ITP001 Axioms: ITP059^5.ax


%------------------------------------------------------------------------------
% File     : ITP059^5 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : ASCIInumbers^2.ax [Gau20]
%          : HL4059^5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   79 (  25 unt;  21 typ;   0 def)
%            Number of atoms       : 4098 (  81 equ;   0 cnn)
%            Maximal formula atoms :  430 (  51 avg)
%            Number of connectives : 4239 (   0   ~;   0   |;  77   &;4138   @)
%                                         (   4 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   37 (   6 avg;4138 nst)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   87 (  86 usr;  80 con; 0-2 aty)
%            Number of variables   :   61 (   9   ^  52   !;   0   ?;  61   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2EASCIInumbers_2EHEX,type,
    c_2EASCIInumbers_2EHEX: $i ).

thf(mem_c_2EASCIInumbers_2EHEX,axiom,
    mem @ c_2EASCIInumbers_2EHEX @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) ).

thf(stp_fo_c_2EASCIInumbers_2EHEX,type,
    fo__c_2EASCIInumbers_2EHEX: tp__ty_2Enum_2Enum > tp__ty_2Estring_2Echar ).

thf(stp_eq_fo_c_2EASCIInumbers_2EHEX,axiom,
    ! [X0: tp__ty_2Enum_2Enum] :
      ( ( inj__ty_2Estring_2Echar @ ( fo__c_2EASCIInumbers_2EHEX @ X0 ) )
      = ( ap @ c_2EASCIInumbers_2EHEX @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).

thf(tp_c_2EASCIInumbers_2EUNHEX,type,
    c_2EASCIInumbers_2EUNHEX: $i ).

thf(mem_c_2EASCIInumbers_2EUNHEX,axiom,
    mem @ c_2EASCIInumbers_2EUNHEX @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2EASCIInumbers_2EUNHEX,type,
    fo__c_2EASCIInumbers_2EUNHEX: tp__ty_2Estring_2Echar > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2EASCIInumbers_2EUNHEX,axiom,
    ! [X0: tp__ty_2Estring_2Echar] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2EASCIInumbers_2EUNHEX @ X0 ) )
      = ( ap @ c_2EASCIInumbers_2EUNHEX @ ( inj__ty_2Estring_2Echar @ X0 ) ) ) ).

thf(tp_c_2EASCIInumbers_2EfromBinString,type,
    c_2EASCIInumbers_2EfromBinString: $i ).

thf(mem_c_2EASCIInumbers_2EfromBinString,axiom,
    mem @ c_2EASCIInumbers_2EfromBinString @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) ).

thf(tp_c_2EASCIInumbers_2EfromDecString,type,
    c_2EASCIInumbers_2EfromDecString: $i ).

thf(mem_c_2EASCIInumbers_2EfromDecString,axiom,
    mem @ c_2EASCIInumbers_2EfromDecString @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) ).

thf(tp_c_2EASCIInumbers_2EfromHexString,type,
    c_2EASCIInumbers_2EfromHexString: $i ).

thf(mem_c_2EASCIInumbers_2EfromHexString,axiom,
    mem @ c_2EASCIInumbers_2EfromHexString @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) ).

thf(tp_c_2EASCIInumbers_2En2s,type,
    c_2EASCIInumbers_2En2s: $i ).

thf(mem_c_2EASCIInumbers_2En2s,axiom,
    mem @ c_2EASCIInumbers_2En2s @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ) ).

thf(tp_c_2EASCIInumbers_2Enum__from__bin__string,type,
    c_2EASCIInumbers_2Enum__from__bin__string: $i ).

thf(mem_c_2EASCIInumbers_2Enum__from__bin__string,axiom,
    mem @ c_2EASCIInumbers_2Enum__from__bin__string @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2EASCIInumbers_2Enum__from__bin__string,type,
    fo__c_2EASCIInumbers_2Enum__from__bin__string: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2EASCIInumbers_2Enum__from__bin__string,axiom,
    ! [X0: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2EASCIInumbers_2Enum__from__bin__string @ X0 ) )
      = ( ap @ c_2EASCIInumbers_2Enum__from__bin__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ X0 ) ) ) ).

