff(thm_2Eind__type_2EINJN,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum,V2x_27_2E0: A_27a] :
( p(c_2Eind__type_2EINJN_2E3(A_27a,V0m_2E0,V1x_2E0,V2x_27_2E0))
<=> ( V1x_2E0 = V0m_2E0 ) ) ).
tff(thm_2Eind__type_2EINJA,axiom,
! [A_27a: $tType,V0a_2E0: A_27a,V1x_2E0: tyop_2Enum_2Enum,V2x_27_2E0: A_27a] :
( p(c_2Eind__type_2EINJA_2E3(A_27a,V0a_2E0,V1x_2E0,V2x_27_2E0))
<=> ( V2x_27_2E0 = V0a_2E0 ) ) ).
tff(thm_2Eind__type_2EINJF,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1x_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2EINJF_2E2(A_27a,V0f_2E0,V1x_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0,c_2Eind__type_2ENUMFST_2E1(V1x_2E0)),c_2Eind__type_2ENUMSND_2E1(V1x_2E0)) ) ).
tff(thm_2Eind__type_2EINJP,axiom,
! [A_27a: $tType,V0f1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2x_2E0: tyop_2Enum_2Enum,V3x_27_2E0: A_27a] : ( c_2Eind__type_2EINJP_2E4(A_27a,V0f1_2E0,V1f2_2E0,V2x_2E0,V3x_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,c_2Eind__type_2ENUMLEFT_2E1(V2x_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f1_2E0,c_2Eind__type_2ENUMRIGHT_2E1(V2x_2E0)),V3x_27_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f2_2E0,c_2Eind__type_2ENUMRIGHT_2E1(V2x_2E0)),V3x_27_2E0)) ) ).
tff(thm_2Eind__type_2EZCONSTR,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Enum_2Enum,V1i_2E0: A_27a,V2r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Eind__type_2EZCONSTR_2E3(A_27a,V0c_2E0,V1i_2E0,V2r_2E0) = c_2Eind__type_2EINJP_2E2(A_27a,c_2Eind__type_2EINJN_2E1(A_27a,c_2Enum_2ESUC_2E1(V0c_2E0)),c_2Eind__type_2EINJP_2E2(A_27a,c_2Eind__type_2EINJA_2E1(A_27a,V1i_2E0),c_2Eind__type_2EINJF_2E1(A_27a,V2r_2E0))) ) ).
tff(thm_2Eind__type_2EZBOT,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
( ! [V0z_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0z_2E0) = c_2Ebool_2ET_2E0 )
=> ( c_2Eind__type_2EZBOT_2E0(A_27a) = c_2Eind__type_2EINJP_2E2(A_27a,c_2Eind__type_2EINJN_2E1(A_27a,c_2Enum_2E0_2E0),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0)) ) ) ).
tff(thm_2Eind__type_2EZRECSPACE__def,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,V0x_2E0))
<=> ! [V1ZRECSPACE_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
( ! [V2a0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ( V2a0_2E0 = c_2Eind__type_2EZBOT_2E0(A_27a) )
| ? [V3c_2E0: tyop_2Enum_2Enum,V4i_2E0: A_27a,V5r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ( V2a0_2E0 = c_2Eind__type_2EZCONSTR_2E3(A_27a,V3c_2E0,V4i_2E0,V5r_2E0) )
& ! [V6n_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V1ZRECSPACE_27_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5r_2E0,V6n_2E0))) ) )
=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V1ZRECSPACE_27_2E0,V2a0_2E0)) )
=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V1ZRECSPACE_27_2E0,V0x_2E0)) ) ) ).
tff(thm_2Eind__type_2Erecspace__TY__DEF,axiom,
! [A_27a: $tType] :
? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EZRECSPACE_2E0(A_27a),V0rep_2E0)) ).
tff(thm_2Eind__type_2Erecspace__repfns,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Eind__type_2Erecspace(A_27a)] : ( c_2Eind__type_2Emk__rec_2E1(A_27a,c_2Eind__type_2Edest__rec_2E1(A_27a,V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,V1r_2E0))
<=> ( c_2Eind__type_2Edest__rec_2E1(A_27a,c_2Eind__type_2Emk__rec_2E1(A_27a,V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Eind__type_2EBOTTOM,axiom,
! [A_27a: $tType] : ( c_2Eind__type_2EBOTTOM_2E0(A_27a) = c_2Eind__type_2Emk__rec_2E1(A_27a,c_2Eind__type_2EZBOT_2E0(A_27a)) ) ).
