ITP001 Axioms: ITP054^7.ax


%------------------------------------------------------------------------------
% File     : ITP054^7 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : string.ax [Gau19]
%          : HL4054^7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  193 (  39 unt;  93 typ;   0 def)
%            Number of atoms       :  242 ( 125 equ;  10 cnn)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives : 1860 (  10   ~;  11   |;  57   &;1715   @)
%                                         (  45 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg;1715 nst)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  195 ( 195   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   92 (  90 usr;   5 con; 0-5 aty)
%            Number of variables   :  312 (  32   ^ 226   !;   9   ?; 312   :)
%                                         (  45  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_SAT_EQU_NAR

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

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

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

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

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

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

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

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

thf(c_2Earithmetic_2E_2B,type,
    c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

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

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

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

thf(c_2Enum_2E0,type,
    c_2Enum_2E0: tyop_2Enum_2Enum ).

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

thf(c_2Earithmetic_2E_3C_3D,type,
    c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

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

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

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

thf(c_2Earithmetic_2E_3E_3D,type,
    c_2Earithmetic_2E_3E_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

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

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

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

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

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

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

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

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

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

thf(c_2Estring_2EDEST__STRING,type,
    c_2Estring_2EDEST__STRING: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) ).

thf(c_2Elist_2EEL,type,
    c_2Elist_2EEL: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).

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

thf(c_2Estring_2EEXTRACT,type,
    c_2Estring_2EEXTRACT: ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2Ebool_2EF,type,
    c_2Ebool_2EF: $o ).

thf(c_2Ecombin_2EFAIL,type,
    c_2Ecombin_2EFAIL: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > A_27a ) ).

thf(c_2Estring_2EFIELDS,type,
    c_2Estring_2EFIELDS: ( tyop_2Estring_2Echar > $o ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ).

thf(c_2Elist_2EFLAT,type,
    c_2Elist_2EFLAT: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a ) ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Elist_2EFOLDR,type,
    c_2Elist_2EFOLDR: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > A_27b ) > A_27b > ( tyop_2Elist_2Elist @ A_27a ) > A_27b ) ).

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

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

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

thf(c_2Ebool_2ELET,type,
    c_2Ebool_2ELET: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > A_27a > A_27b ) ).

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

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

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

thf(c_2Elist_2ENULL,type,
    c_2Elist_2ENULL: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).

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

thf(c_2Estring_2EORD,type,
    c_2Estring_2EORD: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).

thf(c_2Erich__list_2ESEG,type,
    c_2Erich__list_2ESEG: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

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

thf(c_2Erich__list_2ESPLITP,type,
    c_2Erich__list_2ESPLITP: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ).

thf(c_2Estring_2ESTR,type,
    c_2Estring_2ESTR: tyop_2Estring_2Echar > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

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

thf(c_2Estring_2ESUBSTRING,type,
    c_2Estring_2ESUBSTRING: ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

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

thf(c_2Ebool_2ET,type,
    c_2Ebool_2ET: $o ).

thf(c_2Elist_2ETL,type,
    c_2Elist_2ETL: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Estring_2ETOCHAR,type,
    c_2Estring_2ETOCHAR: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Estring_2Echar ).

thf(c_2Estring_2ETOKENS,type,
    c_2Estring_2ETOKENS: ( tyop_2Estring_2Echar > $o ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ).

thf(c_2Estring_2ETRANSLATE,type,
    c_2Estring_2ETRANSLATE: ( tyop_2Estring_2Echar > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2Ebool_2ETYPE__DEFINITION,type,
    c_2Ebool_2ETYPE__DEFINITION: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > A_27a ) > $o ) ).

thf(c_2Epair_2EUNCURRY,type,
    c_2Epair_2EUNCURRY: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27a > A_27b > A_27c ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27c ) ).

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

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

thf(c_2Earithmetic_2EZERO,type,
    c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).

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

thf(c_2Estring_2Echar__ge,type,
    c_2Estring_2Echar__ge: tyop_2Estring_2Echar > tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2Echar__gt,type,
    c_2Estring_2Echar__gt: tyop_2Estring_2Echar > tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2Echar__le,type,
    c_2Estring_2Echar__le: tyop_2Estring_2Echar > tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2Echar__lt,type,
    c_2Estring_2Echar__lt: tyop_2Estring_2Echar > tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2Echar__size,type,
    c_2Estring_2Echar__size: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).

thf(c_2Estring_2EisAlpha,type,
    c_2Estring_2EisAlpha: tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2EisAlphaNum,type,
    c_2Estring_2EisAlphaNum: tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2EisAscii,type,
    c_2Estring_2EisAscii: tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2EisCntrl,type,
    c_2Estring_2EisCntrl: tyop_2Estring_2Echar > $o ).

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

thf(c_2Estring_2EisGraph,type,
    c_2Estring_2EisGraph: tyop_2Estring_2Echar > $o ).

