ITP001 Axioms: ITP094^7.ax
%------------------------------------------------------------------------------
% File : ITP094^7 : 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 : bitstring.ax [Gau19]
% : HL4094^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 268 ( 88 unt; 145 typ; 0 def)
% Number of atoms : 478 ( 170 equ; 3 cnn)
% Maximal formula atoms : 34 ( 1 avg)
% Number of connectives : 3049 ( 3 ~; 1 |; 69 &;2937 @)
% ( 17 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 5 avg;2937 nst)
% Number of types : 5 ( 4 usr)
% Number of type conns : 275 ( 275 >; 0 *; 0 +; 0 <<)
% Number of symbols : 143 ( 141 usr; 5 con; 0-5 aty)
% Number of variables : 562 ( 24 ^ 436 !; 3 ?; 562 :)
% ( 99 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
thf(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: $tType > $tType > $tType ).
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_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(tyop_2Estring_2Echar,type,
tyop_2Estring_2Echar: $tType ).
thf(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: $tType > $tType > $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_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
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_2Emarker_2EAbbrev,type,
c_2Emarker_2EAbbrev: $o > $o ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EBIT2,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Estring_2ECHR,type,
c_2Estring_2ECHR: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Elist_2ECONS,type,
c_2Elist_2ECONS:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EDROP,type,
c_2Elist_2EDROP:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EEL,type,
c_2Elist_2EEL:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).
thf(c_2Elist_2EEVERY,type,
c_2Elist_2EEVERY:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Earithmetic_2EEXP,type,
c_2Earithmetic_2EEXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
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_2Efcp_2EFCP,type,
c_2Efcp_2EFCP:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum > A_27a ) > ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) ) ).
thf(c_2Epred__set_2EFINITE,type,
c_2Epred__set_2EFINITE:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
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_2EFOLDL,type,
c_2Elist_2EFOLDL:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27b > A_27a > A_27b ) > A_27b > ( tyop_2Elist_2Elist @ A_27a ) > A_27b ) ).
thf(c_2Elist_2EGENLIST,type,
c_2Elist_2EGENLIST:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum > A_27a ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EHD,type,
c_2Elist_2EHD:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).
thf(c_2Ecombin_2EK,type,
c_2Ecombin_2EK:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > A_27a ) ).
thf(c_2Elist_2ELAST,type,
c_2Elist_2ELAST:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).
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_2Earithmetic_2EMAX,type,
c_2Earithmetic_2EMAX: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EMIN,type,
c_2Earithmetic_2EMIN: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EMOD,type,
c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebit_2EMOD__2EXP,type,
c_2Ebit_2EMOD__2EXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Elist_2ENIL,type,
c_2Elist_2ENIL:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist @ 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_2Elist_2EPAD__LEFT,type,
c_2Elist_2EPAD__LEFT:
!>[A_27a: $tType] : ( A_27a > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EPAD__RIGHT,type,
c_2Elist_2EPAD__RIGHT:
!>[A_27a: $tType] : ( A_27a > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EREVERSE,type,
c_2Elist_2EREVERSE:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
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_2ETAKE,type,
c_2Elist_2ETAKE:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2ETL,type,
c_2Elist_2ETL:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
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_2Epred__set_2EUNIV,type,
c_2Epred__set_2EUNIV:
!>[A_27a: $tType] : ( A_27a > $o ) ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Elist_2EZIP,type,
c_2Elist_2EZIP:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) > ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ebitstring_2Eadd,type,
c_2Ebitstring_2Eadd: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Eband,type,
c_2Ebitstring_2Eband: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Ebitify,type,
c_2Ebitstring_2Ebitify: ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ).
thf(c_2Ebitstring_2Ebitwise,type,
c_2Ebitstring_2Ebitwise: ( $o > $o > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Ebnand,type,
c_2Ebitstring_2Ebnand: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Ebnor,type,
c_2Ebitstring_2Ebnor: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Ebnot,type,
c_2Ebitstring_2Ebnot: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Eboolify,type,
c_2Ebitstring_2Eboolify: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Ebor,type,
c_2Ebitstring_2Ebor: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Ebxnor,type,
c_2Ebitstring_2Ebxnor: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Ebxor,type,
c_2Ebitstring_2Ebxor: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Efcp_2Edimindex,type,
c_2Efcp_2Edimindex:
!>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ebitstring_2Eextend,type,
c_2Ebitstring_2Eextend: $o > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Efcp_2Efcp__index,type,
c_2Efcp_2Efcp__index:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) > tyop_2Enum_2Enum > A_27a ) ).
thf(c_2Ebitstring_2Efield,type,
c_2Ebitstring_2Efield: tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Efield__insert,type,
c_2Ebitstring_2Efield__insert: tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Efixwidth,type,
c_2Ebitstring_2Efixwidth: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Emodify,type,
c_2Ebitstring_2Emodify: ( tyop_2Enum_2Enum > $o > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2En2v,type,
c_2Ebitstring_2En2v: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ewords_2En2w,type,
c_2Ewords_2En2w:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Enumposrep_2Enum__from__bin__list,type,
c_2Enumposrep_2Enum__from__bin__list: ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
thf(c_2Enumposrep_2Enum__to__bin__list,type,
c_2Enumposrep_2Enum__to__bin__list: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2Ereduce__and,type,
c_2Ewords_2Ereduce__and:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) ).
thf(c_2Ewords_2Ereduce__or,type,
c_2Ewords_2Ereduce__or:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) ).
thf(c_2Ebitstring_2Ereplicate,type,
c_2Ebitstring_2Ereplicate: ( tyop_2Elist_2Elist @ $o ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Erev__count__list,type,
c_2Ebitstring_2Erev__count__list: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ).
thf(c_2Ebitstring_2Erotate,type,
c_2Ebitstring_2Erotate: ( tyop_2Elist_2Elist @ $o ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Es2v,type,
c_2Ebitstring_2Es2v: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Eshiftl,type,
c_2Ebitstring_2Eshiftl: ( tyop_2Elist_2Elist @ $o ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Eshiftr,type,
c_2Ebitstring_2Eshiftr: ( tyop_2Elist_2Elist @ $o ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Esign__extend,type,
c_2Ebitstring_2Esign__extend:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ewords_2Esw2sw,type,
c_2Ewords_2Esw2sw:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).
thf(c_2Ebitstring_2Etestbit,type,
c_2Ebitstring_2Etestbit: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > $o ).
thf(c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself @ A_27a ) ).
thf(c_2Ebitstring_2Ev2n,type,
c_2Ebitstring_2Ev2n: ( tyop_2Elist_2Elist @ $o ) > tyop_2Enum_2Enum ).
thf(c_2Ebitstring_2Ev2s,type,
c_2Ebitstring_2Ev2s: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).
thf(c_2Ebitstring_2Ev2w,type,
c_2Ebitstring_2Ev2w:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Ew2n,type,
c_2Ewords_2Ew2n:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ebitstring_2Ew2v,type,
c_2Ebitstring_2Ew2v:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2Ewords_2Ew2w,type,
c_2Ewords_2Ew2w:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).
thf(c_2Ewords_2Eword__1comp,type,
c_2Ewords_2Eword__1comp:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__2comp,type,
c_2Ewords_2Eword__2comp:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__add,type,
c_2Ewords_2Eword__add:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__and,type,
c_2Ewords_2Eword__and:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__asr,type,
c_2Ewords_2Eword__asr:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__bit,type,
c_2Ewords_2Eword__bit:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__bits,type,
c_2Ewords_2Eword__bits:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__concat,type,
c_2Ewords_2Eword__concat:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) > ( tyop_2Efcp_2Ecart @ $o @ A_27c ) ) ).
thf(c_2Ewords_2Eword__div,type,
c_2Ewords_2Eword__div:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__extract,type,
c_2Ewords_2Eword__extract:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).
thf(c_2Ewords_2Eword__ge,type,
c_2Ewords_2Eword__ge:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__gt,type,
c_2Ewords_2Eword__gt:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__hi,type,
c_2Ewords_2Eword__hi:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__hs,type,
c_2Ewords_2Eword__hs:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__join,type,
c_2Ewords_2Eword__join:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ).
thf(c_2Ewords_2Eword__le,type,
c_2Ewords_2Eword__le:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__lo,type,
c_2Ewords_2Eword__lo:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__log2,type,
c_2Ewords_2Eword__log2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__ls,type,
c_2Ewords_2Eword__ls:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__lsb,type,
c_2Ewords_2Eword__lsb:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__lsl,type,
c_2Ewords_2Eword__lsl:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__lsr,type,
c_2Ewords_2Eword__lsr:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__lt,type,
c_2Ewords_2Eword__lt:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__mod,type,
c_2Ewords_2Eword__mod:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__modify,type,
c_2Ewords_2Eword__modify:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum > $o > $o ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__msb,type,
c_2Ewords_2Eword__msb:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__mul,type,
c_2Ewords_2Eword__mul:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__nand,type,
c_2Ewords_2Eword__nand:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__nor,type,
c_2Ewords_2Eword__nor:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__or,type,
c_2Ewords_2Eword__or:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__quot,type,
c_2Ewords_2Eword__quot:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__reduce,type,
c_2Ewords_2Eword__reduce:
!>[A_27a: $tType] : ( ( $o > $o > $o ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) ).
