TPTP Problem File: ITP014_3.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP014_3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Ebitstring_2Eword__1comp__v2w.p, bushy 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 : thm_2Ebitstring_2Eword__1comp__v2w.p [Gau19]
% : HL406501_3.p [TPAP]
% Status : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 225 ( 66 unt; 93 typ; 0 def)
% Number of atoms : 416 ( 172 equ)
% Maximal formula atoms : 40 ( 1 avg)
% Number of connectives : 336 ( 52 ~; 40 |; 119 &)
% ( 75 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 68 ( 45 >; 23 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 90 ( 90 usr; 28 con; 0-4 aty)
% Number of variables : 393 ( 345 !; 1 ?; 393 :)
% ( 47 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
tff(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: ( $tType * $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(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_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_2Earithmetic_2E_3E_2E0,type,
c_2Earithmetic_2E_3E_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3E_2E2,type,
c_2Earithmetic_2E_3E_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3E_3D_2E0,type,
c_2Earithmetic_2E_3E_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3E_3D_2E2,type,
c_2Earithmetic_2E_3E_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > 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_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_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_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_2Earithmetic_2EEVEN_2E0,type,
c_2Earithmetic_2EEVEN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EEVEN_2E1,type,
c_2Earithmetic_2EEVEN_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
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_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_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Ecombin_2EI_2E1,type,
c_2Ecombin_2EI_2E1:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
tff(c_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_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
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_2E1,type,
c_2Elist_2EMAP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( 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_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EODD_2E0,type,
c_2Earithmetic_2EODD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EODD_2E1,type,
c_2Earithmetic_2EODD_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
tff(c_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_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_2Ebitstring_2Ebnot_2E0,type,
c_2Ebitstring_2Ebnot_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ).
tff(c_2Ebitstring_2Ebnot_2E1,type,
c_2Ebitstring_2Ebnot_2E1: tyop_2Elist_2Elist(tyop_2Emin_2Ebool) > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ).
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__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_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_2Ebitstring_2Efixwidth_2E0,type,
c_2Ebitstring_2Efixwidth_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))) ).
tff(c_2Ebitstring_2Efixwidth_2E2,type,
c_2Ebitstring_2Efixwidth_2E2: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ).
tff(c_2Enumeral_2EiZ_2E0,type,
c_2Enumeral_2EiZ_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enumeral_2EiZ_2E1,type,
c_2Enumeral_2EiZ_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Enumeral_2EiiSUC_2E0,type,
c_2Enumeral_2EiiSUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enumeral_2EiiSUC_2E1,type,
c_2Enumeral_2EiiSUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebitstring_2Etestbit_2E0,type,
c_2Ebitstring_2Etestbit_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebitstring_2Etestbit_2E2,type,
c_2Ebitstring_2Etestbit_2E2: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0:
!>[A_27a: $tType] : tyop_2Ebool_2Eitself(A_27a) ).
tff(c_2Ebitstring_2Ev2w_2E0,type,
c_2Ebitstring_2Ev2w_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ebitstring_2Ev2w_2E1,type,
c_2Ebitstring_2Ev2w_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(tyop_2Emin_2Ebool) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__1comp_2E0,type,
c_2Ewords_2Eword__1comp_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2Eword__1comp_2E1,type,
c_2Ewords_2Eword__1comp_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,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_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(arityeq2_2Ec_2Earithmetic_2E_3E_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_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_3E_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_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_3E_3D_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_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(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : c_2Elist_2EEL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : c_2Elist_2EEL_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),c_2Elist_2EEL_2E0(A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Elist_2EEL_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2EEL_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEVEN_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E0,X0_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(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_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : c_2Efcp_2EFCP_2E1(tyop_2Emin_2Ebool,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Efcp_2EFCP_2E0(tyop_2Emin_2Ebool,A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : c_2Ecombin_2EI_2E1(A_27a,X0_2E0) = app_2E2(A_27a,A_27a,c_2Ecombin_2EI_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : c_2Elist_2ELENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : c_2Elist_2ELENGTH_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Emin_2Ebool),X0_2E0) ).
tff(arityeq2_2Ec_2Ebool_2ELET_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: A_27a] : c_2Ebool_2ELET_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ELET_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),X1_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_2EMAP_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : c_2Elist_2EMAP_2E1(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2EMAP_2E0(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),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_2Earithmetic_2EODD_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EODD_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E0,X0_2E0) ).
