ITP001 Axioms: ITP059

ITP001 Axioms: ITP059_7.ax

%------------------------------------------------------------------------------
% File     : ITP059_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    : ASCIInumbers.ax [Gau19]
%          : HL4059_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  255 (  87 unt; 134 typ;   0 def)
%            Number of atoms       :  330 ( 199 equ)
%            Maximal formula atoms :   48 (   1 avg)
%            Number of connectives :  215 (   6   ~;   4   |;  82   &)
%                                         (  60 <=>;  63  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   52 (   4 avg)
%            Maximal term depth    :   29 (   3 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   94 (  63   >;  31   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  130 ( 130 usr;  43 con; 0-5 aty)
%            Number of variables   :  357 ( 295   !;   1   ?; 357   :)
%                                         (  61  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: $tType > $tType ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: $tType ).

tff(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: $tType > $tType ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

tff(tyop_2Estring_2Echar,type,
    tyop_2Estring_2Echar: $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_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_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_2E1,type,
    c_2Earithmetic_2E_3E_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(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_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_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Ebool_2EARB_2E0,type,
    c_2Ebool_2EARB_2E0: 
      !>[A_27a: $tType] : A_27a ).

tff(c_2Ebit_2EBIT_2E0,type,
    c_2Ebit_2EBIT_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Ebit_2EBIT_2E2,type,
    c_2Ebit_2EBIT_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > 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_2Ebit_2EBITV_2E0,type,
    c_2Ebit_2EBITV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Ebit_2EBITV_2E2,type,
    c_2Ebit_2EBITV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Estring_2ECHR_2E0,type,
    c_2Estring_2ECHR_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar) ).

tff(c_2Estring_2ECHR_2E1,type,
    c_2Estring_2ECHR_2E1: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EEVERY_2E0,type,
    c_2Elist_2EEVERY_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2EEVERY_2E2,type,
    c_2Elist_2EEVERY_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Estring_2EEXPLODE_2E0,type,
    c_2Estring_2EEXPLODE_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).

tff(c_2Estring_2EEXPLODE_2E1,type,
    c_2Estring_2EEXPLODE_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2EASCIInumbers_2EHEX_2E0,type,
    c_2EASCIInumbers_2EHEX_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar) ).

tff(c_2EASCIInumbers_2EHEX_2E1,type,
    c_2EASCIInumbers_2EHEX_2E1: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).

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_2Estring_2EIMPLODE_2E0,type,
    c_2Estring_2EIMPLODE_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).

tff(c_2Estring_2EIMPLODE_2E1,type,
    c_2Estring_2EIMPLODE_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).

tff(c_2Erich__list_2ELASTN_2E0,type,
    c_2Erich__list_2ELASTN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Erich__list_2ELASTN_2E2,type,
    c_2Erich__list_2ELASTN_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(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_2Elogroot_2ELOG_2E0,type,
    c_2Elogroot_2ELOG_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Elogroot_2ELOG_2E2,type,
    c_2Elogroot_2ELOG_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).

tff(c_2Elist_2EMAP_2E2,type,
    c_2Elist_2EMAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: 
      !>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: 
      !>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_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_2Elist_2EREVERSE_2E0,type,
    c_2Elist_2EREVERSE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).

tff(c_2Elist_2EREVERSE_2E1,type,
    c_2Elist_2EREVERSE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).

tff(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Estring_2ESUB_2E0,type,
    c_2Estring_2ESUB_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),tyop_2Estring_2Echar) ).

tff(c_2Estring_2ESUB_2E1,type,
    c_2Estring_2ESUB_2E1: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum) > tyop_2Estring_2Echar ).

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_2EASCIInumbers_2EUNHEX_2E0,type,
    c_2EASCIInumbers_2EUNHEX_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum) ).

tff(c_2EASCIInumbers_2EUNHEX_2E1,type,
    c_2EASCIInumbers_2EUNHEX_2E1: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).

tff(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Erelation_2EWFREC_2E0,type,
    c_2Erelation_2EWFREC_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Erelation_2EWFREC_2E2,type,
    c_2Erelation_2EWFREC_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

tff(c_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_2EASCIInumbers_2EfromBinString_2E0,type,
    c_2EASCIInumbers_2EfromBinString_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)) ).

tff(c_2EASCIInumbers_2EfromBinString_2E1,type,
    c_2EASCIInumbers_2EfromBinString_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Eoption_2Eoption(tyop_2Enum_2Enum) ).