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

thf(c_2Estring_2EisLower,type,
    c_2Estring_2EisLower: tyop_2Estring_2Echar > $o ).

thf(c_2Elist_2EisPREFIX,type,
    c_2Elist_2EisPREFIX: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).

thf(c_2Estring_2EisPrint,type,
    c_2Estring_2EisPrint: tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2EisPunct,type,
    c_2Estring_2EisPunct: tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2EisSpace,type,
    c_2Estring_2EisSpace: tyop_2Estring_2Echar > $o ).

thf(c_2Estring_2EisUpper,type,
    c_2Estring_2EisUpper: tyop_2Estring_2Echar > $o ).

thf(c_2Elist_2Elist__CASE,type,
    c_2Elist_2Elist__CASE: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27b > ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > A_27b ) > A_27b ) ).

thf(c_2Eoption_2Eoption__CASE,type,
    c_2Eoption_2Eoption__CASE: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption @ A_27a ) > A_27b > ( A_27a > A_27b ) > A_27b ) ).

thf(c_2Epair_2Epair__CASE,type,
    c_2Epair_2Epair__CASE: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) > ( A_27b > A_27c > A_27a ) > A_27a ) ).

thf(c_2Estring_2Estring__ge,type,
    c_2Estring_2Estring__ge: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o ).

thf(c_2Estring_2Estring__gt,type,
    c_2Estring_2Estring__gt: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o ).

thf(c_2Estring_2Estring__le,type,
    c_2Estring_2Estring__le: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o ).

thf(c_2Estring_2Estring__lt,type,
    c_2Estring_2Estring__lt: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o ).

thf(c_2Estring_2EtoLower,type,
    c_2Estring_2EtoLower: tyop_2Estring_2Echar > tyop_2Estring_2Echar ).

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

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

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

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

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

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

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

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

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

thf(thm_2Estring_2EDEST__STRING__def,axiom,
    ( ( ( c_2Estring_2EDEST__STRING @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
      = ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) )
    & ! [V0c: tyop_2Estring_2Echar,V1rst: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( c_2Estring_2EDEST__STRING @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ V1rst ) )
        = ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( c_2Epair_2E_2C @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V0c @ V1rst ) ) ) ) ).

thf(thm_2Estring_2Echar__TY__DEF,axiom,
    ? [V0rep: tyop_2Estring_2Echar > tyop_2Enum_2Enum] :
      ( c_2Ebool_2ETYPE__DEFINITION @ tyop_2Enum_2Enum @ tyop_2Estring_2Echar
      @ ^ [V1n: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      @ V0rep ) ).

thf(thm_2Estring_2Echar__BIJ,axiom,
    ( ! [V0a: tyop_2Estring_2Echar] :
        ( ( c_2Estring_2ECHR @ ( c_2Estring_2EORD @ V0a ) )
        = V0a )
    & ! [V1r: tyop_2Enum_2Enum] :
        ( ( ^ [V2n: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ V2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
          @ V1r )
      <=> ( ( c_2Estring_2EORD @ ( c_2Estring_2ECHR @ V1r ) )
          = V1r ) ) ) ).

thf(thm_2Estring_2EisLower__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisLower @ V0c )
    <=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) )
        & ( c_2Earithmetic_2E_3C_3D @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2EisUpper__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisUpper @ V0c )
    <=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) )
        & ( c_2Earithmetic_2E_3C_3D @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2EisDigit__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisDigit @ V0c )
    <=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) )
        & ( c_2Earithmetic_2E_3C_3D @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2EisAlpha__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisAlpha @ V0c )
    <=> ( ( c_2Estring_2EisLower @ V0c )
        | ( c_2Estring_2EisUpper @ V0c ) ) ) ).

thf(thm_2Estring_2EisHexDigit__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisHexDigit @ V0c )
    <=> ( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) )
          & ( c_2Earithmetic_2E_3C_3D @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
        | ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) )
          & ( c_2Earithmetic_2E_3C_3D @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
        | ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) )
          & ( c_2Earithmetic_2E_3C_3D @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2EisAlphaNum__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisAlphaNum @ V0c )
    <=> ( ( c_2Estring_2EisAlpha @ V0c )
        | ( c_2Estring_2EisDigit @ V0c ) ) ) ).

thf(thm_2Estring_2EisPrint__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisPrint @ V0c )
    <=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) )
        & ( c_2Eprim__rec_2E_3C @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2EisSpace__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisSpace @ V0c )
    <=> ( ( ( c_2Estring_2EORD @ V0c )
          = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
        | ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) )
          & ( c_2Earithmetic_2E_3C_3D @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2EisGraph__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisGraph @ V0c )
    <=> ( ( c_2Estring_2EisPrint @ V0c )
        & ( (~) @ ( c_2Estring_2EisSpace @ V0c ) ) ) ) ).

thf(thm_2Estring_2EisPunct__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisPunct @ V0c )
    <=> ( ( c_2Estring_2EisGraph @ V0c )
        & ( (~) @ ( c_2Estring_2EisAlphaNum @ V0c ) ) ) ) ).

thf(thm_2Estring_2EisAscii__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisAscii @ V0c )
      = ( c_2Earithmetic_2E_3C_3D @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2EisCntrl__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EisCntrl @ V0c )
    <=> ( ( c_2Eprim__rec_2E_3C @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
        | ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Estring_2EORD @ V0c ) ) ) ) ).

thf(thm_2Estring_2EtoLower__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EtoLower @ V0c )
      = ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Estring_2EisUpper @ V0c ) @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2E_2B @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ V0c ) ) ).

thf(thm_2Estring_2EtoUpper__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EtoUpper @ V0c )
      = ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ ( c_2Estring_2EisLower @ V0c ) @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2E_2D @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ V0c ) ) ).

thf(thm_2Estring_2Echar__lt__def,axiom,
    ! [V0a: tyop_2Estring_2Echar,V1b: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Echar__lt @ V0a @ V1b )
      = ( c_2Eprim__rec_2E_3C @ ( c_2Estring_2EORD @ V0a ) @ ( c_2Estring_2EORD @ V1b ) ) ) ).

