ITP001 Axioms: ITP059^7.ax


%------------------------------------------------------------------------------
% File     : ITP059^7 : TPTP v9.0.0. 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    :  114 (  28 unt;  70 typ;   0 def)
%            Number of atoms       :  155 (  76 equ;   1 cnn)
%            Maximal formula atoms :   22 (   1 avg)
%            Number of connectives : 2024 (   1   ~;   1   |;  78   &;1922   @)
%                                         (  11 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   34 (   6 avg;1922 nst)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  132 ( 132   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   69 (  67 usr;   3 con; 0-6 aty)
%            Number of variables   :   99 (   9   ^  61   !;   1   ?;  99   :)
%                                         (  28  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_SAT_EQU_NAR

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

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

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: $tType > $tType > $tType ).

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

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

thf(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: $tType > $tType > $tType ).

thf(tyop_2Estring_2Echar,type,
    tyop_2Estring_2Echar: $tType ).

thf(c_2Ebool_2E_21,type,
    c_2Ebool_2E_21: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Epair_2E_2C,type,
    c_2Epair_2E_2C: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).

thf(c_2Earithmetic_2E_2D,type,
    c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Ebool_2E_2F_5C,type,
    c_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(c_2Enum_2E0,type,
    c_2Enum_2E0: tyop_2Enum_2Enum ).

thf(c_2Eprim__rec_2E_3C,type,
    c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Emin_2E_3D,type,
    c_2Emin_2E_3D: 
      !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).

thf(c_2Emin_2E_3D_3D_3E,type,
    c_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(c_2Earithmetic_2E_3E,type,
    c_2Earithmetic_2E_3E: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Ebool_2E_3F,type,
    c_2Ebool_2E_3F: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Emin_2E_40,type,
    c_2Emin_2E_40: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).

thf(c_2Elist_2EAPPEND,type,
    c_2Elist_2EAPPEND: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Ebool_2EARB,type,
    c_2Ebool_2EARB: 
      !>[A_27a: $tType] : A_27a ).

thf(c_2Ebit_2EBIT,type,
    c_2Ebit_2EBIT: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2EBIT1,type,
    c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EBIT2,type,
    c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Ebit_2EBITV,type,
    c_2Ebit_2EBITV: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Estring_2ECHR,type,
    c_2Estring_2ECHR: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).

thf(c_2Ebool_2ECOND,type,
    c_2Ebool_2ECOND: 
      !>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).

thf(c_2Elist_2ECONS,type,
    c_2Elist_2ECONS: 
      !>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Elist_2EEVERY,type,
    c_2Elist_2EEVERY: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).

thf(c_2Estring_2EEXPLODE,type,
    c_2Estring_2EEXPLODE: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2EASCIInumbers_2EHEX,type,
    c_2EASCIInumbers_2EHEX: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).

thf(c_2Ecombin_2EI,type,
    c_2Ecombin_2EI: 
      !>[A_27a: $tType] : ( A_27a > A_27a ) ).

thf(c_2Estring_2EIMPLODE,type,
    c_2Estring_2EIMPLODE: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2Erich__list_2ELASTN,type,
    c_2Erich__list_2ELASTN: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Elist_2ELENGTH,type,
    c_2Elist_2ELENGTH: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > tyop_2Enum_2Enum ) ).

thf(c_2Elogroot_2ELOG,type,
    c_2Elogroot_2ELOG: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Elist_2EMAP,type,
    c_2Elist_2EMAP: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27b ) ) ).

thf(c_2Elist_2ENIL,type,
    c_2Elist_2ENIL: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).

thf(c_2Eoption_2ENONE,type,
    c_2Eoption_2ENONE: 
      !>[A_27a: $tType] : ( tyop_2Eoption_2Eoption @ A_27a ) ).

thf(c_2Earithmetic_2ENUMERAL,type,
    c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Eprim__rec_2EPRE,type,
    c_2Eprim__rec_2EPRE: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Elist_2EREVERSE,type,
    c_2Elist_2EREVERSE: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Eoption_2ESOME,type,
    c_2Eoption_2ESOME: 
      !>[A_27a: $tType] : ( A_27a > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).

