ITP001 Axioms: ITP090^7.ax
%------------------------------------------------------------------------------
% File : ITP090^7 : 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 : words.ax [Gau19]
% : HL4090^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 890 ( 453 unt; 198 typ; 0 def)
% Number of atoms : 1596 ( 743 equ; 70 cnn)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 15359 ( 70 ~; 33 |; 197 &;14857 @)
% ( 79 <=>; 123 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg;14857 nst)
% Number of types : 5 ( 4 usr)
% Number of type conns : 401 ( 401 >; 0 *; 0 +; 0 <<)
% Number of symbols : 196 ( 194 usr; 5 con; 0-6 aty)
% Number of variables : 2157 ( 136 ^1851 !; 6 ?;2157 :)
% ( 164 !>; 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_2Ebit0,type,
tyop_2Efcp_2Ebit0: $tType > $tType ).
thf(tyop_2Efcp_2Ebit1,type,
tyop_2Efcp_2Ebit1: $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_2A,type,
c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
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_2Efcp_2E_3A_2B,type,
c_2Efcp_2E_3A_2B:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Enum_2Enum > A_27a > ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) > ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) ) ).
thf(c_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Earithmetic_2E_3E,type,
c_2Earithmetic_2E_3E: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2E_3E_3D,type,
c_2Earithmetic_2E_3E_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Emin_2E_40,type,
c_2Emin_2E_40:
!>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).
thf(c_2Ebit_2EBIT,type,
c_2Ebit_2EBIT: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $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_2Ebit_2EBITS,type,
c_2Ebit_2EBITS: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebit_2EBITWISE,type,
c_2Ebit_2EBITWISE: tyop_2Enum_2Enum > ( $o > $o > $o ) > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebit_2EBIT__MODIFY,type,
c_2Ebit_2EBIT__MODIFY: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > $o > $o ) > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebit_2EBIT__REVERSE,type,
c_2Ebit_2EBIT__REVERSE: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ewords_2EBIT__SET,type,
c_2Ewords_2EBIT__SET: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Enumposrep_2EBOOLIFY,type,
c_2Enumposrep_2EBOOLIFY: tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
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_2Earithmetic_2EDIV,type,
c_2Earithmetic_2EDIV: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epred__set_2EEMPTY,type,
c_2Epred__set_2EEMPTY:
!>[A_27a: $tType] : ( A_27a > $o ) ).
thf(c_2Earithmetic_2EEVEN,type,
c_2Earithmetic_2EEVEN: tyop_2Enum_2Enum > $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_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_2Epair_2EFST,type,
c_2Epair_2EFST:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27a ) ).
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_2EASCIInumbers_2EHEX,type,
c_2EASCIInumbers_2EHEX: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).
thf(c_2Ecombin_2EI,type,
c_2Ecombin_2EI:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
thf(c_2Ebool_2EIN,type,
c_2Ebool_2EIN:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
thf(c_2Epred__set_2EINSERT,type,
c_2Epred__set_2EINSERT:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > A_27a > $o ) ).
thf(c_2Ewords_2EINT__MAX,type,
c_2Ewords_2EINT__MAX:
!>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2EINT__MIN,type,
c_2Ewords_2EINT__MIN:
!>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ecombin_2EK,type,
c_2Ecombin_2EK:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > A_27a ) ).
thf(c_2Ewhile_2ELEAST,type,
c_2Ewhile_2ELEAST: ( tyop_2Enum_2Enum > $o ) > 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_2Ebit_2ELOG2,type,
c_2Ebit_2ELOG2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
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_2Ebit_2EMOD__2EXP__EQ,type,
c_2Ebit_2EMOD__2EXP__EQ: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Ebit_2EMOD__2EXP__MAX,type,
c_2Ebit_2EMOD__2EXP__MAX: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Elist_2ENIL,type,
c_2Elist_2ENIL:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EODD,type,
c_2Earithmetic_2EODD: tyop_2Enum_2Enum > $o ).
thf(c_2Ebit_2ESBIT,type,
c_2Ebit_2ESBIT: $o > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebit_2ESIGN__EXTEND,type,
c_2Ebit_2ESIGN__EXTEND: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebit_2ESLICE,type,
c_2Ebit_2ESLICE: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Enum_2ESUC,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Esum__num_2ESUM,type,
c_2Esum__num_2ESUM: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Elist_2ETL,type,
c_2Elist_2ETL:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ewords_2EUINT__MAX,type,
c_2Ewords_2EUINT__MAX:
!>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).
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_2EASCIInumbers_2EUNHEX,type,
c_2EASCIInumbers_2EUNHEX: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).
thf(c_2Epred__set_2EUNIV,type,
c_2Epred__set_2EUNIV:
!>[A_27a: $tType] : ( A_27a > $o ) ).
thf(c_2Erelation_2EWF,type,
c_2Erelation_2EWF:
!>[A_27a: $tType] : ( ( A_27a > A_27a > $o ) > $o ) ).
thf(c_2Erelation_2EWFREC,type,
c_2Erelation_2EWFREC:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27a > $o ) > ( ( A_27a > A_27b ) > A_27a > A_27b ) > A_27a > A_27b ) ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ewords_2Eadd__with__carry,type,
c_2Ewords_2Eadd__with__carry:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o ) ) > ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) ).
thf(c_2Ewords_2Ebit__count,type,
c_2Ewords_2Ebit__count:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2Ebit__count__upto,type,
c_2Ewords_2Ebit__count__upto:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2Ebit__field__insert,type,
c_2Ewords_2Ebit__field__insert:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Econcat__word__list,type,
c_2Ewords_2Econcat__word__list:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).
thf(c_2Efcp_2Edimindex,type,
c_2Efcp_2Edimindex:
!>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2Edimword,type,
c_2Ewords_2Edimword:
!>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).
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_2Enumposrep_2El2n,type,
c_2Enumposrep_2El2n: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
thf(c_2Ewords_2El2w,type,
c_2Ewords_2El2w:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Enumposrep_2En2l,type,
c_2Enumposrep_2En2l: tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ).
thf(c_2EASCIInumbers_2En2s,type,
c_2EASCIInumbers_2En2s: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > tyop_2Estring_2Echar ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).
thf(c_2Ewords_2En2w,type,
c_2Ewords_2En2w:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2En2w__itself,type,
c_2Ewords_2En2w__itself:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Enzcv,type,
c_2Ewords_2Enzcv:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) ) ).
thf(c_2Ecombin_2Eo,type,
c_2Ecombin_2Eo:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27c > A_27b ) > ( A_27a > A_27c ) > A_27a > A_27b ) ).
thf(c_2Epair_2Epair__CASE,type,
c_2Epair_2Epair__CASE:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) > ( A_27b > A_27c > A_27a ) > A_27a ) ).
thf(c_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__nand,type,
c_2Ewords_2Ereduce__nand:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) ).
thf(c_2Ewords_2Ereduce__nor,type,
c_2Ewords_2Ereduce__nor:
!>[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_2Ewords_2Ereduce__xnor,type,
c_2Ewords_2Ereduce__xnor:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) ).
thf(c_2Ewords_2Ereduce__xor,type,
c_2Ewords_2Ereduce__xor:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) ).
thf(c_2EASCIInumbers_2Es2n,type,
c_2EASCIInumbers_2Es2n: tyop_2Enum_2Enum > ( tyop_2Estring_2Echar > tyop_2Enum_2Enum ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Enum_2Enum ).
thf(c_2Ewords_2Es2w,type,
c_2Ewords_2Es2w:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Estring_2Echar > tyop_2Enum_2Enum ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Esaturate__add,type,
c_2Ewords_2Esaturate__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_2Esaturate__mul,type,
c_2Ewords_2Esaturate__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_2Esaturate__n2w,type,
c_2Ewords_2Esaturate__n2w:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Esaturate__sub,type,
c_2Ewords_2Esaturate__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_2Esaturate__w2w,type,
c_2Ewords_2Esaturate__w2w:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).
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_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself @ A_27a ) ).
thf(c_2Ewords_2Ew2l,type,
c_2Ewords_2Ew2l:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ).
thf(c_2Ewords_2Ew2n,type,
c_2Ewords_2Ew2n:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2Ew2s,type,
c_2Ewords_2Ew2s:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > tyop_2Estring_2Echar ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ).
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__H,type,
c_2Ewords_2Eword__H:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ).
thf(c_2Ewords_2Eword__L,type,
c_2Ewords_2Eword__L:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ).
thf(c_2Ewords_2Eword__L2,type,
c_2Ewords_2Eword__L2:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ).
thf(c_2Ewords_2Eword__T,type,
c_2Ewords_2Eword__T:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ).
thf(c_2Ewords_2Eword__abs,type,
c_2Ewords_2Eword__abs:
!>[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__asr__bv,type,
c_2Ewords_2Eword__asr__bv:
!>[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__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__compare,type,
c_2Ewords_2Eword__compare:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) ).
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__from__bin__list,type,
c_2Ewords_2Eword__from__bin__list:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__from__bin__string,type,
c_2Ewords_2Eword__from__bin__string:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__from__dec__list,type,
c_2Ewords_2Eword__from__dec__list:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__from__dec__string,type,
c_2Ewords_2Eword__from__dec__string:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__from__hex__list,type,
c_2Ewords_2Eword__from__hex__list:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__from__hex__string,type,
c_2Ewords_2Eword__from__hex__string:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__from__oct__list,type,
c_2Ewords_2Eword__from__oct__list:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__from__oct__string,type,
c_2Ewords_2Eword__from__oct__string:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
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__len,type,
c_2Ewords_2Eword__len:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum ) ).
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__lsl__bv,type,
c_2Ewords_2Eword__lsl__bv:
!>[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__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__lsr__bv,type,
c_2Ewords_2Eword__lsr__bv:
!>[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__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__max,type,
c_2Ewords_2Eword__max:
!>[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__min,type,
c_2Ewords_2Eword__min:
!>[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__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__rem,type,
c_2Ewords_2Eword__rem:
!>[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__replicate,type,
c_2Ewords_2Eword__replicate:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).
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__rol,type,
c_2Ewords_2Eword__rol:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__rol__bv,type,
c_2Ewords_2Eword__rol__bv:
!>[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__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__ror__bv,type,
c_2Ewords_2Eword__ror__bv:
!>[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__rrx,type,
c_2Ewords_2Eword__rrx:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) > ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).
thf(c_2Ewords_2Eword__sign__extend,type,
c_2Ewords_2Eword__sign__extend:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__signed__bits,type,
c_2Ewords_2Eword__signed__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__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__smax,type,
c_2Ewords_2Eword__smax:
!>[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__smin,type,
c_2Ewords_2Eword__smin:
!>[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__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__to__bin__list,type,
c_2Ewords_2Eword__to__bin__list:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ).
thf(c_2Ewords_2Eword__to__bin__string,type,
c_2Ewords_2Eword__to__bin__string:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ).
thf(c_2Ewords_2Eword__to__dec__list,type,
c_2Ewords_2Eword__to__dec__list:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ).
thf(c_2Ewords_2Eword__to__dec__string,type,
c_2Ewords_2Eword__to__dec__string:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ).
thf(c_2Ewords_2Eword__to__hex__list,type,
c_2Ewords_2Eword__to__hex__list:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ).
thf(c_2Ewords_2Eword__to__hex__string,type,
c_2Ewords_2Eword__to__hex__string:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ).
thf(c_2Ewords_2Eword__to__oct__list,type,
c_2Ewords_2Eword__to__oct__list:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ).
thf(c_2Ewords_2Eword__to__oct__string,type,
c_2Ewords_2Eword__to__oct__string:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ).
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_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_2Ewords_2Edimword__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2EUINT__MAX__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2EUINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2EINT__MAX__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2EINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Ew2n__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2n @ A_27a @ V0w )
= ( c_2Esum__num_2ESUM @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Ebit_2ESBIT @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) @ V1i ) ) ) ).
thf(thm_2Ewords_2En2w__def,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2En2w @ A_27a @ V0n )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT @ V1i @ V0n ) ) ) ).
thf(thm_2Ewords_2Ew2w__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w )
= ( c_2Ewords_2En2w @ A_27b @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) ) ) ).
thf(thm_2Ewords_2Esw2sw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esw2sw @ A_27a @ A_27b @ V0w )
= ( c_2Ewords_2En2w @ A_27b @ ( c_2Ebit_2ESIGN__EXTEND @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) ) ) ) ).
thf(thm_2Ewords_2Ew2l__def,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2l @ A_27a @ V0b @ V1w )
= ( c_2Enumposrep_2En2l @ V0b @ ( c_2Ewords_2Ew2n @ A_27a @ V1w ) ) ) ).
thf(thm_2Ewords_2El2w__def,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Ewords_2El2w @ A_27a @ V0b @ V1l )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Enumposrep_2El2n @ V0b @ V1l ) ) ) ).
thf(thm_2Ewords_2Ew2s__def,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1f: tyop_2Enum_2Enum > tyop_2Estring_2Echar,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2s @ A_27a @ V0b @ V1f @ V2w )
= ( c_2EASCIInumbers_2En2s @ V0b @ V1f @ ( c_2Ewords_2Ew2n @ A_27a @ V2w ) ) ) ).
thf(thm_2Ewords_2Es2w__def,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1f: tyop_2Estring_2Echar > tyop_2Enum_2Enum,V2s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( c_2Ewords_2Es2w @ A_27a @ V0b @ V1f @ V2s )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2EASCIInumbers_2Es2n @ V0b @ V1f @ V2s ) ) ) ).
thf(thm_2Ewords_2Eword__from__bin__list__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__from__bin__list @ A_27a )
= ( c_2Ewords_2El2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Eword__from__oct__list__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__from__oct__list @ A_27a )
= ( c_2Ewords_2El2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__from__dec__list__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__from__dec__list @ A_27a )
= ( c_2Ewords_2El2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__from__hex__list__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__from__hex__list @ A_27a )
= ( c_2Ewords_2El2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__to__bin__list__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__to__bin__list @ A_27a )
= ( c_2Ewords_2Ew2l @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Eword__to__oct__list__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__to__oct__list @ A_27a )
= ( c_2Ewords_2Ew2l @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__to__dec__list__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__to__dec__list @ A_27a )
= ( c_2Ewords_2Ew2l @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__to__hex__list__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__to__hex__list @ A_27a )
= ( c_2Ewords_2Ew2l @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__from__bin__string__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__from__bin__string @ A_27a )
= ( c_2Ewords_2Es2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).
thf(thm_2Ewords_2Eword__from__oct__string__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__from__oct__string @ A_27a )
= ( c_2Ewords_2Es2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).
thf(thm_2Ewords_2Eword__from__dec__string__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__from__dec__string @ A_27a )
= ( c_2Ewords_2Es2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).
thf(thm_2Ewords_2Eword__from__hex__string__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__from__hex__string @ A_27a )
= ( c_2Ewords_2Es2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).
thf(thm_2Ewords_2Eword__to__bin__string__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__to__bin__string @ A_27a )
= ( c_2Ewords_2Ew2s @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ c_2EASCIInumbers_2EHEX ) ) ).
thf(thm_2Ewords_2Eword__to__oct__string__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__to__oct__string @ A_27a )
= ( c_2Ewords_2Ew2s @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).
thf(thm_2Ewords_2Eword__to__dec__string__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__to__dec__string @ A_27a )
= ( c_2Ewords_2Ew2s @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).
