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 : 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 ) ) ).
%------------------------------------------------------------------------------