thf(c_2Estring_2ESUB,type,
    c_2Estring_2ESUB: ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Enum_2Enum ) > tyop_2Estring_2Echar ).

thf(c_2Enum_2ESUC,type,
    c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2EASCIInumbers_2EUNHEX,type,
    c_2EASCIInumbers_2EUNHEX: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).

thf(c_2Erelation_2EWF,type,
    c_2Erelation_2EWF: 
      !>[A_27a: $tType] : ( ( A_27a > A_27a > $o ) > $o ) ).

thf(c_2Erelation_2EWFREC,type,
    c_2Erelation_2EWFREC: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27a > $o ) > ( ( A_27a > A_27b ) > A_27a > A_27b ) > A_27a > A_27b ) ).

thf(c_2Earithmetic_2EZERO,type,
    c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).

thf(c_2Ebool_2E_5C_2F,type,
    c_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(c_2EASCIInumbers_2EfromBinString,type,
    c_2EASCIInumbers_2EfromBinString: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ).

thf(c_2EASCIInumbers_2EfromDecString,type,
    c_2EASCIInumbers_2EfromDecString: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ).

thf(c_2EASCIInumbers_2EfromHexString,type,
    c_2EASCIInumbers_2EfromHexString: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ).

thf(c_2Estring_2EisDigit,type,
    c_2Estring_2EisDigit: tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2EisHexDigit,type,
    c_2Estring_2EisHexDigit: tyop_2Estring_2Echar > $o ).

thf(c_2Enumposrep_2El2n,type,
    c_2Enumposrep_2El2n: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

thf(c_2Ebool_2Eliteral__case,type,
    c_2Ebool_2Eliteral__case: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > A_27a > A_27b ) ).

thf(c_2Enumposrep_2En2l,type,
    c_2Enumposrep_2En2l: tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ).

thf(c_2EASCIInumbers_2En2s,type,
    c_2EASCIInumbers_2En2s: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > tyop_2Estring_2Echar ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2EASCIInumbers_2Enum__from__bin__string,type,
    c_2EASCIInumbers_2Enum__from__bin__string: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Enum_2Enum ).

thf(c_2EASCIInumbers_2Enum__from__dec__string,type,
    c_2EASCIInumbers_2Enum__from__dec__string: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Enum_2Enum ).

thf(c_2EASCIInumbers_2Enum__from__hex__string,type,
    c_2EASCIInumbers_2Enum__from__hex__string: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Enum_2Enum ).

thf(c_2EASCIInumbers_2Enum__from__oct__string,type,
    c_2EASCIInumbers_2Enum__from__oct__string: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Enum_2Enum ).

thf(c_2EASCIInumbers_2Enum__to__bin__string,type,
    c_2EASCIInumbers_2Enum__to__bin__string: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2EASCIInumbers_2Enum__to__dec__string,type,
    c_2EASCIInumbers_2Enum__to__dec__string: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2EASCIInumbers_2Enum__to__hex__string,type,
    c_2EASCIInumbers_2Enum__to__hex__string: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2EASCIInumbers_2Enum__to__oct__string,type,
    c_2EASCIInumbers_2Enum__to__oct__string: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2Ecombin_2Eo,type,
    c_2Ecombin_2Eo: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27c > A_27b ) > ( A_27a > A_27c ) > A_27a > A_27b ) ).

thf(c_2EASCIInumbers_2Es2n,type,
    c_2EASCIInumbers_2Es2n: tyop_2Enum_2Enum > ( tyop_2Estring_2Echar > tyop_2Enum_2Enum ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Enum_2Enum ).

thf(c_2Estring_2EtoUpper,type,
    c_2Estring_2EtoUpper: tyop_2Estring_2Echar > tyop_2Estring_2Echar ).

thf(c_2Ebool_2E_7E,type,
    c_2Ebool_2E_7E: $o > $o ).

thf(logicdef_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(logicdef_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(logicdef_2E_7E,axiom,
    ! [V0: $o] :
      ( ( c_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(logicdef_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

thf(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
      ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
    <=> ( V0 = V1 ) ) ).