tff(c_2EASCIInumbers_2EfromDecString_2E0,type,
    c_2EASCIInumbers_2EfromDecString_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)) ).

tff(c_2EASCIInumbers_2EfromDecString_2E1,type,
    c_2EASCIInumbers_2EfromDecString_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Eoption_2Eoption(tyop_2Enum_2Enum) ).

tff(c_2EASCIInumbers_2EfromHexString_2E0,type,
    c_2EASCIInumbers_2EfromHexString_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)) ).

tff(c_2EASCIInumbers_2EfromHexString_2E1,type,
    c_2EASCIInumbers_2EfromHexString_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Eoption_2Eoption(tyop_2Enum_2Enum) ).

tff(c_2Estring_2EisDigit_2E0,type,
    c_2Estring_2EisDigit_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool) ).

tff(c_2Estring_2EisDigit_2E1,type,
    c_2Estring_2EisDigit_2E1: tyop_2Estring_2Echar > tyop_2Emin_2Ebool ).

tff(c_2Estring_2EisHexDigit_2E0,type,
    c_2Estring_2EisHexDigit_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool) ).

tff(c_2Estring_2EisHexDigit_2E1,type,
    c_2Estring_2EisHexDigit_2E1: tyop_2Estring_2Echar > tyop_2Emin_2Ebool ).

tff(c_2Enumposrep_2El2n_2E0,type,
    c_2Enumposrep_2El2n_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum)) ).

tff(c_2Enumposrep_2El2n_2E2,type,
    c_2Enumposrep_2El2n_2E2: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Enum_2Enum) ) > tyop_2Enum_2Enum ).

tff(c_2Ebool_2Eliteral__case_2E0,type,
    c_2Ebool_2Eliteral__case_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_2Eliteral__case_2E2,type,
    c_2Ebool_2Eliteral__case_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(c_2Enumposrep_2En2l_2E0,type,
    c_2Enumposrep_2En2l_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))) ).

tff(c_2Enumposrep_2En2l_2E2,type,
    c_2Enumposrep_2En2l_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Elist_2Elist(tyop_2Enum_2Enum) ).

tff(c_2EASCIInumbers_2En2s_2E0,type,
    c_2EASCIInumbers_2En2s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))) ).

tff(c_2EASCIInumbers_2En2s_2E2,type,
    c_2EASCIInumbers_2En2s_2E2: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).

tff(c_2EASCIInumbers_2En2s_2E3,type,
    c_2EASCIInumbers_2En2s_2E3: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar) * tyop_2Enum_2Enum ) > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).

tff(c_2EASCIInumbers_2Enum__from__bin__string_2E0,type,
    c_2EASCIInumbers_2Enum__from__bin__string_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum) ).

tff(c_2EASCIInumbers_2Enum__from__bin__string_2E1,type,
    c_2EASCIInumbers_2Enum__from__bin__string_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Enum_2Enum ).

tff(c_2EASCIInumbers_2Enum__from__dec__string_2E0,type,
    c_2EASCIInumbers_2Enum__from__dec__string_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum) ).

tff(c_2EASCIInumbers_2Enum__from__dec__string_2E1,type,
    c_2EASCIInumbers_2Enum__from__dec__string_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Enum_2Enum ).

tff(c_2EASCIInumbers_2Enum__from__hex__string_2E0,type,
    c_2EASCIInumbers_2Enum__from__hex__string_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum) ).

tff(c_2EASCIInumbers_2Enum__from__hex__string_2E1,type,
    c_2EASCIInumbers_2Enum__from__hex__string_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Enum_2Enum ).

tff(c_2EASCIInumbers_2Enum__from__oct__string_2E0,type,
    c_2EASCIInumbers_2Enum__from__oct__string_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum) ).

tff(c_2EASCIInumbers_2Enum__to__bin__string_2E0,type,
    c_2EASCIInumbers_2Enum__to__bin__string_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).

tff(c_2EASCIInumbers_2Enum__to__bin__string_2E1,type,
    c_2EASCIInumbers_2Enum__to__bin__string_2E1: tyop_2Enum_2Enum > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).

tff(c_2EASCIInumbers_2Enum__to__dec__string_2E0,type,
    c_2EASCIInumbers_2Enum__to__dec__string_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).

tff(c_2EASCIInumbers_2Enum__to__dec__string_2E1,type,
    c_2EASCIInumbers_2Enum__to__dec__string_2E1: tyop_2Enum_2Enum > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).