thf(c_2Ewords_2Eword__reverse,type,
c_2Ewords_2Eword__reverse:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__ror,type,
c_2Ewords_2Eword__ror:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__slice,type,
c_2Ewords_2Eword__slice:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__sub,type,
c_2Ewords_2Eword__sub:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__xnor,type,
c_2Ewords_2Eword__xnor:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__xor,type,
c_2Ewords_2Eword__xor:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ebitstring_2Ezero__extend,type,
c_2Ebitstring_2Ezero__extend: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
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_2Ebitstring_2Eextend__def,axiom,
( ! [V0v0: $o,V1l: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eextend @ V0v0 @ c_2Enum_2E0 @ V1l )
= V1l )
& ! [V2c: $o,V3n: tyop_2Enum_2Enum,V4l: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eextend @ V2c @ ( c_2Enum_2ESUC @ V3n ) @ V4l )
= ( c_2Ebitstring_2Eextend @ V2c @ V3n @ ( c_2Elist_2ECONS @ $o @ V2c @ V4l ) ) ) ) ).
thf(thm_2Ebitstring_2Eboolify__def,axiom,
( ! [V0a: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eboolify @ V0a @ ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) )
= V0a )
& ! [V1a: tyop_2Elist_2Elist @ $o,V2n: tyop_2Enum_2Enum,V3l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Eboolify @ V1a @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ V2n @ V3l ) )
= ( c_2Ebitstring_2Eboolify @ ( c_2Elist_2ECONS @ $o @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2n @ c_2Enum_2E0 ) ) @ V1a ) @ V3l ) ) ) ).
thf(thm_2Ebitstring_2En2v__def,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2En2v @ V0n )
= ( c_2Ebitstring_2Eboolify @ ( c_2Elist_2ENIL @ $o ) @ ( c_2Enumposrep_2Enum__to__bin__list @ V0n ) ) ) ).
thf(thm_2Ebitstring_2Ev2n__def,axiom,
! [V0l: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Ev2n @ V0l )
= ( c_2Enumposrep_2Enum__from__bin__list @ ( c_2Ebitstring_2Ebitify @ ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) @ V0l ) ) ) ).
thf(thm_2Ebitstring_2Es2v__def,axiom,
( c_2Ebitstring_2Es2v
= ( c_2Elist_2EMAP @ tyop_2Estring_2Echar @ $o
@ ^ [V0c: tyop_2Estring_2Echar] : ( c_2Ebool_2E_5C_2F @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V0c @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( c_2Emin_2E_3D @ tyop_2Estring_2Echar @ V0c @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ebitstring_2Ev2s__def,axiom,
( c_2Ebitstring_2Ev2s
= ( c_2Elist_2EMAP @ $o @ tyop_2Estring_2Echar
@ ^ [V0b: $o] : ( c_2Ebool_2ECOND @ tyop_2Estring_2Echar @ V0b @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ebitstring_2Ezero__extend__def,axiom,
! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Ezero__extend @ V0n @ V1v )
= ( c_2Elist_2EPAD__LEFT @ $o @ c_2Ebool_2EF @ V0n @ V1v ) ) ).
thf(thm_2Ebitstring_2Esign__extend__def,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Ebitstring_2Esign__extend @ A_27a @ V0n @ V1v )
= ( c_2Elist_2EPAD__LEFT @ A_27a @ ( c_2Elist_2EHD @ A_27a @ V1v ) @ V0n @ V1v ) ) ).
thf(thm_2Ebitstring_2Efixwidth__def,axiom,
! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Efixwidth @ V0n @ V1v )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V2l: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Eprim__rec_2E_3C @ V2l @ V0n ) @ ( c_2Ebitstring_2Ezero__extend @ V0n @ V1v ) @ ( c_2Elist_2EDROP @ $o @ ( c_2Earithmetic_2E_2D @ V2l @ V0n ) @ V1v ) )
@ ( c_2Elist_2ELENGTH @ $o @ V1v ) ) ) ).
thf(thm_2Ebitstring_2Eshiftl__def,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1m: tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Eshiftl @ V0v @ V1m )
= ( c_2Elist_2EPAD__RIGHT @ $o @ c_2Ebool_2EF @ ( c_2Earithmetic_2E_2B @ ( c_2Elist_2ELENGTH @ $o @ V0v ) @ V1m ) @ V0v ) ) ).
thf(thm_2Ebitstring_2Eshiftr__def,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1m: tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Eshiftr @ V0v @ V1m )
= ( c_2Elist_2ETAKE @ $o @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ $o @ V0v ) @ V1m ) @ V0v ) ) ).
thf(thm_2Ebitstring_2Efield__def,axiom,
! [V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Efield @ V0h @ V1l @ V2v )
= ( c_2Ebitstring_2Efixwidth @ ( c_2Earithmetic_2E_2D @ ( c_2Enum_2ESUC @ V0h ) @ V1l ) @ ( c_2Ebitstring_2Eshiftr @ V2v @ V1l ) ) ) ).
thf(thm_2Ebitstring_2Erotate__def,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1m: tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Erotate @ V0v @ V1m )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V2l: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V3x: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2l @ c_2Enum_2E0 ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V3x @ c_2Enum_2E0 ) ) @ V0v @ ( c_2Elist_2EAPPEND @ $o @ ( c_2Ebitstring_2Efield @ ( c_2Earithmetic_2E_2D @ V3x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V0v ) @ ( c_2Ebitstring_2Efield @ ( c_2Earithmetic_2E_2D @ V2l @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V3x @ V0v ) ) )
@ ( c_2Earithmetic_2EMOD @ V1m @ V2l ) )
@ ( c_2Elist_2ELENGTH @ $o @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Etestbit__def,axiom,
! [V0b: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Etestbit @ V0b @ V1v )
<=> ( ( c_2Ebitstring_2Efield @ V0b @ V0b @ V1v )
= ( c_2Elist_2ECONS @ $o @ c_2Ebool_2ET @ ( c_2Elist_2ENIL @ $o ) ) ) ) ).
thf(thm_2Ebitstring_2Ew2v__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ebitstring_2Ew2v @ A_27a @ V0w )
= ( c_2Elist_2EGENLIST @ $o
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1i ) )
@ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ebitstring_2Ev2w__def,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Ev2w @ A_27a @ V0v )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Ebitstring_2Etestbit @ V1i @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Erev__count__list__def,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Erev__count__list @ V0n )
= ( c_2Elist_2EGENLIST @ tyop_2Enum_2Enum
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1i )
@ V0n ) ) ).
thf(thm_2Ebitstring_2Emodify__def,axiom,
! [V0f: tyop_2Enum_2Enum > $o > $o,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Emodify @ V0f @ V1v )
= ( c_2Elist_2EMAP @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ $o ) @ $o @ ( c_2Epair_2EUNCURRY @ tyop_2Enum_2Enum @ $o @ $o @ V0f ) @ ( c_2Elist_2EZIP @ tyop_2Enum_2Enum @ $o @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Ebitstring_2Erev__count__list @ ( c_2Elist_2ELENGTH @ $o @ V1v ) ) @ V1v ) ) ) ) ).
thf(thm_2Ebitstring_2Efield__insert__def,axiom,
! [V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2s: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Efield__insert @ V0h @ V1l @ V2s )
= ( c_2Ebitstring_2Emodify
@ ^ [V3i: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2E_3C_3D @ V1l @ V3i ) @ ( c_2Earithmetic_2E_3C_3D @ V3i @ V0h ) ) @ ( c_2Ebitstring_2Etestbit @ ( c_2Earithmetic_2E_2D @ V3i @ V1l ) @ V2s ) ) ) ) ).
thf(thm_2Ebitstring_2Eadd__def,axiom,
! [V0a: tyop_2Elist_2Elist @ $o,V1b: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eadd @ V0a @ V1b )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V2m: tyop_2Enum_2Enum] : ( c_2Ebitstring_2Ezero__extend @ V2m @ ( c_2Ebitstring_2En2v @ ( c_2Earithmetic_2E_2B @ ( c_2Ebitstring_2Ev2n @ V0a ) @ ( c_2Ebitstring_2Ev2n @ V1b ) ) ) )
@ ( c_2Earithmetic_2EMAX @ ( c_2Elist_2ELENGTH @ $o @ V0a ) @ ( c_2Elist_2ELENGTH @ $o @ V1b ) ) ) ) ).