thf(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
    <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
    <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(thm_2EASCIInumbers_2Es2n__def,axiom,
    ! [V0b: tyop_2Enum_2Enum,V1f: tyop_2Estring_2Echar > tyop_2Enum_2Enum,V2s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2EASCIInumbers_2Es2n @ V0b @ V1f @ V2s )
      = ( c_2Enumposrep_2El2n @ V0b @ ( c_2Elist_2EMAP @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum @ V1f @ ( c_2Elist_2EREVERSE @ tyop_2Estring_2Echar @ V2s ) ) ) ) ).

thf(thm_2EASCIInumbers_2En2s__def,axiom,
    ! [V0b: tyop_2Enum_2Enum,V1f: tyop_2Enum_2Enum > tyop_2Estring_2Echar,V2n: tyop_2Enum_2Enum] :
      ( ( c_2EASCIInumbers_2En2s @ V0b @ V1f @ V2n )
      = ( c_2Elist_2EREVERSE @ tyop_2Estring_2Echar @ ( c_2Elist_2EMAP @ tyop_2Enum_2Enum @ tyop_2Estring_2Echar @ V1f @ ( c_2Enumposrep_2En2l @ V0b @ V2n ) ) ) ) ).

thf(thm_2EASCIInumbers_2EHEX__primitive__def,axiom,
    ( c_2EASCIInumbers_2EHEX
    = ( c_2Erelation_2EWFREC @ tyop_2Enum_2Enum @ tyop_2Estring_2Echar
      @ ( c_2Emin_2E_40 @ ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o )
        @ ^ [V0R: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o] : ( c_2Erelation_2EWF @ tyop_2Enum_2Enum @ V0R ) )
      @ ^ [V1HEX: tyop_2Enum_2Enum > tyop_2Estring_2Echar,V2a: tyop_2Enum_2Enum] :
          ( c_2Ebool_2Eliteral__case @ tyop_2Enum_2Enum @ tyop_2Estring_2Echar
          @ ^ [V3v: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ c_2Enum_2E0 ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3v @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ebool_2EARB @ tyop_2Estring_2Echar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ V2a ) ) ) ).

thf(thm_2EASCIInumbers_2EUNHEX__primitive__def,axiom,
    ( c_2EASCIInumbers_2EUNHEX
    = ( c_2Erelation_2EWFREC @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum
      @ ( c_2Emin_2E_40 @ ( tyop_2Estring_2Echar > tyop_2Estring_2Echar > $o )
        @ ^ [V0R: tyop_2Estring_2Echar > tyop_2Estring_2Echar > $o] : ( c_2Erelation_2EWF @ tyop_2Estring_2Echar @ V0R ) )
      @ ^ [V1UNHEX: tyop_2Estring_2Echar > tyop_2Enum_2Enum,V2a: tyop_2Estring_2Echar] :
          ( c_2Ebool_2Eliteral__case @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum
          @ ^ [V3v: tyop_2Estring_2Echar] : ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ c_2Enum_2E0 ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V3v @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ebool_2EARB @ tyop_2Enum_2Enum ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ V2a ) ) ) ).

thf(thm_2EASCIInumbers_2Enum__from__bin__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__from__bin__string
    = ( c_2EASCIInumbers_2Es2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).

thf(thm_2EASCIInumbers_2Enum__from__oct__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__from__oct__string
    = ( c_2EASCIInumbers_2Es2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).

thf(thm_2EASCIInumbers_2Enum__from__dec__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__from__dec__string
    = ( c_2EASCIInumbers_2Es2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).

thf(thm_2EASCIInumbers_2Enum__from__hex__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__from__hex__string
    = ( c_2EASCIInumbers_2Es2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).

thf(thm_2EASCIInumbers_2Enum__to__bin__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__to__bin__string
    = ( c_2EASCIInumbers_2En2s @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ c_2EASCIInumbers_2EHEX ) ) ).

thf(thm_2EASCIInumbers_2Enum__to__oct__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__to__oct__string
    = ( c_2EASCIInumbers_2En2s @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).

