ITP001 Axioms: ITP094^7.ax


%------------------------------------------------------------------------------
% File     : ITP094^7 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

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

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