thf(thm_2Estring_2Echar__le__def,axiom,
    ! [V0a: tyop_2Estring_2Echar,V1b: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Echar__le @ V0a @ V1b )
      = ( c_2Earithmetic_2E_3C_3D @ ( c_2Estring_2EORD @ V0a ) @ ( c_2Estring_2EORD @ V1b ) ) ) ).

thf(thm_2Estring_2Echar__gt__def,axiom,
    ! [V0a: tyop_2Estring_2Echar,V1b: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Echar__gt @ V0a @ V1b )
      = ( c_2Earithmetic_2E_3E @ ( c_2Estring_2EORD @ V0a ) @ ( c_2Estring_2EORD @ V1b ) ) ) ).

thf(thm_2Estring_2Echar__ge__def,axiom,
    ! [V0a: tyop_2Estring_2Echar,V1b: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Echar__ge @ V0a @ V1b )
      = ( c_2Earithmetic_2E_3E_3D @ ( c_2Estring_2EORD @ V0a ) @ ( c_2Estring_2EORD @ V1b ) ) ) ).

thf(thm_2Estring_2Echar__size__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Echar__size @ V0c )
      = c_2Enum_2E0 ) ).

thf(thm_2Estring_2ESUB__def,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1n: tyop_2Enum_2Enum] :
      ( ( c_2Estring_2ESUB @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Enum_2Enum @ V0s @ V1n ) )
      = ( c_2Elist_2EEL @ tyop_2Estring_2Echar @ V1n @ V0s ) ) ).

thf(thm_2Estring_2ESTR__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2ESTR @ V0c )
      = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) ) ).

thf(thm_2Estring_2ETOCHAR__primitive__def,axiom,
    ( c_2Estring_2ETOCHAR
    = ( c_2Erelation_2EWFREC @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Estring_2Echar
      @ ( c_2Emin_2E_40 @ ( ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o )
        @ ^ [V0R: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o] : ( c_2Erelation_2EWF @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V0R ) )
      @ ^ [V1TOCHAR: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Estring_2Echar,V2a: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
          ( c_2Elist_2Elist__CASE @ tyop_2Estring_2Echar @ tyop_2Estring_2Echar @ V2a @ ( c_2Ebool_2EARB @ tyop_2Estring_2Echar )
          @ ^ [V3c: tyop_2Estring_2Echar,V4v1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
              ( c_2Elist_2Elist__CASE @ tyop_2Estring_2Echar @ tyop_2Estring_2Echar @ V4v1 @ ( c_2Ecombin_2EI @ tyop_2Estring_2Echar @ V3c )
              @ ^ [V5v2: tyop_2Estring_2Echar,V6v3: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( c_2Ebool_2EARB @ tyop_2Estring_2Echar ) ) ) ) ) ).

thf(thm_2Estring_2ESUBSTRING__def,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1i: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
      ( ( c_2Estring_2ESUBSTRING @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1i @ V2n ) ) )
      = ( c_2Erich__list_2ESEG @ tyop_2Estring_2Echar @ V2n @ V1i @ V0s ) ) ).

thf(thm_2Estring_2ETRANSLATE__def,axiom,
    ! [V0f: tyop_2Estring_2Echar > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ),V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Estring_2ETRANSLATE @ V0f @ V1s )
      = ( c_2Elist_2EFLAT @ tyop_2Estring_2Echar @ ( c_2Elist_2EMAP @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V0f @ V1s ) ) ) ).

thf(thm_2Estring_2EIMPLODE__def,axiom,
    ( ( ( c_2Estring_2EIMPLODE @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
      = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
    & ! [V0c: tyop_2Estring_2Echar,V1cs: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( c_2Estring_2EIMPLODE @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ V1cs ) )
        = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ ( c_2Estring_2EIMPLODE @ V1cs ) ) ) ) ).

thf(thm_2Estring_2EEXPLODE__def,axiom,
    ( ( ( c_2Estring_2EEXPLODE @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
      = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
    & ! [V0c: tyop_2Estring_2Echar,V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( c_2Estring_2EEXPLODE @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ V1s ) )
        = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ ( c_2Estring_2EEXPLODE @ V1s ) ) ) ) ).

thf(thm_2Estring_2EEXTRACT__primitive__def,axiom,
    ( c_2Estring_2EEXTRACT
    = ( c_2Erelation_2EWFREC @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )
      @ ( c_2Emin_2E_40 @ ( ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) > ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) > $o )
        @ ^ [V0R: ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) > ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) > $o] : ( c_2Erelation_2EWF @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0R ) )
      @ ^ [V1EXTRACT: ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ),V2a: tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) )] :
          ( c_2Epair_2Epair__CASE @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V2a
          @ ^ [V3s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V4v1: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum )] :
              ( c_2Epair_2Epair__CASE @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ V4v1
              @ ^ [V5i: tyop_2Enum_2Enum,V6v3: tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum] :
                  ( c_2Eoption_2Eoption__CASE @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V6v3 @ ( c_2Ecombin_2EI @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Estring_2ESUBSTRING @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V3s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V5i @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V3s ) @ V5i ) ) ) ) )
                  @ ^ [V7n: tyop_2Enum_2Enum] : ( c_2Ecombin_2EI @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Estring_2ESUBSTRING @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V3s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V5i @ V7n ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2Estring__le__def,axiom,
    ! [V0s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Estring__le @ V0s1 @ V1s2 )
    <=> ( ( V0s1 = V1s2 )
        | ( c_2Estring_2Estring__lt @ V0s1 @ V1s2 ) ) ) ).