thf(thm_2Ebitstring_2Ebitwise__def,axiom,
! [V0f: $o > $o > $o,V1v1: tyop_2Elist_2Elist @ $o,V2v2: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Ebitwise @ V0f @ V1v1 @ V2v2 )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V3m: tyop_2Enum_2Enum] : ( c_2Elist_2EMAP @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ $o @ ( c_2Epair_2EUNCURRY @ $o @ $o @ $o @ V0f ) @ ( c_2Elist_2EZIP @ $o @ $o @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ $o ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Ebitstring_2Efixwidth @ V3m @ V1v1 ) @ ( c_2Ebitstring_2Efixwidth @ V3m @ V2v2 ) ) ) )
@ ( c_2Earithmetic_2EMAX @ ( c_2Elist_2ELENGTH @ $o @ V1v1 ) @ ( c_2Elist_2ELENGTH @ $o @ V2v2 ) ) ) ) ).
thf(thm_2Ebitstring_2Ebnot__def,axiom,
( c_2Ebitstring_2Ebnot
= ( c_2Elist_2EMAP @ $o @ $o @ c_2Ebool_2E_7E ) ) ).
thf(thm_2Ebitstring_2Ebor__def,axiom,
( c_2Ebitstring_2Ebor
= ( c_2Ebitstring_2Ebitwise @ c_2Ebool_2E_5C_2F ) ) ).
thf(thm_2Ebitstring_2Eband__def,axiom,
( c_2Ebitstring_2Eband
= ( c_2Ebitstring_2Ebitwise @ c_2Ebool_2E_2F_5C ) ) ).
thf(thm_2Ebitstring_2Ebxor__def,axiom,
( c_2Ebitstring_2Ebxor
= ( c_2Ebitstring_2Ebitwise
@ ^ [V0x: $o,V1y: $o] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ V0x @ V1y ) ) ) ) ).
thf(thm_2Ebitstring_2Ebnor__def,axiom,
( c_2Ebitstring_2Ebnor
= ( c_2Ebitstring_2Ebitwise
@ ^ [V0x: $o,V1y: $o] : ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_5C_2F @ V0x @ V1y ) ) ) ) ).
thf(thm_2Ebitstring_2Ebxnor__def,axiom,
( c_2Ebitstring_2Ebxnor
= ( c_2Ebitstring_2Ebitwise @ ( c_2Emin_2E_3D @ $o ) ) ) ).
thf(thm_2Ebitstring_2Ebnand__def,axiom,
( c_2Ebitstring_2Ebnand
= ( c_2Ebitstring_2Ebitwise
@ ^ [V0x: $o,V1y: $o] : ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_2F_5C @ V0x @ V1y ) ) ) ) ).
thf(thm_2Ebitstring_2Ereplicate__def,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1n: tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Ereplicate @ V0v @ V1n )
= ( c_2Elist_2EFLAT @ $o @ ( c_2Elist_2EGENLIST @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Ecombin_2EK @ ( tyop_2Elist_2Elist @ $o ) @ tyop_2Enum_2Enum @ V0v ) @ V1n ) ) ) ).
thf(thm_2Ebitstring_2Eextend__def__compute,axiom,
( ! [V0v0: $o,V1l: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eextend @ V0v0 @ c_2Enum_2E0 @ V1l )
= V1l )
& ! [V2c: $o,V3n: tyop_2Enum_2Enum,V4l: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eextend @ V2c @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V3n ) ) @ V4l )
= ( c_2Ebitstring_2Eextend @ V2c @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V3n ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Elist_2ECONS @ $o @ V2c @ V4l ) ) )
& ! [V5c: $o,V6n: tyop_2Enum_2Enum,V7l: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eextend @ V5c @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V6n ) ) @ V7l )
= ( c_2Ebitstring_2Eextend @ V5c @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V6n ) ) @ ( c_2Elist_2ECONS @ $o @ V5c @ V7l ) ) ) ) ).
thf(thm_2Ebitstring_2Ebitify__ind,axiom,
! [V0P: ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > ( tyop_2Elist_2Elist @ $o ) > $o] :
( ( ! [V1a: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] : ( V0P @ V1a @ ( c_2Elist_2ENIL @ $o ) )
& ! [V2a: tyop_2Elist_2Elist @ tyop_2Enum_2Enum,V3l: tyop_2Elist_2Elist @ $o] :
( ( V0P @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ c_2Enum_2E0 @ V2a ) @ V3l )
=> ( V0P @ V2a @ ( c_2Elist_2ECONS @ $o @ c_2Ebool_2EF @ V3l ) ) )
& ! [V4a: tyop_2Elist_2Elist @ tyop_2Enum_2Enum,V5l: tyop_2Elist_2Elist @ $o] :
( ( V0P @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V4a ) @ V5l )
=> ( V0P @ V4a @ ( c_2Elist_2ECONS @ $o @ c_2Ebool_2ET @ V5l ) ) ) )
=> ! [V6v: tyop_2Elist_2Elist @ tyop_2Enum_2Enum,V7v1: tyop_2Elist_2Elist @ $o] : ( V0P @ V6v @ V7v1 ) ) ).
thf(thm_2Ebitstring_2Ebitify__def,axiom,
( ! [V0a: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Ebitify @ V0a @ ( c_2Elist_2ENIL @ $o ) )
= V0a )
& ! [V1l: tyop_2Elist_2Elist @ $o,V2a: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Ebitify @ V2a @ ( c_2Elist_2ECONS @ $o @ c_2Ebool_2EF @ V1l ) )
= ( c_2Ebitstring_2Ebitify @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ c_2Enum_2E0 @ V2a ) @ V1l ) )
& ! [V3l: tyop_2Elist_2Elist @ $o,V4a: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Ebitify @ V4a @ ( c_2Elist_2ECONS @ $o @ c_2Ebool_2ET @ V3l ) )
= ( c_2Ebitstring_2Ebitify @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V4a ) @ V3l ) ) ) ).
thf(thm_2Ebitstring_2Eextend__cons,axiom,
! [V0n: tyop_2Enum_2Enum,V1c: $o,V2l: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eextend @ V1c @ ( c_2Enum_2ESUC @ V0n ) @ V2l )
= ( c_2Elist_2ECONS @ $o @ V1c @ ( c_2Ebitstring_2Eextend @ V1c @ V0n @ V2l ) ) ) ).
thf(thm_2Ebitstring_2Epad__left__extend,axiom,
! [V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ $o,V2c: $o] :
( ( c_2Elist_2EPAD__LEFT @ $o @ V2c @ V0n @ V1l )
= ( c_2Ebitstring_2Eextend @ V2c @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Elist_2ELENGTH @ $o @ V1l ) ) @ V1l ) ) ).
thf(thm_2Ebitstring_2Eextend,axiom,
( ! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Ezero__extend @ V0n @ V1v )
= ( c_2Ebitstring_2Eextend @ c_2Ebool_2EF @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Elist_2ELENGTH @ $o @ V1v ) ) @ V1v ) )
& ! [V2n: tyop_2Enum_2Enum,V3v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Esign__extend @ $o @ V2n @ V3v )
= ( c_2Ebitstring_2Eextend @ ( c_2Elist_2EHD @ $o @ V3v ) @ ( c_2Earithmetic_2E_2D @ V2n @ ( c_2Elist_2ELENGTH @ $o @ V3v ) ) @ V3v ) ) ) ).
thf(thm_2Ebitstring_2Efixwidth,axiom,
! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Efixwidth @ V0n @ V1v )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V2l: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Eprim__rec_2E_3C @ V2l @ V0n ) @ ( c_2Ebitstring_2Eextend @ c_2Ebool_2EF @ ( c_2Earithmetic_2E_2D @ V0n @ V2l ) @ V1v ) @ ( c_2Elist_2EDROP @ $o @ ( c_2Earithmetic_2E_2D @ V2l @ V0n ) @ V1v ) )
@ ( c_2Elist_2ELENGTH @ $o @ V1v ) ) ) ).
thf(thm_2Ebitstring_2Efixwidth__id,axiom,
! [V0w: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Efixwidth @ ( c_2Elist_2ELENGTH @ $o @ V0w ) @ V0w )
= V0w ) ).
thf(thm_2Ebitstring_2Efixwidth__id__imp,axiom,
! [V0n: tyop_2Enum_2Enum,V1w: tyop_2Elist_2Elist @ $o] :
( ( V0n
= ( c_2Elist_2ELENGTH @ $o @ V1w ) )
=> ( ( c_2Ebitstring_2Efixwidth @ V0n @ V1w )
= V1w ) ) ).