thf(thm_2Ewords_2Eword__to__hex__string__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__to__hex__string @ A_27a )
= ( c_2Ewords_2Ew2s @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).
thf(thm_2Ewords_2Eword__T__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__T @ A_27a )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ewords_2EUINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2Eword__L__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__L @ A_27a )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2Eword__H__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__H @ A_27a )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ewords_2EINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2Eword__1comp__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__1comp @ A_27a @ V0w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) ) ) ) ).
thf(thm_2Ewords_2Eword__and__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V0v @ V1w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0v @ V2i ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) ) ) ) ).
thf(thm_2Ewords_2Eword__or__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ V0v @ V1w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0v @ V2i ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) ) ) ) ).
thf(thm_2Ewords_2Eword__xor__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ V0v @ V1w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0v @ V2i ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__nand__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__nand @ A_27a @ V0v @ V1w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_2F_5C @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0v @ V2i ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__nor__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__nor @ A_27a @ V0v @ V1w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_5C_2F @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0v @ V2i ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__xnor__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xnor @ A_27a @ V0v @ V1w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ $o @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0v @ V2i ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) ) ) ) ).
thf(thm_2Ewords_2Eword__reduce__def,axiom,
! [A_27a: $tType,V0f: $o > $o > $o,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__reduce @ A_27a @ V0f @ V1w )
= ( c_2Efcp_2EFCP @ $o @ tyop_2Eone_2Eone
@ ( c_2Ecombin_2EK @ $o @ tyop_2Enum_2Enum
@ ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ $o ) @ $o
@ ^ [V2l: tyop_2Elist_2Elist @ $o] : ( c_2Elist_2EFOLDL @ $o @ $o @ V0f @ ( c_2Elist_2EHD @ $o @ V2l ) @ ( c_2Elist_2ETL @ $o @ V2l ) )
@ ( c_2Elist_2EGENLIST @ $o
@ ^ [V3i: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ ( 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 ) ) ) @ V3i ) )
@ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__compare__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__compare @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0a @ V1b ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Ereduce__and__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Ereduce__and @ A_27a )
= ( c_2Ewords_2Eword__reduce @ A_27a @ c_2Ebool_2E_2F_5C ) ) ).
thf(thm_2Ewords_2Ereduce__or__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Ereduce__or @ A_27a )
= ( c_2Ewords_2Eword__reduce @ A_27a @ c_2Ebool_2E_5C_2F ) ) ).
thf(thm_2Ewords_2Ereduce__xor__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Ereduce__xor @ A_27a )
= ( c_2Ewords_2Eword__reduce @ A_27a
@ ^ [V0x: $o,V1y: $o] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ V0x @ V1y ) ) ) ) ).
thf(thm_2Ewords_2Ereduce__nand__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Ereduce__nand @ A_27a )
= ( c_2Ewords_2Eword__reduce @ A_27a
@ ^ [V0a: $o,V1b: $o] : ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_2F_5C @ V0a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2Ereduce__nor__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Ereduce__nor @ A_27a )
= ( c_2Ewords_2Eword__reduce @ A_27a
@ ^ [V0a: $o,V1b: $o] : ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_5C_2F @ V0a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2Ereduce__xnor__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Ereduce__xnor @ A_27a )
= ( c_2Ewords_2Eword__reduce @ A_27a @ ( c_2Emin_2E_3D @ $o ) ) ) ).
thf(thm_2Ewords_2Eword__lsb__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lsb @ A_27a @ V0w )
= ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2Eword__msb__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__msb @ A_27a @ V0w )
= ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__slice__def,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1l )
= ( ^ [V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V3i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2E_3C_3D @ V1l @ V3i ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2E_3C_3D @ V3i @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V2w @ V3i ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__bits__def,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l )
= ( ^ [V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V3i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V3i @ V1l ) @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V2w @ ( c_2Earithmetic_2E_2B @ V3i @ V1l ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__signed__bits__def,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__signed__bits @ A_27a @ V0h @ V1l )
= ( ^ [V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V3i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2E_3C_3D @ V1l @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V2w @ ( c_2Earithmetic_2EMIN @ ( c_2Earithmetic_2E_2B @ V3i @ V1l ) @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__extract__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l )
= ( c_2Ecombin_2Eo @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l ) ) ) ).
thf(thm_2Ewords_2Eword__bit__def,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__bit @ A_27a @ V0b @ V1w )
<=> ( ( c_2Earithmetic_2E_3C_3D @ V0b @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V0b ) ) ) ).
thf(thm_2Ewords_2Eword__reverse__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__reverse @ A_27a @ V0w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [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 ) ) ) ) ).
thf(thm_2Ewords_2Eword__modify__def,axiom,
! [A_27a: $tType,V0f: tyop_2Enum_2Enum > $o > $o,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__modify @ A_27a @ V0f @ V1w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( V0f @ V2i @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) ) ) ) ).
thf(thm_2Ewords_2Ebit__field__insert__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2a: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Ewords_2Ebit__field__insert @ A_27a @ A_27b @ V0h @ V1l @ V2a )
= ( c_2Ewords_2Eword__modify @ A_27a
@ ^ [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_2Efcp_2Efcp__index @ $o @ A_27b @ V2a @ ( c_2Earithmetic_2E_2D @ V3i @ V1l ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__sign__extend__def,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sign__extend @ A_27a @ V0n @ V1w )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2ESIGN__EXTEND @ V0n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1w ) ) ) ) ).
thf(thm_2Ewords_2Eword__len__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__len @ A_27a @ V0w )
= ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2Ebit__count__upto__def,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ebit__count__upto @ A_27a @ V0n @ V1w )
= ( c_2Esum__num_2ESUM @ V0n
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Ebit__count__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ebit__count @ A_27a @ V0w )
= ( c_2Ewords_2Ebit__count__upto @ A_27a @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0w ) ) ).
thf(thm_2Ewords_2Eword__2comp__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ V0w )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) ) ) ) ).
thf(thm_2Ewords_2Eword__add__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2B @ ( c_2Ewords_2Ew2n @ A_27a @ V0v ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1w ) ) ) ) ).
thf(thm_2Ewords_2Eword__mul__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2A @ ( c_2Ewords_2Ew2n @ A_27a @ V0v ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1w ) ) ) ) ).
thf(thm_2Ewords_2Eword__log2__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__log2 @ A_27a @ V0w )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2ELOG2 @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) ) ) ) ).
thf(thm_2Ewords_2Eadd__with__carry__def,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a,V2carry__in: $o] :
( ( c_2Ewords_2Eadd__with__carry @ A_27a @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o ) @ V0x @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o @ V1y @ V2carry__in ) ) )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) )
@ ^ [V3unsigned__sum: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) )
@ ^ [V4result: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( c_2Ebool_2ELET @ $o @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) )
@ ( c_2Ebool_2ELET @ $o @ ( $o > ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) )
@ ^ [V5carry__out: $o,V6overflow: $o] : ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ V4result @ ( c_2Epair_2E_2C @ $o @ $o @ V5carry__out @ V6overflow ) )
@ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Ewords_2Ew2n @ A_27a @ V4result ) @ V3unsigned__sum ) ) )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Emin_2E_3D @ $o @ ( c_2Ewords_2Eword__msb @ A_27a @ V0x ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1y ) ) @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ ( c_2Ewords_2Eword__msb @ A_27a @ V0x ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V4result ) ) ) ) )
@ ( c_2Ewords_2En2w @ A_27a @ V3unsigned__sum ) )
@ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2B @ ( c_2Ewords_2Ew2n @ A_27a @ V0x ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1y ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ V2carry__in @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2Ewords_2Eword__sub__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2Eword__add @ A_27a @ V0v @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1w ) ) ) ).
thf(thm_2Ewords_2Eword__div__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__div @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EDIV @ ( c_2Ewords_2Ew2n @ A_27a @ V0v ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1w ) ) ) ) ).
thf(thm_2Ewords_2Eword__mod__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mod @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EMOD @ ( c_2Ewords_2Ew2n @ A_27a @ V0v ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1w ) ) ) ) ).
thf(thm_2Ewords_2Eword__quot__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__quot @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) @ ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) @ ( c_2Ewords_2Eword__div @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1b ) ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__div @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) @ V1b ) ) ) @ ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__div @ A_27a @ V0a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1b ) ) ) @ ( c_2Ewords_2Eword__div @ A_27a @ V0a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2Eword__rem__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__rem @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) @ ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__mod @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1b ) ) ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__mod @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) @ V1b ) ) ) @ ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) @ ( c_2Ewords_2Eword__mod @ A_27a @ V0a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1b ) ) @ ( c_2Ewords_2Eword__mod @ A_27a @ V0a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2Eword__L2__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__L2 @ A_27a )
= ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(thm_2Ewords_2Enzcv__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Enzcv @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) )
@ ^ [V2q: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) )
@ ^ [V3r: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V3r ) @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V3r @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) @ ( c_2Epair_2E_2C @ $o @ $o @ ( c_2Ebool_2E_5C_2F @ ( c_2Ebit_2EBIT @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V2q ) @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V1b @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) ) ) @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ ( c_2Ewords_2Eword__msb @ A_27a @ V3r ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) ) ) ) ) ) )
@ ( c_2Ewords_2En2w @ A_27a @ V2q ) )
@ ( c_2Earithmetic_2E_2B @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1b ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__lt__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) @ $o
@ ( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) @ $o
@ ^ [V2n: $o] :
( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ $o
@ ^ [V3z: $o] :
( c_2Epair_2EUNCURRY @ $o @ $o @ $o
@ ^ [V4c: $o,V5v: $o] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ V2n @ V5v ) ) ) ) )
@ ( c_2Ewords_2Enzcv @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__gt__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__gt @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) @ $o
@ ( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) @ $o
@ ^ [V2n: $o] :
( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ $o
@ ^ [V3z: $o] :
( c_2Epair_2EUNCURRY @ $o @ $o @ $o
@ ^ [V4c: $o,V5v: $o] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ V3z ) @ ( c_2Emin_2E_3D @ $o @ V2n @ V5v ) ) ) ) )
@ ( c_2Ewords_2Enzcv @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__le__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) @ $o
@ ( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) @ $o
@ ^ [V2n: $o] :
( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ $o
@ ^ [V3z: $o] :
( c_2Epair_2EUNCURRY @ $o @ $o @ $o
@ ^ [V4c: $o,V5v: $o] : ( c_2Ebool_2E_5C_2F @ V3z @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ V2n @ V5v ) ) ) ) ) )
@ ( c_2Ewords_2Enzcv @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__ge__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ge @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) @ $o
@ ( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) @ $o
@ ^ [V2n: $o] :
( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ $o
@ ^ [V3z: $o] :
( c_2Epair_2EUNCURRY @ $o @ $o @ $o
@ ^ [V4c: $o,V5v: $o] : ( c_2Emin_2E_3D @ $o @ V2n @ V5v ) ) ) )
@ ( c_2Ewords_2Enzcv @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__ls__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) @ $o
@ ( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) @ $o
@ ^ [V2n: $o] :
( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ $o
@ ^ [V3z: $o] :
( c_2Epair_2EUNCURRY @ $o @ $o @ $o
@ ^ [V4c: $o,V5v: $o] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ V4c ) @ V3z ) ) ) )
@ ( c_2Ewords_2Enzcv @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__hi__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hi @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) @ $o
@ ( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) @ $o
@ ^ [V2n: $o] :
( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ $o
@ ^ [V3z: $o] :
( c_2Epair_2EUNCURRY @ $o @ $o @ $o
@ ^ [V4c: $o,V5v: $o] : ( c_2Ebool_2E_2F_5C @ V4c @ ( c_2Ebool_2E_7E @ V3z ) ) ) ) )
@ ( c_2Ewords_2Enzcv @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__lo__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) @ $o
@ ( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) @ $o
@ ^ [V2n: $o] :
( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ $o
@ ^ [V3z: $o] :
( c_2Epair_2EUNCURRY @ $o @ $o @ $o
@ ^ [V4c: $o,V5v: $o] : ( c_2Ebool_2E_7E @ V4c ) ) ) )
@ ( c_2Ewords_2Enzcv @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__hs__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hs @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) ) @ $o
@ ( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) ) @ $o
@ ^ [V2n: $o] :
( c_2Epair_2EUNCURRY @ $o @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ $o
@ ^ [V3z: $o] :
( c_2Epair_2EUNCURRY @ $o @ $o @ $o
@ ^ [V4c: $o,V5v: $o] : V4c ) ) )
@ ( c_2Ewords_2Enzcv @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__min__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__min @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b ) @ V0a @ V1b ) ) ).
thf(thm_2Ewords_2Eword__max__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__max @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b ) @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2Eword__smin__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__smin @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b ) @ V0a @ V1b ) ) ).
thf(thm_2Ewords_2Eword__smax__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__smax @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b ) @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2Eword__abs__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__abs @ A_27a @ V0w )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__lt @ A_27a @ V0w @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) @ V0w ) ) ).
thf(thm_2Ewords_2Eword__lsl__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ V1n )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Eprim__rec_2E_3C @ V2i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2E_3C_3D @ V1n @ V2i ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ ( c_2Earithmetic_2E_2D @ V2i @ V1n ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__lsr__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ V1n )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2B @ V2i @ V1n ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ ( c_2Earithmetic_2E_2B @ V2i @ V1n ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__asr__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__asr @ A_27a @ V0w @ V1n )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2E_2B @ V2i @ V1n ) ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0w ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ ( c_2Earithmetic_2E_2B @ V2i @ V1n ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__ror__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ V1n )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ V2i @ V1n ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__rol__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__rol @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2EMOD @ V1n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__rrx__def,axiom,
! [A_27a: $tType,V0c: $o,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__rrx @ A_27a @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0c @ V1w ) )
= ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__lsb @ A_27a @ V1w )
@ ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2i @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0c @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V1w @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2i ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__lsl__bv__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lsl__bv @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ ( c_2Ewords_2Ew2n @ A_27a @ V1n ) ) ) ).
thf(thm_2Ewords_2Eword__lsr__bv__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lsr__bv @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ ( c_2Ewords_2Ew2n @ A_27a @ V1n ) ) ) ).
thf(thm_2Ewords_2Eword__asr__bv__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__asr__bv @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2Eword__asr @ A_27a @ V0w @ ( c_2Ewords_2Ew2n @ A_27a @ V1n ) ) ) ).
thf(thm_2Ewords_2Eword__ror__bv__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ror__bv @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ ( c_2Ewords_2Ew2n @ A_27a @ V1n ) ) ) ).
thf(thm_2Ewords_2Eword__rol__bv__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__rol__bv @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2Eword__rol @ A_27a @ V0w @ ( c_2Ewords_2Ew2n @ A_27a @ V1n ) ) ) ).
thf(thm_2Ewords_2Eword__join__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Ewords_2Eword__join @ A_27a @ A_27b @ V0v @ V1w )
= ( c_2Ebool_2ELET @ ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) )
@ ( c_2Ebool_2ELET @ ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) )
@ ^ [V2cv: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ),V3cw: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b )] : ( c_2Ewords_2Eword__or @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ewords_2Eword__lsl @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V2cv @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ V3cw )
@ ( c_2Ewords_2Ew2w @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0v ) )
@ ( c_2Ewords_2Ew2w @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V1w ) ) ) ).
thf(thm_2Ewords_2Eword__concat__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ V0v @ V1w )
= ( c_2Ewords_2Ew2w @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b @ V0v @ V1w ) ) ) ).