tff(arityeq1_2Ec_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(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_2Ebitstring_2Ebnot_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Ebitstring_2Ebnot_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Ebitstring_2Ebnot_2E0,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(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_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Enum_2Enum] : c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Efcp_2Efcp__index_2E0(tyop_2Emin_2Ebool,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebitstring_2Efixwidth_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Ebitstring_2Efixwidth_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Ebitstring_2Efixwidth_2E0,X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Enumeral_2EiZ_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Enumeral_2EiZ_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Enumeral_2EiiSUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Enumeral_2EiiSUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E0,X0_2E0) ).
tff(arityeq2_2Ec_2Ebitstring_2Etestbit_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Ebitstring_2Etestbit_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebitstring_2Etestbit_2E0,X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Ebitstring_2Ev2w_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Ebitstring_2Ev2w_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebitstring_2Ev2w_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Eword__1comp_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__1comp_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__1comp_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_2Earithmetic_2EADD__CLAUSES,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B_2E2(c_2Enum_2E0_2E0,V1m_2E0) = V1m_2E0 )
& ( c_2Earithmetic_2E_2B_2E2(V1m_2E0,c_2Enum_2E0_2E0) = V1m_2E0 )
& ( c_2Earithmetic_2E_2B_2E2(c_2Enum_2ESUC_2E1(V1m_2E0),V0n_2E0) = c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V1m_2E0,V0n_2E0)) )
& ( c_2Earithmetic_2E_2B_2E2(V1m_2E0,c_2Enum_2ESUC_2E1(V0n_2E0)) = c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V1m_2E0,V0n_2E0)) ) ) ).
tff(thm_2Earithmetic_2EADD__SYM,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0) = c_2Earithmetic_2E_2B_2E2(V1n_2E0,V0m_2E0) ).
tff(thm_2Earithmetic_2EADD__COMM,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0) = c_2Earithmetic_2E_2B_2E2(V1n_2E0,V0m_2E0) ).
tff(thm_2Earithmetic_2EADD__ASSOC,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(V0m_2E0,c_2Earithmetic_2E_2B_2E2(V1n_2E0,V2p_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0),V2p_2E0) ).
tff(thm_2Earithmetic_2ELESS__EQ,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0) = c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2ESUC_2E1(V0m_2E0),V1n_2E0) ).
tff(thm_2Earithmetic_2EZERO__LESS__EQ,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2E0_2E0,V0n_2E0)) ).
tff(thm_2Earithmetic_2ENOT__LESS,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( ~ p(c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0))
<=> p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V0m_2E0)) ) ).
tff(thm_2Earithmetic_2ELESS__EQ__0,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Enum_2E0_2E0))
<=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Earithmetic_2EMULT__CLAUSES,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A_2E2(c_2Enum_2E0_2E0,V0m_2E0) = c_2Enum_2E0_2E0 )
& ( c_2Earithmetic_2E_2A_2E2(V0m_2E0,c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 )
& ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0m_2E0) = V0m_2E0 )
& ( c_2Earithmetic_2E_2A_2E2(V0m_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V0m_2E0 )
& ( c_2Earithmetic_2E_2A_2E2(c_2Enum_2ESUC_2E1(V0m_2E0),V1n_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(V0m_2E0,V1n_2E0),V1n_2E0) )
& ( c_2Earithmetic_2E_2A_2E2(V0m_2E0,c_2Enum_2ESUC_2E1(V1n_2E0)) = c_2Earithmetic_2E_2B_2E2(V0m_2E0,c_2Earithmetic_2E_2A_2E2(V0m_2E0,V1n_2E0)) ) ) ).
tff(thm_2Earithmetic_2ELESS__EQ__TRANS,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V2p_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V2p_2E0)) ) ).
tff(thm_2Earithmetic_2EEQ__LESS__EQ,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( ( V0m_2E0 = V1n_2E0 )
<=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V0m_2E0)) ) ) ).
tff(thm_2Earithmetic_2EADD__MONO__LESS__EQ,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0),c_2Earithmetic_2E_2B_2E2(V0m_2E0,V2p_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V2p_2E0) ).
tff(thm_2Earithmetic_2ENOT__LEQ,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( ~ p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0))
<=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V0m_2E0)) ) ).