tff(c_2EASCIInumbers_2Enum__to__hex__string_2E0,type,
    c_2EASCIInumbers_2Enum__to__hex__string_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).

tff(c_2EASCIInumbers_2Enum__to__oct__string_2E0,type,
    c_2EASCIInumbers_2Enum__to__oct__string_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

tff(c_2EASCIInumbers_2Es2n_2E0,type,
    c_2EASCIInumbers_2Es2n_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum))) ).

tff(c_2EASCIInumbers_2Es2n_2E2,type,
    c_2EASCIInumbers_2Es2n_2E2: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum) ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum) ).

tff(c_2EASCIInumbers_2Es2n_2E3,type,
    c_2EASCIInumbers_2Es2n_2E3: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum) * tyop_2Elist_2Elist(tyop_2Estring_2Echar) ) > tyop_2Enum_2Enum ).

tff(c_2Estring_2EtoUpper_2E0,type,
    c_2Estring_2EtoUpper_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar) ).

tff(c_2Estring_2EtoUpper_2E1,type,
    c_2Estring_2EtoUpper_2E1: tyop_2Estring_2Echar > tyop_2Estring_2Echar ).

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_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
      ( ( X0_2E0 = X1_2E0 )
    <=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Earithmetic_2E_3E_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_2E0,X0_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_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Elist_2EAPPEND_2E2(tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2EAPPEND_2E0(tyop_2Estring_2Echar),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebit_2EBIT_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT_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_2Ebit_2EBIT_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(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(arityeq2_2Ec_2Ebit_2EBITV_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBITV_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_2Ebit_2EBITV_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Estring_2ECHR_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Estring_2ECHR_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,c_2Estring_2ECHR_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Estring_2Echar,X2_2E0: tyop_2Estring_2Echar] : ( c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2Estring_2Echar,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar)),c_2Ebool_2ECOND_2E0(tyop_2Estring_2Echar),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),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_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Estring_2Echar,X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ECONS_2E0(tyop_2Estring_2Echar),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Elist_2EEVERY_2E2(tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(tyop_2Estring_2Echar),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Estring_2EEXPLODE_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Estring_2EEXPLODE_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EASCIInumbers_2EHEX_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2EHEX_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,c_2EASCIInumbers_2EHEX_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Estring_2Echar] : ( c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2Estring_2Echar,c_2Ecombin_2EI_2E0(tyop_2Estring_2Echar),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Estring_2EIMPLODE_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Estring_2EIMPLODE_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EIMPLODE_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Erich__list_2ELASTN_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Erich__list_2ELASTN_2E2(tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Erich__list_2ELASTN_2E0(tyop_2Estring_2Echar),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Elist_2ELENGTH_2E1(tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Estring_2Echar),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elogroot_2ELOG_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Elogroot_2ELOG_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_2Elogroot_2ELOG_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Elist_2EMAP_2E2(tyop_2Estring_2Echar,tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2EMAP_2E0(tyop_2Estring_2Echar,tyop_2Estring_2Echar),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Elist_2EMAP_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2EMAP_2E0(tyop_2Enum_2Enum,tyop_2Estring_2Echar),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_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_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Elist_2EREVERSE_2E1(tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EREVERSE_2E0(tyop_2Estring_2Echar),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Estring_2ESUB_2E1,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum)] : ( c_2Estring_2ESUB_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),tyop_2Estring_2Echar,c_2Estring_2ESUB_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EASCIInumbers_2EUNHEX_2E1,axiom,