thf(thm_2Ebitstring_2Eboolify__reverse__map,axiom,
! [V0v: tyop_2Elist_2Elist @ tyop_2Enum_2Enum,V1a: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eboolify @ V1a @ V0v )
= ( c_2Elist_2EAPPEND @ $o
@ ( c_2Elist_2EREVERSE @ $o
@ ( c_2Elist_2EMAP @ tyop_2Enum_2Enum @ $o
@ ^ [V2n: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2n @ c_2Enum_2E0 ) )
@ V0v ) )
@ V1a ) ) ).
thf(thm_2Ebitstring_2Ebitify__reverse__map,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1a: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Ebitify @ V1a @ V0v )
= ( c_2Elist_2EAPPEND @ tyop_2Enum_2Enum
@ ( c_2Elist_2EREVERSE @ tyop_2Enum_2Enum
@ ( c_2Elist_2EMAP @ $o @ tyop_2Enum_2Enum
@ ^ [V2b: $o] : ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ V2b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 )
@ V0v ) )
@ V1a ) ) ).
thf(thm_2Ebitstring_2Eevery__bit__bitify,axiom,
! [V0v: tyop_2Elist_2Elist @ $o] : ( c_2Elist_2EEVERY @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_3E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebitstring_2Ebitify @ ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) @ V0v ) ) ).
thf(thm_2Ebitstring_2Elength__pad__left,axiom,
! [A_27a: $tType,V0x: A_27a,V1n: tyop_2Enum_2Enum,V2a: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Elist_2EPAD__LEFT @ A_27a @ V0x @ V1n @ V2a ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Eprim__rec_2E_3C @ ( c_2Elist_2ELENGTH @ A_27a @ V2a ) @ V1n ) @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V2a ) ) ) ).
thf(thm_2Ebitstring_2Elength__pad__right,axiom,
! [A_27a: $tType,V0x: A_27a,V1n: tyop_2Enum_2Enum,V2a: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Elist_2EPAD__RIGHT @ A_27a @ V0x @ V1n @ V2a ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Eprim__rec_2E_3C @ ( c_2Elist_2ELENGTH @ A_27a @ V2a ) @ V1n ) @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V2a ) ) ) ).
thf(thm_2Ebitstring_2Elength__zero__extend,axiom,
! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Elist_2ELENGTH @ $o @ V1v ) @ V0n )
=> ( ( c_2Elist_2ELENGTH @ $o @ ( c_2Ebitstring_2Ezero__extend @ V0n @ V1v ) )
= V0n ) ) ).
thf(thm_2Ebitstring_2Elength__sign__extend,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Elist_2ELENGTH @ A_27a @ V1v ) @ V0n )
=> ( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Ebitstring_2Esign__extend @ A_27a @ V0n @ V1v ) )
= V0n ) ) ).
thf(thm_2Ebitstring_2Elength__fixwidth,axiom,
! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Elist_2ELENGTH @ $o @ ( c_2Ebitstring_2Efixwidth @ V0n @ V1v ) )
= V0n ) ).
thf(thm_2Ebitstring_2Elength__field,axiom,
! [V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2v: tyop_2Elist_2Elist @ $o] :
( ( c_2Elist_2ELENGTH @ $o @ ( c_2Ebitstring_2Efield @ V0h @ V1l @ V2v ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Enum_2ESUC @ V0h ) @ V1l ) ) ).
thf(thm_2Ebitstring_2Elength__bitify,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Elist_2ELENGTH @ tyop_2Enum_2Enum @ ( c_2Ebitstring_2Ebitify @ V1l @ V0v ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Elist_2ELENGTH @ tyop_2Enum_2Enum @ V1l ) @ ( c_2Elist_2ELENGTH @ $o @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Elength__bitify__null,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o,V1l: A_27a] :
( ( c_2Elist_2ELENGTH @ tyop_2Enum_2Enum @ ( c_2Ebitstring_2Ebitify @ ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) @ V0v ) )
= ( c_2Elist_2ELENGTH @ $o @ V0v ) ) ).
thf(thm_2Ebitstring_2Elength__shiftr,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1n: tyop_2Enum_2Enum] :
( ( c_2Elist_2ELENGTH @ $o @ ( c_2Ebitstring_2Eshiftr @ V0v @ V1n ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ $o @ V0v ) @ V1n ) ) ).
thf(thm_2Ebitstring_2Elength__rev__count__list,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Elist_2ELENGTH @ tyop_2Enum_2Enum @ ( c_2Ebitstring_2Erev__count__list @ V0n ) )
= V0n ) ).
thf(thm_2Ebitstring_2Elength__w2v,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Elist_2ELENGTH @ $o @ ( c_2Ebitstring_2Ew2v @ A_27a @ V0w ) )
= ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ebitstring_2Elength__rotate,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1n: tyop_2Enum_2Enum] :
( ( c_2Elist_2ELENGTH @ $o @ ( c_2Ebitstring_2Erotate @ V0v @ V1n ) )
= ( c_2Elist_2ELENGTH @ $o @ V0v ) ) ).
thf(thm_2Ebitstring_2Eel__rev__count__list,axiom,
! [V0n: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1i @ V0n )
=> ( ( c_2Elist_2EEL @ tyop_2Enum_2Enum @ V1i @ ( c_2Ebitstring_2Erev__count__list @ V0n ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1i ) ) ) ).
thf(thm_2Ebitstring_2Eel__zero__extend,axiom,
! [V0n: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum,V2v: tyop_2Elist_2Elist @ $o] :
( ( c_2Elist_2EEL @ $o @ V1i @ ( c_2Ebitstring_2Ezero__extend @ V0n @ V2v ) )
<=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Elist_2ELENGTH @ $o @ V2v ) ) @ V1i )
& ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2D @ V1i @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Elist_2ELENGTH @ $o @ V2v ) ) ) @ V2v ) ) ) ).
thf(thm_2Ebitstring_2Eel__sign__extend,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum,V2v: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEL @ A_27a @ V1i @ ( c_2Ebitstring_2Esign__extend @ A_27a @ V0n @ V2v ) )
= ( c_2Ebool_2ECOND @ A_27a @ ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V2v ) ) ) @ ( c_2Elist_2EEL @ A_27a @ c_2Enum_2E0 @ V2v ) @ ( c_2Elist_2EEL @ A_27a @ ( c_2Earithmetic_2E_2D @ V1i @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V2v ) ) ) @ V2v ) ) ) ).
thf(thm_2Ebitstring_2Eel__fixwidth,axiom,
! [V0i: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2w: tyop_2Elist_2Elist @ $o] :
( ( c_2Eprim__rec_2E_3C @ V0i @ V1n )
=> ( ( c_2Elist_2EEL @ $o @ V0i @ ( c_2Ebitstring_2Efixwidth @ V1n @ V2w ) )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Eprim__rec_2E_3C @ ( c_2Elist_2ELENGTH @ $o @ V2w ) @ V1n ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ $o @ V2w ) ) @ V0i ) @ ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2D @ V0i @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ $o @ V2w ) ) ) @ V2w ) ) @ ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2B @ V0i @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ $o @ V2w ) @ V1n ) ) @ V2w ) ) ) ) ).
thf(thm_2Ebitstring_2Eel__field,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1h: tyop_2Enum_2Enum,V2l: tyop_2Enum_2Enum,V3i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V3i @ ( c_2Earithmetic_2E_2D @ ( c_2Enum_2ESUC @ V1h ) @ V2l ) )
=> ( ( c_2Elist_2EEL @ $o @ V3i @ ( c_2Ebitstring_2Efield @ V1h @ V2l @ V0v ) )
<=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Enum_2ESUC @ V1h ) @ ( c_2Earithmetic_2E_2B @ V3i @ ( c_2Elist_2ELENGTH @ $o @ V0v ) ) )
& ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ V3i @ ( c_2Elist_2ELENGTH @ $o @ V0v ) ) @ ( c_2Enum_2ESUC @ V1h ) ) @ V0v ) ) ) ) ).
thf(thm_2Ebitstring_2Eel__w2v,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Elist_2EEL @ $o @ V1n @ ( c_2Ebitstring_2Ew2v @ A_27a @ V0w ) )
= ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1n ) ) ) ) ).
thf(thm_2Ebitstring_2Eel__shiftr,axiom,
! [V0i: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o,V2n: tyop_2Enum_2Enum,V3d: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ V2n @ V3d )
& ( c_2Eprim__rec_2E_3C @ V0i @ ( c_2Earithmetic_2E_2D @ V3d @ V2n ) )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V3d ) )
=> ( ( c_2Elist_2EEL @ $o @ V0i @ ( c_2Ebitstring_2Eshiftr @ ( c_2Ebitstring_2Efixwidth @ V3d @ V1v ) @ V2n ) )
<=> ( ( c_2Earithmetic_2E_3C_3D @ V3d @ ( c_2Earithmetic_2E_2B @ V0i @ ( c_2Elist_2ELENGTH @ $o @ V1v ) ) )
& ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ V0i @ ( c_2Elist_2ELENGTH @ $o @ V1v ) ) @ V3d ) @ V1v ) ) ) ) ).