thf(thm_2EASCIInumbers_2Enum__to__dec__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__to__dec__string
    = ( c_2EASCIInumbers_2En2s @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).

thf(thm_2EASCIInumbers_2Enum__to__hex__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__to__hex__string
    = ( c_2EASCIInumbers_2En2s @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).

thf(thm_2EASCIInumbers_2EfromBinString__def,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2EASCIInumbers_2EfromBinString @ V0s )
      = ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum )
        @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V0s @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) )
          @ ( c_2Elist_2EEVERY @ tyop_2Estring_2Echar
            @ ^ [V1c: tyop_2Estring_2Echar] : ( c_2Ebool_2E_5C_2F @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V1c @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V1c @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
            @ V0s ) )
        @ ( c_2Eoption_2ESOME @ tyop_2Enum_2Enum @ ( c_2EASCIInumbers_2Enum__from__bin__string @ V0s ) )
        @ ( c_2Eoption_2ENONE @ tyop_2Enum_2Enum ) ) ) ).

thf(thm_2EASCIInumbers_2EfromDecString__def,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2EASCIInumbers_2EfromDecString @ V0s )
      = ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V0s @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) ) @ ( c_2Elist_2EEVERY @ tyop_2Estring_2Echar @ c_2Estring_2EisDigit @ V0s ) ) @ ( c_2Eoption_2ESOME @ tyop_2Enum_2Enum @ ( c_2EASCIInumbers_2Enum__from__dec__string @ V0s ) ) @ ( c_2Eoption_2ENONE @ tyop_2Enum_2Enum ) ) ) ).

thf(thm_2EASCIInumbers_2EfromHexString__def,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2EASCIInumbers_2EfromHexString @ V0s )
      = ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V0s @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) ) @ ( c_2Elist_2EEVERY @ tyop_2Estring_2Echar @ c_2Estring_2EisHexDigit @ V0s ) ) @ ( c_2Eoption_2ESOME @ tyop_2Enum_2Enum @ ( c_2EASCIInumbers_2Enum__from__hex__string @ V0s ) ) @ ( c_2Eoption_2ENONE @ tyop_2Enum_2Enum ) ) ) ).

thf(thm_2EASCIInumbers_2EHEX__ind,axiom,
    ! [V0P: tyop_2Enum_2Enum > $o] :
      ( ( ( V0P @ c_2Enum_2E0 )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( V0P @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
        & ! [V1v18: tyop_2Enum_2Enum] : ( V0P @ V1v18 ) )
     => ! [V2v: tyop_2Enum_2Enum] : ( V0P @ V2v ) ) ).

thf(thm_2EASCIInumbers_2EHEX__def,axiom,
    ( ( ( c_2EASCIInumbers_2EHEX @ c_2Enum_2E0 )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EHEX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
      = ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2EASCIInumbers_2EUNHEX__ind,axiom,
    ! [V0P: tyop_2Estring_2Echar > $o] :
      ( ( ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ( V0P @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        & ! [V1v24: tyop_2Estring_2Echar] : ( V0P @ V1v24 ) )
     => ! [V2v: tyop_2Estring_2Echar] : ( V0P @ V2v ) ) ).

thf(thm_2EASCIInumbers_2EUNHEX__def,axiom,
    ( ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = c_2Enum_2E0 )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(thm_2EASCIInumbers_2Es2n__compute,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1f: tyop_2Estring_2Echar > tyop_2Enum_2Enum,V2b: tyop_2Enum_2Enum] :
      ( ( c_2EASCIInumbers_2Es2n @ V2b @ V1f @ V0s )
      = ( c_2Enumposrep_2El2n @ V2b @ ( c_2Elist_2EMAP @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum @ V1f @ ( c_2Elist_2EREVERSE @ tyop_2Estring_2Echar @ ( c_2Estring_2EEXPLODE @ V0s ) ) ) ) ) ).