    ! [X0_2E0: tyop_2Estring_2Echar] : ( c_2EASCIInumbers_2EUNHEX_2E1(X0_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,c_2EASCIInumbers_2EUNHEX_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Estring_2Echar,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Estring_2Echar),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum)),c_2Erelation_2EWFREC_2E0(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar)),c_2Erelation_2EWFREC_2E0(tyop_2Enum_2Enum,tyop_2Estring_2Echar),X0_2E0),X1_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_2EASCIInumbers_2EfromBinString_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2EfromBinString_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2EASCIInumbers_2EfromBinString_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EASCIInumbers_2EfromDecString_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2EfromDecString_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2EASCIInumbers_2EfromDecString_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EASCIInumbers_2EfromHexString_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2EfromHexString_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2EASCIInumbers_2EfromHexString_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Estring_2EisDigit_2E1,axiom,
    ! [X0_2E0: tyop_2Estring_2Echar] : ( c_2Estring_2EisDigit_2E1(X0_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,c_2Estring_2EisDigit_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Estring_2EisHexDigit_2E1,axiom,
    ! [X0_2E0: tyop_2Estring_2Echar] : ( c_2Estring_2EisHexDigit_2E1(X0_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,c_2Estring_2EisHexDigit_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Enumposrep_2El2n_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Enumposrep_2El2n_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Enumposrep_2El2n_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X1_2E0: tyop_2Estring_2Echar] : ( c_2Ebool_2Eliteral__case_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Ebool_2Eliteral__case_2E0(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2Eliteral__case_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),c_2Ebool_2Eliteral__case_2E0(tyop_2Enum_2Enum,tyop_2Estring_2Echar),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Enumposrep_2En2l_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Enumposrep_2En2l_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Enumposrep_2En2l_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EASCIInumbers_2En2s_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2En2s_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2EASCIInumbers_2En2s_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EASCIInumbers_2En2s_2E3,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),X2_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2En2s_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2EASCIInumbers_2En2s_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EASCIInumbers_2Enum__from__bin__string_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2Enum__from__bin__string_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__bin__string_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EASCIInumbers_2Enum__from__dec__string_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2Enum__from__dec__string_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EASCIInumbers_2Enum__from__hex__string_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2Enum__from__hex__string_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__hex__string_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EASCIInumbers_2Enum__to__bin__string_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2Enum__to__bin__string_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__to__bin__string_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EASCIInumbers_2Enum__to__dec__string_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2Enum__to__dec__string_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__to__dec__string_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar))] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E0(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),X1_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Estring_2Echar,tyop_2Estring_2Echar,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Estring_2Echar)),c_2Ecombin_2Eo_2E0(tyop_2Estring_2Echar,tyop_2Estring_2Echar,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EASCIInumbers_2Es2n_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum)] : ( c_2EASCIInumbers_2Es2n_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum)),c_2EASCIInumbers_2Es2n_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EASCIInumbers_2Es2n_2E3,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X2_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2Es2n_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum)),c_2EASCIInumbers_2Es2n_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Estring_2EtoUpper_2E1,axiom,
    ! [X0_2E0: tyop_2Estring_2Echar] : ( c_2Estring_2EtoUpper_2E1(X0_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2Estring_2Echar,c_2Estring_2EtoUpper_2E0,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_2EASCIInumbers_2Es2n__def,axiom,
    ! [V0b_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),V2s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2Es2n_2E3(V0b_2E0,V1f_2E0,V2s_2E0) = c_2Enumposrep_2El2n_2E2(V0b_2E0,c_2Elist_2EMAP_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,V1f_2E0,c_2Elist_2EREVERSE_2E1(tyop_2Estring_2Echar,V2s_2E0))) ) ).