thf(tp_c_2EASCIInumbers_2Enum__from__dec__string,type,
    c_2EASCIInumbers_2Enum__from__dec__string: $i ).

thf(mem_c_2EASCIInumbers_2Enum__from__dec__string,axiom,
    mem @ c_2EASCIInumbers_2Enum__from__dec__string @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2EASCIInumbers_2Enum__from__dec__string,type,
    fo__c_2EASCIInumbers_2Enum__from__dec__string: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2EASCIInumbers_2Enum__from__dec__string,axiom,
    ! [X0: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2EASCIInumbers_2Enum__from__dec__string @ X0 ) )
      = ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ X0 ) ) ) ).

thf(tp_c_2EASCIInumbers_2Enum__from__hex__string,type,
    c_2EASCIInumbers_2Enum__from__hex__string: $i ).

thf(mem_c_2EASCIInumbers_2Enum__from__hex__string,axiom,
    mem @ c_2EASCIInumbers_2Enum__from__hex__string @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2EASCIInumbers_2Enum__from__hex__string,type,
    fo__c_2EASCIInumbers_2Enum__from__hex__string: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2EASCIInumbers_2Enum__from__hex__string,axiom,
    ! [X0: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2EASCIInumbers_2Enum__from__hex__string @ X0 ) )
      = ( ap @ c_2EASCIInumbers_2Enum__from__hex__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ X0 ) ) ) ).

thf(tp_c_2EASCIInumbers_2Enum__from__oct__string,type,
    c_2EASCIInumbers_2Enum__from__oct__string: $i ).

thf(mem_c_2EASCIInumbers_2Enum__from__oct__string,axiom,
    mem @ c_2EASCIInumbers_2Enum__from__oct__string @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2EASCIInumbers_2Enum__from__oct__string,type,
    fo__c_2EASCIInumbers_2Enum__from__oct__string: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2EASCIInumbers_2Enum__from__oct__string,axiom,
    ! [X0: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2EASCIInumbers_2Enum__from__oct__string @ X0 ) )
      = ( ap @ c_2EASCIInumbers_2Enum__from__oct__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ X0 ) ) ) ).

thf(tp_c_2EASCIInumbers_2Enum__to__bin__string,type,
    c_2EASCIInumbers_2Enum__to__bin__string: $i ).

thf(mem_c_2EASCIInumbers_2Enum__to__bin__string,axiom,
    mem @ c_2EASCIInumbers_2Enum__to__bin__string @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ).

thf(tp_c_2EASCIInumbers_2Enum__to__dec__string,type,
    c_2EASCIInumbers_2Enum__to__dec__string: $i ).

thf(mem_c_2EASCIInumbers_2Enum__to__dec__string,axiom,
    mem @ c_2EASCIInumbers_2Enum__to__dec__string @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ).

thf(tp_c_2EASCIInumbers_2Enum__to__hex__string,type,
    c_2EASCIInumbers_2Enum__to__hex__string: $i ).

thf(mem_c_2EASCIInumbers_2Enum__to__hex__string,axiom,
    mem @ c_2EASCIInumbers_2Enum__to__hex__string @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ).

thf(tp_c_2EASCIInumbers_2Enum__to__oct__string,type,
    c_2EASCIInumbers_2Enum__to__oct__string: $i ).

thf(mem_c_2EASCIInumbers_2Enum__to__oct__string,axiom,
    mem @ c_2EASCIInumbers_2Enum__to__oct__string @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ).

thf(tp_c_2EASCIInumbers_2Es2n,type,
    c_2EASCIInumbers_2Es2n: $i ).

thf(mem_c_2EASCIInumbers_2Es2n,axiom,
    mem @ c_2EASCIInumbers_2Es2n @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) ) ) ).