thf(thm_2Ewords_2Eword__replicate__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__replicate @ A_27a @ A_27b @ V0n @ V1w )
= ( c_2Efcp_2EFCP @ $o @ A_27b
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Eprim__rec_2E_3C @ V2i @ ( c_2Earithmetic_2E_2A @ V0n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ ( c_2Earithmetic_2EMOD @ V2i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Econcat__word__list__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( ( c_2Ewords_2Econcat__word__list @ A_27a @ A_27b @ ( c_2Elist_2ENIL @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) )
= ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) )
& ! [V0h: tyop_2Efcp_2Ecart @ $o @ A_27a,V1t: tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ A_27a )] :
( ( c_2Ewords_2Econcat__word__list @ A_27a @ A_27b @ ( c_2Elist_2ECONS @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0h @ V1t ) )
= ( c_2Ewords_2Eword__or @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0h ) @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Econcat__word__list @ A_27a @ A_27b @ V1t ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(thm_2Ewords_2Esaturate__n2w__def,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Esaturate__n2w @ A_27a @ V0n )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0n ) @ ( c_2Ewords_2Eword__T @ A_27a ) @ ( c_2Ewords_2En2w @ A_27a @ V0n ) ) ) ).
thf(thm_2Ewords_2Esaturate__w2w__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esaturate__w2w @ A_27a @ A_27b @ V0w )
= ( c_2Ewords_2Esaturate__n2w @ A_27b @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) ) ) ).
thf(thm_2Ewords_2Esaturate__add__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esaturate__add @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Esaturate__n2w @ A_27a @ ( c_2Earithmetic_2E_2B @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2Esaturate__sub__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esaturate__sub @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2Esaturate__mul__def,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esaturate__mul @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Esaturate__n2w @ A_27a @ ( c_2Earithmetic_2E_2A @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2En2w__itself__primitive__def,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2En2w__itself @ A_27a )
= ( c_2Erelation_2EWFREC @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a )
@ ( c_2Emin_2E_40 @ ( ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) ) > $o )
@ ^ [V0R: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) ) > $o] : ( c_2Erelation_2EWF @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) ) @ V0R ) )
@ ^ [V1n2w__itself: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ),V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) @ V2a
@ ^ [V3v: tyop_2Enum_2Enum,V4v1: tyop_2Ebool_2Eitself @ A_27a] : ( c_2Ecombin_2EI @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2En2w @ A_27a @ V3v ) ) ) ) ) ).
thf(thm_2Ewords_2EBIT__SET__ind,axiom,
! [V0P: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o] :
( ! [V1i: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( ( ( ( (~) @ ( V2n = c_2Enum_2E0 ) )
& ( c_2Earithmetic_2EODD @ V2n ) )
=> ( V0P @ ( c_2Enum_2ESUC @ V1i ) @ ( c_2Earithmetic_2EDIV @ V2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( ( ( (~) @ ( V2n = c_2Enum_2E0 ) )
& ( (~) @ ( c_2Earithmetic_2EODD @ V2n ) ) )
=> ( V0P @ ( c_2Enum_2ESUC @ V1i ) @ ( c_2Earithmetic_2EDIV @ V2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
=> ( V0P @ V1i @ V2n ) )
=> ! [V3v: tyop_2Enum_2Enum,V4v1: tyop_2Enum_2Enum] : ( V0P @ V3v @ V4v1 ) ) ).
thf(thm_2Ewords_2EBIT__SET__def,axiom,
! [V0n: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum] :
( ( c_2Ewords_2EBIT__SET @ V1i @ V0n )
= ( c_2Ebool_2ECOND @ ( tyop_2Enum_2Enum > $o ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V0n @ c_2Enum_2E0 ) @ ( c_2Epred__set_2EEMPTY @ tyop_2Enum_2Enum ) @ ( c_2Ebool_2ECOND @ ( tyop_2Enum_2Enum > $o ) @ ( c_2Earithmetic_2EODD @ V0n ) @ ( c_2Epred__set_2EINSERT @ tyop_2Enum_2Enum @ V1i @ ( c_2Ewords_2EBIT__SET @ ( c_2Enum_2ESUC @ V1i ) @ ( c_2Earithmetic_2EDIV @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ewords_2EBIT__SET @ ( c_2Enum_2ESUC @ V1i ) @ ( c_2Earithmetic_2EDIV @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2EZERO__LT__dimword,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2EDIMINDEX__GT__0,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2Edimword__IS__TWICE__INT__MIN,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2Edimword__sub__int__min,axiom,
! [A_27a: $tType] :
( ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2EONE__LT__dimword,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2EEXISTS__HB,axiom,
! [A_27a: $tType] :
? [V0m: tyop_2Enum_2Enum] :
( ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Enum_2ESUC @ V0m ) ) ).
thf(thm_2Ewords_2EMOD__DIMINDEX,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V0n ) ) ).
thf(thm_2Ewords_2EBITS__ZEROL__DIMINDEX,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V0n )
= V0n ) ) ).
thf(thm_2Ewords_2EMOD__2EXP__DIMINDEX,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Ebit_2EMOD__2EXP @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0n ) ) ).
thf(thm_2Ewords_2EINT__MIN__SUM,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( 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_2Earithmetic_2E_2A @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EINT__MIN @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( c_2Ewords_2EINT__MIN @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) ) ).
thf(thm_2Ewords_2EZERO__LT__INT__MIN,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2EZERO__LT__INT__MAX,axiom,
! [A_27a: $tType] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Ewords_2EINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2EZERO__LE__INT__MAX,axiom,
! [A_27a: $tType] : ( c_2Earithmetic_2E_3C_3D @ c_2Enum_2E0 @ ( c_2Ewords_2EINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2EZERO__LT__UINT__MAX,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Ewords_2EUINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__LT__DIMWORD,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2EINT__MAX__LT__DIMWORD,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2EINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2Edimindex__lt__dimword,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2EBOUND__ORDER,axiom,
! [A_27a: $tType] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2EINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EUINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
& ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2EUINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__dimword__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
<=> ( ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__dimword__le__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( c_2Earithmetic_2E_3C_3D @ ( 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_3C_3D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__dimword__lt__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( 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_2Eprim__rec_2E_3C @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__int__min__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
<=> ( ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Ewords_2EINT__MIN @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__int__min__le__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( c_2Earithmetic_2E_3C_3D @ ( 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_3C_3D @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EINT__MIN @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__int__min__lt__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( 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_2Eprim__rec_2E_3C @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EINT__MIN @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__int__max__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
<=> ( ( c_2Ewords_2EINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Ewords_2EINT__MAX @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__int__max__le__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( c_2Earithmetic_2E_3C_3D @ ( 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_3C_3D @ ( c_2Ewords_2EINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EINT__MAX @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__int__max__lt__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( 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_2Eprim__rec_2E_3C @ ( c_2Ewords_2EINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EINT__MAX @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__uint__max__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
<=> ( ( c_2Ewords_2EUINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Ewords_2EUINT__MAX @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__uint__max__le__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( c_2Earithmetic_2E_3C_3D @ ( 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_3C_3D @ ( c_2Ewords_2EUINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EUINT__MAX @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__uint__max__lt__iso,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( 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_2Eprim__rec_2E_3C @ ( c_2Ewords_2EUINT__MAX @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2EUINT__MAX @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Ew2n__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2En2w__w2n,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2En2w @ A_27a @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) )
= V0w ) ).
thf(thm_2Ewords_2Eword__nchotomy,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
? [V1n: tyop_2Enum_2Enum] :
( V0w
= ( c_2Ewords_2En2w @ A_27a @ V1n ) ) ).
thf(thm_2Ewords_2En2w__mod,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( c_2Ewords_2En2w @ A_27a @ V0n ) ) ).
thf(thm_2Ewords_2En2w__11,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( ( c_2Ewords_2En2w @ A_27a @ V0m )
= ( c_2Ewords_2En2w @ A_27a @ V1n ) )
<=> ( ( c_2Earithmetic_2EMOD @ V0m @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Earithmetic_2EMOD @ V1n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Eranged__word__nchotomy,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
? [V1n: tyop_2Enum_2Enum] :
( ( V0w
= ( c_2Ewords_2En2w @ A_27a @ V1n ) )
& ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__1__cases,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
=> ( ( V0a
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
| ( V0a
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Emod__dimindex,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2EWORD__INDUCT,axiom,
! [A_27a: $tType,V0P: ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o] :
( ( ( V0P @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ! [V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ V1n ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( V0P @ ( c_2Ewords_2En2w @ A_27a @ V1n ) )
=> ( V0P @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Enum_2ESUC @ V1n ) ) ) ) ) )
=> ! [V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( V0P @ V2x ) ) ).
thf(thm_2Ewords_2Ew2n__11,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Ew2n @ A_27a @ V0v )
= ( c_2Ewords_2Ew2n @ A_27a @ V1w ) )
<=> ( V0v = V1w ) ) ).
thf(thm_2Ewords_2Ew2n__lt,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__0__n2w,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= c_2Enum_2E0 ) ).
thf(thm_2Ewords_2Eword__1__n2w,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Ewords_2Ew2n__eq__0,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Ew2n @ A_27a @ V0w )
= c_2Enum_2E0 )
<=> ( V0w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2En2w__dimword,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2En2w @ A_27a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2Eword__2comp__dimindex__1,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
=> ( ( c_2Ewords_2Eword__2comp @ A_27a @ V0w )
= V0w ) ) ).
thf(thm_2Ewords_2Eword__add__n2w,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0m ) @ ( c_2Ewords_2En2w @ A_27a @ V1n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2B @ V0m @ V1n ) ) ) ).
thf(thm_2Ewords_2Eword__mul__n2w,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0m ) @ ( c_2Ewords_2En2w @ A_27a @ V1n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ).
thf(thm_2Ewords_2Eword__log2__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__log2 @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2ELOG2 @ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__1comp__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__2comp__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__lsb,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__lsb @ A_27a )
= ( c_2Ewords_2Eword__bit @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2Eword__msb,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__msb @ A_27a )
= ( c_2Ewords_2Eword__bit @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__lsb__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsb @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Earithmetic_2EODD @ V0n ) ) ).
thf(thm_2Ewords_2Eword__msb__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Ebit_2EBIT @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0n ) ) ).
thf(thm_2Ewords_2Eword__msb__n2w__numeric,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__and__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ V1m ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBITWISE @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ c_2Ebool_2E_2F_5C @ V0n @ V1m ) ) ) ).
thf(thm_2Ewords_2Eword__or__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ V1m ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBITWISE @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ c_2Ebool_2E_5C_2F @ V0n @ V1m ) ) ) ).
thf(thm_2Ewords_2Eword__xor__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ V1m ) )
= ( c_2Ewords_2En2w @ A_27a
@ ( c_2Ebit_2EBITWISE @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
@ ^ [V2x: $o,V3y: $o] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ V2x @ V3y ) )
@ V0n
@ V1m ) ) ) ).
thf(thm_2Ewords_2Eword__nand__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__nand @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ V1m ) )
= ( c_2Ewords_2En2w @ A_27a
@ ( c_2Ebit_2EBITWISE @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
@ ^ [V2x: $o,V3y: $o] : ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_2F_5C @ V2x @ V3y ) )
@ V0n
@ V1m ) ) ) ).
thf(thm_2Ewords_2Eword__nor__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__nor @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ V1m ) )
= ( c_2Ewords_2En2w @ A_27a
@ ( c_2Ebit_2EBITWISE @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
@ ^ [V2x: $o,V3y: $o] : ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_5C_2F @ V2x @ V3y ) )
@ V0n
@ V1m ) ) ) ).
thf(thm_2Ewords_2Eword__xnor__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__xnor @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ V1m ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBITWISE @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Emin_2E_3D @ $o ) @ V0n @ V1m ) ) ) ).
thf(thm_2Ewords_2El2w__w2l,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0b )
=> ( ( c_2Ewords_2El2w @ A_27a @ V0b @ ( c_2Ewords_2Ew2l @ A_27a @ V0b @ V1w ) )
= V1w ) ) ).
thf(thm_2Ewords_2Ew2l__l2w,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Ewords_2Ew2l @ A_27a @ V0b @ ( c_2Ewords_2El2w @ A_27a @ V0b @ V1l ) )
= ( c_2Enumposrep_2En2l @ V0b @ ( c_2Earithmetic_2EMOD @ ( c_2Enumposrep_2El2n @ V0b @ V1l ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Es2w__w2s,axiom,
! [A_27a: $tType,V0c2n: tyop_2Estring_2Echar > tyop_2Enum_2Enum,V1n2c: tyop_2Enum_2Enum > tyop_2Estring_2Echar,V2b: tyop_2Enum_2Enum,V3w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V2b )
& ! [V4x: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V4x @ V2b )
=> ( ( V0c2n @ ( V1n2c @ V4x ) )
= V4x ) ) )
=> ( ( c_2Ewords_2Es2w @ A_27a @ V2b @ V0c2n @ ( c_2Ewords_2Ew2s @ A_27a @ V2b @ V1n2c @ V3w ) )
= V3w ) ) ).
thf(thm_2Ewords_2Ew2s__s2w,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1c2n: tyop_2Estring_2Echar > tyop_2Enum_2Enum,V2n2c: tyop_2Enum_2Enum > tyop_2Estring_2Echar,V3s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( c_2Ewords_2Ew2s @ A_27a @ V0b @ V2n2c @ ( c_2Ewords_2Es2w @ A_27a @ V0b @ V1c2n @ V3s ) )
= ( c_2EASCIInumbers_2En2s @ V0b @ V2n2c @ ( c_2Earithmetic_2EMOD @ ( c_2EASCIInumbers_2Es2n @ V0b @ V1c2n @ V3s ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2ENUMERAL__LESS__THM,axiom,
( ! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) )
<=> ( ( V0m
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( c_2Eprim__rec_2E_3C @ V0m @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V2m: tyop_2Enum_2Enum,V3n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V2m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V3n ) ) )
<=> ( ( V2m
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V3n ) ) )
| ( c_2Eprim__rec_2E_3C @ V2m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V3n ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__bin__list,axiom,
! [A_27a: $tType] :
( ( c_2Ecombin_2Eo @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Ewords_2Eword__from__bin__list @ A_27a ) @ ( c_2Ewords_2Eword__to__bin__list @ A_27a ) )
= ( c_2Ecombin_2EI @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__oct__list,axiom,
! [A_27a: $tType] :
( ( c_2Ecombin_2Eo @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Ewords_2Eword__from__oct__list @ A_27a ) @ ( c_2Ewords_2Eword__to__oct__list @ A_27a ) )
= ( c_2Ecombin_2EI @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__dec__list,axiom,
! [A_27a: $tType] :
( ( c_2Ecombin_2Eo @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Ewords_2Eword__from__dec__list @ A_27a ) @ ( c_2Ewords_2Eword__to__dec__list @ A_27a ) )
= ( c_2Ecombin_2EI @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__hex__list,axiom,
! [A_27a: $tType] :
( ( c_2Ecombin_2Eo @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Ewords_2Eword__from__hex__list @ A_27a ) @ ( c_2Ewords_2Eword__to__hex__list @ A_27a ) )
= ( c_2Ecombin_2EI @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__bin__string,axiom,
! [A_27a: $tType] :
( ( c_2Ecombin_2Eo @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Ewords_2Eword__from__bin__string @ A_27a ) @ ( c_2Ewords_2Eword__to__bin__string @ A_27a ) )
= ( c_2Ecombin_2EI @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__oct__string,axiom,
! [A_27a: $tType] :
( ( c_2Ecombin_2Eo @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Ewords_2Eword__from__oct__string @ A_27a ) @ ( c_2Ewords_2Eword__to__oct__string @ A_27a ) )
= ( c_2Ecombin_2EI @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__dec__string,axiom,
! [A_27a: $tType] :
( ( c_2Ecombin_2Eo @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Ewords_2Eword__from__dec__string @ A_27a ) @ ( c_2Ewords_2Eword__to__dec__string @ A_27a ) )
= ( c_2Ecombin_2EI @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__hex__string,axiom,
! [A_27a: $tType] :
( ( c_2Ecombin_2Eo @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Ewords_2Eword__from__hex__string @ A_27a ) @ ( c_2Ewords_2Eword__to__hex__string @ A_27a ) )
= ( c_2Ecombin_2EI @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__0,axiom,
! [A_27a: $tType,V0i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0i ) ) ) ).