tff(thm_2EASCIInumbers_2En2s__def,axiom,
    ! [V0b_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),V2n_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2En2s_2E3(V0b_2E0,V1f_2E0,V2n_2E0) = c_2Elist_2EREVERSE_2E1(tyop_2Estring_2Echar,c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,V1f_2E0,c_2Enumposrep_2En2l_2E2(V0b_2E0,V2n_2E0))) ) ).

tff(thm_2EASCIInumbers_2EHEX__primitive__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F17_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F13_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F9_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F15_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F11_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F7_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F5_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F16_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F12_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F8_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F14_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F18_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F10_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F6_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F4_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar))] :
      ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0) = c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,V0R_2E0) )
     => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F17_2E0,V3v_2E0))
          <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
       => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F13_2E0,V3v_2E0))
            <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
         => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F9_2E0,V3v_2E0))
              <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) ) )
           => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                  ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F15_2E0,V3v_2E0))
                <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
             => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                    ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F11_2E0,V3v_2E0))
                  <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
               => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                      ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F7_2E0,V3v_2E0))
                    <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) )
                 => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                        ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F5_2E0,V3v_2E0))
                      <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)) ) )
                   => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F16_2E0,V3v_2E0))
                        <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
                     => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F12_2E0,V3v_2E0))
                          <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
                       => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F8_2E0,V3v_2E0))
                            <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) ) )
                         => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F14_2E0,V3v_2E0))
                              <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
                           => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                                  ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F18_2E0,V3v_2E0))
                                <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) )
                             => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                                    ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F10_2E0,V3v_2E0))
                                  <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
                               => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                                      ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F6_2E0,V3v_2E0))
                                    <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) )
                                 => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                                        ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F4_2E0,V3v_2E0))
                                      <=> ( V3v_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) )
                                   => ( ! [V3v_2E0: tyop_2Enum_2Enum] :
                                          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V3v_2E0))
                                        <=> ( V3v_2E0 = c_2Enum_2E0_2E0 ) )
                                     => ( ! [V3v_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,F2_2E0,V3v_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F4_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F5_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F6_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F7_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F8_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F9_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F10_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F11_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F12_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F13_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F14_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F15_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F16_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F17_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Ebool_2ECOND_2E3(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F18_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Ebool_2EARB_2E0(tyop_2Estring_2Echar))))))))))))))))) )
                                       => ( ! [V1HEX_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),V2a_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),F1_2E0,V1HEX_2E0),V2a_2E0) = c_2Ebool_2Eliteral__case_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,F2_2E0,V2a_2E0) )
                                         => ( c_2EASCIInumbers_2EHEX_2E0 = c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2EASCIInumbers_2EUNHEX__primitive__def,axiom,
    ! [F9_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F18_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F24_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F5_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F14_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F20_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F7_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F16_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F22_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F11_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F3_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F8_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F17_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F23_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F12_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F4_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F13_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F19_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F6_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F15_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F21_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F10_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
      ( ! [V3v_2E0: tyop_2Estring_2Echar] :
          ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F9_2E0,V3v_2E0))
        <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
     => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
            ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F18_2E0,V3v_2E0))
          <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
       => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
              ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F24_2E0,V3v_2E0))
            <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
         => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F5_2E0,V3v_2E0))
              <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
           => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                  ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F14_2E0,V3v_2E0))
                <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
             => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                    ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F20_2E0,V3v_2E0))
                  <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
               => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                      ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F7_2E0,V3v_2E0))
                    <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
                 => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                        ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F16_2E0,V3v_2E0))
                      <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
                   => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                          ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F22_2E0,V3v_2E0))
                        <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
                     => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                            ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F11_2E0,V3v_2E0))
                          <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
                       => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                              ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F3_2E0,V3v_2E0))
                            <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
                         => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F8_2E0,V3v_2E0))
                              <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
                           => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                  ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F17_2E0,V3v_2E0))
                                <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
                             => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                    ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F23_2E0,V3v_2E0))
                                  <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
                               => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                      ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F12_2E0,V3v_2E0))
                                    <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
                                 => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                        ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F4_2E0,V3v_2E0))
                                      <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
                                   => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                          ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F13_2E0,V3v_2E0))
                                        <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
                                     => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                            ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F19_2E0,V3v_2E0))
                                          <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
                                       => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                              ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F6_2E0,V3v_2E0))
                                            <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
                                         => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                                ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F15_2E0,V3v_2E0))
                                              <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
                                           => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                                  ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F21_2E0,V3v_2E0))
                                                <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
                                             => ( ! [V3v_2E0: tyop_2Estring_2Echar] :
                                                    ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F10_2E0,V3v_2E0))
                                                  <=> ( V3v_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
                                               => ( ! [V3v_2E0: tyop_2Estring_2Echar] : ( app_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,F2_2E0,V3v_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F3_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F4_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F5_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F6_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F7_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F8_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F9_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F10_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F11_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F12_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F13_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F14_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F15_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F16_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F17_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F18_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F19_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F20_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F21_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F22_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F23_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F24_2E0,V3v_2E0),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))),c_2Ebool_2EARB_2E0(tyop_2Enum_2Enum))))))))))))))))))))))) )
                                                 => ( ! [V1UNHEX_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),V2a_2E0: tyop_2Estring_2Echar] : ( app_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),F1_2E0,V1UNHEX_2E0),V2a_2E0) = c_2Ebool_2Eliteral__case_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,F2_2E0,V2a_2E0) )
                                                   => ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0) = c_2Erelation_2EWF_2E1(tyop_2Estring_2Echar,V0R_2E0) )
                                                     => ( c_2EASCIInumbers_2EUNHEX_2E0 = c_2Erelation_2EWFREC_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

tff(thm_2EASCIInumbers_2Enum__from__bin__string__def,axiom,
    c_2EASCIInumbers_2Enum__from__bin__string_2E0 = c_2EASCIInumbers_2Es2n_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2EASCIInumbers_2EUNHEX_2E0) ).