tff(thm_2Earithmetic_2ENOT__NUM__EQ,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( ( V0m_2E0 != V1n_2E0 )
<=> ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2ESUC_2E1(V0m_2E0),V1n_2E0))
| p(c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V0m_2E0)) ) ) ).
tff(thm_2Earithmetic_2ESUC__ONE__ADD,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : c_2Enum_2ESUC_2E1(V0n_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0) ).
tff(thm_2Earithmetic_2ESUB__RIGHT__SUB,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2D_2E2(V0m_2E0,V1n_2E0),V2p_2E0) = c_2Earithmetic_2E_2D_2E2(V0m_2E0,c_2Earithmetic_2E_2B_2E2(V1n_2E0,V2p_2E0)) ).
tff(thm_2Earithmetic_2ESUB__LEFT__LESS__EQ,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Earithmetic_2E_2D_2E2(V1n_2E0,V2p_2E0)))
<=> ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0m_2E0,V2p_2E0),V1n_2E0))
| p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Enum_2E0_2E0)) ) ) ).
tff(thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2D_2E2(V0m_2E0,V1n_2E0),V2p_2E0) = c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Earithmetic_2E_2B_2E2(V1n_2E0,V2p_2E0)) ).
tff(thm_2Earithmetic_2ESUB__RIGHT__LESS,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2E_2D_2E2(V0m_2E0,V1n_2E0),V2p_2E0))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(V0m_2E0,c_2Earithmetic_2E_2B_2E2(V1n_2E0,V2p_2E0)))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V2p_2E0)) ) ) ).
tff(thm_2Earithmetic_2ESUB__ELIM__THM,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,c_2Earithmetic_2E_2D_2E2(V1a_2E0,V0b_2E0)))
<=> ! [V3d_2E0: tyop_2Enum_2Enum] :
( ( ( V0b_2E0 = c_2Earithmetic_2E_2B_2E2(V1a_2E0,V3d_2E0) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,c_2Enum_2E0_2E0)) )
& ( ( V1a_2E0 = c_2Earithmetic_2E_2B_2E2(V0b_2E0,V3d_2E0) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,V3d_2E0)) ) ) ) ).
tff(thm_2Ebitstring_2Ev2w__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ! [V0v_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1i_2E0: tyop_2Enum_2Enum] : app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0v_2E0),V1i_2E0) = c_2Ebitstring_2Etestbit_2E2(V1i_2E0,V0v_2E0)
=> ! [V0v_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Ebitstring_2Ev2w_2E1(A_27a,V0v_2E0) = c_2Efcp_2EFCP_2E1(tyop_2Emin_2Ebool,A_27a,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0v_2E0)) ) ).
tff(thm_2Ebitstring_2Ebnot__def,axiom,
c_2Ebitstring_2Ebnot_2E0 = c_2Elist_2EMAP_2E1(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) ).
tff(thm_2Ebitstring_2Elength__fixwidth,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1v_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,c_2Ebitstring_2Efixwidth_2E2(V0n_2E0,V1v_2E0)) = V0n_2E0 ).
tff(thm_2Ebitstring_2Eel__fixwidth,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
( ! [V1n_2E0: tyop_2Enum_2Enum,V2w_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0i_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1n_2E0),V2w_2E0),V0i_2E0))
<=> ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,V2w_2E0)),V0i_2E0))
& p(c_2Elist_2EEL_2E2(tyop_2Emin_2Ebool,c_2Earithmetic_2E_2D_2E2(V0i_2E0,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,V2w_2E0))),V2w_2E0)) ) )
=> ! [V0i_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2w_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0i_2E0,V1n_2E0))
=> ( c_2Elist_2EEL_2E2(tyop_2Emin_2Ebool,V0i_2E0,c_2Ebitstring_2Efixwidth_2E2(V1n_2E0,V2w_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,V2w_2E0),V1n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1n_2E0),V2w_2E0),V0i_2E0),c_2Elist_2EEL_2E2(tyop_2Emin_2Ebool,c_2Earithmetic_2E_2B_2E2(V0i_2E0,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,V2w_2E0),V1n_2E0)),V2w_2E0)) ) ) ) ).