thf(thm_2Ebitstring_2Eshiftr__0,axiom,
! [V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eshiftr @ V0v @ c_2Enum_2E0 )
= V0v ) ).
thf(thm_2Ebitstring_2Efield__fixwidth,axiom,
! [V0h: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Efield @ V0h @ c_2Enum_2E0 @ V1v )
= ( c_2Ebitstring_2Efixwidth @ ( c_2Enum_2ESUC @ V0h ) @ V1v ) ) ).
thf(thm_2Ebitstring_2Etestbit,axiom,
! [V0b: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Etestbit @ V0b @ V1v )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ $o
@ ^ [V2n: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Eprim__rec_2E_3C @ V0b @ V2n ) @ ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2D @ V2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0b ) @ V1v ) )
@ ( c_2Elist_2ELENGTH @ $o @ V1v ) ) ) ).
thf(thm_2Ebitstring_2Etestbit__geq__len,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1i: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ $o @ V0v ) @ V1i )
=> ( (~) @ ( c_2Ebitstring_2Etestbit @ V1i @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Etestbit__el,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Elist_2ELENGTH @ $o @ V0v ) )
=> ( ( c_2Ebitstring_2Etestbit @ V1i @ V0v )
= ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ $o @ V0v ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1i ) @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Ebit__v2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__bit @ A_27a @ V0n @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) )
<=> ( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
& ( c_2Ebitstring_2Etestbit @ V0n @ V1v ) ) ) ).
thf(thm_2Ebitstring_2Eword__index__v2w,axiom,
! [A_27a: $tType,V0index_20too_20large: $o,V1v: tyop_2Elist_2Elist @ $o,V2i: tyop_2Enum_2Enum] :
( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) @ V2i )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Eprim__rec_2E_3C @ V2i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Ebitstring_2Etestbit @ V2i @ V1v ) @ ( c_2Ecombin_2EFAIL @ ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum > $o ) @ $o @ ( c_2Efcp_2Efcp__index @ $o @ A_27a ) @ V0index_20too_20large @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) @ V2i ) ) ) ).
thf(thm_2Ebitstring_2Etestbit__w2v,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ebitstring_2Etestbit @ V0n @ ( c_2Ebitstring_2Ew2v @ A_27a @ V1w ) )
= ( c_2Ewords_2Eword__bit @ A_27a @ V0n @ V1w ) ) ).
thf(thm_2Ebitstring_2Ew2v__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Ew2v @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v ) ) ).
thf(thm_2Ebitstring_2Ev2w__w2v,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Ew2v @ A_27a @ V0w ) )
= V0w ) ).
thf(thm_2Ebitstring_2Ev2w__fixwidth,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) ) ).
thf(thm_2Ebitstring_2Efixwidth__fixwidth,axiom,
! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Efixwidth @ V0n @ ( c_2Ebitstring_2Efixwidth @ V0n @ V1v ) )
= ( c_2Ebitstring_2Efixwidth @ V0n @ V1v ) ) ).
thf(thm_2Ebitstring_2Ebitstring__nchotomy,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
? [V1v: tyop_2Elist_2Elist @ $o] :
( V0w
= ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) ) ).
thf(thm_2Ebitstring_2Eranged__bitstring__nchotomy,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
? [V1v: tyop_2Elist_2Elist @ $o] :
( ( V0w
= ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) )
& ( c_2Emarker_2EAbbrev @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH @ $o @ V1v ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ebitstring_2Efixwidth__eq,axiom,
! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o,V2w: tyop_2Elist_2Elist @ $o] :
( ( ( c_2Ebitstring_2Efixwidth @ V0n @ V1v )
= ( c_2Ebitstring_2Efixwidth @ V0n @ V2w ) )
<=> ! [V3i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V3i @ V0n )
=> ( ( c_2Ebitstring_2Etestbit @ V3i @ V1v )
= ( c_2Ebitstring_2Etestbit @ V3i @ V2w ) ) ) ) ).
thf(thm_2Ebitstring_2Ev2w__11,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o,V1w: tyop_2Elist_2Elist @ $o] :
( ( ( c_2Ebitstring_2Ev2w @ A_27a @ V0v )
= ( c_2Ebitstring_2Ev2w @ A_27a @ V1w ) )
<=> ( ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v )
= ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1w ) ) ) ).
thf(thm_2Ebitstring_2Efield__concat__right,axiom,
! [V0h: tyop_2Enum_2Enum,V1a: tyop_2Elist_2Elist @ $o,V2b: tyop_2Elist_2Elist @ $o] :
( ( ( c_2Elist_2ELENGTH @ $o @ V2b )
= ( c_2Enum_2ESUC @ V0h ) )
=> ( ( c_2Ebitstring_2Efield @ V0h @ c_2Enum_2E0 @ ( c_2Elist_2EAPPEND @ $o @ V1a @ V2b ) )
= V2b ) ) ).
thf(thm_2Ebitstring_2Efield__concat__left,axiom,
! [V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2a: tyop_2Elist_2Elist @ $o,V3b: tyop_2Elist_2Elist @ $o] :
( ( ( c_2Earithmetic_2E_3C_3D @ V1l @ V0h )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ $o @ V3b ) @ V1l ) )
=> ( ( c_2Ebitstring_2Efield @ V0h @ V1l @ ( c_2Elist_2EAPPEND @ $o @ V2a @ V3b ) )
= ( c_2Ebitstring_2Efield @ ( c_2Earithmetic_2E_2D @ V0h @ ( c_2Elist_2ELENGTH @ $o @ V3b ) ) @ ( c_2Earithmetic_2E_2D @ V1l @ ( c_2Elist_2ELENGTH @ $o @ V3b ) ) @ V2a ) ) ) ).
thf(thm_2Ebitstring_2Efield__id__imp,axiom,
! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( ( c_2Enum_2ESUC @ V0n )
= ( c_2Elist_2ELENGTH @ $o @ V1v ) )
=> ( ( c_2Ebitstring_2Efield @ V0n @ c_2Enum_2E0 @ V1v )
= V1v ) ) ).
thf(thm_2Ebitstring_2Eshiftl__replicate__F,axiom,
! [V0v: tyop_2Elist_2Elist @ $o,V1n: tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Eshiftl @ V0v @ V1n )
= ( c_2Elist_2EAPPEND @ $o @ V0v @ ( c_2Ebitstring_2Ereplicate @ ( c_2Elist_2ECONS @ $o @ c_2Ebool_2EF @ ( c_2Elist_2ENIL @ $o ) ) @ V1n ) ) ) ).
thf(thm_2Ebitstring_2Eword__lsb__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__lsb @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
<=> ( ( (~)
@ ( V0v
= ( c_2Elist_2ENIL @ $o ) ) )
& ( c_2Elist_2ELAST @ $o @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Eword__msb__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ebitstring_2Etestbit @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0v ) ) ).
thf(thm_2Ebitstring_2Ew2w__v2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ebitstring_2Ev2w @ A_27b @ ( c_2Ebitstring_2Efixwidth @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Eprim__rec_2E_3C @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Esw2sw__v2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Esw2sw @ A_27a @ A_27b @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( c_2Eprim__rec_2E_3C @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ ( c_2Ebitstring_2Esign__extend @ $o @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v ) ) ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V0v ) ) ) ) ).
thf(thm_2Ebitstring_2En2w__v2n,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V0v ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) ) ).
thf(thm_2Ebitstring_2Ev2n__n2v,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Ev2n @ ( c_2Ebitstring_2En2v @ V0n ) )
= V0n ) ).
thf(thm_2Ebitstring_2Ev2w__n2v,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2En2v @ V0n ) )
= ( c_2Ewords_2En2w @ A_27a @ V0n ) ) ).
thf(thm_2Ebitstring_2Ew2n__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ebit_2EMOD__2EXP @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ebitstring_2Ev2n @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Ev2n__lt,axiom,
! [V0v: tyop_2Elist_2Elist @ $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebitstring_2Ev2n @ V0v ) @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Elist_2ELENGTH @ $o @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Eword__and__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o,V1w: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1w ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Eband @ V0v @ V1w ) ) ) ).
thf(thm_2Ebitstring_2Eword__or__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o,V1w: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1w ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Ebor @ V0v @ V1w ) ) ) ).
thf(thm_2Ebitstring_2Eword__xor__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o,V1w: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1w ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Ebxor @ V0v @ V1w ) ) ) ).
thf(thm_2Ebitstring_2Eword__nand__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o,V1w: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__nand @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1w ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Ebnand @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v ) @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1w ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__nor__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o,V1w: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__nor @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1w ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Ebnor @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v ) @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1w ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__xnor__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o,V1w: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__xnor @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1w ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Ebxnor @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v ) @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1w ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__1comp__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Ebnot @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__lsl__v2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) @ V0n )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Eshiftl @ V1v @ V0n ) ) ) ).