thf(thm_2Ewords_2Eword__eq__0,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( V0w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
<=> ! [V1i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) ) ) ) ).
thf(thm_2Ewords_2Eword__T,axiom,
! [A_27a: $tType,V0i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) @ V0i ) ) ).
thf(thm_2Ewords_2EFCP__T__F,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( ( c_2Efcp_2EFCP @ $o @ A_27a @ ( c_2Ecombin_2EK @ $o @ tyop_2Enum_2Enum @ c_2Ebool_2ET ) )
= ( c_2Ewords_2Eword__T @ A_27a ) )
& ( ( c_2Efcp_2EFCP @ $o @ A_27b @ ( c_2Ecombin_2EK @ $o @ tyop_2Enum_2Enum @ c_2Ebool_2EF ) )
= ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Eword__L,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) @ V0n )
<=> ( V0n
= ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__H,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__H @ A_27a ) @ V0n )
= ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__L2,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__L2 @ A_27a )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(thm_2Ewords_2EWORD__NEG__1,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(thm_2Ewords_2EWORD__NEG__1__T,axiom,
! [A_27a: $tType,V0i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0i ) ) ).
thf(thm_2Ewords_2EWORD__MSB__1COMP,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0w ) )
<=> ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0w ) ) ) ).
thf(thm_2Ewords_2Ew2n__minus1,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Ew2n__plus1,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Earithmetic_2E_2B @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0a @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__NOT__NOT,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) )
= V0a ) ).
thf(thm_2Ewords_2EWORD__DE__MORGAN__THM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b ) )
= ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) @ ( c_2Ewords_2Eword__1comp @ A_27a @ V1b ) ) )
& ( ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V1b ) )
= ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) @ ( c_2Ewords_2Eword__1comp @ A_27a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__NOT__XOR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) @ ( c_2Ewords_2Eword__1comp @ A_27a @ V1b ) )
= ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V1b ) )
& ( ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V1b ) )
= ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V1b ) ) )
& ( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) @ V1b )
= ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__AND__CLAUSES,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) @ V0a )
= V0a )
& ( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ ( c_2Ewords_2Eword__T @ A_27a ) )
= V0a )
& ( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0a )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V0a )
= V0a ) ) ).
thf(thm_2Ewords_2EWORD__OR__CLAUSES,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) @ V0a )
= ( c_2Ewords_2Eword__T @ A_27a ) )
& ( ( c_2Ewords_2Eword__or @ A_27a @ V0a @ ( c_2Ewords_2Eword__T @ A_27a ) )
= ( c_2Ewords_2Eword__T @ A_27a ) )
& ( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0a )
= V0a )
& ( ( c_2Ewords_2Eword__or @ A_27a @ V0a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= V0a )
& ( ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V0a )
= V0a ) ) ).
thf(thm_2Ewords_2EWORD__XOR__CLAUSES,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) @ V0a )
= ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) )
& ( ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ ( c_2Ewords_2Eword__T @ A_27a ) )
= ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) )
& ( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0a )
= V0a )
& ( ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= V0a )
& ( ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V0a )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__AND__ASSOC,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b ) @ V2c )
= ( c_2Ewords_2Eword__and @ A_27a @ V0a @ ( c_2Ewords_2Eword__and @ A_27a @ V1b @ V2c ) ) ) ).
thf(thm_2Ewords_2EWORD__OR__ASSOC,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V1b ) @ V2c )
= ( c_2Ewords_2Eword__or @ A_27a @ V0a @ ( c_2Ewords_2Eword__or @ A_27a @ V1b @ V2c ) ) ) ).
thf(thm_2Ewords_2EWORD__XOR__ASSOC,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V1b ) @ V2c )
= ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ ( c_2Ewords_2Eword__xor @ A_27a @ V1b @ V2c ) ) ) ).
thf(thm_2Ewords_2EWORD__AND__COMM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__and @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__OR__COMM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__or @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__XOR__COMM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__xor @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__AND__IDEM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V0a )
= V0a ) ).
thf(thm_2Ewords_2EWORD__OR__IDEM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V0a )
= V0a ) ).
thf(thm_2Ewords_2EWORD__AND__ABSORD,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ V0a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b ) )
= V0a ) ).
thf(thm_2Ewords_2EWORD__OR__ABSORB,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V1b ) )
= V0a ) ).
thf(thm_2Ewords_2EWORD__AND__COMP,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__OR__COMP,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ V0a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(thm_2Ewords_2EWORD__XOR__COMP,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(thm_2Ewords_2EWORD__RIGHT__AND__OVER__OR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V1b ) @ V2c )
= ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V2c ) @ ( c_2Ewords_2Eword__and @ A_27a @ V1b @ V2c ) ) ) ).
thf(thm_2Ewords_2EWORD__RIGHT__OR__OVER__AND,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b ) @ V2c )
= ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V2c ) @ ( c_2Ewords_2Eword__or @ A_27a @ V1b @ V2c ) ) ) ).
thf(thm_2Ewords_2EWORD__RIGHT__AND__OVER__XOR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V1b ) @ V2c )
= ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V2c ) @ ( c_2Ewords_2Eword__and @ A_27a @ V1b @ V2c ) ) ) ).
thf(thm_2Ewords_2EWORD__LEFT__AND__OVER__OR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ ( c_2Ewords_2Eword__or @ A_27a @ V1b @ V2c ) )
= ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b ) @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V2c ) ) ) ).
thf(thm_2Ewords_2EWORD__LEFT__OR__OVER__AND,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ V0a @ ( c_2Ewords_2Eword__and @ A_27a @ V1b @ V2c ) )
= ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V1b ) @ ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V2c ) ) ) ).
thf(thm_2Ewords_2EWORD__LEFT__AND__OVER__XOR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ ( c_2Ewords_2Eword__xor @ A_27a @ V1b @ V2c ) )
= ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b ) @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V2c ) ) ) ).
thf(thm_2Ewords_2EWORD__XOR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V1b ) ) @ ( c_2Ewords_2Eword__and @ A_27a @ V1b @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0a ) ) ) ) ).
thf(thm_2Ewords_2EWORD__NAND__NOT__AND,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__nand @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__NOR__NOT__OR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__nor @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__XNOR__NOT__XOR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xnor @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__OR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
=> ( ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__or @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__XOR,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__and @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
=> ( ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__xor @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__AND__EXP__SUB1,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V1n ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0m ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EMOD @ V1n @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0m ) ) ) ) ).
thf(thm_2Ewords_2Eword__msb__add__word__L,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0a @ ( c_2Ewords_2Eword__L @ A_27a ) ) )
<=> ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) ) ) ).
thf(thm_2Ewords_2Ew2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) @ V1i )
<=> ( ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
& ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) ) ) ) ).
thf(thm_2Ewords_2Esw2sw,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27b @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b @ V0w ) @ V1i )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Ebool_2E_5C_2F @ ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( 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_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0w ) ) ) ) ).
thf(thm_2Ewords_2Ew2w__id,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2w @ A_27a @ A_27a @ V0w )
= V0w ) ).
thf(thm_2Ewords_2Esw2sw__id,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esw2sw @ A_27a @ A_27a @ V0w )
= V0w ) ).
thf(thm_2Ewords_2Ew2w__w2w,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2w @ A_27b @ A_27c @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) )
= ( c_2Ewords_2Ew2w @ A_27a @ A_27c @ ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V0w ) ) ) ).
thf(thm_2Ewords_2Esw2sw__sw2sw,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esw2sw @ A_27b @ A_27c @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b @ V0w ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ ( c_2Ebool_2E_2F_5C @ ( 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_2Eprim__rec_2E_3C @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) ) @ ( c_2Ewords_2Esw2sw @ A_27b @ A_27c @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) ) @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27c @ V0w ) ) ) ).
thf(thm_2Ewords_2Esw2sw__w2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esw2sw @ A_27a @ A_27b @ V0w )
= ( c_2Ewords_2Eword__or @ A_27b @ ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0w ) @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) ) ) ).
thf(thm_2Ewords_2Eword__bit,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1b @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1b )
= ( c_2Ewords_2Eword__bit @ A_27a @ V1b @ V0w ) ) ) ).
thf(thm_2Ewords_2Eword__slice__n2w,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1l @ ( c_2Ewords_2En2w @ A_27a @ V2n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2ESLICE @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1l @ V2n ) ) ) ).
thf(thm_2Ewords_2Eword__bits__n2w,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ ( c_2Ewords_2En2w @ A_27a @ V2n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1l @ V2n ) ) ) ).
thf(thm_2Ewords_2Eword__bit__n2w,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__bit @ A_27a @ V0b @ ( c_2Ewords_2En2w @ A_27a @ V1n ) )
<=> ( ( c_2Earithmetic_2E_3C_3D @ V0b @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ( c_2Ebit_2EBIT @ V0b @ V1n ) ) ) ).
thf(thm_2Ewords_2Eword__signed__bits__n2w,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__signed__bits @ A_27a @ V0h @ V1l @ ( c_2Ewords_2En2w @ A_27a @ V2n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2ESIGN__EXTEND @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EMIN @ ( c_2Enum_2ESUC @ V0h ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ V1l ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1l @ V2n ) ) ) ) ).
thf(thm_2Ewords_2Eword__sign__extend__bits,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__signed__bits @ A_27a @ V0h @ V1l @ V2w )
= ( c_2Ewords_2Eword__sign__extend @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EMIN @ ( c_2Enum_2ESUC @ V0h ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ V1l ) @ ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2w ) ) ) ).
thf(thm_2Ewords_2Eword__index__n2w,axiom,
! [A_27a: $tType,V0index_20too_20large: $o,V1n: tyop_2Enum_2Enum,V2i: tyop_2Enum_2Enum] :
( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V1n ) @ V2i )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Eprim__rec_2E_3C @ V2i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Ebit_2EBIT @ V2i @ V1n ) @ ( 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_2Ewords_2En2w @ A_27a @ V1n ) @ V2i ) ) ) ).
thf(thm_2Ewords_2Eword__index,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ V1i )
= ( c_2Ebit_2EBIT @ V1i @ V0n ) ) ) ).
thf(thm_2Ewords_2Eword__bits__w2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1h: tyop_2Enum_2Enum,V2l: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__bits @ A_27b @ V1h @ V2l @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) )
= ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2EMIN @ V1h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2l @ V0w ) ) ) ).
thf(thm_2Ewords_2Eword__reverse__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBIT__REVERSE @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0n ) ) ) ).
thf(thm_2Ewords_2Eword__modify__n2w,axiom,
! [A_27a: $tType,V0f: tyop_2Enum_2Enum > $o > $o,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__modify @ A_27a @ V0f @ ( c_2Ewords_2En2w @ A_27a @ V1n ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBIT__MODIFY @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0f @ V1n ) ) ) ).
thf(thm_2Ewords_2Efcp__n2w,axiom,
! [A_27a: $tType,V0f: tyop_2Enum_2Enum > $o] :
( ( c_2Efcp_2EFCP @ $o @ A_27a @ V0f )
= ( c_2Ewords_2Eword__modify @ A_27a
@ ^ [V1i: tyop_2Enum_2Enum,V2b: $o] : ( V0f @ V1i )
@ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Ew2n__w2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2n @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) @ ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V0w ) ) ) ) ).
thf(thm_2Ewords_2Ew2n__w2w__le,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) ) @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) ) ).
thf(thm_2Ewords_2Ew2w__lt,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ewords_2Ew2w__n2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( 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_2En2w @ A_27b @ V0n ) @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V0n ) ) ) ) ).
thf(thm_2Ewords_2Ew2w__0,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( c_2Ewords_2Ew2w @ A_27b @ A_27a @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2Ew2n__11__lift,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
=> ( ( ( c_2Ewords_2Ew2n @ A_27a @ V0a )
= ( c_2Ewords_2Ew2n @ A_27b @ V1b ) )
<=> ( ( c_2Ewords_2Ew2w @ A_27a @ A_27c @ V0a )
= ( c_2Ewords_2Ew2w @ A_27b @ A_27c @ V1b ) ) ) ) ).
thf(thm_2Ewords_2Eword__extract__n2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2h: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ V1l @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( 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_2En2w @ A_27b @ ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2EMIN @ V2h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1l @ V0n ) ) @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2EMIN @ ( c_2Earithmetic_2EMIN @ V2h @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1l ) ) @ V1l @ V0n ) ) ) ) ).
thf(thm_2Ewords_2En2w__BITS,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0h @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBITS @ V0h @ V1l @ V2n ) )
= ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ ( c_2Ewords_2En2w @ A_27a @ V2n ) ) ) ) ).
thf(thm_2Ewords_2Eword__extract__w2w,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1h: tyop_2Enum_2Enum,V2l: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Ewords_2Eword__extract @ A_27b @ A_27c @ V1h @ V2l @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27c @ V1h @ V2l @ V0w ) ) ) ).
thf(thm_2Ewords_2EWORD__w2w__EXTRACT,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V0w ) ) ).
thf(thm_2Ewords_2EWORD__EQ,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ! [V2x: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V2x @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__bit @ A_27a @ V2x @ V0v )
= ( c_2Ewords_2Eword__bit @ A_27a @ V2x @ V1w ) ) )
<=> ( V0v = V1w ) ) ).
thf(thm_2Ewords_2EBIT__UPDATE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1x: $o] :
( ( c_2Efcp_2E_3A_2B @ $o @ A_27a @ V0n @ V1x )
= ( c_2Ewords_2Eword__modify @ A_27a
@ ^ [V2i: tyop_2Enum_2Enum,V3b: $o] : ( c_2Ebool_2ECOND @ $o @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2i @ V0n ) @ V1x @ V3b ) ) ) ).
thf(thm_2Ewords_2EWORD__MODIFY__BIT,axiom,
! [A_27a: $tType,V0f: tyop_2Enum_2Enum > $o > $o,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V2i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__modify @ A_27a @ V0f @ V1w ) @ V2i )
= ( V0f @ V2i @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) ) ) ) ).
