ITP001 Axioms: ITP054^7.ax
%------------------------------------------------------------------------------
% File : ITP054^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : 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 ) ) ).
%------------------------------------------------------------------------------