thf(thm_2Ebitstring_2Eword__lsr__v2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) @ V0n )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Eshiftr @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1v ) @ V0n ) ) ) ).
thf(thm_2Ebitstring_2Eword__modify__v2w,axiom,
! [A_27a: $tType,V0f: tyop_2Enum_2Enum > $o > $o,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__modify @ A_27a @ V0f @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Emodify @ V0f @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1v ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__bits__v2w,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ ( c_2Ebitstring_2Ev2w @ A_27a @ V2v ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Efield @ V0h @ V1l @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V2v ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__extract__v2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ ( c_2Ebitstring_2Ev2w @ A_27a @ V2v ) )
= ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ ( c_2Ebitstring_2Ev2w @ A_27a @ V2v ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__slice__v2w,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1l @ ( c_2Ebitstring_2Ev2w @ A_27a @ V2v ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Eshiftl @ ( c_2Ebitstring_2Efield @ V0h @ V1l @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V2v ) ) @ V1l ) ) ) ).
thf(thm_2Ebitstring_2Eword__asr__v2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__asr @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) @ V0n )
= ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ $o ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a )
@ ^ [V2l: tyop_2Elist_2Elist @ $o] : ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Esign__extend @ $o @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0n ) @ ( c_2Elist_2ECONS @ $o @ ( c_2Elist_2EHD @ $o @ V2l ) @ ( c_2Elist_2ENIL @ $o ) ) @ ( c_2Ebitstring_2Eshiftr @ V2l @ V0n ) ) ) )
@ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1v ) ) ) ).
thf(thm_2Ebitstring_2Eword__ror__v2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__ror @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) @ V0n )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Erotate @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1v ) @ V0n ) ) ) ).
thf(thm_2Ebitstring_2Eword__reverse__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Elist_2EREVERSE @ $o @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__join__v2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0v1: tyop_2Elist_2Elist @ $o,V1v2: tyop_2Elist_2Elist @ $o] :
( ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
& ( c_2Epred__set_2EFINITE @ A_27b @ ( c_2Epred__set_2EUNIV @ A_27b ) ) )
=> ( ( c_2Ewords_2Eword__join @ A_27a @ A_27b @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v1 ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ V1v2 ) )
= ( c_2Ebitstring_2Ev2w @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Elist_2EAPPEND @ $o @ V0v1 @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V1v2 ) ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__concat__v2w,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v1: tyop_2Elist_2Elist @ $o,V1v2: tyop_2Elist_2Elist @ $o] :
( ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
& ( c_2Epred__set_2EFINITE @ A_27b @ ( c_2Epred__set_2EUNIV @ A_27b ) ) )
=> ( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v1 ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ V1v2 ) )
= ( c_2Ebitstring_2Ev2w @ A_27c @ ( c_2Ebitstring_2Efixwidth @ ( c_2Earithmetic_2EMIN @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) @ ( c_2Elist_2EAPPEND @ $o @ V0v1 @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V1v2 ) ) ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__join__v2w__rwt,axiom,
! [A_27a: $tType,A_27b: $tType,V0bad_20domain: $o,V1v1: tyop_2Elist_2Elist @ $o,V2v2: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__join @ A_27a @ A_27b @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v1 ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ V2v2 ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ ( c_2Epred__set_2EFINITE @ A_27b @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) @ ( c_2Ebitstring_2Ev2w @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Elist_2EAPPEND @ $o @ V1v1 @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V2v2 ) ) ) @ ( c_2Ecombin_2EFAIL @ ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ $o @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b ) @ V0bad_20domain @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v1 ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ V2v2 ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__concat__v2w__rwt,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0bad_20domain: $o,V1v1: tyop_2Elist_2Elist @ $o,V2v2: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v1 ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ V2v2 ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ ( c_2Epred__set_2EFINITE @ A_27b @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) @ ( c_2Ebitstring_2Ev2w @ A_27c @ ( c_2Ebitstring_2Efixwidth @ ( c_2Earithmetic_2EMIN @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) @ ( c_2Elist_2EAPPEND @ $o @ V1v1 @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V2v2 ) ) ) ) @ ( c_2Ecombin_2EFAIL @ ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) > ( tyop_2Efcp_2Ecart @ $o @ A_27c ) ) @ $o @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ V0bad_20domain @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v1 ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ V2v2 ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__reduce__v2w,axiom,
! [A_27a: $tType,V0f: $o > $o > $o,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__reduce @ A_27a @ V0f @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) )
= ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ $o ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V2l: tyop_2Elist_2Elist @ $o] : ( c_2Ebitstring_2Ev2w @ tyop_2Eone_2Eone @ ( c_2Elist_2ECONS @ $o @ ( c_2Elist_2EFOLDL @ $o @ $o @ V0f @ ( c_2Elist_2EHD @ $o @ V2l ) @ ( c_2Elist_2ETL @ $o @ V2l ) ) @ ( c_2Elist_2ENIL @ $o ) ) )
@ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1v ) ) ) ).
thf(thm_2Ebitstring_2Ereduce__and__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Ereduce__and @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ewords_2Eword__reduce @ A_27a @ c_2Ebool_2E_2F_5C @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Ereduce__or__v2w,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Ereduce__or @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ewords_2Eword__reduce @ A_27a @ c_2Ebool_2E_5C_2F @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Eextract__v2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2v: tyop_2Elist_2Elist @ $o] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ $o @ V2v ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
& ( ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Enum_2ESUC @ V0h ) @ V1l ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ ( c_2Ebitstring_2Ev2w @ A_27a @ V2v ) )
= ( c_2Ebitstring_2Ev2w @ A_27b @ ( c_2Ebitstring_2Efield @ V0h @ V1l @ V2v ) ) ) ) ).
thf(thm_2Ebitstring_2Eword__bit__last__shiftr,axiom,
! [A_27a: $tType,V0i: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Eprim__rec_2E_3C @ V0i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__bit @ A_27a @ V0i @ ( c_2Ebitstring_2Ev2w @ A_27a @ V1v ) )
= ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ $o ) @ $o
@ ^ [V2l: tyop_2Elist_2Elist @ $o] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Elist_2ENULL @ $o @ V2l ) ) @ ( c_2Elist_2ELAST @ $o @ V2l ) )
@ ( c_2Ebitstring_2Eshiftr @ V1v @ V0i ) ) ) ) ).