tff(thm_2Ebitstring_2Etestbit,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
( ! [V0b_2E0: tyop_2Enum_2Enum,V1v_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0b_2E0),V1v_2E0),V2n_2E0))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(V0b_2E0,V2n_2E0))
& p(c_2Elist_2EEL_2E2(tyop_2Emin_2Ebool,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0b_2E0),V1v_2E0)) ) )
=> ! [V0b_2E0: tyop_2Enum_2Enum,V1v_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Ebitstring_2Etestbit_2E2(V0b_2E0,V1v_2E0) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0b_2E0),V1v_2E0),c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,V1v_2E0)) ) ).
tff(thm_2Ebool_2ETRUTH,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
=> p(V1t2_2E0) )
=> ( ( p(V1t2_2E0)
=> p(V0t1_2E0) )
=> ( V0t1_2E0 = V1t2_2E0 ) ) ) ).
tff(thm_2Ebool_2EFALSITY,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2EF_2E0)
=> p(V0t_2E0) ) ).
tff(thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( p(V0t_2E0)
| ~ p(V0t_2E0) ) ).
tff(thm_2Ebool_2ELET__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a] : c_2Ebool_2ELET_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) ).
tff(thm_2Ebool_2EFORALL__SIMP,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Ebool] :
( ! [V1x_2E0: A_27a] : p(V0t_2E0)
<=> p(V0t_2E0) ) ).
tff(thm_2Ebool_2ECONJ__ASSOC,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool,V2t3_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
& p(V1t2_2E0)
& p(V2t3_2E0) )
<=> ( p(V0t1_2E0)
& p(V1t2_2E0)
& p(V2t3_2E0) ) ) ).
tff(thm_2Ebool_2EAND__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2ET_2E0)
& p(V0t_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
& p(c_2Ebool_2ET_2E0) )
<=> p(V0t_2E0) )
& ( ( p(c_2Ebool_2EF_2E0)
& p(V0t_2E0) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( p(V0t_2E0)
& p(c_2Ebool_2EF_2E0) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( p(V0t_2E0)
& p(V0t_2E0) )
<=> p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2EOR__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2ET_2E0)
| p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
| p(c_2Ebool_2ET_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(c_2Ebool_2EF_2E0)
| p(V0t_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
| p(c_2Ebool_2EF_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
| p(V0t_2E0) )
<=> p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2ET_2E0)
=> p(V0t_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
=> p(c_2Ebool_2ET_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(c_2Ebool_2EF_2E0)
=> p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
=> p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
=> p(c_2Ebool_2EF_2E0) )
<=> ~ p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t_2E0: tyop_2Emin_2Ebool] :
( ~ ~ p(V0t_2E0)
<=> p(V0t_2E0) )
& ( ~ p(c_2Ebool_2ET_2E0)
<=> p(c_2Ebool_2EF_2E0) )
& ( ~ p(c_2Ebool_2EF_2E0)
<=> p(c_2Ebool_2ET_2E0) ) ) ).
tff(thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] :
( ( V0x_2E0 = V0x_2E0 )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
( ( V0x_2E0 = V1y_2E0 )
<=> ( V1y_2E0 = V0x_2E0 ) ) ).
tff(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = V0t_2E0 )
<=> p(V0t_2E0) )
& ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
<=> p(V0t_2E0) )
& ( ( c_2Ebool_2EF_2E0 = V0t_2E0 )
<=> ~ p(V0t_2E0) )
& ( ( V0t_2E0 = c_2Ebool_2EF_2E0 )
<=> ~ p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2ECOND__ID,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Ebool,V1t_2E0: A_27a] : c_2Ebool_2ECOND_2E3(A_27a,V0b_2E0,V1t_2E0,V1t_2E0) = V1t_2E0 ).
tff(thm_2Ebool_2EDISJ__ASSOC,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool,V2C_2E0: tyop_2Emin_2Ebool] :
( ( p(V0A_2E0)
| p(V1B_2E0)
| p(V2C_2E0) )
<=> ( p(V0A_2E0)
| p(V1B_2E0)
| p(V2C_2E0) ) ) ).
tff(thm_2Ebool_2EDE__MORGAN__THM,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool] :
( ( ~ ( p(V0A_2E0)
& p(V1B_2E0) )
<=> ( ~ p(V0A_2E0)
| ~ p(V1B_2E0) ) )
& ( ~ ( p(V0A_2E0)
| p(V1B_2E0) )
<=> ( ~ p(V0A_2E0)
& ~ p(V1B_2E0) ) ) ) ).