thf(ax_thm_2EASCIInumbers_2Es2n__def,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1f: $i] :
      ( ( mem @ V1f @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) )
     => ! [V2s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
          ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1f ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2s ) ) )
          = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) @ V1f ) @ ( ap @ ( c_2Elist_2EREVERSE @ ty_2Estring_2Echar ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2s ) ) ) ) ) ) ) ).

thf(ax_thm_2EASCIInumbers_2En2s__def,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1f: $i] :
      ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) )
     => ! [V2n: tp__ty_2Enum_2Enum] :
          ( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
          = ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( c_2Elist_2EREVERSE @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) @ V1f ) @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).

thf(ax_thm_2EASCIInumbers_2EHEX__primitive__def,axiom,
    ( c_2EASCIInumbers_2EHEX
    = ( ap
      @ ( ap @ ( c_2Erelation_2EWFREC @ ty_2Enum_2Enum @ ty_2Estring_2Echar )
        @ ( ap @ ( c_2Emin_2E_40 @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
          @ ( lam @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) )
            @ ^ [V0R: $i] : ( ap @ ( c_2Erelation_2EWF @ ty_2Enum_2Enum ) @ V0R ) ) ) )
      @ ( lam @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar )
        @ ^ [V1HEX: $i] :
            ( lam @ ty_2Enum_2Enum
            @ ^ [V2a: $i] :
                ( ap
                @ ( ap @ ( c_2Ebool_2Eliteral__case @ ty_2Enum_2Enum @ ty_2Estring_2Echar )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V3v: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3v ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ebool_2EARB @ ty_2Estring_2Echar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
                @ V2a ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2EHEX__ind,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
          & ! [V1v18: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1v18 ) ) ) )
       => ! [V2v: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2v ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2EHEX__def,axiom,
    ( ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2EASCIInumbers_2EUNHEX__primitive__def,axiom,
    ( c_2EASCIInumbers_2EUNHEX
    = ( ap
      @ ( ap @ ( c_2Erelation_2EWFREC @ ty_2Estring_2Echar @ ty_2Enum_2Enum )
        @ ( ap @ ( c_2Emin_2E_40 @ ( arr @ ty_2Estring_2Echar @ ( arr @ ty_2Estring_2Echar @ bool ) ) )
          @ ( lam @ ( arr @ ty_2Estring_2Echar @ ( arr @ ty_2Estring_2Echar @ bool ) )
            @ ^ [V0R: $i] : ( ap @ ( c_2Erelation_2EWF @ ty_2Estring_2Echar ) @ V0R ) ) ) )
      @ ( lam @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum )
        @ ^ [V1UNHEX: $i] :
            ( lam @ ty_2Estring_2Echar
            @ ^ [V2a: $i] :
                ( ap
                @ ( ap @ ( c_2Ebool_2Eliteral__case @ ty_2Estring_2Echar @ ty_2Enum_2Enum )
                  @ ( lam @ ty_2Estring_2Echar
                    @ ^ [V3v: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V3v ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Ebool_2EARB @ ty_2Enum_2Enum ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
                @ V2a ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2EUNHEX__ind,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Estring_2Echar @ bool ) )
     => ( ( ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ( p @ ( ap @ V0P @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
          & ! [V1v24: tp__ty_2Estring_2Echar] : ( p @ ( ap @ V0P @ ( inj__ty_2Estring_2Echar @ V1v24 ) ) ) )
       => ! [V2v: tp__ty_2Estring_2Echar] : ( p @ ( ap @ V0P @ ( inj__ty_2Estring_2Echar @ V2v ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2EUNHEX__def,axiom,
    ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = fo__c_2Enum_2E0 )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2EASCIInumbers_2Enum__from__bin__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__from__bin__string
    = ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).

thf(ax_thm_2EASCIInumbers_2Enum__from__oct__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__from__oct__string
    = ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).