tff(thm_2EASCIInumbers_2Enum__from__oct__string__def,axiom,
    c_2EASCIInumbers_2Enum__from__oct__string_2E0 = c_2EASCIInumbers_2Es2n_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2EASCIInumbers_2EUNHEX_2E0) ).

tff(thm_2EASCIInumbers_2Enum__from__dec__string__def,axiom,
    c_2EASCIInumbers_2Enum__from__dec__string_2E0 = c_2EASCIInumbers_2Es2n_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2EASCIInumbers_2EUNHEX_2E0) ).

tff(thm_2EASCIInumbers_2Enum__from__hex__string__def,axiom,
    c_2EASCIInumbers_2Enum__from__hex__string_2E0 = c_2EASCIInumbers_2Es2n_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2EASCIInumbers_2EUNHEX_2E0) ).

tff(thm_2EASCIInumbers_2Enum__to__bin__string__def,axiom,
    c_2EASCIInumbers_2Enum__to__bin__string_2E0 = c_2EASCIInumbers_2En2s_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2EASCIInumbers_2EHEX_2E0) ).

tff(thm_2EASCIInumbers_2Enum__to__oct__string__def,axiom,
    c_2EASCIInumbers_2Enum__to__oct__string_2E0 = c_2EASCIInumbers_2En2s_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2EASCIInumbers_2EHEX_2E0) ).

tff(thm_2EASCIInumbers_2Enum__to__dec__string__def,axiom,
    c_2EASCIInumbers_2Enum__to__dec__string_2E0 = c_2EASCIInumbers_2En2s_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2EASCIInumbers_2EHEX_2E0) ).

tff(thm_2EASCIInumbers_2Enum__to__hex__string__def,axiom,
    c_2EASCIInumbers_2Enum__to__hex__string_2E0 = c_2EASCIInumbers_2En2s_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2EASCIInumbers_2EHEX_2E0) ).

tff(thm_2EASCIInumbers_2EfromBinString__def,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)] :
      ( ! [V1c_2E0: tyop_2Estring_2Echar] :
          ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F1_2E0,V1c_2E0))
        <=> ( ( V1c_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
            | ( V1c_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) ) )
     => ( ! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0))
          <=> ( ( V0s_2E0 != c_2Elist_2ENIL_2E0(tyop_2Estring_2Echar) )
              & p(c_2Elist_2EEVERY_2E2(tyop_2Estring_2Echar,F1_2E0,V0s_2E0)) ) )
       => ! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2EfromBinString_2E1(V0s_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__bin__string_2E1(V0s_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) ) ) ) ).

tff(thm_2EASCIInumbers_2EfromDecString__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)] :
      ( ! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
          ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0))
        <=> ( ( V0s_2E0 != c_2Elist_2ENIL_2E0(tyop_2Estring_2Echar) )
            & p(c_2Elist_2EEVERY_2E2(tyop_2Estring_2Echar,c_2Estring_2EisDigit_2E0,V0s_2E0)) ) )
     => ! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2EfromDecString_2E1(V0s_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(V0s_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) ) ) ).

tff(thm_2EASCIInumbers_2EfromHexString__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)] :
      ( ! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
          ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0))
        <=> ( ( V0s_2E0 != c_2Elist_2ENIL_2E0(tyop_2Estring_2Echar) )
            & p(c_2Elist_2EEVERY_2E2(tyop_2Estring_2Echar,c_2Estring_2EisHexDigit_2E0,V0s_2E0)) ) )
     => ! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2EfromHexString_2E1(V0s_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__hex__string_2E1(V0s_2E0)),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) ) ) ).

tff(thm_2EASCIInumbers_2EHEX__ind,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Enum_2E0_2E0))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
        & ! [V1v18_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V1v18_2E0)) )
     => ! [V2v_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V2v_2E0)) ) ).

tff(thm_2EASCIInumbers_2EHEX__def,axiom,
    ( ( c_2EASCIInumbers_2EHEX_2E1(c_2Enum_2E0_2E0) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) )
    & ( c_2EASCIInumbers_2EHEX_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) ) ).

tff(thm_2EASCIInumbers_2EUNHEX__ind,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))))
        & ! [V1v24_2E0: tyop_2Estring_2Echar] : p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,V1v24_2E0)) )
     => ! [V2v_2E0: tyop_2Estring_2Echar] : p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,V0P_2E0,V2v_2E0)) ) ).

tff(thm_2EASCIInumbers_2EUNHEX__def,axiom,
    ( ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Enum_2E0_2E0 )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
    & ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) ).