thf(thm_2Ewords_2EWORD__BIT__BITS,axiom,
! [A_27a: $tType,V0b: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__bit @ A_27a @ V0b @ V1w )
<=> ( ( c_2Ewords_2Eword__bits @ A_27a @ V0b @ V0b @ V1w )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__BITS__COMP__THM,axiom,
! [A_27a: $tType,V0h1: tyop_2Enum_2Enum,V1l1: tyop_2Enum_2Enum,V2h2: tyop_2Enum_2Enum,V3l2: tyop_2Enum_2Enum,V4w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__bits @ A_27a @ V2h2 @ V3l2 @ ( c_2Ewords_2Eword__bits @ A_27a @ V0h1 @ V1l1 @ V4w ) )
= ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2EMIN @ V0h1 @ ( c_2Earithmetic_2E_2B @ V2h2 @ V1l1 ) ) @ ( c_2Earithmetic_2E_2B @ V3l2 @ V1l1 ) @ V4w ) ) ).
thf(thm_2Ewords_2EWORD__BITS__EXTRACT,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2w )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27a @ V0h @ V1l @ V2w ) ) ).
thf(thm_2Ewords_2EWORD__BITS__LSR,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a,V3n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2w ) @ V3n )
= ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ ( c_2Earithmetic_2E_2B @ V1l @ V3n ) @ V2w ) ) ).
thf(thm_2Ewords_2EWORD__BITS__ZERO,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0h @ V1l )
=> ( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2w )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__BITS__ZERO2,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__BITS__ZERO3,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1l )
=> ( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2w )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__BITS__LT,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2w ) ) @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Enum_2ESUC @ V0h ) @ V1l ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__LT,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ V2w ) ) @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Enum_2ESUC @ V0h ) @ V1l ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__ZERO,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0h @ V1l )
=> ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ V2w )
= ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__ZERO2,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__extract @ A_27b @ A_27a @ V0h @ V1l @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__ZERO3,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1l )
=> ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ V2w )
= ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__SLICE__THM,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1l @ V2w )
= ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2w ) @ V1l ) ) ).
thf(thm_2Ewords_2EWORD__SLICE__ZERO,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0h @ V1l )
=> ( ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1l @ V2w )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__SLICE__ZERO2,axiom,
! [A_27a: $tType,V0l: tyop_2Enum_2Enum,V1h: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__slice @ A_27a @ V1h @ V0l @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__SLICE__BITS__THM,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ c_2Enum_2E0 @ V1w )
= ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ c_2Enum_2E0 @ V1w ) ) ).
thf(thm_2Ewords_2EWORD__BITS__SLICE__THM,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1l @ V2w ) )
= ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2w ) ) ).
thf(thm_2Ewords_2EWORD__SLICE__COMP__THM,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1m_27: tyop_2Enum_2Enum,V2m: tyop_2Enum_2Enum,V3l: tyop_2Enum_2Enum,V4w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Earithmetic_2E_3C_3D @ V3l @ V2m )
& ( V1m_27
= ( c_2Earithmetic_2E_2B @ V2m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ( c_2Eprim__rec_2E_3C @ V2m @ V0h ) )
=> ( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1m_27 @ V4w ) @ ( c_2Ewords_2Eword__slice @ A_27a @ V2m @ V3l @ V4w ) )
= ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V3l @ V4w ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__COMP__THM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27c,V1h: tyop_2Enum_2Enum,V2l: tyop_2Enum_2Enum,V3m: tyop_2Enum_2Enum,V4n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__extract @ A_27b @ A_27a @ V1h @ V2l @ ( c_2Ewords_2Eword__extract @ A_27c @ A_27b @ V3m @ V4n @ V0w ) )
= ( c_2Ewords_2Eword__extract @ A_27c @ A_27a @ ( c_2Earithmetic_2EMIN @ V3m @ ( c_2Earithmetic_2EMIN @ ( c_2Earithmetic_2E_2B @ V1h @ V4n ) @ ( c_2Earithmetic_2EMIN @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V4n ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Earithmetic_2E_2B @ V2l @ V4n ) @ V0w ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__BITS__COMP,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Efcp_2Ecart @ $o @ A_27a,V1l: tyop_2Enum_2Enum,V2k: tyop_2Enum_2Enum,V3j: tyop_2Enum_2Enum,V4h: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V3j @ V2k @ ( c_2Ewords_2Eword__bits @ A_27a @ V4h @ V1l @ V0n ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2EMIN @ V4h @ ( c_2Earithmetic_2E_2B @ V3j @ V1l ) ) @ ( c_2Earithmetic_2E_2B @ V2k @ V1l ) @ V0n ) ) ).
thf(thm_2Ewords_2EWORD__ALL__BITS,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1h: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1h )
=> ( ( c_2Ewords_2Eword__bits @ A_27a @ V1h @ c_2Enum_2E0 @ V0w )
= V0w ) ) ).
thf(thm_2Ewords_2EEXTRACT__ALL__BITS,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0h )
=> ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ c_2Enum_2E0 @ V1w )
= ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V1w ) ) ) ).
thf(thm_2Ewords_2EWORD__BITS__MIN__HIGH,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1h: tyop_2Enum_2Enum,V2l: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1h )
=> ( ( c_2Ewords_2Eword__bits @ A_27a @ V1h @ V2l @ V0w )
= ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2l @ V0w ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__MIN__HIGH,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V1l ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0h ) )
=> ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ V2w )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1l @ V2w ) ) )
& ! [V3h: tyop_2Enum_2Enum,V4l: tyop_2Enum_2Enum,V5w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V4l ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V4l ) @ V3h ) )
=> ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V3h @ V4l @ V5w )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V4l ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V4l @ V5w ) ) ) ) ).
thf(thm_2Ewords_2ECONCAT__EXTRACT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0h: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Enum_2Enum,V3w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( ( c_2Earithmetic_2E_2D @ V0h @ V1m )
= ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
& ( ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ V1m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2l )
= ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
& ( ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ V0h @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2l )
= ( c_2Efcp_2Edimindex @ A_27d @ ( c_2Ebool_2Ethe__value @ A_27d ) ) )
& ( (~)
@ ( ( c_2Efcp_2Edimindex @ ( tyop_2Esum_2Esum @ A_27b @ A_27c ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Esum_2Esum @ A_27b @ A_27c ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
=> ( ( c_2Ewords_2Eword__concat @ A_27b @ A_27c @ A_27d @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ ( c_2Earithmetic_2E_2B @ V1m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V3w ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c @ V1m @ V2l @ V3w ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27d @ V0h @ V2l @ V3w ) ) ) ).
thf(thm_2Ewords_2EEXTRACT__CONCAT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( ( 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_2Earithmetic_2E_3C_3D @ ( 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_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
=> ( ( ( c_2Ewords_2Eword__extract @ A_27c @ A_27b @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ V0v @ V1w ) )
= V1w )
& ( ( c_2Ewords_2Eword__extract @ A_27c @ A_27a @ ( c_2Earithmetic_2E_2D @ ( 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_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ V0v @ V1w ) )
= V0v ) ) ) ).
thf(thm_2Ewords_2EEXTRACT__JOIN,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2m_27: tyop_2Enum_2Enum,V3l: tyop_2Enum_2Enum,V4s: tyop_2Enum_2Enum,V5w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Earithmetic_2E_3C_3D @ V3l @ V1m )
& ( c_2Earithmetic_2E_3C_3D @ V2m_27 @ V0h )
& ( V2m_27
= ( c_2Earithmetic_2E_2B @ V1m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ( V4s
= ( c_2Earithmetic_2E_2D @ V2m_27 @ V3l ) ) )
=> ( ( c_2Ewords_2Eword__or @ A_27b @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V2m_27 @ V5w ) @ V4s ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V1m @ V3l @ V5w ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2EMIN @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V3l ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ V3l @ V5w ) ) ) ).
thf(thm_2Ewords_2EEXTRACT__JOIN__ADD,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2m_27: tyop_2Enum_2Enum,V3l: tyop_2Enum_2Enum,V4s: tyop_2Enum_2Enum,V5w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Earithmetic_2E_3C_3D @ V3l @ V1m )
& ( c_2Earithmetic_2E_3C_3D @ V2m_27 @ V0h )
& ( V2m_27
= ( c_2Earithmetic_2E_2B @ V1m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ( V4s
= ( c_2Earithmetic_2E_2D @ V2m_27 @ V3l ) ) )
=> ( ( c_2Ewords_2Eword__add @ A_27b @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V2m_27 @ V5w ) @ V4s ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V1m @ V3l @ V5w ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2EMIN @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V3l ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ V3l @ V5w ) ) ) ).
thf(thm_2Ewords_2EEXTEND__EXTRACT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ V0h @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1l ) )
=> ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ V2w )
= ( c_2Ewords_2Ew2w @ A_27c @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c @ V0h @ V1l @ V2w ) ) ) ) ).
thf(thm_2Ewords_2EWORD__SLICE__OVER__BITWISE,axiom,
! [A_27a: $tType] :
( ! [V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2v: tyop_2Efcp_2Ecart @ $o @ A_27a,V3w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1l @ V2v ) @ ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1l @ V3w ) )
= ( c_2Ewords_2Eword__slice @ A_27a @ V0h @ V1l @ ( c_2Ewords_2Eword__and @ A_27a @ V2v @ V3w ) ) )
& ! [V4h: tyop_2Enum_2Enum,V5l: tyop_2Enum_2Enum,V6v: tyop_2Efcp_2Ecart @ $o @ A_27a,V7w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__slice @ A_27a @ V4h @ V5l @ V6v ) @ ( c_2Ewords_2Eword__slice @ A_27a @ V4h @ V5l @ V7w ) )
= ( c_2Ewords_2Eword__slice @ A_27a @ V4h @ V5l @ ( c_2Ewords_2Eword__or @ A_27a @ V6v @ V7w ) ) )
& ! [V8h: tyop_2Enum_2Enum,V9l: tyop_2Enum_2Enum,V10v: tyop_2Efcp_2Ecart @ $o @ A_27a,V11w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__slice @ A_27a @ V8h @ V9l @ V10v ) @ ( c_2Ewords_2Eword__slice @ A_27a @ V8h @ V9l @ V11w ) )
= ( c_2Ewords_2Eword__slice @ A_27a @ V8h @ V9l @ ( c_2Ewords_2Eword__xor @ A_27a @ V10v @ V11w ) ) ) ) ).
thf(thm_2Ewords_2EWORD__BITS__OVER__BITWISE,axiom,
! [A_27a: $tType] :
( ! [V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2v: tyop_2Efcp_2Ecart @ $o @ A_27a,V3w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2v ) @ ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V3w ) )
= ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ ( c_2Ewords_2Eword__and @ A_27a @ V2v @ V3w ) ) )
& ! [V4h: tyop_2Enum_2Enum,V5l: tyop_2Enum_2Enum,V6v: tyop_2Efcp_2Ecart @ $o @ A_27a,V7w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ V4h @ V5l @ V6v ) @ ( c_2Ewords_2Eword__bits @ A_27a @ V4h @ V5l @ V7w ) )
= ( c_2Ewords_2Eword__bits @ A_27a @ V4h @ V5l @ ( c_2Ewords_2Eword__or @ A_27a @ V6v @ V7w ) ) )
& ! [V8h: tyop_2Enum_2Enum,V9l: tyop_2Enum_2Enum,V10v: tyop_2Efcp_2Ecart @ $o @ A_27a,V11w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ V8h @ V9l @ V10v ) @ ( c_2Ewords_2Eword__bits @ A_27a @ V8h @ V9l @ V11w ) )
= ( c_2Ewords_2Eword__bits @ A_27a @ V8h @ V9l @ ( c_2Ewords_2Eword__xor @ A_27a @ V10v @ V11w ) ) ) ) ).
thf(thm_2Ewords_2EWORD__w2w__OVER__BITWISE,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0v ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V1w ) )
= ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2Eword__and @ A_27a @ V0v @ V1w ) ) )
& ! [V2v: tyop_2Efcp_2Ecart @ $o @ A_27a,V3w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V2v ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V3w ) )
= ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2Eword__or @ A_27a @ V2v @ V3w ) ) )
& ! [V4v: tyop_2Efcp_2Ecart @ $o @ A_27a,V5w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V4v ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V5w ) )
= ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2Eword__xor @ A_27a @ V4v @ V5w ) ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__OVER__BITWISE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
( ! [V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2v: tyop_2Efcp_2Ecart @ $o @ A_27a,V3w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ V2v ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ V3w ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ ( c_2Ewords_2Eword__and @ A_27a @ V2v @ V3w ) ) )
& ! [V4h: tyop_2Enum_2Enum,V5l: tyop_2Enum_2Enum,V6v: tyop_2Efcp_2Ecart @ $o @ A_27a,V7w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27c @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c @ V4h @ V5l @ V6v ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c @ V4h @ V5l @ V7w ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27c @ V4h @ V5l @ ( c_2Ewords_2Eword__or @ A_27a @ V6v @ V7w ) ) )
& ! [V8h: tyop_2Enum_2Enum,V9l: tyop_2Enum_2Enum,V10v: tyop_2Efcp_2Ecart @ $o @ A_27a,V11w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27d @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27d @ V8h @ V9l @ V10v ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27d @ V8h @ V9l @ V11w ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27d @ V8h @ V9l @ ( c_2Ewords_2Eword__xor @ A_27a @ V10v @ V11w ) ) ) ) ).
thf(thm_2Ewords_2EWORD__w2w__OVER__ADD,axiom,
! [A_27a: $tType,A_27b: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b ) )
= ( c_2Ewords_2Eword__bits @ A_27b @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__add @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0a ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__w2w__OVER__MUL,axiom,
! [A_27a: $tType,A_27b: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2Eword__mul @ A_27a @ V0a @ V1b ) )
= ( c_2Ewords_2Eword__bits @ A_27b @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__mul @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0a ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__OVER__ADD,axiom,
! [A_27a: $tType,A_27b: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2h: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2h )
& ( 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 @ V2h @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b ) )
= ( c_2Ewords_2Eword__add @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ V0a ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__OVER__MUL,axiom,
! [A_27a: $tType,A_27b: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2h: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2h )
& ( 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 @ V2h @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__mul @ A_27a @ V0a @ V1b ) )
= ( c_2Ewords_2Eword__mul @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ V0a ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__OVER__ADD2,axiom,
! [A_27a: $tType,A_27b: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2h: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V2h @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__extract @ A_27b @ A_27b @ V2h @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__add @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ V0a ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ V1b ) ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__OVER__MUL2,axiom,
! [A_27a: $tType,A_27b: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2h: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V2h @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__extract @ A_27b @ A_27b @ V2h @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__mul @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ V0a ) @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ V1b ) ) )
= ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V2h @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__mul @ A_27a @ V0a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__ID,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1h: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ V1h ) ) )
=> ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27a @ V1h @ c_2Enum_2E0 @ V0w )
= V0w ) ) ).
thf(thm_2Ewords_2EBIT__SET,axiom,
! [V0i: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Ebit_2EBIT @ V0i @ V1n )
= ( c_2Ebool_2EIN @ tyop_2Enum_2Enum @ V0i @ ( c_2Ewords_2EBIT__SET @ c_2Enum_2E0 @ V1n ) ) ) ).