thf(thm_2Estring_2Estring__gt__def,axiom,
    ! [V0s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Estring__gt @ V0s1 @ V1s2 )
      = ( c_2Estring_2Estring__lt @ V1s2 @ V0s1 ) ) ).

thf(thm_2Estring_2Estring__ge__def,axiom,
    ! [V0s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Estring__ge @ V0s1 @ V1s2 )
      = ( c_2Estring_2Estring__le @ V1s2 @ V0s1 ) ) ).

thf(thm_2Estring_2EIMPLODE__STRING,axiom,
    ! [V0clist: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EIMPLODE @ V0clist )
      = ( c_2Elist_2EFOLDR @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar ) @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) @ V0clist ) ) ).

thf(thm_2Estring_2EEXPLODE__DEST__STRING,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EEXPLODE @ V0s )
      = ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Estring_2EDEST__STRING @ V0s ) @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar )
        @ ^ [V1v: tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )] :
            ( c_2Epair_2Epair__CASE @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V1v
            @ ^ [V2c: tyop_2Estring_2Echar,V3t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V2c @ ( c_2Estring_2EEXPLODE @ V3t ) ) ) ) ) ).

thf(thm_2Estring_2EIMPLODE__EQ__THM,axiom,
    ! [V0c: tyop_2Estring_2Echar,V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ V1s )
          = ( c_2Estring_2EIMPLODE @ V2l ) )
      <=> ( V2l
          = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ ( c_2Estring_2EEXPLODE @ V1s ) ) ) )
      & ( ( ( c_2Estring_2EIMPLODE @ V2l )
          = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ V1s ) )
      <=> ( V2l
          = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ ( c_2Estring_2EEXPLODE @ V1s ) ) ) ) ) ).

thf(thm_2Estring_2EEXPLODE__EQ__THM,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1h: tyop_2Estring_2Echar,V2t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V1h @ V2t )
          = ( c_2Estring_2EEXPLODE @ V0s ) )
      <=> ( V0s
          = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V1h @ ( c_2Estring_2EIMPLODE @ V2t ) ) ) )
      & ( ( ( c_2Estring_2EEXPLODE @ V0s )
          = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V1h @ V2t ) )
      <=> ( V0s
          = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V1h @ ( c_2Estring_2EIMPLODE @ V2t ) ) ) ) ) ).

thf(thm_2Estring_2EEXPLODE__EQ__NIL,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( ( c_2Estring_2EEXPLODE @ V0s )
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
      <=> ( V0s
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) )
      & ( ( ( c_2Elist_2ENIL @ tyop_2Estring_2Echar )
          = ( c_2Estring_2EEXPLODE @ V0s ) )
      <=> ( V0s
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) ) ) ).

thf(thm_2Estring_2EIMPLODE__EQ__EMPTYSTRING,axiom,
    ! [V0l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( ( c_2Estring_2EIMPLODE @ V0l )
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
      <=> ( V0l
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) )
      & ( ( ( c_2Elist_2ENIL @ tyop_2Estring_2Echar )
          = ( c_2Estring_2EIMPLODE @ V0l ) )
      <=> ( V0l
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) ) ) ).

thf(thm_2Estring_2EIMPLODE__EQNS,axiom,
    ( ( ( c_2Estring_2EIMPLODE @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
      = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
    & ! [V0c: tyop_2Estring_2Echar,V1cs: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( c_2Estring_2EIMPLODE @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ V1cs ) )
        = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ ( c_2Estring_2EIMPLODE @ V1cs ) ) ) ) ).

thf(thm_2Estring_2EEXPLODE__EQNS,axiom,
    ( ( ( c_2Estring_2EEXPLODE @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
      = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
    & ! [V0c: tyop_2Estring_2Echar,V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( c_2Estring_2EEXPLODE @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ V1s ) )
        = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ ( c_2Estring_2EEXPLODE @ V1s ) ) ) ) ).

thf(thm_2Estring_2EDEST__STRING__LEMS,axiom,
    ! [V0t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1c: tyop_2Estring_2Echar,V2s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( ( c_2Estring_2EDEST__STRING @ V2s )
          = ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) )
      <=> ( V2s
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) )
      & ( ( ( c_2Estring_2EDEST__STRING @ V2s )
          = ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( c_2Epair_2E_2C @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V1c @ V0t ) ) )
      <=> ( V2s
          = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V1c @ V0t ) ) ) ) ).

thf(thm_2Estring_2ESTRLEN__EXPLODE__THM,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V0s )
      = ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ ( c_2Estring_2EEXPLODE @ V0s ) ) ) ).

thf(thm_2Estring_2EORD__11,axiom,
    ! [V0a: tyop_2Estring_2Echar,V1a_27: tyop_2Estring_2Echar] :
      ( ( ( c_2Estring_2EORD @ V0a )
        = ( c_2Estring_2EORD @ V1a_27 ) )
    <=> ( V0a = V1a_27 ) ) ).

thf(thm_2Estring_2ECHR__11,axiom,
    ! [V0r: tyop_2Enum_2Enum,V1r_27: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
     => ( ( c_2Eprim__rec_2E_3C @ V1r_27 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
       => ( ( ( c_2Estring_2ECHR @ V0r )
            = ( c_2Estring_2ECHR @ V1r_27 ) )
        <=> ( V0r = V1r_27 ) ) ) ) ).