thf(thm_2Ebitstring_2Eops__to__v2w,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,A_27h: $tType,A_27i: $tType,A_27j: $tType,A_27k: $tType,A_27l: $tType,A_27m: $tType,A_27n: $tType,A_27o: $tType,A_27p: $tType,A_27q: $tType,A_27r: $tType,A_27s: $tType,A_27t: $tType] :
( ! [V0v: tyop_2Elist_2Elist @ $o,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__or @ A_27c @ ( c_2Ebitstring_2Ev2w @ A_27c @ V0v ) @ ( c_2Ewords_2En2w @ A_27c @ V1n ) )
= ( c_2Ewords_2Eword__or @ A_27c @ ( c_2Ebitstring_2Ev2w @ A_27c @ V0v ) @ ( c_2Ebitstring_2Ev2w @ A_27c @ ( c_2Ebitstring_2En2v @ V1n ) ) ) )
& ! [V2v: tyop_2Elist_2Elist @ $o,V3n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__or @ A_27d @ ( c_2Ewords_2En2w @ A_27d @ V3n ) @ ( c_2Ebitstring_2Ev2w @ A_27d @ V2v ) )
= ( c_2Ewords_2Eword__or @ A_27d @ ( c_2Ebitstring_2Ev2w @ A_27d @ ( c_2Ebitstring_2En2v @ V3n ) ) @ ( c_2Ebitstring_2Ev2w @ A_27d @ V2v ) ) )
& ! [V4v: tyop_2Elist_2Elist @ $o,V5n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__and @ A_27e @ ( c_2Ebitstring_2Ev2w @ A_27e @ V4v ) @ ( c_2Ewords_2En2w @ A_27e @ V5n ) )
= ( c_2Ewords_2Eword__and @ A_27e @ ( c_2Ebitstring_2Ev2w @ A_27e @ V4v ) @ ( c_2Ebitstring_2Ev2w @ A_27e @ ( c_2Ebitstring_2En2v @ V5n ) ) ) )
& ! [V6v: tyop_2Elist_2Elist @ $o,V7n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__and @ A_27f @ ( c_2Ewords_2En2w @ A_27f @ V7n ) @ ( c_2Ebitstring_2Ev2w @ A_27f @ V6v ) )
= ( c_2Ewords_2Eword__and @ A_27f @ ( c_2Ebitstring_2Ev2w @ A_27f @ ( c_2Ebitstring_2En2v @ V7n ) ) @ ( c_2Ebitstring_2Ev2w @ A_27f @ V6v ) ) )
& ! [V8v: tyop_2Elist_2Elist @ $o,V9n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__xor @ A_27g @ ( c_2Ebitstring_2Ev2w @ A_27g @ V8v ) @ ( c_2Ewords_2En2w @ A_27g @ V9n ) )
= ( c_2Ewords_2Eword__xor @ A_27g @ ( c_2Ebitstring_2Ev2w @ A_27g @ V8v ) @ ( c_2Ebitstring_2Ev2w @ A_27g @ ( c_2Ebitstring_2En2v @ V9n ) ) ) )
& ! [V10v: tyop_2Elist_2Elist @ $o,V11n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__xor @ A_27h @ ( c_2Ewords_2En2w @ A_27h @ V11n ) @ ( c_2Ebitstring_2Ev2w @ A_27h @ V10v ) )
= ( c_2Ewords_2Eword__xor @ A_27h @ ( c_2Ebitstring_2Ev2w @ A_27h @ ( c_2Ebitstring_2En2v @ V11n ) ) @ ( c_2Ebitstring_2Ev2w @ A_27h @ V10v ) ) )
& ! [V12v: tyop_2Elist_2Elist @ $o,V13n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__nor @ A_27i @ ( c_2Ebitstring_2Ev2w @ A_27i @ V12v ) @ ( c_2Ewords_2En2w @ A_27i @ V13n ) )
= ( c_2Ewords_2Eword__nor @ A_27i @ ( c_2Ebitstring_2Ev2w @ A_27i @ V12v ) @ ( c_2Ebitstring_2Ev2w @ A_27i @ ( c_2Ebitstring_2En2v @ V13n ) ) ) )
& ! [V14v: tyop_2Elist_2Elist @ $o,V15n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__nor @ A_27j @ ( c_2Ewords_2En2w @ A_27j @ V15n ) @ ( c_2Ebitstring_2Ev2w @ A_27j @ V14v ) )
= ( c_2Ewords_2Eword__nor @ A_27j @ ( c_2Ebitstring_2Ev2w @ A_27j @ ( c_2Ebitstring_2En2v @ V15n ) ) @ ( c_2Ebitstring_2Ev2w @ A_27j @ V14v ) ) )
& ! [V16v: tyop_2Elist_2Elist @ $o,V17n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__nand @ A_27k @ ( c_2Ebitstring_2Ev2w @ A_27k @ V16v ) @ ( c_2Ewords_2En2w @ A_27k @ V17n ) )
= ( c_2Ewords_2Eword__nand @ A_27k @ ( c_2Ebitstring_2Ev2w @ A_27k @ V16v ) @ ( c_2Ebitstring_2Ev2w @ A_27k @ ( c_2Ebitstring_2En2v @ V17n ) ) ) )
& ! [V18v: tyop_2Elist_2Elist @ $o,V19n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__nand @ A_27l @ ( c_2Ewords_2En2w @ A_27l @ V19n ) @ ( c_2Ebitstring_2Ev2w @ A_27l @ V18v ) )
= ( c_2Ewords_2Eword__nand @ A_27l @ ( c_2Ebitstring_2Ev2w @ A_27l @ ( c_2Ebitstring_2En2v @ V19n ) ) @ ( c_2Ebitstring_2Ev2w @ A_27l @ V18v ) ) )
& ! [V20v: tyop_2Elist_2Elist @ $o,V21n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__xnor @ A_27m @ ( c_2Ebitstring_2Ev2w @ A_27m @ V20v ) @ ( c_2Ewords_2En2w @ A_27m @ V21n ) )
= ( c_2Ewords_2Eword__xnor @ A_27m @ ( c_2Ebitstring_2Ev2w @ A_27m @ V20v ) @ ( c_2Ebitstring_2Ev2w @ A_27m @ ( c_2Ebitstring_2En2v @ V21n ) ) ) )
& ! [V22v: tyop_2Elist_2Elist @ $o,V23n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__xnor @ A_27n @ ( c_2Ewords_2En2w @ A_27n @ V23n ) @ ( c_2Ebitstring_2Ev2w @ A_27n @ V22v ) )
= ( c_2Ewords_2Eword__xnor @ A_27n @ ( c_2Ebitstring_2Ev2w @ A_27n @ ( c_2Ebitstring_2En2v @ V23n ) ) @ ( c_2Ebitstring_2Ev2w @ A_27n @ V22v ) ) )
& ! [V24v: tyop_2Elist_2Elist @ $o,V25n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27o @ ( c_2Ebitstring_2Ev2w @ A_27a @ V24v ) @ ( c_2Ewords_2En2w @ A_27b @ V25n ) )
= ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27o @ ( c_2Ebitstring_2Ev2w @ A_27a @ V24v ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ ( c_2Ebitstring_2En2v @ V25n ) ) ) )
& ! [V26v: tyop_2Elist_2Elist @ $o,V27n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27p @ ( c_2Ewords_2En2w @ A_27a @ V27n ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ V26v ) )
= ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27p @ ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2En2v @ V27n ) ) @ ( c_2Ebitstring_2Ev2w @ A_27b @ V26v ) ) )
& ! [V28v: tyop_2Elist_2Elist @ $o,V29n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__join @ A_27q @ A_27r @ ( c_2Ebitstring_2Ev2w @ A_27q @ V28v ) @ ( c_2Ewords_2En2w @ A_27r @ V29n ) )
= ( c_2Ewords_2Eword__join @ A_27q @ A_27r @ ( c_2Ebitstring_2Ev2w @ A_27q @ V28v ) @ ( c_2Ebitstring_2Ev2w @ A_27r @ ( c_2Ebitstring_2En2v @ V29n ) ) ) )
& ! [V30v: tyop_2Elist_2Elist @ $o,V31n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__join @ A_27s @ A_27t @ ( c_2Ewords_2En2w @ A_27s @ V31n ) @ ( c_2Ebitstring_2Ev2w @ A_27t @ V30v ) )
= ( c_2Ewords_2Eword__join @ A_27s @ A_27t @ ( c_2Ebitstring_2Ev2w @ A_27s @ ( c_2Ebitstring_2En2v @ V31n ) ) @ ( c_2Ebitstring_2Ev2w @ A_27t @ V30v ) ) ) ) ).