thf(thm_2Ewords_2EWORD__LITERAL__AND,axiom,
! [A_27a: $tType] :
( ! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ V1m ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBITWISE @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2EMIN @ ( c_2Ebit_2ELOG2 @ V0n ) @ ( c_2Ebit_2ELOG2 @ V1m ) ) ) @ c_2Ebool_2E_2F_5C @ V0n @ V1m ) ) )
& ! [V2n: tyop_2Enum_2Enum,V3m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V2n ) @ ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V3m ) ) )
= ( c_2Ewords_2En2w @ A_27a
@ ( c_2Ebit_2EBITWISE @ ( c_2Enum_2ESUC @ ( c_2Ebit_2ELOG2 @ V2n ) )
@ ^ [V4a: $o,V5b: $o] : ( c_2Ebool_2E_2F_5C @ V4a @ ( c_2Ebool_2E_7E @ V5b ) )
@ V2n
@ V3m ) ) )
& ! [V6n: tyop_2Enum_2Enum,V7m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V7m ) ) @ ( c_2Ewords_2En2w @ A_27a @ V6n ) )
= ( c_2Ewords_2En2w @ A_27a
@ ( c_2Ebit_2EBITWISE @ ( c_2Enum_2ESUC @ ( c_2Ebit_2ELOG2 @ V6n ) )
@ ^ [V8a: $o,V9b: $o] : ( c_2Ebool_2E_2F_5C @ V8a @ ( c_2Ebool_2E_7E @ V9b ) )
@ V6n
@ V7m ) ) )
& ! [V10n: tyop_2Enum_2Enum,V11m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V10n ) ) @ ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V11m ) ) )
= ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBITWISE @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2EMAX @ ( c_2Ebit_2ELOG2 @ V10n ) @ ( c_2Ebit_2ELOG2 @ V11m ) ) ) @ c_2Ebool_2E_5C_2F @ V10n @ V11m ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LITERAL__OR,axiom,
! [A_27a: $tType] :
( ! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ V1m ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBITWISE @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2EMAX @ ( c_2Ebit_2ELOG2 @ V0n ) @ ( c_2Ebit_2ELOG2 @ V1m ) ) ) @ c_2Ebool_2E_5C_2F @ V0n @ V1m ) ) )
& ! [V2n: tyop_2Enum_2Enum,V3m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V2n ) @ ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V3m ) ) )
= ( c_2Ewords_2Eword__1comp @ A_27a
@ ( c_2Ewords_2En2w @ A_27a
@ ( c_2Ebit_2EBITWISE @ ( c_2Enum_2ESUC @ ( c_2Ebit_2ELOG2 @ V3m ) )
@ ^ [V4a: $o,V5b: $o] : ( c_2Ebool_2E_2F_5C @ V4a @ ( c_2Ebool_2E_7E @ V5b ) )
@ V3m
@ V2n ) ) ) )
& ! [V6n: tyop_2Enum_2Enum,V7m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V7m ) ) @ ( c_2Ewords_2En2w @ A_27a @ V6n ) )
= ( c_2Ewords_2Eword__1comp @ A_27a
@ ( c_2Ewords_2En2w @ A_27a
@ ( c_2Ebit_2EBITWISE @ ( c_2Enum_2ESUC @ ( c_2Ebit_2ELOG2 @ V7m ) )
@ ^ [V8a: $o,V9b: $o] : ( c_2Ebool_2E_2F_5C @ V8a @ ( c_2Ebool_2E_7E @ V9b ) )
@ V7m
@ V6n ) ) ) )
& ! [V10n: tyop_2Enum_2Enum,V11m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V10n ) ) @ ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V11m ) ) )
= ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Ebit_2EBITWISE @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2EMIN @ ( c_2Ebit_2ELOG2 @ V10n ) @ ( c_2Ebit_2ELOG2 @ V11m ) ) ) @ c_2Ebool_2E_2F_5C @ V10n @ V11m ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LITERAL__XOR,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ V1m ) )
= ( c_2Ewords_2En2w @ A_27a
@ ( c_2Ebit_2EBITWISE @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2EMAX @ ( c_2Ebit_2ELOG2 @ V0n ) @ ( c_2Ebit_2ELOG2 @ V1m ) ) )
@ ^ [V2x: $o,V3y: $o] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ V2x @ V3y ) )
@ V0n
@ V1m ) ) ) ).
thf(thm_2Ewords_2Eword__replicate__concat__word__list,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__replicate @ A_27a @ A_27b @ V0n @ V1w )
= ( c_2Ewords_2Econcat__word__list @ A_27a @ A_27b @ ( c_2Elist_2EGENLIST @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ecombin_2EK @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ tyop_2Enum_2Enum @ V1w ) @ V0n ) ) ) ).
thf(thm_2Ewords_2Ebit__field__insert,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2a: tyop_2Efcp_2Ecart @ $o @ A_27a,V3b: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Eprim__rec_2E_3C @ V0h @ ( c_2Earithmetic_2E_2B @ V1l @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( c_2Ewords_2Ebit__field__insert @ A_27b @ A_27a @ V0h @ V1l @ V2a @ V3b )
= ( c_2Ebool_2ELET @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( tyop_2Efcp_2Ecart @ $o @ A_27b )
@ ^ [V4mask: tyop_2Efcp_2Ecart @ $o @ A_27b] : ( c_2Ewords_2Eword__or @ A_27b @ ( c_2Ewords_2Eword__and @ A_27b @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V2a ) @ V1l ) @ V4mask ) @ ( c_2Ewords_2Eword__and @ A_27b @ V3b @ ( c_2Ewords_2Eword__1comp @ A_27b @ V4mask ) ) )
@ ( c_2Ewords_2Eword__slice @ A_27b @ V0h @ V1l @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__join__index,axiom,
! [A_27a: $tType,A_27b: $tType,V0i: tyop_2Enum_2Enum,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a,V2b: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( ( 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_2Eprim__rec_2E_3C @ V0i @ ( c_2Efcp_2Edimindex @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b @ V1a @ V2b ) @ V0i )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Eprim__rec_2E_3C @ V0i @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27b @ V2b @ V0i ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1a @ ( c_2Earithmetic_2E_2D @ V0i @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efoldl__reduce__and,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ereduce__and @ A_27a @ V0w )
= ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V1l: tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )] : ( c_2Elist_2EFOLDL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( c_2Ewords_2Eword__and @ tyop_2Eone_2Eone ) @ ( c_2Elist_2EHD @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) @ ( c_2Elist_2ETL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) )
@ ( c_2Elist_2EGENLIST @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V2i: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V3n: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__extract @ A_27a @ tyop_2Eone_2Eone @ V3n @ V3n @ 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 ) ) ) @ V2i ) )
@ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Efoldl__reduce__or,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ereduce__or @ A_27a @ V0w )
= ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V1l: tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )] : ( c_2Elist_2EFOLDL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( c_2Ewords_2Eword__or @ tyop_2Eone_2Eone ) @ ( c_2Elist_2EHD @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) @ ( c_2Elist_2ETL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) )
@ ( c_2Elist_2EGENLIST @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V2i: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V3n: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__extract @ A_27a @ tyop_2Eone_2Eone @ V3n @ V3n @ 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 ) ) ) @ V2i ) )
@ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Efoldl__reduce__xor,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ereduce__xor @ A_27a @ V0w )
= ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V1l: tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )] : ( c_2Elist_2EFOLDL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( c_2Ewords_2Eword__xor @ tyop_2Eone_2Eone ) @ ( c_2Elist_2EHD @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) @ ( c_2Elist_2ETL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) )
@ ( c_2Elist_2EGENLIST @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V2i: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V3n: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__extract @ A_27a @ tyop_2Eone_2Eone @ V3n @ V3n @ 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 ) ) ) @ V2i ) )
@ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Efoldl__reduce__nand,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ereduce__nand @ A_27a @ V0w )
= ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V1l: tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )] : ( c_2Elist_2EFOLDL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( c_2Ewords_2Eword__nand @ tyop_2Eone_2Eone ) @ ( c_2Elist_2EHD @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) @ ( c_2Elist_2ETL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) )
@ ( c_2Elist_2EGENLIST @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V2i: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V3n: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__extract @ A_27a @ tyop_2Eone_2Eone @ V3n @ V3n @ 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 ) ) ) @ V2i ) )
@ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Efoldl__reduce__nor,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ereduce__nor @ A_27a @ V0w )
= ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V1l: tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )] : ( c_2Elist_2EFOLDL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( c_2Ewords_2Eword__nor @ tyop_2Eone_2Eone ) @ ( c_2Elist_2EHD @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) @ ( c_2Elist_2ETL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) )
@ ( c_2Elist_2EGENLIST @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V2i: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V3n: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__extract @ A_27a @ tyop_2Eone_2Eone @ V3n @ V3n @ 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 ) ) ) @ V2i ) )
@ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Efoldl__reduce__xnor,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ereduce__xnor @ A_27a @ V0w )
= ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V1l: tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )] : ( c_2Elist_2EFOLDL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( c_2Ewords_2Eword__xnor @ tyop_2Eone_2Eone ) @ ( c_2Elist_2EHD @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) @ ( c_2Elist_2ETL @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1l ) )
@ ( c_2Elist_2EGENLIST @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V2i: tyop_2Enum_2Enum] :
( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone )
@ ^ [V3n: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__extract @ A_27a @ tyop_2Eone_2Eone @ V3n @ V3n @ 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 ) ) ) @ V2i ) )
@ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2ELOG2__w2n__lt,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~)
@ ( V0w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Ebit_2ELOG2 @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2ELOG2__w2n,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~)
@ ( V0w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
=> ( ( c_2Ebit_2ELOG2 @ ( c_2Ewords_2Ew2n @ 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 ) ) )
@ ( c_2Ewhile_2ELEAST
@ ^ [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 ) ) ) ) ) ) ).
thf(thm_2Ewords_2ELEAST__BIT__LT,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~)
@ ( V0w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
=> ( c_2Eprim__rec_2E_3C
@ ( c_2Ewhile_2ELEAST
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) )
@ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2Eword__reduce__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1f: $o > $o > $o] :
( ( c_2Ewords_2Eword__reduce @ A_27a @ V1f @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Efcp_2EFCP @ $o @ tyop_2Eone_2Eone
@ ( c_2Ecombin_2EK @ $o @ tyop_2Enum_2Enum
@ ( c_2Ebool_2ELET @ ( tyop_2Elist_2Elist @ $o ) @ $o
@ ^ [V2l: tyop_2Elist_2Elist @ $o] : ( c_2Elist_2EFOLDL @ $o @ $o @ V1f @ ( c_2Elist_2EHD @ $o @ V2l ) @ ( c_2Elist_2ETL @ $o @ V2l ) )
@ ( c_2Enumposrep_2EBOOLIFY @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0n @ ( c_2Elist_2ENIL @ $o ) ) ) ) ) ) ).
thf(thm_2Ewords_2ENOT__UINTMAXw,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~)
@ ( V0w
= ( c_2Ewords_2Eword__T @ A_27a ) ) )
=> ? [V1i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
& ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) ) ) ) ).
thf(thm_2Ewords_2ENOT__0w,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~)
@ ( V0w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
=> ? [V1i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
& ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) ) ) ).
thf(thm_2Ewords_2Ereduce__and,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ereduce__and @ A_27a @ V0w )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0w @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Ereduce__or,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ereduce__or @ A_27a @ V0w )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0w @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__0,axiom,
! [A_27a: $tType] :
( ! [V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ V0w @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= V0w )
& ! [V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1w )
= V1w ) ) ).
thf(thm_2Ewords_2EWORD__ADD__ASSOC,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ ( c_2Ewords_2Eword__add @ A_27a @ V1w @ V2x ) )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w ) @ V2x ) ) ).
thf(thm_2Ewords_2EWORD__MULT__ASSOC,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ ( c_2Ewords_2Eword__mul @ A_27a @ V1w @ V2x ) )
= ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V1w ) @ V2x ) ) ).
thf(thm_2Ewords_2EWORD__ADD__COMM,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2Eword__add @ A_27a @ V1w @ V0v ) ) ).
thf(thm_2Ewords_2EWORD__MULT__COMM,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2Eword__mul @ A_27a @ V1w @ V0v ) ) ).
thf(thm_2Ewords_2EWORD__MULT__CLAUSES,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0v )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ( ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0v )
= V0v )
& ( ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= V0v )
& ( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1w )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V1w ) @ V1w ) )
& ( ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ ( c_2Ewords_2Eword__add @ A_27a @ V1w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ewords_2Eword__add @ A_27a @ V0v @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V1w ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LEFT__ADD__DISTRIB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ ( c_2Ewords_2Eword__add @ A_27a @ V1w @ V2x ) )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V1w ) @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V2x ) ) ) ).
thf(thm_2Ewords_2EWORD__RIGHT__ADD__DISTRIB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w ) @ V2x )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V2x ) @ ( c_2Ewords_2Eword__mul @ A_27a @ V1w @ V2x ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__SUB__ASSOC,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w ) @ V2x )
= ( c_2Ewords_2Eword__add @ A_27a @ V0v @ ( c_2Ewords_2Eword__sub @ A_27a @ V1w @ V2x ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__SUB__SYM,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w ) @ V2x )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V2x ) @ V1w ) ) ).
thf(thm_2Ewords_2EWORD__ADD__LINV,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) @ V0w )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__ADD__RINV,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ V0w @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__SUB__REFL,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V0w @ V0w )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__SUB__ADD2,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ ( c_2Ewords_2Eword__sub @ A_27a @ V1w @ V0v ) )
= V1w ) ).
thf(thm_2Ewords_2EWORD__ADD__SUB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w ) @ V1w )
= V0v ) ).
thf(thm_2Ewords_2EWORD__SUB__ADD,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w ) @ V1w )
= V0v ) ).
thf(thm_2Ewords_2EWORD__ADD__EQ__SUB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w )
= V2x )
<=> ( V0v
= ( c_2Ewords_2Eword__sub @ A_27a @ V2x @ V1w ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__INV__0__EQ,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w )
= V0v )
<=> ( V1w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__EQ__ADD__LCANCEL,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V2x ) )
<=> ( V1w = V2x ) ) ).
thf(thm_2Ewords_2EWORD__EQ__ADD__RCANCEL,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2Eword__add @ A_27a @ V2x @ V1w ) )
<=> ( V0v = V2x ) ) ).
thf(thm_2Ewords_2EWORD__NEG,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ V0w )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0w ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__NOT,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__1comp @ A_27a @ V0w )
= ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__NEG__0,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__NEG__ADD,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w ) )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0v ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1w ) ) ) ).
thf(thm_2Ewords_2EWORD__NEG__NEG,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) )
= V0w ) ).
thf(thm_2Ewords_2EWORD__SUB__LNEG,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0v ) @ V1w )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w ) ) ) ).
thf(thm_2Ewords_2EWORD__SUB__RNEG,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1w ) )
= ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w ) ) ).
thf(thm_2Ewords_2EWORD__SUB__SUB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ ( c_2Ewords_2Eword__sub @ A_27a @ V1w @ V2x ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V2x ) @ V1w ) ) ).
thf(thm_2Ewords_2EWORD__SUB__SUB2,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w ) )
= V1w ) ).
thf(thm_2Ewords_2EWORD__EQ__SUB__LADD,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( V0v
= ( c_2Ewords_2Eword__sub @ A_27a @ V1w @ V2x ) )
<=> ( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V2x )
= V1w ) ) ).
thf(thm_2Ewords_2EWORD__EQ__SUB__RADD,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w )
= V2x )
<=> ( V0v
= ( c_2Ewords_2Eword__add @ A_27a @ V2x @ V1w ) ) ) ).
thf(thm_2Ewords_2EWORD__EQ__SUB__ZERO,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1v: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__sub @ A_27a @ V1v @ V0w )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
<=> ( V1v = V0w ) ) ).
