ITP001 Axioms: ITP059^5.ax
%------------------------------------------------------------------------------
% File : ITP059^5 : TPTP v8.2.0. 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 ) ) ).
%------------------------------------------------------------------------------