tff(thm_2Eind__type_2ECONSTR,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V2r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V3n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2r_2E0),V3n_2E0) = c_2Eind__type_2Edest__rec_2E1(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),V2r_2E0,V3n_2E0)) )
=> ! [V0c_2E0: tyop_2Enum_2Enum,V1i_2E0: A_27a,V2r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2ECONSTR_2E3(A_27a,V0c_2E0,V1i_2E0,V2r_2E0) = c_2Eind__type_2Emk__rec_2E1(A_27a,c_2Eind__type_2EZCONSTR_2E3(A_27a,V0c_2E0,V1i_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2r_2E0))) ) ) ).
tff(thm_2Eind__type_2EFCONS,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Eind__type_2EFCONS_2E3(A_27a,V0a_2E0,V1f_2E0,c_2Enum_2E0_2E0) = V0a_2E0 )
& ! [V2a_2E0: A_27a,V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4n_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2EFCONS_2E3(A_27a,V2a_2E0,V3f_2E0,c_2Enum_2ESUC_2E1(V4n_2E0)) = app_2E2(tyop_2Enum_2Enum,A_27a,V3f_2E0,V4n_2E0) ) ) ).
tff(thm_2Eind__type_2EFNIL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : ( c_2Eind__type_2EFNIL_2E1(A_27a,V0n_2E0) = c_2Ebool_2EARB_2E0(A_27a) ) ).
tff(thm_2Eind__type_2EISO,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Eind__type_2EISO_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0))
<=> ( ! [V2x_2E0: A_27b] : ( app_2E2(A_27a,A_27b,V0f_2E0,app_2E2(A_27b,A_27a,V1g_2E0,V2x_2E0)) = V2x_2E0 )
& ! [V3y_2E0: A_27a] : ( app_2E2(A_27b,A_27a,V1g_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0)) = V3y_2E0 ) ) ) ).
tff(thm_2Eind__type_2EINJ__INVERSE2,axiom,
! [A_27A: $tType,A_27B: $tType,A_27C: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27A,tyop_2Emin_2Efun(A_27B,A_27C))] :
( ! [V1x1_2E0: A_27A,V2y1_2E0: A_27B,V3x2_2E0: A_27A,V4y2_2E0: A_27B] :
( ( app_2E2(A_27B,A_27C,app_2E2(A_27A,tyop_2Emin_2Efun(A_27B,A_27C),V0P_2E0,V1x1_2E0),V2y1_2E0) = app_2E2(A_27B,A_27C,app_2E2(A_27A,tyop_2Emin_2Efun(A_27B,A_27C),V0P_2E0,V3x2_2E0),V4y2_2E0) )
<=> ( ( V1x1_2E0 = V3x2_2E0 )
& ( V2y1_2E0 = V4y2_2E0 ) ) )
=> ? [V5X_2E0: tyop_2Emin_2Efun(A_27C,A_27A),V6Y_2E0: tyop_2Emin_2Efun(A_27C,A_27B)] :
! [V7x_2E0: A_27A,V8y_2E0: A_27B] :
( ( app_2E2(A_27C,A_27A,V5X_2E0,app_2E2(A_27B,A_27C,app_2E2(A_27A,tyop_2Emin_2Efun(A_27B,A_27C),V0P_2E0,V7x_2E0),V8y_2E0)) = V7x_2E0 )
& ( app_2E2(A_27C,A_27B,V6Y_2E0,app_2E2(A_27B,A_27C,app_2E2(A_27A,tyop_2Emin_2Efun(A_27B,A_27C),V0P_2E0,V7x_2E0),V8y_2E0)) = V8y_2E0 ) ) ) ).
tff(thm_2Eind__type_2ENUMPAIR__INJ__LEMMA,axiom,
! [V0x1_2E0: tyop_2Enum_2Enum,V1y1_2E0: tyop_2Enum_2Enum,V2x2_2E0: tyop_2Enum_2Enum,V3y2_2E0: tyop_2Enum_2Enum] :
( ( c_2Eind__type_2ENUMPAIR_2E2(V0x1_2E0,V1y1_2E0) = c_2Eind__type_2ENUMPAIR_2E2(V2x2_2E0,V3y2_2E0) )
=> ( V0x1_2E0 = V2x2_2E0 ) ) ).