thf(thm_2Estring_2EORD__ONTO,axiom,
    ! [V0r: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    <=> ? [V1a: tyop_2Estring_2Echar] :
          ( V0r
          = ( c_2Estring_2EORD @ V1a ) ) ) ).

thf(thm_2Estring_2ECHR__ONTO,axiom,
    ! [V0a: tyop_2Estring_2Echar] :
    ? [V1r: tyop_2Enum_2Enum] :
      ( ( V0a
        = ( c_2Estring_2ECHR @ V1r ) )
      & ( c_2Eprim__rec_2E_3C @ V1r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2ECHR__ORD,axiom,
    ! [V0a: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2ECHR @ ( c_2Estring_2EORD @ V0a ) )
      = V0a ) ).

thf(thm_2Estring_2EORD__CHR,axiom,
    ! [V0r: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
    <=> ( ( c_2Estring_2EORD @ ( c_2Estring_2ECHR @ V0r ) )
        = V0r ) ) ).

thf(thm_2Estring_2EORD__CHR__RWT,axiom,
    ! [V0r: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
     => ( ( c_2Estring_2EORD @ ( c_2Estring_2ECHR @ V0r ) )
        = V0r ) ) ).

thf(thm_2Estring_2EORD__CHR__COMPUTE,axiom,
    ! [V0_3E_20255: $o,V1n: tyop_2Enum_2Enum] :
      ( ( c_2Estring_2EORD @ ( c_2Estring_2ECHR @ V1n ) )
      = ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ V1n @ ( c_2Ecombin_2EFAIL @ ( tyop_2Estring_2Echar > tyop_2Enum_2Enum ) @ $o @ c_2Estring_2EORD @ V0_3E_20255 @ ( c_2Estring_2ECHR @ V1n ) ) ) ) ).

thf(thm_2Estring_2EORD__BOUND,axiom,
    ! [V0c: tyop_2Estring_2Echar] : ( c_2Eprim__rec_2E_3C @ ( c_2Estring_2EORD @ V0c ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2Echar__nchotomy,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
    ? [V1n: tyop_2Enum_2Enum] :
      ( V0c
      = ( c_2Estring_2ECHR @ V1n ) ) ).

thf(thm_2Estring_2Eranged__char__nchotomy,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
    ? [V1n: tyop_2Enum_2Enum] :
      ( ( V0c
        = ( c_2Estring_2ECHR @ V1n ) )
      & ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2ECHAR__EQ__THM,axiom,
    ! [V0c1: tyop_2Estring_2Echar,V1c2: tyop_2Estring_2Echar] :
      ( ( V0c1 = V1c2 )
    <=> ( ( c_2Estring_2EORD @ V0c1 )
        = ( c_2Estring_2EORD @ V1c2 ) ) ) ).

thf(thm_2Estring_2ECHAR__INDUCT__THM,axiom,
    ! [V0P: tyop_2Estring_2Echar > $o] :
      ( ! [V1n: tyop_2Enum_2Enum] :
          ( ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
         => ( V0P @ ( c_2Estring_2ECHR @ V1n ) ) )
     => ! [V2c: tyop_2Estring_2Echar] : ( V0P @ V2c ) ) ).

thf(thm_2Estring_2ETOCHAR__ind,axiom,
    ! [V0P: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o] :
      ( ( ! [V1c: tyop_2Estring_2Echar] : ( V0P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V1c @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) )
        & ( V0P @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
        & ! [V2v6: tyop_2Estring_2Echar,V3v4: tyop_2Estring_2Echar,V4v5: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( V0P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V2v6 @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3v4 @ V4v5 ) ) ) )
     => ! [V5v: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( V0P @ V5v ) ) ).

thf(thm_2Estring_2ETOCHAR__def,axiom,
    ! [V0c: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2ETOCHAR @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) )
      = V0c ) ).

thf(thm_2Estring_2ETOKENS__ind,axiom,
    ! [V0P_27: ( tyop_2Estring_2Echar > $o ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o] :
      ( ( ! [V1P: tyop_2Estring_2Echar > $o] : ( V0P_27 @ V1P @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
        & ! [V2P: tyop_2Estring_2Echar > $o,V3h: tyop_2Estring_2Echar,V4t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
            ( ( ! [V5l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V6r: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
                  ( ( ( ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V5l @ V6r )
                      = ( c_2Erich__list_2ESPLITP @ tyop_2Estring_2Echar @ V2P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3h @ V4t ) ) )
                    & ( c_2Elist_2ENULL @ tyop_2Estring_2Echar @ V5l ) )
                 => ( V0P_27 @ V2P @ ( c_2Elist_2ETL @ tyop_2Estring_2Echar @ V6r ) ) )
              & ! [V7l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V8r: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
                  ( ( ( ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V7l @ V8r )
                      = ( c_2Erich__list_2ESPLITP @ tyop_2Estring_2Echar @ V2P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3h @ V4t ) ) )
                    & ( (~) @ ( c_2Elist_2ENULL @ tyop_2Estring_2Echar @ V7l ) ) )
                 => ( V0P_27 @ V2P @ V8r ) ) )
           => ( V0P_27 @ V2P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3h @ V4t ) ) ) )
     => ! [V9v: tyop_2Estring_2Echar > $o,V10v1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( V0P_27 @ V9v @ V10v1 ) ) ).