thf(thm_2Ewords_2EWORD__LCANCEL__SUB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2Eword__sub @ A_27a @ V2x @ V1w ) )
<=> ( V0v = V2x ) ) ).
thf(thm_2Ewords_2EWORD__RCANCEL__SUB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V2x ) )
<=> ( V1w = V2x ) ) ).
thf(thm_2Ewords_2EWORD__SUB__PLUS,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ ( c_2Ewords_2Eword__add @ A_27a @ V1w @ V2x ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w ) @ V2x ) ) ).
thf(thm_2Ewords_2EWORD__SUB__LZERO,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0w )
= ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) ) ).
thf(thm_2Ewords_2EWORD__SUB__RZERO,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V0w @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= V0w ) ).
thf(thm_2Ewords_2EWORD__ADD__LID__UNIQ,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w )
= V1w )
<=> ( V0v
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__RID__UNIQ,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1w )
= V0v )
<=> ( V1w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__SUM__ZERO,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
<=> ( V0a
= ( c_2Ewords_2Eword__2comp @ A_27a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__SUB2,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V1w @ V0v ) @ V1w )
= V0v ) ).
thf(thm_2Ewords_2EWORD__ADD__SUB3,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ ( c_2Ewords_2Eword__add @ A_27a @ V0v @ V1x ) )
= ( c_2Ewords_2Eword__2comp @ A_27a @ V1x ) ) ).
thf(thm_2Ewords_2EWORD__SUB__SUB3,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1v: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V1v @ V0w ) @ V1v )
= ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) ) ).
thf(thm_2Ewords_2EWORD__EQ__NEG,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__2comp @ A_27a @ V0v )
= ( c_2Ewords_2Eword__2comp @ A_27a @ V1w ) )
<=> ( V0v = V1w ) ) ).
thf(thm_2Ewords_2EWORD__NEG__EQ,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1v: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__2comp @ A_27a @ V1v )
= V0w )
<=> ( V1v
= ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) ) ) ).
thf(thm_2Ewords_2EWORD__NEG__EQ__0,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__2comp @ A_27a @ V0v )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
<=> ( V0v
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__SUB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1w ) @ V0v )
= ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w ) ) ).
thf(thm_2Ewords_2EWORD__SUB__NEG,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0v ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1w ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ V1w @ V0v ) ) ).
thf(thm_2Ewords_2EWORD__NEG__SUB,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1v: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V1v @ V0w ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ V0w @ V1v ) ) ).
thf(thm_2Ewords_2EWORD__SUB__TRIANGLE,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w ) @ ( c_2Ewords_2Eword__sub @ A_27a @ V1w @ V2x ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V2x ) ) ).
thf(thm_2Ewords_2EWORD__NOT__0,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(thm_2Ewords_2EWORD__NOT__T,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__NEG__T,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2EWORD__MULT__SUC,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2B @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ ( c_2Ewords_2En2w @ A_27a @ V1n ) ) @ V0v ) ) ).
thf(thm_2Ewords_2EWORD__NEG__LMUL,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V1w ) )
= ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0v ) @ V1w ) ) ).
thf(thm_2Ewords_2EWORD__NEG__RMUL,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V1w ) )
= ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1w ) ) ) ).
thf(thm_2Ewords_2EWORD__NEG__MUL,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ V0w )
= ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0w ) ) ).
thf(thm_2Ewords_2Esw2sw__w2w__add,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esw2sw @ A_27a @ A_27b @ V0w )
= ( c_2Ewords_2Eword__add @ A_27b @ ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0w ) @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__BIT0,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b ) @ c_2Enum_2E0 )
<=> ( (~)
@ ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0a @ c_2Enum_2E0 )
= ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1b @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__BIT,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a,V2b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V1a @ V2b ) @ V0n )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V0n @ c_2Enum_2E0 ) @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1a @ c_2Enum_2E0 ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V2b @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2ECOND @ $o @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V1a ) @ ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V2b ) ) @ V0n ) @ ( c_2Emin_2E_3D @ $o @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1a @ V0n ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V2b @ V0n ) ) @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1a @ V0n ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V2b @ V0n ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LEFT__SUB__DISTRIB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ ( c_2Ewords_2Eword__sub @ A_27a @ V1w @ V2x ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V1w ) @ ( c_2Ewords_2Eword__mul @ A_27a @ V0v @ V2x ) ) ) ).
thf(thm_2Ewords_2EWORD__RIGHT__SUB__DISTRIB,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V1w @ V2x ) @ V0v )
= ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V1w @ V0v ) @ ( c_2Ewords_2Eword__mul @ A_27a @ V2x @ V0v ) ) ) ).
thf(thm_2Ewords_2EWORD__LITERAL__MULT,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0m ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V1n ) ) )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) )
& ! [V2m: tyop_2Enum_2Enum,V3n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ A_27b @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ V2m ) ) @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ V3n ) ) )
= ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2E_2A @ V2m @ V3n ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0m ) ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V1n ) ) )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2B @ V0m @ V1n ) ) ) )
& ! [V2m: tyop_2Enum_2Enum,V3n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ V2m ) @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ V3n ) ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( c_2Earithmetic_2E_3C_3D @ V3n @ V2m ) @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2E_2D @ V2m @ V3n ) ) @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2E_2D @ V3n @ V2m ) ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__SUB__INTRO,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1y ) @ V0x )
= ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ V1y ) )
& ! [V2x: tyop_2Efcp_2Ecart @ $o @ A_27a,V3y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ V2x @ ( c_2Ewords_2Eword__2comp @ A_27a @ V3y ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ V2x @ V3y ) )
& ! [V4x: tyop_2Efcp_2Ecart @ $o @ A_27a,V5y: tyop_2Efcp_2Ecart @ $o @ A_27a,V6z: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V4x ) @ V5y ) @ V6z )
= ( c_2Ewords_2Eword__sub @ A_27a @ V6z @ ( c_2Ewords_2Eword__mul @ A_27a @ V4x @ V5y ) ) )
& ! [V7x: tyop_2Efcp_2Ecart @ $o @ A_27a,V8y: tyop_2Efcp_2Ecart @ $o @ A_27a,V9z: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ V9z @ ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V7x ) @ V8y ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ V9z @ ( c_2Ewords_2Eword__mul @ A_27a @ V7x @ V8y ) ) )
& ! [V10x: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Ewords_2Eword__mul @ A_27b @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V10x )
= ( c_2Ewords_2Eword__2comp @ A_27b @ V10x ) )
& ! [V11x: tyop_2Efcp_2Ecart @ $o @ A_27a,V12y: tyop_2Efcp_2Ecart @ $o @ A_27a,V13z: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V13z @ ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V11x ) @ V12y ) )
= ( c_2Ewords_2Eword__add @ A_27a @ V13z @ ( c_2Ewords_2Eword__mul @ A_27a @ V11x @ V12y ) ) )
& ! [V14x: tyop_2Efcp_2Ecart @ $o @ A_27a,V15y: tyop_2Efcp_2Ecart @ $o @ A_27a,V16z: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V14x ) @ V15y ) @ V16z )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ V14x @ V15y ) @ V16z ) ) ) ) ).
thf(thm_2Ewords_2En2w__SUC,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2En2w @ A_27a @ ( c_2Enum_2ESUC @ V0n ) )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2En2w__sub,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V1b @ V0a )
=> ( ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ V0a @ V1b ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2En2w__sub__eq__0,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V0a @ V1b )
=> ( ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ V0a @ V1b ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__H__WORD__L,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__H @ A_27a )
= ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__L__MULT,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) @ ( c_2Ewords_2Eword__L @ A_27a ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Earithmetic_2EEVEN @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(thm_2Ewords_2EASR__ADD,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1m: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__asr @ A_27a @ ( c_2Ewords_2Eword__asr @ A_27a @ V0w @ V1m ) @ V2n )
= ( c_2Ewords_2Eword__asr @ A_27a @ V0w @ ( c_2Earithmetic_2E_2B @ V1m @ V2n ) ) ) ).
thf(thm_2Ewords_2ELSR__ADD,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1m: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ V1m ) @ V2n )
= ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ ( c_2Earithmetic_2E_2B @ V1m @ V2n ) ) ) ).
thf(thm_2Ewords_2EROR__ADD,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1m: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ror @ A_27a @ ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ V1m ) @ V2n )
= ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ ( c_2Earithmetic_2E_2B @ V1m @ V2n ) ) ) ).
thf(thm_2Ewords_2ELSL__ADD,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1m: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ V1m ) @ V2n )
= ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ ( c_2Earithmetic_2E_2B @ V1m @ V2n ) ) ) ).
thf(thm_2Ewords_2EASR__LIMIT,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1n )
=> ( ( c_2Ewords_2Eword__asr @ A_27a @ V0w @ V1n )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0w ) @ ( c_2Ewords_2Eword__T @ A_27a ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2Ewords_2EASR__UINT__MAX,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__asr @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) @ V0n )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(thm_2Ewords_2ELSR__LIMIT,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1n )
=> ( ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2ELSL__LIMIT,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1n )
=> ( ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EROR__CYCLE,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ ( c_2Earithmetic_2E_2A @ V1n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= V0w ) ).
thf(thm_2Ewords_2EROR__MOD,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ ( c_2Earithmetic_2EMOD @ V1n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ V1n ) ) ).
thf(thm_2Ewords_2EROL__MOD,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__rol @ A_27a @ V0w @ ( c_2Earithmetic_2EMOD @ V1n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( c_2Ewords_2Eword__rol @ A_27a @ V0w @ V1n ) ) ).
thf(thm_2Ewords_2ELSL__ONE,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ewords_2Eword__add @ A_27a @ V0w @ V0w ) ) ).
thf(thm_2Ewords_2EROR__UINT__MAX,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ror @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) @ V0n )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(thm_2Ewords_2EROR__ROL,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( ( c_2Ewords_2Eword__rol @ A_27a @ ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ V1n ) @ V1n )
= V0w )
& ( ( c_2Ewords_2Eword__ror @ A_27a @ ( c_2Ewords_2Eword__rol @ A_27a @ V0w @ V1n ) @ V1n )
= V0w ) ) ).
thf(thm_2Ewords_2EMOD__COMPLEMENT,axiom,
! [V0n: tyop_2Enum_2Enum,V1q: tyop_2Enum_2Enum,V2a: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0n )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V1q )
& ( c_2Eprim__rec_2E_3C @ V2a @ ( c_2Earithmetic_2E_2A @ V1q @ V0n ) ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ V1q @ V0n ) @ V2a ) @ V0n )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Earithmetic_2EMOD @ V2a @ V0n ) ) @ V0n ) ) ) ).
thf(thm_2Ewords_2EROL__ADD,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1m: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__rol @ A_27a @ ( c_2Ewords_2Eword__rol @ A_27a @ V0w @ V1m ) @ V2n )
= ( c_2Ewords_2Eword__rol @ A_27a @ V0w @ ( c_2Earithmetic_2E_2B @ V1m @ V2n ) ) ) ).
thf(thm_2Ewords_2EZERO__SHIFT,axiom,
! [A_27a: $tType] :
( ! [V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0n )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ! [V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__asr @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1n )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ! [V2n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V2n )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ! [V3n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__rol @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V3n )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ! [V4n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ror @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V4n )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2ESHIFT__ZERO,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType] :
( ! [V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ V0a @ c_2Enum_2E0 )
= V0a )
& ! [V1a: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Ewords_2Eword__asr @ A_27b @ V1a @ c_2Enum_2E0 )
= V1a )
& ! [V2a: tyop_2Efcp_2Ecart @ $o @ A_27c] :
( ( c_2Ewords_2Eword__lsr @ A_27c @ V2a @ c_2Enum_2E0 )
= V2a )
& ! [V3a: tyop_2Efcp_2Ecart @ $o @ A_27d] :
( ( c_2Ewords_2Eword__rol @ A_27d @ V3a @ c_2Enum_2E0 )
= V3a )
& ! [V4a: tyop_2Efcp_2Ecart @ $o @ A_27e] :
( ( c_2Ewords_2Eword__ror @ A_27e @ V4a @ c_2Enum_2E0 )
= V4a ) ) ).
thf(thm_2Ewords_2Eword__lsl__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V1m ) @ V0n )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2A @ V1m @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0n ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__1__lsl,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0n )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0n ) ) ) ).
thf(thm_2Ewords_2Eword__lsr__n2w,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2Eword__bits @ A_27a @ ( 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 @ V0w ) ) ).
thf(thm_2Ewords_2ELSL__UINT__MAX,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) @ V0n )
= ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0n ) ) ) ) ).
thf(thm_2Ewords_2Eword__asr__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__asr @ A_27a @ V1w @ V0n )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1w ) @ ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2EMIN @ V0n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) @ ( c_2Ewords_2Eword__lsr @ A_27a @ V1w @ V0n ) ) @ ( c_2Ewords_2Eword__lsr @ A_27a @ V1w @ V0n ) ) ) ).
thf(thm_2Ewords_2Eword__ror__n2w,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ror @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V1a ) @ V0n )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ A_27a )
@ ^ [V2x: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2B @ ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2x @ V1a ) @ ( c_2Earithmetic_2E_2A @ ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2E_2D @ V2x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V1a ) @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V2x ) ) ) ) )
@ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__rrx__n2w,axiom,
! [A_27a: $tType,V0c: $o,V1a: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__rrx @ A_27a @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0c @ ( c_2Ewords_2En2w @ A_27a @ V1a ) ) )
= ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Earithmetic_2EODD @ V1a ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2B @ ( c_2Ebit_2EBITS @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V1a ) @ ( c_2Ebit_2ESBIT @ V0c @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__ror,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ror @ A_27a @ V0w @ V1n )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ A_27a )
@ ^ [V2x: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2x @ V0w ) @ ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2E_2D @ V2x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V0w ) @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V2x ) ) )
@ ( c_2Earithmetic_2EMOD @ V1n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__asr,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__asr @ A_27a @ V0w @ V1n )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0w ) @ ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__slice @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V1n ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ V1n ) ) @ ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ V1n ) ) ) ).
thf(thm_2Ewords_2Ew2n__lsr,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1m: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ V1m ) )
= ( c_2Earithmetic_2EDIV @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V1m ) ) ) ).
thf(thm_2Ewords_2EWORD__MUL__LSL,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ V0a @ V1n )
= ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V1n ) ) @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__ADD__LSL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a,V2b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V1a @ V2b ) @ V0n )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ V1a @ V0n ) @ ( c_2Ewords_2Eword__lsl @ A_27a @ V2b @ V0n ) ) ) ).
thf(thm_2Ewords_2EWORD__DIV__LSR,axiom,
! [A_27a: $tType,V0m: 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_2Ewords_2Eword__lsr @ A_27a @ V0m @ V1n )
= ( c_2Ewords_2Eword__div @ A_27a @ V0m @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V1n ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__MOD__1,axiom,
! [A_27a: $tType,V0m: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mod @ A_27a @ V0m @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2EWORD__MOD__POW2,axiom,
! [A_27a: $tType,V0m: tyop_2Efcp_2Ecart @ $o @ A_27a,V1v: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1v @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
=> ( ( c_2Ewords_2Eword__mod @ A_27a @ V0m @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ V1v ) ) ) )
= ( c_2Ewords_2Eword__bits @ A_27a @ V1v @ c_2Enum_2E0 @ V0m ) ) ) ).