tff(thm_2Ebool_2EIMP__DISJ__THM,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool] :
( ( p(V0A_2E0)
=> p(V1B_2E0) )
<=> ( ~ p(V0A_2E0)
| p(V1B_2E0) ) ) ).
tff(thm_2Ebool_2EIMP__F__EQ__F,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
=> p(c_2Ebool_2EF_2E0) )
<=> ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Ebool_2EAND__IMP__INTRO,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool,V2t3_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
=> ( p(V1t2_2E0)
=> p(V2t3_2E0) ) )
<=> ( ( p(V0t1_2E0)
& p(V1t2_2E0) )
=> p(V2t3_2E0) ) ) ).
tff(thm_2Ebool_2EEQ__EXPAND,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( ( V0t1_2E0 = V1t2_2E0 )
<=> ( ( p(V0t1_2E0)
& p(V1t2_2E0) )
| ( ~ p(V0t1_2E0)
& ~ p(V1t2_2E0) ) ) ) ).
tff(thm_2Ebool_2EIMP__CONG,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool,V1x_27_2E0: tyop_2Emin_2Ebool,V2y_2E0: tyop_2Emin_2Ebool,V3y_27_2E0: tyop_2Emin_2Ebool] :
( ( ( V0x_2E0 = V1x_27_2E0 )
& ( p(V1x_27_2E0)
=> ( V2y_2E0 = V3y_27_2E0 ) ) )
=> ( ( p(V0x_2E0)
=> p(V2y_2E0) )
<=> ( p(V1x_27_2E0)
=> p(V3y_27_2E0) ) ) ) ).
tff(thm_2Ebool_2ECOND__CONG,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool,V2x_2E0: A_27a,V3x_27_2E0: A_27a,V4y_2E0: A_27a,V5y_27_2E0: A_27a] :
( ( ( V0P_2E0 = V1Q_2E0 )
& ( p(V1Q_2E0)
=> ( V2x_2E0 = V3x_27_2E0 ) )
& ( ~ p(V1Q_2E0)
=> ( V4y_2E0 = V5y_27_2E0 ) ) )
=> ( c_2Ebool_2ECOND_2E3(A_27a,V0P_2E0,V2x_2E0,V4y_2E0) = c_2Ebool_2ECOND_2E3(A_27a,V1Q_2E0,V3x_27_2E0,V5y_27_2E0) ) ) ).
tff(thm_2Ebool_2Ebool__case__thm,axiom,
! [A_27a: $tType] :
( ! [V0t1_2E0: A_27a,V1t2_2E0: A_27a] : c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2ET_2E0,V0t1_2E0,V1t2_2E0) = V0t1_2E0
& ! [V2t1_2E0: A_27a,V3t2_2E0: A_27a] : c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2EF_2E0,V2t1_2E0,V3t2_2E0) = V3t2_2E0 ) ).
tff(thm_2Ecombin_2EI__THM,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : c_2Ecombin_2EI_2E1(A_27a,V0x_2E0) = V0x_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_2Elist_2ELENGTH__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : c_2Elist_2ELENGTH_2E1(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V1f_2E0,V0l_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) ).
tff(thm_2Elist_2EEL__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : c_2Elist_2EEL_2E2(A_27b,V0n_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V2f_2E0,V1l_2E0)) = app_2E2(A_27a,A_27b,V2f_2E0,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ).