thf(thm_2EASCIInumbers_2En2s__compute,axiom,
    ! [V0n: tyop_2Enum_2Enum,V1f: tyop_2Enum_2Enum > tyop_2Estring_2Echar,V2b: tyop_2Enum_2Enum] :
      ( ( c_2EASCIInumbers_2En2s @ V2b @ V1f @ V0n )
      = ( c_2Estring_2EIMPLODE @ ( c_2Elist_2EREVERSE @ tyop_2Estring_2Echar @ ( c_2Elist_2EMAP @ tyop_2Enum_2Enum @ tyop_2Estring_2Echar @ V1f @ ( c_2Enumposrep_2En2l @ V2b @ V0n ) ) ) ) ) ).

thf(thm_2EASCIInumbers_2EUNHEX__HEX,axiom,
    ! [V0n: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
     => ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2EASCIInumbers_2EHEX @ V0n ) )
        = V0n ) ) ).

thf(thm_2EASCIInumbers_2EHEX__UNHEX,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisHexDigit @ V0c )
     => ( ( c_2EASCIInumbers_2EHEX @ ( c_2EASCIInumbers_2EUNHEX @ V0c ) )
        = ( c_2Estring_2EtoUpper @ V0c ) ) ) ).

thf(thm_2EASCIInumbers_2EDEC__UNDEC,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisDigit @ V0c )
     => ( ( c_2EASCIInumbers_2EHEX @ ( c_2EASCIInumbers_2EUNHEX @ V0c ) )
        = V0c ) ) ).

thf(thm_2EASCIInumbers_2Es2n__n2s,axiom,
    ! [V0c2n: tyop_2Estring_2Echar > tyop_2Enum_2Enum,V1n2c: tyop_2Enum_2Enum > tyop_2Estring_2Echar,V2b: tyop_2Enum_2Enum,V3n: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V2b )
        & ! [V4x: tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ V4x @ V2b )
           => ( ( V0c2n @ ( V1n2c @ V4x ) )
              = V4x ) ) )
     => ( ( c_2EASCIInumbers_2Es2n @ V2b @ V0c2n @ ( c_2EASCIInumbers_2En2s @ V2b @ V1n2c @ V3n ) )
        = V3n ) ) ).

thf(thm_2EASCIInumbers_2En2s__s2n,axiom,
    ! [V0c2n: tyop_2Estring_2Echar > tyop_2Enum_2Enum,V1n2c: tyop_2Enum_2Enum > tyop_2Estring_2Echar,V2b: tyop_2Enum_2Enum,V3s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V2b )
        & ( c_2Elist_2EEVERY @ tyop_2Estring_2Echar @ ( c_2Ecombin_2Eo @ tyop_2Estring_2Echar @ $o @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_3E @ V2b ) @ V0c2n ) @ V3s ) )
     => ( ( c_2EASCIInumbers_2En2s @ V2b @ V1n2c @ ( c_2EASCIInumbers_2Es2n @ V2b @ V0c2n @ V3s ) )
        = ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2EASCIInumbers_2Es2n @ V2b @ V0c2n @ V3s ) @ c_2Enum_2E0 ) @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ ( V1n2c @ c_2Enum_2E0 ) @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) @ ( c_2Elist_2EMAP @ tyop_2Estring_2Echar @ tyop_2Estring_2Echar @ ( c_2Ecombin_2Eo @ tyop_2Estring_2Echar @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum @ V1n2c @ V0c2n ) @ ( c_2Erich__list_2ELASTN @ tyop_2Estring_2Echar @ ( c_2Enum_2ESUC @ ( c_2Elogroot_2ELOG @ V2b @ ( c_2EASCIInumbers_2Es2n @ V2b @ V0c2n @ V3s ) ) ) @ V3s ) ) ) ) ) ).

thf(thm_2EASCIInumbers_2EtoNum__toString,axiom,
    ! [V0n: tyop_2Enum_2Enum] :
      ( ( c_2EASCIInumbers_2Enum__from__dec__string @ ( c_2EASCIInumbers_2Enum__to__dec__string @ V0n ) )
      = V0n ) ).