thf(ax_thm_2EASCIInumbers_2Enum__from__dec__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__from__dec__string
    = ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).

thf(ax_thm_2EASCIInumbers_2Enum__from__hex__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__from__hex__string
    = ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).

thf(ax_thm_2EASCIInumbers_2Enum__to__bin__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__to__bin__string
    = ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).

thf(ax_thm_2EASCIInumbers_2Enum__to__oct__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__to__oct__string
    = ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).

thf(ax_thm_2EASCIInumbers_2Enum__to__dec__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__to__dec__string
    = ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).

thf(ax_thm_2EASCIInumbers_2Enum__to__hex__string__def,axiom,
    ( c_2EASCIInumbers_2Enum__to__hex__string
    = ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).

thf(ax_thm_2EASCIInumbers_2EfromBinString__def,axiom,
    ! [V0s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
      ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EfromBinString @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) )
      = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum
        @ ( ap
          @ ( ap
            @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) )
              @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) @ ( c_2Elist_2ENIL @ ty_2Estring_2Echar ) ) ) )
                @ ( ap
                  @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Estring_2Echar )
                    @ ( lam @ ty_2Estring_2Echar
                      @ ^ [V1c: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V1c ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V1c ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
                  @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) ) )
            @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ c_2EASCIInumbers_2Enum__from__bin__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) ) )
          @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ).

thf(ax_thm_2EASCIInumbers_2EfromDecString__def,axiom,
    ! [V0s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
      ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EfromDecString @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) )
      = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) @ ( c_2Elist_2ENIL @ ty_2Estring_2Echar ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Estring_2Echar ) @ c_2Estring_2EisDigit ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) ) ) @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ).

thf(ax_thm_2EASCIInumbers_2EfromHexString__def,axiom,
    ! [V0s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
      ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EfromHexString @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) )
      = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) @ ( c_2Elist_2ENIL @ ty_2Estring_2Echar ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Estring_2Echar ) @ c_2Estring_2EisHexDigit ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ c_2EASCIInumbers_2Enum__from__hex__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) ) ) @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2Es2n__compute,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1f: $i] :
      ( ( mem @ V1f @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) )
     => ! [V2s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
          ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1f ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2s ) ) )
          = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) @ V1f ) @ ( ap @ ( c_2Elist_2EREVERSE @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2EEXPLODE @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2s ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2En2s__compute,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1f: $i] :
      ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) )
     => ! [V2n: tp__ty_2Enum_2Enum] :
          ( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
          = ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2Estring_2EIMPLODE @ ( ap @ ( c_2Elist_2EREVERSE @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) @ V1f ) @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2EUNHEX__HEX,axiom,
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2EASCIInumbers_2EHEX @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
        = V0n ) ) ).

thf(conj_thm_2EASCIInumbers_2EHEX__UNHEX,axiom,
    ! [V0c: tp__ty_2Estring_2Echar] :
      ( ( p @ ( ap @ c_2Estring_2EisHexDigit @ ( inj__ty_2Estring_2Echar @ V0c ) ) )
     => ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( inj__ty_2Estring_2Echar @ V0c ) ) ) )
        = ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2EtoUpper @ ( inj__ty_2Estring_2Echar @ V0c ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2EDEC__UNDEC,axiom,
    ! [V0c: tp__ty_2Estring_2Echar] :
      ( ( p @ ( ap @ c_2Estring_2EisDigit @ ( inj__ty_2Estring_2Echar @ V0c ) ) )
     => ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( inj__ty_2Estring_2Echar @ V0c ) ) ) )
        = V0c ) ) ).