tff(thm_2Enumeral_2Enumeral__distrib,axiom,
( ! [V0n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(c_2Enum_2E0_2E0,V0n_2E0) = V0n_2E0
& ! [V1n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(V1n_2E0,c_2Enum_2E0_2E0) = V1n_2E0
& ! [V2n_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(V2n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V3m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V2n_2E0,V3m_2E0)))
& ! [V4n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2A_2E2(c_2Enum_2E0_2E0,V4n_2E0) = c_2Enum_2E0_2E0
& ! [V5n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2A_2E2(V5n_2E0,c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0
& ! [V6n_2E0: tyop_2Enum_2Enum,V7m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(V6n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V7m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2E_2A_2E2(V6n_2E0,V7m_2E0))
& ! [V8n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_2E2(c_2Enum_2E0_2E0,V8n_2E0) = c_2Enum_2E0_2E0
& ! [V9n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_2E2(V9n_2E0,c_2Enum_2E0_2E0) = V9n_2E0
& ! [V10n_2E0: tyop_2Enum_2Enum,V11m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V10n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V11m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2E_2D_2E2(V10n_2E0,V11m_2E0))
& ! [V12n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V12n_2E0))) = c_2Enum_2E0_2E0
& ! [V13n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V13n_2E0))) = c_2Enum_2E0_2E0
& ! [V14n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(V14n_2E0,c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))
& ! [V15n_2E0: tyop_2Enum_2Enum,V16m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(V15n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V16m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EEXP_2E2(V15n_2E0,V16m_2E0))
& ( c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V17n_2E0: tyop_2Enum_2Enum] : c_2Enum_2ESUC_2E1(c_2Earithmetic_2ENUMERAL_2E1(V17n_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enum_2ESUC_2E1(V17n_2E0))
& ( c_2Eprim__rec_2EPRE_2E1(c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 )
& ! [V18n_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2ENUMERAL_2E1(V18n_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Eprim__rec_2EPRE_2E1(V18n_2E0))
& ! [V19n_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2ENUMERAL_2E1(V19n_2E0) = c_2Enum_2E0_2E0 )
<=> ( V19n_2E0 = c_2Earithmetic_2EZERO_2E0 ) )
& ! [V20n_2E0: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0_2E0 = c_2Earithmetic_2ENUMERAL_2E1(V20n_2E0) )
<=> ( V20n_2E0 = c_2Earithmetic_2EZERO_2E0 ) )
& ! [V21n_2E0: tyop_2Enum_2Enum,V22m_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2ENUMERAL_2E1(V21n_2E0) = c_2Earithmetic_2ENUMERAL_2E1(V22m_2E0) )
<=> ( V21n_2E0 = V22m_2E0 ) )
& ! [V23n_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(V23n_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0
& ! [V24n_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(V24n_2E0)) = c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,V24n_2E0)
& ! [V25n_2E0: tyop_2Enum_2Enum,V26m_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(V25n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V26m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V25n_2E0,V26m_2E0)
& ! [V27n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_2E2(c_2Enum_2E0_2E0,V27n_2E0) = c_2Ebool_2EF_2E0
& ! [V28n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_2E2(c_2Earithmetic_2ENUMERAL_2E1(V28n_2E0),c_2Enum_2E0_2E0) = c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,V28n_2E0)
& ! [V29n_2E0: tyop_2Enum_2Enum,V30m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_2E2(c_2Earithmetic_2ENUMERAL_2E1(V29n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V30m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V30m_2E0,V29n_2E0)
& ! [V31n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2E0_2E0,V31n_2E0) = c_2Ebool_2ET_2E0
& ! [V32n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V32n_2E0),c_2Enum_2E0_2E0) = c_2Earithmetic_2E_3C_3D_2E2(V32n_2E0,c_2Earithmetic_2EZERO_2E0)
& ! [V33n_2E0: tyop_2Enum_2Enum,V34m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V33n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V34m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V33n_2E0,V34m_2E0)
& ! [V35n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_3D_2E2(V35n_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2ET_2E0
& ! [V36n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3E_3D_2E2(c_2Enum_2E0_2E0,V36n_2E0))
<=> ( V36n_2E0 = c_2Enum_2E0_2E0 ) )
& ! [V37n_2E0: tyop_2Enum_2Enum,V38m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V37n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V38m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V38m_2E0,V37n_2E0)
& ! [V39n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EODD_2E1(c_2Earithmetic_2ENUMERAL_2E1(V39n_2E0)) = c_2Earithmetic_2EODD_2E1(V39n_2E0)
& ! [V40n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEVEN_2E1(c_2Earithmetic_2ENUMERAL_2E1(V40n_2E0)) = c_2Earithmetic_2EEVEN_2E1(V40n_2E0)
& ~ p(c_2Earithmetic_2EODD_2E1(c_2Enum_2E0_2E0))
& p(c_2Earithmetic_2EEVEN_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2Enumeral_2Enumeral__add,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0)) = V0n_2E0 )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0)) = V0n_2E0 )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0)) = c_2Enum_2ESUC_2E1(V0n_2E0) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0)) = c_2Enum_2ESUC_2E1(V0n_2E0) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0)) = c_2Enumeral_2EiiSUC_2E1(V0n_2E0) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0)) = c_2Enumeral_2EiiSUC_2E1(V0n_2E0) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) ) ) ).