tff(thm_2EASCIInumbers_2Es2n__compute,axiom,
    ! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1f_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),V2b_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2Es2n_2E3(V2b_2E0,V1f_2E0,V0s_2E0) = c_2Enumposrep_2El2n_2E2(V2b_2E0,c_2Elist_2EMAP_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,V1f_2E0,c_2Elist_2EREVERSE_2E1(tyop_2Estring_2Echar,c_2Estring_2EEXPLODE_2E1(V0s_2E0)))) ) ).

tff(thm_2EASCIInumbers_2En2s__compute,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),V2b_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2En2s_2E3(V2b_2E0,V1f_2E0,V0n_2E0) = c_2Estring_2EIMPLODE_2E1(c_2Elist_2EREVERSE_2E1(tyop_2Estring_2Echar,c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,V1f_2E0,c_2Enumposrep_2En2l_2E2(V2b_2E0,V0n_2E0)))) ) ).

tff(thm_2EASCIInumbers_2EUNHEX__HEX,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
     => ( c_2EASCIInumbers_2EUNHEX_2E1(c_2EASCIInumbers_2EHEX_2E1(V0n_2E0)) = V0n_2E0 ) ) ).

tff(thm_2EASCIInumbers_2EHEX__UNHEX,axiom,
    ! [V0c_2E0: tyop_2Estring_2Echar] :
      ( p(c_2Estring_2EisHexDigit_2E1(V0c_2E0))
     => ( c_2EASCIInumbers_2EHEX_2E1(c_2EASCIInumbers_2EUNHEX_2E1(V0c_2E0)) = c_2Estring_2EtoUpper_2E1(V0c_2E0) ) ) ).

tff(thm_2EASCIInumbers_2EDEC__UNDEC,axiom,
    ! [V0c_2E0: tyop_2Estring_2Echar] :
      ( p(c_2Estring_2EisDigit_2E1(V0c_2E0))
     => ( c_2EASCIInumbers_2EHEX_2E1(c_2EASCIInumbers_2EUNHEX_2E1(V0c_2E0)) = V0c_2E0 ) ) ).

tff(thm_2EASCIInumbers_2Es2n__n2s,axiom,
    ! [V0c2n_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),V1n2c_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),V2b_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V2b_2E0))
        & ! [V4x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V4x_2E0,V2b_2E0))
           => ( app_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,V0c2n_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,V1n2c_2E0,V4x_2E0)) = V4x_2E0 ) ) )
     => ( c_2EASCIInumbers_2Es2n_2E3(V2b_2E0,V0c2n_2E0,c_2EASCIInumbers_2En2s_2E3(V2b_2E0,V1n2c_2E0,V3n_2E0)) = V3n_2E0 ) ) ).

tff(thm_2EASCIInumbers_2En2s__s2n,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)))] :
      ( ! [V2b_2E0: tyop_2Enum_2Enum,V0c2n_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),V3s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
          ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),F0_2E0,V2b_2E0),V0c2n_2E0),V3s_2E0))
        <=> ( c_2EASCIInumbers_2Es2n_2E3(V2b_2E0,V0c2n_2E0,V3s_2E0) = c_2Enum_2E0_2E0 ) )
     => ! [V0c2n_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),V1n2c_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),V2b_2E0: tyop_2Enum_2Enum,V3s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
          ( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V2b_2E0))
            & p(c_2Elist_2EEVERY_2E2(tyop_2Estring_2Echar,c_2Ecombin_2Eo_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,tyop_2Enum_2Enum,c_2Earithmetic_2E_3E_2E1(V2b_2E0),V0c2n_2E0),V3s_2E0)) )
         => ( c_2EASCIInumbers_2En2s_2E3(V2b_2E0,V1n2c_2E0,c_2EASCIInumbers_2Es2n_2E3(V2b_2E0,V0c2n_2E0,V3s_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),F0_2E0,V2b_2E0),V0c2n_2E0),V3s_2E0),c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,V1n2c_2E0,c_2Enum_2E0_2E0),c_2Elist_2ENIL_2E0(tyop_2Estring_2Echar)),c_2Elist_2EMAP_2E2(tyop_2Estring_2Echar,tyop_2Estring_2Echar,c_2Ecombin_2Eo_2E2(tyop_2Estring_2Echar,tyop_2Estring_2Echar,tyop_2Enum_2Enum,V1n2c_2E0,V0c2n_2E0),c_2Erich__list_2ELASTN_2E2(tyop_2Estring_2Echar,c_2Enum_2ESUC_2E1(c_2Elogroot_2ELOG_2E2(V2b_2E0,c_2EASCIInumbers_2Es2n_2E3(V2b_2E0,V0c2n_2E0,V3s_2E0))),V3s_2E0))) ) ) ) ).