thf(thm_2Estring_2ETOKENS__def,axiom,
    ( ! [V0P: tyop_2Estring_2Echar > $o] :
        ( ( c_2Estring_2ETOKENS @ V0P @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
        = ( c_2Elist_2ENIL @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) )
    & ! [V1t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2h: tyop_2Estring_2Echar,V3P: tyop_2Estring_2Echar > $o] :
        ( ( c_2Estring_2ETOKENS @ V3P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V2h @ V1t ) )
        = ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) )
          @ ( c_2Epair_2EUNCURRY @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) )
            @ ^ [V4l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V5r: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( c_2Elist_2ENULL @ tyop_2Estring_2Echar @ V4l ) @ ( c_2Estring_2ETOKENS @ V3P @ ( c_2Elist_2ETL @ tyop_2Estring_2Echar @ V5r ) ) @ ( c_2Elist_2ECONS @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V4l @ ( c_2Estring_2ETOKENS @ V3P @ V5r ) ) ) )
          @ ( c_2Erich__list_2ESPLITP @ tyop_2Estring_2Echar @ V3P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V2h @ V1t ) ) ) ) ) ).

thf(thm_2Estring_2EFIELDS__ind,axiom,
    ! [V0P_27: ( tyop_2Estring_2Echar > $o ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o] :
      ( ( ! [V1P: tyop_2Estring_2Echar > $o] : ( V0P_27 @ V1P @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
        & ! [V2P: tyop_2Estring_2Echar > $o,V3h: tyop_2Estring_2Echar,V4t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
            ( ( ! [V5l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V6r: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
                  ( ( ( ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V5l @ V6r )
                      = ( c_2Erich__list_2ESPLITP @ tyop_2Estring_2Echar @ V2P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3h @ V4t ) ) )
                    & ( c_2Elist_2ENULL @ tyop_2Estring_2Echar @ V5l ) )
                 => ( V0P_27 @ V2P @ ( c_2Elist_2ETL @ tyop_2Estring_2Echar @ V6r ) ) )
              & ! [V7l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V8r: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
                  ( ( ( ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V7l @ V8r )
                      = ( c_2Erich__list_2ESPLITP @ tyop_2Estring_2Echar @ V2P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3h @ V4t ) ) )
                    & ( (~) @ ( c_2Elist_2ENULL @ tyop_2Estring_2Echar @ V7l ) )
                    & ( (~) @ ( c_2Elist_2ENULL @ tyop_2Estring_2Echar @ V8r ) ) )
                 => ( V0P_27 @ V2P @ ( c_2Elist_2ETL @ tyop_2Estring_2Echar @ V8r ) ) ) )
           => ( V0P_27 @ V2P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3h @ V4t ) ) ) )
     => ! [V9v: tyop_2Estring_2Echar > $o,V10v1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( V0P_27 @ V9v @ V10v1 ) ) ).

thf(thm_2Estring_2EFIELDS__def,axiom,
    ( ! [V0P: tyop_2Estring_2Echar > $o] :
        ( ( c_2Estring_2EFIELDS @ V0P @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
        = ( c_2Elist_2ECONS @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) @ ( c_2Elist_2ENIL @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) )
    & ! [V1t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2h: tyop_2Estring_2Echar,V3P: tyop_2Estring_2Echar > $o] :
        ( ( c_2Estring_2EFIELDS @ V3P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V2h @ V1t ) )
        = ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) )
          @ ( c_2Epair_2EUNCURRY @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) )
            @ ^ [V4l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V5r: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( c_2Elist_2ENULL @ tyop_2Estring_2Echar @ V4l ) @ ( c_2Elist_2ECONS @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) @ ( c_2Estring_2EFIELDS @ V3P @ ( c_2Elist_2ETL @ tyop_2Estring_2Echar @ V5r ) ) ) @ ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( c_2Elist_2ENULL @ tyop_2Estring_2Echar @ V5r ) @ ( c_2Elist_2ECONS @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V4l @ ( c_2Elist_2ENIL @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) @ ( c_2Elist_2ECONS @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V4l @ ( c_2Estring_2EFIELDS @ V3P @ ( c_2Elist_2ETL @ tyop_2Estring_2Echar @ V5r ) ) ) ) ) )
          @ ( c_2Erich__list_2ESPLITP @ tyop_2Estring_2Echar @ V3P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V2h @ V1t ) ) ) ) ) ).

thf(thm_2Estring_2EIMPLODE__EXPLODE__I,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Estring_2EEXPLODE @ V0s )
        = V0s )
      & ( ( c_2Estring_2EIMPLODE @ V0s )
        = V0s ) ) ).

thf(thm_2Estring_2EIMPLODE__EXPLODE,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EIMPLODE @ ( c_2Estring_2EEXPLODE @ V0s ) )
      = V0s ) ).

thf(thm_2Estring_2EEXPLODE__IMPLODE,axiom,
    ! [V0cs: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Estring_2EEXPLODE @ ( c_2Estring_2EIMPLODE @ V0cs ) )
      = V0cs ) ).

thf(thm_2Estring_2EEXPLODE__ONTO,axiom,
    ! [V0cs: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
    ? [V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( V0cs
      = ( c_2Estring_2EEXPLODE @ V1s ) ) ).

thf(thm_2Estring_2EIMPLODE__ONTO,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
    ? [V1cs: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( V0s
      = ( c_2Estring_2EIMPLODE @ V1cs ) ) ).

thf(thm_2Estring_2EEXPLODE__11,axiom,
    ! [V0s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Estring_2EEXPLODE @ V1s1 )
        = ( c_2Estring_2EEXPLODE @ V0s2 ) )
    <=> ( V1s1 = V0s2 ) ) ).