tff(thm_2Enumeral_2Enumeral__lte,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0) = c_2Ebool_2ET_2E0 )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EZERO_2E0) = c_2Ebool_2EF_2E0 )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EZERO_2E0) = c_2Ebool_2EF_2E0 )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0) )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0) )
& ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0)))
<=> ~ p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V0n_2E0)) )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0) ) ) ).
tff(thm_2Esat_2ENOT__NOT,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ~ ~ p(V0t_2E0)
<=> p(V0t_2E0) ) ).
tff(thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool] :
( p(V0A_2E0)
=> ( ~ p(V0A_2E0)
=> p(c_2Ebool_2EF_2E0) ) ) ).
tff(thm_2Esat_2EOR__DUAL2,axiom,
! [V0B_2E0: tyop_2Emin_2Ebool,V1A_2E0: tyop_2Emin_2Ebool] :
( ( ~ ( p(V1A_2E0)
| p(V0B_2E0) )
=> p(c_2Ebool_2EF_2E0) )
<=> ( ( p(V1A_2E0)
=> p(c_2Ebool_2EF_2E0) )
=> ( ~ p(V0B_2E0)
=> p(c_2Ebool_2EF_2E0) ) ) ) ).
tff(thm_2Esat_2EOR__DUAL3,axiom,
! [V0B_2E0: tyop_2Emin_2Ebool,V1A_2E0: tyop_2Emin_2Ebool] :
( ( ~ ( ~ p(V1A_2E0)
| p(V0B_2E0) )
=> p(c_2Ebool_2EF_2E0) )
<=> ( p(V1A_2E0)
=> ( ~ p(V0B_2E0)
=> p(c_2Ebool_2EF_2E0) ) ) ) ).
tff(thm_2Esat_2EAND__INV2,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V0A_2E0)
=> p(c_2Ebool_2EF_2E0) )
=> ( ( p(V0A_2E0)
=> p(c_2Ebool_2EF_2E0) )
=> p(c_2Ebool_2EF_2E0) ) ) ).
tff(thm_2Esat_2Edc__eq,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( V1q_2E0 = V0r_2E0 ) )
<=> ( ( p(V2p_2E0)
| p(V1q_2E0)
| p(V0r_2E0) )
& ( p(V2p_2E0)
| ~ p(V0r_2E0)
| ~ p(V1q_2E0) )
& ( p(V1q_2E0)
| ~ p(V0r_2E0)
| ~ p(V2p_2E0) )
& ( p(V0r_2E0)
| ~ p(V1q_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__conj,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( p(V1q_2E0)
& p(V0r_2E0) ) )
<=> ( ( p(V2p_2E0)
| ~ p(V1q_2E0)
| ~ p(V0r_2E0) )
& ( p(V1q_2E0)
| ~ p(V2p_2E0) )
& ( p(V0r_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__disj,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( p(V1q_2E0)
| p(V0r_2E0) ) )
<=> ( ( p(V2p_2E0)
| ~ p(V1q_2E0) )
& ( p(V2p_2E0)
| ~ p(V0r_2E0) )
& ( p(V1q_2E0)
| p(V0r_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__neg,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
<=> ~ p(V0q_2E0) )
<=> ( ( p(V1p_2E0)
| p(V0q_2E0) )
& ( ~ p(V0q_2E0)
| ~ p(V1p_2E0) ) ) ) ).
tff(thm_2Ewords_2Eword__1comp__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ! [V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1i_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0w_2E0),V1i_2E0))
<=> ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,A_27a,V0w_2E0,V1i_2E0)) )
=> ! [V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__1comp_2E1(A_27a,V0w_2E0) = c_2Efcp_2EFCP_2E1(tyop_2Emin_2Ebool,A_27a,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0w_2E0)) ) ).
tff(thm_2Ewords_2EDIMINDEX__GT__0,axiom,
! [A_27a: $tType] : p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ).
tff(thm_2Ebitstring_2Eword__1comp__v2w,conjecture,
! [A_27a: $tType,V0v_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : c_2Ewords_2Eword__1comp_2E1(A_27a,c_2Ebitstring_2Ev2w_2E1(A_27a,V0v_2E0)) = c_2Ebitstring_2Ev2w_2E1(A_27a,c_2Ebitstring_2Ebnot_2E1(c_2Ebitstring_2Efixwidth_2E2(c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V0v_2E0))) ).
%------------------------------------------------------------------------------