tff(thm_2EASCIInumbers_2EtoNum__toString,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2Enum__from__dec__string_2E1(c_2EASCIInumbers_2Enum__to__dec__string_2E1(V0n_2E0)) = V0n_2E0 ) ).

tff(thm_2EASCIInumbers_2EtoString__toNum__cancel,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2Enum__from__dec__string_2E1(c_2EASCIInumbers_2Enum__to__dec__string_2E1(V0n_2E0)) = V0n_2E0 ) ).

tff(thm_2EASCIInumbers_2EtoString__inj,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
      ( ( c_2EASCIInumbers_2Enum__to__dec__string_2E1(V0n_2E0) = c_2EASCIInumbers_2Enum__to__dec__string_2E1(V1m_2E0) )
    <=> ( V0n_2E0 = V1m_2E0 ) ) ).

tff(thm_2EASCIInumbers_2EtoString__11,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
      ( ( c_2EASCIInumbers_2Enum__to__dec__string_2E1(V0n_2E0) = c_2EASCIInumbers_2Enum__to__dec__string_2E1(V1m_2E0) )
    <=> ( V0n_2E0 = V1m_2E0 ) ) ).

tff(thm_2EASCIInumbers_2ESTRCAT__toString__inj,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
      ( ( c_2Elist_2EAPPEND_2E2(tyop_2Estring_2Echar,V2s_2E0,c_2EASCIInumbers_2Enum__to__dec__string_2E1(V0n_2E0)) = c_2Elist_2EAPPEND_2E2(tyop_2Estring_2Echar,V2s_2E0,c_2EASCIInumbers_2Enum__to__dec__string_2E1(V1m_2E0)) )
    <=> ( V0n_2E0 = V1m_2E0 ) ) ).

tff(thm_2EASCIInumbers_2EBIT__num__from__bin__string,axiom,
    ! [V0x_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
      ( ( p(c_2Elist_2EEVERY_2E2(tyop_2Estring_2Echar,c_2Ecombin_2Eo_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,tyop_2Enum_2Enum,c_2Earithmetic_2E_3E_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2EASCIInumbers_2EUNHEX_2E0),V1s_2E0))
        & p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Estring_2Echar,V1s_2E0))) )
     => ( p(c_2Ebit_2EBIT_2E2(V0x_2E0,c_2EASCIInumbers_2Enum__from__bin__string_2E1(V1s_2E0)))
      <=> ( c_2EASCIInumbers_2EUNHEX_2E1(c_2Estring_2ESUB_2E1(c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,V1s_2E0,c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(tyop_2Estring_2Echar,V1s_2E0),V0x_2E0))))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ) ).

tff(thm_2EASCIInumbers_2ESUB__num__to__bin__string,axiom,
    ! [V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Estring_2Echar,c_2EASCIInumbers_2Enum__to__bin__string_2E1(V1n_2E0))))
     => ( c_2Estring_2ESUB_2E1(c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__to__bin__string_2E1(V1n_2E0),V0x_2E0)) = c_2EASCIInumbers_2EHEX_2E1(c_2Ebit_2EBITV_2E2(V1n_2E0,c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(tyop_2Estring_2Echar,c_2EASCIInumbers_2Enum__to__bin__string_2E1(V1n_2E0)),V0x_2E0)))) ) ) ).

tff(thm_2EASCIInumbers_2Enum__bin__string,axiom,
    c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__from__bin__string_2E0,c_2EASCIInumbers_2Enum__to__bin__string_2E0) = c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum) ).

tff(thm_2EASCIInumbers_2Enum__oct__string,axiom,
    c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__from__oct__string_2E0,c_2EASCIInumbers_2Enum__to__oct__string_2E0) = c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum) ).

tff(thm_2EASCIInumbers_2Enum__dec__string,axiom,
    c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__from__dec__string_2E0,c_2EASCIInumbers_2Enum__to__dec__string_2E0) = c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum) ).

tff(thm_2EASCIInumbers_2Enum__hex__string,axiom,
    c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__from__hex__string_2E0,c_2EASCIInumbers_2Enum__to__hex__string_2E0) = c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum) ).

%------------------------------------------------------------------------------