thf(thm_2Estring_2EIMPLODE__11,axiom,
    ! [V0cs2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1cs1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Estring_2EIMPLODE @ V1cs1 )
        = ( c_2Estring_2EIMPLODE @ V0cs2 ) )
    <=> ( V1cs1 = V0cs2 ) ) ).

thf(thm_2Estring_2ESTRING__ACYCLIC,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1c: tyop_2Estring_2Echar] :
      ( ( (~)
        @ ( ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V1c @ V0s )
          = V0s ) )
      & ( (~)
        @ ( V0s
          = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V1c @ V0s ) ) ) ) ).

thf(thm_2Estring_2EEXTRACT__ind,axiom,
    ! [V0P: ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) > $o] :
      ( ( ! [V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2i: tyop_2Enum_2Enum] : ( V0P @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V1s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ V2i @ ( c_2Eoption_2ENONE @ tyop_2Enum_2Enum ) ) ) )
        & ! [V3s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V4i: tyop_2Enum_2Enum,V5n: tyop_2Enum_2Enum] : ( V0P @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V3s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ V4i @ ( c_2Eoption_2ESOME @ tyop_2Enum_2Enum @ V5n ) ) ) ) )
     => ! [V6v: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V7v1: tyop_2Enum_2Enum,V8v2: tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum] : ( V0P @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V6v @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ V7v1 @ V8v2 ) ) ) ) ).

thf(thm_2Estring_2EEXTRACT__def,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1n: tyop_2Enum_2Enum,V2i: tyop_2Enum_2Enum] :
      ( ( ( c_2Estring_2EEXTRACT @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ V2i @ ( c_2Eoption_2ENONE @ tyop_2Enum_2Enum ) ) ) )
        = ( c_2Estring_2ESUBSTRING @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V2i @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V0s ) @ V2i ) ) ) ) )
      & ( ( c_2Estring_2EEXTRACT @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ V2i @ ( c_2Eoption_2ESOME @ tyop_2Enum_2Enum @ V1n ) ) ) )
        = ( c_2Estring_2ESUBSTRING @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V2i @ V1n ) ) ) ) ) ).

thf(thm_2Estring_2ESTRLEN__EQ__0,axiom,
    ! [V0l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V0l )
        = c_2Enum_2E0 )
    <=> ( V0l
        = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) ) ).

thf(thm_2Estring_2ESTRLEN__THM,axiom,
    ( ( ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
      = c_2Enum_2E0 )
    & ! [V0h: tyop_2Estring_2Echar,V1t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0h @ V1t ) )
        = ( c_2Enum_2ESUC @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V1t ) ) ) ) ).

thf(thm_2Estring_2ESTRLEN__DEF,axiom,
    ( ( ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
      = c_2Enum_2E0 )
    & ! [V0h: tyop_2Estring_2Echar,V1t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0h @ V1t ) )
        = ( c_2Enum_2ESUC @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V1t ) ) ) ) ).

thf(thm_2Estring_2ESTRCAT__def,axiom,
    ( ! [V0l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) @ V0l )
        = V0l )
    & ! [V1l1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2l2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V3h: tyop_2Estring_2Echar] :
        ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3h @ V1l1 ) @ V2l2 )
        = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3h @ ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V1l1 @ V2l2 ) ) ) ) ).

thf(thm_2Estring_2ESTRCAT,axiom,
    ! [V0s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V1s1 @ V0s2 )
      = ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V1s1 @ V0s2 ) ) ).

thf(thm_2Estring_2ESTRCAT__EQNS,axiom,
    ! [V0s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V3c: tyop_2Estring_2Echar] :
      ( ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) @ V2s )
        = V2s )
      & ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V2s @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
        = V2s )
      & ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3c @ V1s1 ) @ V0s2 )
        = ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V3c @ ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V1s1 @ V0s2 ) ) ) ) ).

thf(thm_2Estring_2ESTRCAT__ASSOC,axiom,
    ! [V0l1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1l2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2l3: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V0l1 @ ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V1l2 @ V2l3 ) )
      = ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V0l1 @ V1l2 ) @ V2l3 ) ) ).

thf(thm_2Estring_2ESTRCAT__11,axiom,
    ( ! [V0l1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1l2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2l3: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V0l1 @ V1l2 )
          = ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V0l1 @ V2l3 ) )
      <=> ( V1l2 = V2l3 ) )
    & ! [V3l1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V4l2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V5l3: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V4l2 @ V3l1 )
          = ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V5l3 @ V3l1 ) )
      <=> ( V4l2 = V5l3 ) ) ) ).

thf(thm_2Estring_2ESTRCAT__ACYCLIC,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( V0s
          = ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V0s @ V1s1 ) )
      <=> ( V1s1
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) )
      & ( ( V0s
          = ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V1s1 @ V0s ) )
      <=> ( V1s1
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) ) ) ).

thf(thm_2Estring_2ESTRCAT__EXPLODE,axiom,
    ! [V0s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V0s1 @ V1s2 )
      = ( c_2Elist_2EFOLDR @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar ) @ V1s2 @ ( c_2Estring_2EEXPLODE @ V0s1 ) ) ) ).

thf(thm_2Estring_2ESTRCAT__EQ__EMPTY,axiom,
    ! [V0l1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1l2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V0l1 @ V1l2 )
        = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
    <=> ( ( V0l1
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
        & ( V1l2
          = ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) ) ) ) ).