thf(thm_2EASCIInumbers_2EtoString__toNum__cancel,axiom,
    ! [V0n: tyop_2Enum_2Enum] :
      ( ( c_2EASCIInumbers_2Enum__from__dec__string @ ( c_2EASCIInumbers_2Enum__to__dec__string @ V0n ) )
      = V0n ) ).

thf(thm_2EASCIInumbers_2EtoString__inj,axiom,
    ! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
      ( ( ( c_2EASCIInumbers_2Enum__to__dec__string @ V0n )
        = ( c_2EASCIInumbers_2Enum__to__dec__string @ V1m ) )
    <=> ( V0n = V1m ) ) ).

thf(thm_2EASCIInumbers_2EtoString__11,axiom,
    ! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
      ( ( ( c_2EASCIInumbers_2Enum__to__dec__string @ V0n )
        = ( c_2EASCIInumbers_2Enum__to__dec__string @ V1m ) )
    <=> ( V0n = V1m ) ) ).

thf(thm_2EASCIInumbers_2ESTRCAT__toString__inj,axiom,
    ! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V2s @ ( c_2EASCIInumbers_2Enum__to__dec__string @ V0n ) )
        = ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V2s @ ( c_2EASCIInumbers_2Enum__to__dec__string @ V1m ) ) )
    <=> ( V0n = V1m ) ) ).

thf(thm_2EASCIInumbers_2EBIT__num__from__bin__string,axiom,
    ! [V0x: tyop_2Enum_2Enum,V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Elist_2EEVERY @ tyop_2Estring_2Echar @ ( c_2Ecombin_2Eo @ tyop_2Estring_2Echar @ $o @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_3E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ c_2EASCIInumbers_2EUNHEX ) @ V1s )
        & ( c_2Eprim__rec_2E_3C @ V0x @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V1s ) ) )
     => ( ( c_2Ebit_2EBIT @ V0x @ ( c_2EASCIInumbers_2Enum__from__bin__string @ V1s ) )
      <=> ( ( c_2EASCIInumbers_2EUNHEX @ ( c_2Estring_2ESUB @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Enum_2Enum @ V1s @ ( c_2Eprim__rec_2EPRE @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V1s ) @ V0x ) ) ) ) )
          = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2EASCIInumbers_2ESUB__num__to__bin__string,axiom,
    ! [V0x: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0x @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ ( c_2EASCIInumbers_2Enum__to__bin__string @ V1n ) ) )
     => ( ( c_2Estring_2ESUB @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Enum_2Enum @ ( c_2EASCIInumbers_2Enum__to__bin__string @ V1n ) @ V0x ) )
        = ( c_2EASCIInumbers_2EHEX @ ( c_2Ebit_2EBITV @ V1n @ ( c_2Eprim__rec_2EPRE @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ ( c_2EASCIInumbers_2Enum__to__bin__string @ V1n ) ) @ V0x ) ) ) ) ) ) ).

thf(thm_2EASCIInumbers_2Enum__bin__string,axiom,
    ( ( c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ c_2EASCIInumbers_2Enum__from__bin__string @ c_2EASCIInumbers_2Enum__to__bin__string )
    = ( c_2Ecombin_2EI @ tyop_2Enum_2Enum ) ) ).

thf(thm_2EASCIInumbers_2Enum__oct__string,axiom,
    ( ( c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ c_2EASCIInumbers_2Enum__from__oct__string @ c_2EASCIInumbers_2Enum__to__oct__string )
    = ( c_2Ecombin_2EI @ tyop_2Enum_2Enum ) ) ).

thf(thm_2EASCIInumbers_2Enum__dec__string,axiom,
    ( ( c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ c_2EASCIInumbers_2Enum__from__dec__string @ c_2EASCIInumbers_2Enum__to__dec__string )
    = ( c_2Ecombin_2EI @ tyop_2Enum_2Enum ) ) ).

thf(thm_2EASCIInumbers_2Enum__hex__string,axiom,
    ( ( c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ c_2EASCIInumbers_2Enum__from__hex__string @ c_2EASCIInumbers_2Enum__to__hex__string )
    = ( c_2Ecombin_2EI @ tyop_2Enum_2Enum ) ) ).

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