thf(thm_2Ebitstring_2Eops__to__n2w,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,A_27h: $tType,A_27i: $tType,A_27j: $tType,A_27k: $tType,A_27l: $tType,A_27m: $tType,A_27n: $tType,A_27o: $tType] :
( ! [V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ebitstring_2Ev2w @ A_27b @ V0v ) )
= ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Ebitstring_2Ev2n @ V0v ) ) ) )
& ! [V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__log2 @ A_27c @ ( c_2Ebitstring_2Ev2w @ A_27c @ V1v ) )
= ( c_2Ewords_2Eword__log2 @ A_27c @ ( c_2Ewords_2En2w @ A_27c @ ( c_2Ebitstring_2Ev2n @ V1v ) ) ) )
& ! [V2v: tyop_2Elist_2Elist @ $o,V3n: tyop_2Enum_2Enum] :
( ( ( c_2Ebitstring_2Ev2w @ A_27a @ V2v )
= ( c_2Ewords_2En2w @ A_27a @ V3n ) )
<=> ( ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V2v ) )
= ( c_2Ewords_2En2w @ A_27a @ V3n ) ) )
& ! [V4v: tyop_2Elist_2Elist @ $o,V5n: tyop_2Enum_2Enum] :
( ( ( c_2Ewords_2En2w @ A_27a @ V5n )
= ( c_2Ebitstring_2Ev2w @ A_27a @ V4v ) )
<=> ( ( c_2Ewords_2En2w @ A_27a @ V5n )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V4v ) ) ) )
& ! [V6v: tyop_2Elist_2Elist @ $o,V7w: tyop_2Efcp_2Ecart @ $o @ A_27d] :
( ( c_2Ewords_2Eword__add @ A_27d @ ( c_2Ebitstring_2Ev2w @ A_27d @ V6v ) @ V7w )
= ( c_2Ewords_2Eword__add @ A_27d @ ( c_2Ewords_2En2w @ A_27d @ ( c_2Ebitstring_2Ev2n @ V6v ) ) @ V7w ) )
& ! [V8v: tyop_2Elist_2Elist @ $o,V9w: tyop_2Efcp_2Ecart @ $o @ A_27e] :
( ( c_2Ewords_2Eword__add @ A_27e @ V9w @ ( c_2Ebitstring_2Ev2w @ A_27e @ V8v ) )
= ( c_2Ewords_2Eword__add @ A_27e @ V9w @ ( c_2Ewords_2En2w @ A_27e @ ( c_2Ebitstring_2Ev2n @ V8v ) ) ) )
& ! [V10v: tyop_2Elist_2Elist @ $o,V11w: tyop_2Efcp_2Ecart @ $o @ A_27f] :
( ( c_2Ewords_2Eword__sub @ A_27f @ ( c_2Ebitstring_2Ev2w @ A_27f @ V10v ) @ V11w )
= ( c_2Ewords_2Eword__sub @ A_27f @ ( c_2Ewords_2En2w @ A_27f @ ( c_2Ebitstring_2Ev2n @ V10v ) ) @ V11w ) )
& ! [V12v: tyop_2Elist_2Elist @ $o,V13w: tyop_2Efcp_2Ecart @ $o @ A_27g] :
( ( c_2Ewords_2Eword__sub @ A_27g @ V13w @ ( c_2Ebitstring_2Ev2w @ A_27g @ V12v ) )
= ( c_2Ewords_2Eword__sub @ A_27g @ V13w @ ( c_2Ewords_2En2w @ A_27g @ ( c_2Ebitstring_2Ev2n @ V12v ) ) ) )
& ! [V14v: tyop_2Elist_2Elist @ $o,V15w: tyop_2Efcp_2Ecart @ $o @ A_27h] :
( ( c_2Ewords_2Eword__mul @ A_27h @ ( c_2Ebitstring_2Ev2w @ A_27h @ V14v ) @ V15w )
= ( c_2Ewords_2Eword__mul @ A_27h @ ( c_2Ewords_2En2w @ A_27h @ ( c_2Ebitstring_2Ev2n @ V14v ) ) @ V15w ) )
& ! [V16v: tyop_2Elist_2Elist @ $o,V17w: tyop_2Efcp_2Ecart @ $o @ A_27i] :
( ( c_2Ewords_2Eword__mul @ A_27i @ V17w @ ( c_2Ebitstring_2Ev2w @ A_27i @ V16v ) )
= ( c_2Ewords_2Eword__mul @ A_27i @ V17w @ ( c_2Ewords_2En2w @ A_27i @ ( c_2Ebitstring_2Ev2n @ V16v ) ) ) )
& ! [V18v: tyop_2Elist_2Elist @ $o,V19w: tyop_2Efcp_2Ecart @ $o @ A_27j] :
( ( c_2Ewords_2Eword__quot @ A_27j @ ( c_2Ebitstring_2Ev2w @ A_27j @ V18v ) @ V19w )
= ( c_2Ewords_2Eword__quot @ A_27j @ ( c_2Ewords_2En2w @ A_27j @ ( c_2Ebitstring_2Ev2n @ V18v ) ) @ V19w ) )
& ! [V20v: tyop_2Elist_2Elist @ $o,V21w: tyop_2Efcp_2Ecart @ $o @ A_27k] :
( ( c_2Ewords_2Eword__quot @ A_27k @ V21w @ ( c_2Ebitstring_2Ev2w @ A_27k @ V20v ) )
= ( c_2Ewords_2Eword__quot @ A_27k @ V21w @ ( c_2Ewords_2En2w @ A_27k @ ( c_2Ebitstring_2Ev2n @ V20v ) ) ) )
& ! [V22v: tyop_2Elist_2Elist @ $o,V23w: tyop_2Efcp_2Ecart @ $o @ A_27l] :
( ( c_2Ewords_2Eword__div @ A_27l @ ( c_2Ebitstring_2Ev2w @ A_27l @ V22v ) @ V23w )
= ( c_2Ewords_2Eword__div @ A_27l @ ( c_2Ewords_2En2w @ A_27l @ ( c_2Ebitstring_2Ev2n @ V22v ) ) @ V23w ) )
& ! [V24v: tyop_2Elist_2Elist @ $o,V25w: tyop_2Efcp_2Ecart @ $o @ A_27m] :
( ( c_2Ewords_2Eword__div @ A_27m @ V25w @ ( c_2Ebitstring_2Ev2w @ A_27m @ V24v ) )
= ( c_2Ewords_2Eword__div @ A_27m @ V25w @ ( c_2Ewords_2En2w @ A_27m @ ( c_2Ebitstring_2Ev2n @ V24v ) ) ) )
& ! [V26v: tyop_2Elist_2Elist @ $o,V27w: tyop_2Efcp_2Ecart @ $o @ A_27n] :
( ( c_2Ewords_2Eword__mod @ A_27n @ ( c_2Ebitstring_2Ev2w @ A_27n @ V26v ) @ V27w )
= ( c_2Ewords_2Eword__mod @ A_27n @ ( c_2Ewords_2En2w @ A_27n @ ( c_2Ebitstring_2Ev2n @ V26v ) ) @ V27w ) )
& ! [V28v: tyop_2Elist_2Elist @ $o,V29w: tyop_2Efcp_2Ecart @ $o @ A_27o] :
( ( c_2Ewords_2Eword__mod @ A_27o @ V29w @ ( c_2Ebitstring_2Ev2w @ A_27o @ V28v ) )
= ( c_2Ewords_2Eword__mod @ A_27o @ V29w @ ( c_2Ewords_2En2w @ A_27o @ ( c_2Ebitstring_2Ev2n @ V28v ) ) ) )
& ! [V30v: tyop_2Elist_2Elist @ $o,V31w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V30v ) @ V31w )
= ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V30v ) ) @ V31w ) )
& ! [V32v: tyop_2Elist_2Elist @ $o,V33w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lt @ A_27a @ V33w @ ( c_2Ebitstring_2Ev2w @ A_27a @ V32v ) )
= ( c_2Ewords_2Eword__lt @ A_27a @ V33w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V32v ) ) ) )
& ! [V34v: tyop_2Elist_2Elist @ $o,V35w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__gt @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V34v ) @ V35w )
= ( c_2Ewords_2Eword__gt @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V34v ) ) @ V35w ) )
& ! [V36v: tyop_2Elist_2Elist @ $o,V37w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__gt @ A_27a @ V37w @ ( c_2Ebitstring_2Ev2w @ A_27a @ V36v ) )
= ( c_2Ewords_2Eword__gt @ A_27a @ V37w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V36v ) ) ) )
& ! [V38v: tyop_2Elist_2Elist @ $o,V39w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V38v ) @ V39w )
= ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V38v ) ) @ V39w ) )
& ! [V40v: tyop_2Elist_2Elist @ $o,V41w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__le @ A_27a @ V41w @ ( c_2Ebitstring_2Ev2w @ A_27a @ V40v ) )
= ( c_2Ewords_2Eword__le @ A_27a @ V41w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V40v ) ) ) )
& ! [V42v: tyop_2Elist_2Elist @ $o,V43w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ge @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V42v ) @ V43w )
= ( c_2Ewords_2Eword__ge @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V42v ) ) @ V43w ) )
& ! [V44v: tyop_2Elist_2Elist @ $o,V45w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ge @ A_27a @ V45w @ ( c_2Ebitstring_2Ev2w @ A_27a @ V44v ) )
= ( c_2Ewords_2Eword__ge @ A_27a @ V45w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V44v ) ) ) )
& ! [V46v: tyop_2Elist_2Elist @ $o,V47w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V46v ) @ V47w )
= ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V46v ) ) @ V47w ) )
& ! [V48v: tyop_2Elist_2Elist @ $o,V49w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V49w @ ( c_2Ebitstring_2Ev2w @ A_27a @ V48v ) )
= ( c_2Ewords_2Eword__lo @ A_27a @ V49w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V48v ) ) ) )
& ! [V50v: tyop_2Elist_2Elist @ $o,V51w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hi @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V50v ) @ V51w )
= ( c_2Ewords_2Eword__hi @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V50v ) ) @ V51w ) )
& ! [V52v: tyop_2Elist_2Elist @ $o,V53w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hi @ A_27a @ V53w @ ( c_2Ebitstring_2Ev2w @ A_27a @ V52v ) )
= ( c_2Ewords_2Eword__hi @ A_27a @ V53w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V52v ) ) ) )
& ! [V54v: tyop_2Elist_2Elist @ $o,V55w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V54v ) @ V55w )
= ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V54v ) ) @ V55w ) )
& ! [V56v: tyop_2Elist_2Elist @ $o,V57w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ V57w @ ( c_2Ebitstring_2Ev2w @ A_27a @ V56v ) )
= ( c_2Ewords_2Eword__ls @ A_27a @ V57w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V56v ) ) ) )
& ! [V58v: tyop_2Elist_2Elist @ $o,V59w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hs @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V58v ) @ V59w )
= ( c_2Ewords_2Eword__hs @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V58v ) ) @ V59w ) )
& ! [V60v: tyop_2Elist_2Elist @ $o,V61w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hs @ A_27a @ V61w @ ( c_2Ebitstring_2Ev2w @ A_27a @ V60v ) )
= ( c_2Ewords_2Eword__hs @ A_27a @ V61w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebitstring_2Ev2n @ V60v ) ) ) ) ) ).
%------------------------------------------------------------------------------