tff(thm_2Eind__type_2ENUMPAIR__INJ,axiom,
! [V0x1_2E0: tyop_2Enum_2Enum,V1y1_2E0: tyop_2Enum_2Enum,V2x2_2E0: tyop_2Enum_2Enum,V3y2_2E0: tyop_2Enum_2Enum] :
( ( c_2Eind__type_2ENUMPAIR_2E2(V0x1_2E0,V1y1_2E0) = c_2Eind__type_2ENUMPAIR_2E2(V2x2_2E0,V3y2_2E0) )
<=> ( ( V0x1_2E0 = V2x2_2E0 )
& ( V1y1_2E0 = V3y2_2E0 ) ) ) ).
tff(thm_2Eind__type_2ENUMSUM__INJ,axiom,
! [V0b1_2E0: tyop_2Emin_2Ebool,V1x1_2E0: tyop_2Enum_2Enum,V2b2_2E0: tyop_2Emin_2Ebool,V3x2_2E0: tyop_2Enum_2Enum] :
( ( c_2Eind__type_2ENUMSUM_2E2(V0b1_2E0,V1x1_2E0) = c_2Eind__type_2ENUMSUM_2E2(V2b2_2E0,V3x2_2E0) )
<=> ( ( V0b1_2E0 = V2b2_2E0 )
& ( V1x1_2E0 = V3x2_2E0 ) ) ) ).
tff(thm_2Eind__type_2EINJN__INJ,axiom,
! [A_27a: $tType,V0n1_2E0: tyop_2Enum_2Enum,V1n2_2E0: tyop_2Enum_2Enum] :
( ( c_2Eind__type_2EINJN_2E1(A_27a,V0n1_2E0) = c_2Eind__type_2EINJN_2E1(A_27a,V1n2_2E0) )
<=> ( V0n1_2E0 = V1n2_2E0 ) ) ).
tff(thm_2Eind__type_2EINJA__INJ,axiom,
! [A_27a: $tType,V0a1_2E0: A_27a,V1a2_2E0: A_27a] :
( ( c_2Eind__type_2EINJA_2E1(A_27a,V0a1_2E0) = c_2Eind__type_2EINJA_2E1(A_27a,V1a2_2E0) )
<=> ( V0a1_2E0 = V1a2_2E0 ) ) ).
tff(thm_2Eind__type_2EINJF__INJ,axiom,
! [A_27a: $tType,V0f1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1f2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ( c_2Eind__type_2EINJF_2E1(A_27a,V0f1_2E0) = c_2Eind__type_2EINJF_2E1(A_27a,V1f2_2E0) )
<=> ( V0f1_2E0 = V1f2_2E0 ) ) ).
tff(thm_2Eind__type_2EINJP__INJ,axiom,
! [A_27a: $tType,V0f1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f1_27_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3f2_27_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Eind__type_2EINJP_2E2(A_27a,V0f1_2E0,V2f2_2E0) = c_2Eind__type_2EINJP_2E2(A_27a,V1f1_27_2E0,V3f2_27_2E0) )
<=> ( ( V0f1_2E0 = V1f1_27_2E0 )
& ( V2f2_2E0 = V3f2_27_2E0 ) ) ) ).
tff(thm_2Eind__type_2EZCONSTR__ZBOT,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Enum_2Enum,V1i_2E0: A_27a,V2r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Eind__type_2EZCONSTR_2E3(A_27a,V0c_2E0,V1i_2E0,V2r_2E0) != c_2Eind__type_2EZBOT_2E0(A_27a) ) ).
tff(thm_2Eind__type_2EZRECSPACE__rules,axiom,
! [A_27a: $tType] :
( p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,c_2Eind__type_2EZBOT_2E0(A_27a)))
& ! [V0c_2E0: tyop_2Enum_2Enum,V1i_2E0: A_27a,V2r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2r_2E0,V3n_2E0)))
=> p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,c_2Eind__type_2EZCONSTR_2E3(A_27a,V0c_2E0,V1i_2E0,V2r_2E0))) ) ) ).