thf(thm_2Estring_2ESTRLEN__CAT,axiom,
    ! [V0l1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1l2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V0l1 @ V1l2 ) )
      = ( c_2Earithmetic_2E_2B @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V0l1 ) @ ( c_2Elist_2ELENGTH @ tyop_2Estring_2Echar @ V1l2 ) ) ) ).

thf(thm_2Estring_2EisPREFIX__DEF,axiom,
    ! [V0s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Elist_2EisPREFIX @ tyop_2Estring_2Echar @ V0s1 @ V1s2 )
      = ( c_2Epair_2Epair__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) @ ( c_2Estring_2EDEST__STRING @ V0s1 ) @ ( c_2Estring_2EDEST__STRING @ V1s2 ) )
        @ ^ [V2v: tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ),V3v1: tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) )] :
            ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ $o @ V2v @ c_2Ebool_2ET
            @ ^ [V4v2: tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )] :
                ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ $o @ V3v1 @ c_2Ebool_2EF
                @ ^ [V5v3: tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar )] :
                    ( c_2Epair_2Epair__CASE @ $o @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V5v3
                    @ ^ [V6c2: tyop_2Estring_2Echar,V7t2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
                        ( c_2Epair_2Epair__CASE @ $o @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V4v2
                        @ ^ [V8c1: tyop_2Estring_2Echar,V9t1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( c_2Ebool_2E_2F_5C @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V8c1 @ V6c2 ) @ ( c_2Elist_2EisPREFIX @ tyop_2Estring_2Echar @ V9t1 @ V7t2 ) ) ) ) ) ) ) ) ).

thf(thm_2Estring_2EisPREFIX__IND,axiom,
    ! [V0P: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o] :
      ( ! [V1s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
          ( ! [V3c: tyop_2Estring_2Echar,V4t1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V5t2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
              ( ( ( ( c_2Estring_2EDEST__STRING @ V1s1 )
                  = ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( c_2Epair_2E_2C @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V3c @ V4t1 ) ) )
                & ( ( c_2Estring_2EDEST__STRING @ V2s2 )
                  = ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( c_2Epair_2E_2C @ tyop_2Estring_2Echar @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V3c @ V5t2 ) ) ) )
             => ( V0P @ V4t1 @ V5t2 ) )
         => ( V0P @ V1s1 @ V2s2 ) )
     => ! [V6v: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V7v1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( V0P @ V6v @ V7v1 ) ) ).

thf(thm_2Estring_2EisPREFIX__STRCAT,axiom,
    ! [V0s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Elist_2EisPREFIX @ tyop_2Estring_2Echar @ V0s1 @ V1s2 )
    <=> ? [V2s3: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
          ( V1s2
          = ( c_2Elist_2EAPPEND @ tyop_2Estring_2Echar @ V0s1 @ V2s3 ) ) ) ).

thf(thm_2Estring_2Estring__lt__ind,axiom,
    ! [V0P: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o] :
      ( ( ! [V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( V0P @ V1s @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
        & ! [V2c: tyop_2Estring_2Echar,V3s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( V0P @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V2c @ V3s ) )
        & ! [V4c1: tyop_2Estring_2Echar,V5s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V6c2: tyop_2Estring_2Echar,V7s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
            ( ( V0P @ V5s1 @ V7s2 )
           => ( V0P @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V4c1 @ V5s1 ) @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V6c2 @ V7s2 ) ) ) )
     => ! [V8v: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V9v1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( V0P @ V8v @ V9v1 ) ) ).

thf(thm_2Estring_2Estring__lt__def,axiom,
    ( ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
        ( ( c_2Estring_2Estring__lt @ V0s @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) )
        = c_2Ebool_2EF )
    & ! [V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2c: tyop_2Estring_2Echar] :
        ( ( c_2Estring_2Estring__lt @ ( c_2Elist_2ENIL @ tyop_2Estring_2Echar ) @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V2c @ V1s ) )
        = c_2Ebool_2ET )
    & ! [V3s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V4s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V5c2: tyop_2Estring_2Echar,V6c1: tyop_2Estring_2Echar] :
        ( ( c_2Estring_2Estring__lt @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V6c1 @ V4s1 ) @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V5c2 @ V3s2 ) )
      <=> ( ( c_2Estring_2Echar__lt @ V6c1 @ V5c2 )
          | ( ( V6c1 = V5c2 )
            & ( c_2Estring_2Estring__lt @ V4s1 @ V3s2 ) ) ) ) ) ).

thf(thm_2Estring_2Estring__lt__nonrefl,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( (~) @ ( c_2Estring_2Estring__lt @ V0s @ V0s ) ) ).

thf(thm_2Estring_2Estring__lt__antisym,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( (~)
      @ ( ( c_2Estring_2Estring__lt @ V0s @ V1t )
        & ( c_2Estring_2Estring__lt @ V1t @ V0s ) ) ) ).

thf(thm_2Estring_2Estring__lt__cases,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( V0s = V1t )
      | ( c_2Estring_2Estring__lt @ V0s @ V1t )
      | ( c_2Estring_2Estring__lt @ V1t @ V0s ) ) ).

thf(thm_2Estring_2Estring__lt__trans,axiom,
    ! [V0s1: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1s2: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2s3: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Estring_2Estring__lt @ V0s1 @ V1s2 )
        & ( c_2Estring_2Estring__lt @ V1s2 @ V2s3 ) )
     => ( c_2Estring_2Estring__lt @ V0s1 @ V2s3 ) ) ).

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