thf(conj_thm_2EASCIInumbers_2Es2n__n2s,axiom,
    ! [V0c2n: $i] :
      ( ( mem @ V0c2n @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) )
     => ! [V1n2c: $i] :
          ( ( mem @ V1n2c @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) )
         => ! [V2b: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
                & ! [V4x: tp__ty_2Enum_2Enum] :
                    ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
                   => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0c2n @ ( ap @ V1n2c @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) )
                      = V4x ) ) )
             => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ V0c2n ) @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ V1n2c ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
                = V3n ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2En2s__s2n,axiom,
    ! [V0c2n: $i] :
      ( ( mem @ V0c2n @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) )
     => ! [V1n2c: $i] :
          ( ( mem @ V1n2c @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) )
         => ! [V2b: tp__ty_2Enum_2Enum,V3s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
              ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
                & ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Estring_2Echar @ bool @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) @ V0c2n ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V3s ) ) ) )
             => ( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ V1n2c ) @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ V0c2n ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V3s ) ) ) )
                = ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ V0c2n ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V3s ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( ap @ V1n2c @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Elist_2ENIL @ ty_2Estring_2Echar ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Estring_2Echar @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Estring_2Echar @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) @ V1n2c ) @ V0c2n ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ ty_2Estring_2Echar ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ V0c2n ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V3s ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V3s ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2EtoNum__toString,axiom,
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
      = V0n ) ).

thf(conj_thm_2EASCIInumbers_2EtoString__toNum__cancel,axiom,
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
      = V0n ) ).

thf(conj_thm_2EASCIInumbers_2EtoString__inj,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
      ( ( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
        = ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
    <=> ( V0n = V1m ) ) ).

thf(conj_thm_2EASCIInumbers_2EtoString__11,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
      ( ( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
        = ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
    <=> ( V0n = V1m ) ) ).

thf(conj_thm_2EASCIInumbers_2ESTRCAT__toString__inj,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
      ( ( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ty_2Estring_2Echar ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2s ) ) @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
        = ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ty_2Estring_2Echar ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2s ) ) @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
    <=> ( V0n = V1m ) ) ).

thf(conj_thm_2EASCIInumbers_2EBIT__num__from__bin__string,axiom,
    ! [V0x: tp__ty_2Enum_2Enum,V1s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
      ( ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Estring_2Echar @ bool @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1s ) ) )
        & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Estring_2Echar ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1s ) ) ) ) )
     => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2EASCIInumbers_2Enum__from__bin__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1s ) ) ) )
      <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EASCIInumbers_2EUNHEX @ ( ap @ c_2Estring_2ESUB @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1s ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Estring_2Echar ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1s ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ) )
          = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2ESUB__num__to__bin__string,axiom,
    ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Estring_2Echar ) @ ( ap @ c_2EASCIInumbers_2Enum__to__bin__string @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
     => ( ( surj__ty_2Estring_2Echar @ ( ap @ c_2Estring_2ESUB @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) @ ( ap @ c_2EASCIInumbers_2Enum__to__bin__string @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) )
        = ( surj__ty_2Estring_2Echar @ ( ap @ c_2EASCIInumbers_2EHEX @ ( ap @ ( ap @ c_2Ebit_2EBITV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Estring_2Echar ) @ ( ap @ c_2EASCIInumbers_2Enum__to__bin__string @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EASCIInumbers_2Enum__bin__string,axiom,
    ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ c_2EASCIInumbers_2Enum__from__bin__string ) @ c_2EASCIInumbers_2Enum__to__bin__string )
    = ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ).

thf(conj_thm_2EASCIInumbers_2Enum__oct__string,axiom,
    ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ c_2EASCIInumbers_2Enum__from__oct__string ) @ c_2EASCIInumbers_2Enum__to__oct__string )
    = ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ).

thf(conj_thm_2EASCIInumbers_2Enum__dec__string,axiom,
    ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ c_2EASCIInumbers_2Enum__from__dec__string ) @ c_2EASCIInumbers_2Enum__to__dec__string )
    = ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ).

thf(conj_thm_2EASCIInumbers_2Enum__hex__string,axiom,
    ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ c_2EASCIInumbers_2Enum__from__hex__string ) @ c_2EASCIInumbers_2Enum__to__hex__string )
    = ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ).

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