tff(thm_2Eind__type_2EZRECSPACE__ind,axiom,
! [A_27a: $tType,V0ZRECSPACE_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V0ZRECSPACE_27_2E0,c_2Eind__type_2EZBOT_2E0(A_27a)))
& ! [V1c_2E0: tyop_2Enum_2Enum,V2i_2E0: A_27a,V3r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V4n_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V0ZRECSPACE_27_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3r_2E0,V4n_2E0)))
=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V0ZRECSPACE_27_2E0,c_2Eind__type_2EZCONSTR_2E3(A_27a,V1c_2E0,V2i_2E0,V3r_2E0))) ) )
=> ! [V5a0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,V5a0_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V0ZRECSPACE_27_2E0,V5a0_2E0)) ) ) ).
tff(thm_2Eind__type_2EZRECSPACE__strongind,axiom,
! [A_27a: $tType,V0ZRECSPACE_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V0ZRECSPACE_27_2E0,c_2Eind__type_2EZBOT_2E0(A_27a)))
& ! [V1c_2E0: tyop_2Enum_2Enum,V2i_2E0: A_27a,V3r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3r_2E0,V4n_2E0)))
& p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V0ZRECSPACE_27_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3r_2E0,V4n_2E0))) )
=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V0ZRECSPACE_27_2E0,c_2Eind__type_2EZCONSTR_2E3(A_27a,V1c_2E0,V2i_2E0,V3r_2E0))) ) )
=> ! [V5a0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,V5a0_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,V0ZRECSPACE_27_2E0,V5a0_2E0)) ) ) ).
tff(thm_2Eind__type_2EZRECSPACE__cases,axiom,
! [A_27a: $tType,V0a0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,V0a0_2E0))
<=> ( ( V0a0_2E0 = c_2Eind__type_2EZBOT_2E0(A_27a) )
| ? [V1c_2E0: tyop_2Enum_2Enum,V2i_2E0: A_27a,V3r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ( V0a0_2E0 = c_2Eind__type_2EZCONSTR_2E3(A_27a,V1c_2E0,V2i_2E0,V3r_2E0) )
& ! [V4n_2E0: tyop_2Enum_2Enum] : p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3r_2E0,V4n_2E0))) ) ) ) ).
tff(thm_2Eind__type_2EMK__REC__INJ,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1y_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Eind__type_2Emk__rec_2E1(A_27a,V0x_2E0) = c_2Eind__type_2Emk__rec_2E1(A_27a,V1y_2E0) )
=> ( ( p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,V0x_2E0))
& p(c_2Eind__type_2EZRECSPACE_2E1(A_27a,V1y_2E0)) )
=> ( V0x_2E0 = V1y_2E0 ) ) ) ).
tff(thm_2Eind__type_2EDEST__REC__INJ,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eind__type_2Erecspace(A_27a),V1y_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( c_2Eind__type_2Edest__rec_2E1(A_27a,V0x_2E0) = c_2Eind__type_2Edest__rec_2E1(A_27a,V1y_2E0) )
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Eind__type_2ECONSTR__BOT,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Enum_2Enum,V1i_2E0: A_27a,V2r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2ECONSTR_2E3(A_27a,V0c_2E0,V1i_2E0,V2r_2E0) != c_2Eind__type_2EBOTTOM_2E0(A_27a) ) ).
tff(thm_2Eind__type_2ECONSTR__INJ,axiom,
! [A_27a: $tType,V0c1_2E0: tyop_2Enum_2Enum,V1i1_2E0: A_27a,V2r1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V3c2_2E0: tyop_2Enum_2Enum,V4i2_2E0: A_27a,V5r2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] :
( ( c_2Eind__type_2ECONSTR_2E3(A_27a,V0c1_2E0,V1i1_2E0,V2r1_2E0) = c_2Eind__type_2ECONSTR_2E3(A_27a,V3c2_2E0,V4i2_2E0,V5r2_2E0) )
<=> ( ( V0c1_2E0 = V3c2_2E0 )
& ( V1i1_2E0 = V4i2_2E0 )
& ( V2r1_2E0 = V5r2_2E0 ) ) ) ).
tff(thm_2Eind__type_2ECONSTR__IND,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Eind__type_2EBOTTOM_2E0(A_27a)))
& ! [V1c_2E0: tyop_2Enum_2Enum,V2i_2E0: A_27a,V3r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] :
( ! [V4n_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V0P_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),V3r_2E0,V4n_2E0)))
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Eind__type_2ECONSTR_2E3(A_27a,V1c_2E0,V2i_2E0,V3r_2E0))) ) )
=> ! [V5x_2E0: tyop_2Eind__type_2Erecspace(A_27a)] : p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V5x_2E0)) ) ).
tff(thm_2Eind__type_2ECONSTR__REC,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),V4r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V5n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),F0_2E0,V1f_2E0),V4r_2E0),V5n_2E0) = app_2E2(tyop_2Eind__type_2Erecspace(A_27a),A_27b,V1f_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),V4r_2E0,V5n_2E0)) )
=> ! [V0Fn_2E0: 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_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b))))] :
? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b)] :
! [V2c_2E0: tyop_2Enum_2Enum,V3i_2E0: A_27a,V4r_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( app_2E2(tyop_2Eind__type_2Erecspace(A_27a),A_27b,V1f_2E0,c_2Eind__type_2ECONSTR_2E3(A_27a,V2c_2E0,V3i_2E0,V4r_2E0)) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b)),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_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b))),V0Fn_2E0,V2c_2E0),V3i_2E0),V4r_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),F0_2E0,V1f_2E0),V4r_2E0)) ) ) ).
tff(thm_2Eind__type_2EFCONS__DEST,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V0n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0))
<=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2a_2E0: A_27a] : ( c_2Eind__type_2EFCONS_2E3(A_27a,V2a_2E0,V1f_2E0,V0n_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0),V2a_2E0,app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) ).
tff(thm_2Eind__type_2EISO__REFL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( ! [V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,F0_2E0,V0x_2E0) = V0x_2E0 )
=> p(c_2Eind__type_2EISO_2E2(A_27a,A_27a,F0_2E0,F0_2E0)) ) ).
tff(thm_2Eind__type_2EISO__FUN,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))))] :
( ! [V0g_27_2E0: tyop_2Emin_2Efun(A_27d,A_27b),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V6h_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V7a_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),F1_2E0,V0g_27_2E0),V3f_2E0),V6h_2E0),V7a_2E0) = app_2E2(A_27d,A_27b,V0g_27_2E0,app_2E2(A_27c,A_27d,V6h_2E0,app_2E2(A_27a,A_27c,V3f_2E0,V7a_2E0))) )
=> ( ! [V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V2f_27_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V4h_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V5a_27_2E0: A_27c] : ( app_2E2(A_27c,A_27d,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),F0_2E0,V1g_2E0),V2f_27_2E0),V4h_2E0),V5a_27_2E0) = app_2E2(A_27b,A_27d,V1g_2E0,app_2E2(A_27a,A_27b,V4h_2E0,app_2E2(A_27c,A_27a,V2f_27_2E0,V5a_27_2E0))) )
=> ! [V0g_27_2E0: tyop_2Emin_2Efun(A_27d,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V2f_27_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27c)] :
( ( p(c_2Eind__type_2EISO_2E2(A_27a,A_27c,V3f_2E0,V2f_27_2E0))
& p(c_2Eind__type_2EISO_2E2(A_27b,A_27d,V1g_2E0,V0g_27_2E0)) )
=> p(c_2Eind__type_2EISO_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),F0_2E0,V1g_2E0),V2f_27_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),F1_2E0,V0g_27_2E0),V3f_2E0))) ) ) ) ).
tff(thm_2Eind__type_2EISO__USAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Eind__type_2EISO_2E2(A_27a,A_27b,V1f_2E0,V0g_2E0))
=> ( ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3x_2E0))
<=> ! [V4x_2E0: A_27b] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,app_2E2(A_27b,A_27a,V0g_2E0,V4x_2E0))) )
& ! [V5P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V6x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V5P_2E0,V6x_2E0))
<=> ? [V7x_2E0: A_27b] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V5P_2E0,app_2E2(A_27b,A_27a,V0g_2E0,V7x_2E0))) )
& ! [V8a_2E0: A_27a,V9b_2E0: A_27b] :
( ( V8a_2E0 = app_2E2(A_27b,A_27a,V0g_2E0,V9b_2E0) )
<=> ( app_2E2(A_27a,A_27b,V1f_2E0,V8a_2E0) = V9b_2E0 ) ) ) ) ).
%------------------------------------------------------------------------------