thf(thm_2Ewords_2ESHIFT__1__SUB__1,axiom,
! [A_27a: $tType,V0i: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0i @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1n ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0i )
= ( c_2Eprim__rec_2E_3C @ V0i @ V1n ) ) ) ).
thf(thm_2Ewords_2ELSR__BITWISE,axiom,
! [A_27a: $tType] :
( ! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Efcp_2Ecart @ $o @ A_27a,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V2w @ V0n ) @ ( c_2Ewords_2Eword__lsr @ A_27a @ V1v @ V0n ) )
= ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V2w @ V1v ) @ V0n ) )
& ! [V3n: tyop_2Enum_2Enum,V4v: tyop_2Efcp_2Ecart @ $o @ A_27a,V5w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V5w @ V3n ) @ ( c_2Ewords_2Eword__lsr @ A_27a @ V4v @ V3n ) )
= ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V5w @ V4v ) @ V3n ) )
& ! [V6n: tyop_2Enum_2Enum,V7v: tyop_2Efcp_2Ecart @ $o @ A_27a,V8w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V8w @ V6n ) @ ( c_2Ewords_2Eword__lsr @ A_27a @ V7v @ V6n ) )
= ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2Eword__xor @ A_27a @ V8w @ V7v ) @ V6n ) ) ) ).
thf(thm_2Ewords_2ELSL__BITWISE,axiom,
! [A_27a: $tType] :
( ! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Efcp_2Ecart @ $o @ A_27a,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ V2w @ V0n ) @ ( c_2Ewords_2Eword__lsl @ A_27a @ V1v @ V0n ) )
= ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V2w @ V1v ) @ V0n ) )
& ! [V3n: tyop_2Enum_2Enum,V4v: tyop_2Efcp_2Ecart @ $o @ A_27a,V5w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ V5w @ V3n ) @ ( c_2Ewords_2Eword__lsl @ A_27a @ V4v @ V3n ) )
= ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V5w @ V4v ) @ V3n ) )
& ! [V6n: tyop_2Enum_2Enum,V7v: tyop_2Efcp_2Ecart @ $o @ A_27a,V8w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ V8w @ V6n ) @ ( c_2Ewords_2Eword__lsl @ A_27a @ V7v @ V6n ) )
= ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__xor @ A_27a @ V8w @ V7v ) @ V6n ) ) ) ).
thf(thm_2Ewords_2EROR__BITWISE,axiom,
! [A_27a: $tType] :
( ! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Efcp_2Ecart @ $o @ A_27a,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__ror @ A_27a @ V2w @ V0n ) @ ( c_2Ewords_2Eword__ror @ A_27a @ V1v @ V0n ) )
= ( c_2Ewords_2Eword__ror @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V2w @ V1v ) @ V0n ) )
& ! [V3n: tyop_2Enum_2Enum,V4v: tyop_2Efcp_2Ecart @ $o @ A_27a,V5w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__ror @ A_27a @ V5w @ V3n ) @ ( c_2Ewords_2Eword__ror @ A_27a @ V4v @ V3n ) )
= ( c_2Ewords_2Eword__ror @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V5w @ V4v ) @ V3n ) )
& ! [V6n: tyop_2Enum_2Enum,V7v: tyop_2Efcp_2Ecart @ $o @ A_27a,V8w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__ror @ A_27a @ V8w @ V6n ) @ ( c_2Ewords_2Eword__ror @ A_27a @ V7v @ V6n ) )
= ( c_2Ewords_2Eword__ror @ A_27a @ ( c_2Ewords_2Eword__xor @ A_27a @ V8w @ V7v ) @ V6n ) ) ) ).
thf(thm_2Ewords_2EROL__BITWISE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
( ! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Efcp_2Ecart @ $o @ A_27a,V2w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__rol @ A_27a @ V2w @ V0n ) @ ( c_2Ewords_2Eword__rol @ A_27a @ V1v @ V0n ) )
= ( c_2Ewords_2Eword__rol @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V2w @ V1v ) @ V0n ) )
& ! [V3n: tyop_2Enum_2Enum,V4v: tyop_2Efcp_2Ecart @ $o @ A_27b,V5w: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Ewords_2Eword__or @ A_27b @ ( c_2Ewords_2Eword__rol @ A_27b @ V5w @ V3n ) @ ( c_2Ewords_2Eword__rol @ A_27b @ V4v @ V3n ) )
= ( c_2Ewords_2Eword__rol @ A_27b @ ( c_2Ewords_2Eword__or @ A_27b @ V5w @ V4v ) @ V3n ) )
& ! [V6n: tyop_2Enum_2Enum,V7v: tyop_2Efcp_2Ecart @ $o @ A_27c,V8w: tyop_2Efcp_2Ecart @ $o @ A_27c] :
( ( c_2Ewords_2Eword__xor @ A_27c @ ( c_2Ewords_2Eword__rol @ A_27c @ V8w @ V6n ) @ ( c_2Ewords_2Eword__rol @ A_27c @ V7v @ V6n ) )
= ( c_2Ewords_2Eword__rol @ A_27c @ ( c_2Ewords_2Eword__xor @ A_27c @ V8w @ V7v ) @ V6n ) ) ) ).
thf(thm_2Ewords_2EWORD__2COMP__LSL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1a ) @ V0n )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ V1a @ V0n ) ) ) ).
thf(thm_2Ewords_2Ew2w__LSL,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ V1n ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2Eword__bits @ A_27a @ ( 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 ) @ c_2Enum_2E0 @ V0w ) ) @ V1n ) @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2En2w__DIV,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EDIV @ V0a @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V1n ) ) )
= ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ V1n ) ) ) ).
thf(thm_2Ewords_2EWORD__BITS__LSL,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum,V3w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0h @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ ( c_2Ewords_2Eword__lsl @ A_27a @ V3w @ V2n ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Earithmetic_2E_3C_3D @ V2n @ V0h ) @ ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__bits @ A_27a @ ( c_2Earithmetic_2E_2D @ V0h @ V2n ) @ ( c_2Earithmetic_2E_2D @ V1l @ V2n ) @ V3w ) @ ( c_2Earithmetic_2E_2D @ V2n @ V1l ) ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__LSL,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum,V3w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0h @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ ( c_2Ewords_2Eword__lsl @ A_27a @ V3w @ V2n ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( c_2Earithmetic_2E_3C_3D @ V2n @ V0h ) @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2E_2D @ V0h @ V2n ) @ ( c_2Earithmetic_2E_2D @ V1l @ V2n ) @ V3w ) @ ( c_2Earithmetic_2E_2D @ V2n @ V1l ) ) @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2Ewords_2EWORD__EXTRACT__LSL2,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum,V3w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V1l ) @ ( c_2Earithmetic_2E_2B @ V0h @ V2n ) )
=> ( ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ V3w ) @ V2n )
= ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V1l ) @ ( c_2Earithmetic_2E_2B @ V2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1l @ V3w ) @ V2n ) ) ) ).
thf(thm_2Ewords_2EEXTRACT__JOIN__LSL,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2m_27: tyop_2Enum_2Enum,V3l: tyop_2Enum_2Enum,V4s: tyop_2Enum_2Enum,V5n: tyop_2Enum_2Enum,V6w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Earithmetic_2E_3C_3D @ V3l @ V1m )
& ( c_2Earithmetic_2E_3C_3D @ V2m_27 @ V0h )
& ( V2m_27
= ( c_2Earithmetic_2E_2B @ V1m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ( V4s
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2D @ V2m_27 @ V3l ) @ V5n ) ) )
=> ( ( c_2Ewords_2Eword__or @ A_27b @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V2m_27 @ V6w ) @ V4s ) @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V1m @ V3l @ V6w ) @ V5n ) )
= ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2EMIN @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V3l ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ V3l @ V6w ) @ V5n ) ) ) ).
thf(thm_2Ewords_2EEXTRACT__JOIN__ADD__LSL,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2m_27: tyop_2Enum_2Enum,V3l: tyop_2Enum_2Enum,V4s: tyop_2Enum_2Enum,V5n: tyop_2Enum_2Enum,V6w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Earithmetic_2E_3C_3D @ V3l @ V1m )
& ( c_2Earithmetic_2E_3C_3D @ V2m_27 @ V0h )
& ( V2m_27
= ( c_2Earithmetic_2E_2B @ V1m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ( V4s
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2D @ V2m_27 @ V3l ) @ V5n ) ) )
=> ( ( c_2Ewords_2Eword__add @ A_27b @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V2m_27 @ V6w ) @ V4s ) @ ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V1m @ V3l @ V6w ) @ V5n ) )
= ( c_2Ewords_2Eword__lsl @ A_27b @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ ( c_2Earithmetic_2EMIN @ V0h @ ( c_2Earithmetic_2EMIN @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V3l ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ V3l @ V6w ) @ V5n ) ) ) ).
thf(thm_2Ewords_2Eword__extract__mask,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__extract @ A_27a @ A_27a @ V0h @ V1l @ V2a )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Earithmetic_2E_3C_3D @ V1l @ V0h ) @ ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V2a @ V1l ) @ ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ V0h @ V1l ) ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Eword__bits__mask,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__bits @ A_27a @ V0h @ V1l @ V2a )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Earithmetic_2E_3C_3D @ V1l @ V0h ) @ ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V2a @ V1l ) @ ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ V0h @ V1l ) ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Eword__extract__w2w__mask,axiom,
! [A_27a: $tType,A_27b: $tType,V0h: tyop_2Enum_2Enum,V1l: tyop_2Enum_2Enum,V2a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V0h @ V1l @ V2a )
= ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Earithmetic_2E_3C_3D @ V1l @ V0h ) @ ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V2a @ V1l ) @ ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ V0h @ V1l ) ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2Ewords_2Eword__shift__bv,axiom,
! [A_27a: $tType] :
( ! [V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ V1n )
= ( c_2Ewords_2Eword__lsl__bv @ A_27a @ V0w @ ( c_2Ewords_2En2w @ A_27a @ V1n ) ) ) )
& ! [V2w: tyop_2Efcp_2Ecart @ $o @ A_27a,V3n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V3n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__asr @ A_27a @ V2w @ V3n )
= ( c_2Ewords_2Eword__asr__bv @ A_27a @ V2w @ ( c_2Ewords_2En2w @ A_27a @ V3n ) ) ) )
& ! [V4w: tyop_2Efcp_2Ecart @ $o @ A_27a,V5n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V5n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__lsr @ A_27a @ V4w @ V5n )
= ( c_2Ewords_2Eword__lsr__bv @ A_27a @ V4w @ ( c_2Ewords_2En2w @ A_27a @ V5n ) ) ) )
& ! [V6w: tyop_2Efcp_2Ecart @ $o @ A_27a,V7n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ror @ A_27a @ V6w @ V7n )
= ( c_2Ewords_2Eword__ror__bv @ A_27a @ V6w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EMOD @ V7n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) )
& ! [V8w: tyop_2Efcp_2Ecart @ $o @ A_27a,V9n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__rol @ A_27a @ V8w @ V9n )
= ( c_2Ewords_2Eword__rol__bv @ A_27a @ V8w @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2EMOD @ V9n @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Elsl__lsr,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V1n ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ V1n ) @ V1n )
= V0w ) ) ).
thf(thm_2Ewords_2EWORD__NEG__L,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) )
= ( c_2Ewords_2Eword__L @ A_27a ) ) ).
thf(thm_2Ewords_2Eword__L__MULT__NEG,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0n ) ) @ ( c_2Ewords_2Eword__L @ A_27a ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Earithmetic_2EEVEN @ V0n ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(thm_2Ewords_2Eword__L2__MULT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
( ( ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__L2 @ A_27a ) @ ( c_2Ewords_2Eword__L2 @ A_27a ) )
= ( c_2Ewords_2Eword__L2 @ A_27a ) )
& ( ( c_2Ewords_2Eword__mul @ A_27b @ ( c_2Ewords_2Eword__L @ A_27b ) @ ( c_2Ewords_2Eword__L2 @ A_27b ) )
= ( c_2Ewords_2Eword__L2 @ A_27b ) )
& ! [V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ A_27c @ ( c_2Ewords_2En2w @ A_27c @ V0n ) @ ( c_2Ewords_2Eword__L2 @ A_27c ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ ( c_2Earithmetic_2EEVEN @ V0n ) @ ( c_2Ewords_2En2w @ A_27c @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L2 @ A_27c ) ) )
& ! [V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ A_27d @ ( c_2Ewords_2Eword__2comp @ A_27d @ ( c_2Ewords_2En2w @ A_27d @ V1n ) ) @ ( c_2Ewords_2Eword__L2 @ A_27d ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27d ) @ ( c_2Earithmetic_2EEVEN @ V1n ) @ ( c_2Ewords_2En2w @ A_27d @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L2 @ A_27d ) ) ) ) ).
thf(thm_2Ewords_2ETWO__COMP__NEG,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__msb @ A_27a @ V0a )
=> ( c_2Ebool_2ECOND @ $o @ ( c_2Ebool_2E_5C_2F @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0a @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) @ ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) ) @ ( c_2Ebool_2E_7E @ ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) ) ) ) ) ).
thf(thm_2Ewords_2ETWO__COMP__POS__NEG,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( (~)
@ ( V0a
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( (~)
@ ( V0a
= ( c_2Ewords_2Eword__L @ A_27a ) ) ) )
=> ( ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) )
<=> ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) ) ) ) ).
thf(thm_2Ewords_2EWORD__0__POS,axiom,
! [A_27a: $tType] : ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2ETWO__COMP__POS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) )
=> ( ( V0a
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) ) ) ) ).
thf(thm_2Ewords_2EWORD__H__POS,axiom,
! [A_27a: $tType] : ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__H @ A_27a ) ) ) ).
thf(thm_2Ewords_2EWORD__L__NEG,axiom,
! [A_27a: $tType] : ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) ) ).
thf(thm_2Ewords_2EWORD__GREATER,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__gt @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__lt @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__GREATER__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ge @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__le @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__NOT__LESS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~) @ ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b ) )
<=> ( c_2Ewords_2Eword__le @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LT,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
<=> ( ( ( ( c_2Ewords_2Eword__msb @ A_27a @ V0a )
= ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) )
& ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) )
| ( ( c_2Ewords_2Eword__msb @ A_27a @ V0a )
& ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__GT,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__gt @ A_27a @ V0a @ V1b )
<=> ( ( ( ( c_2Ewords_2Eword__msb @ A_27a @ V1b )
= ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) )
& ( c_2Earithmetic_2E_3E @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) )
| ( ( c_2Ewords_2Eword__msb @ A_27a @ V1b )
& ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LE,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b )
<=> ( ( ( ( c_2Ewords_2Eword__msb @ A_27a @ V0a )
= ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) )
| ( ( c_2Ewords_2Eword__msb @ A_27a @ V0a )
& ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__GE,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ge @ A_27a @ V0a @ V1b )
<=> ( ( ( ( c_2Ewords_2Eword__msb @ A_27a @ V1b )
= ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) )
& ( c_2Earithmetic_2E_3E_3D @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) )
| ( ( c_2Ewords_2Eword__msb @ A_27a @ V1b )
& ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LO,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
= ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__LS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__HI,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hi @ A_27a @ V0a @ V1b )
= ( c_2Earithmetic_2E_3E @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__HS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hs @ A_27a @ V0a @ V1b )
= ( c_2Earithmetic_2E_3E_3D @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__NOT__LESS__EQUAL,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~) @ ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b ) )
<=> ( c_2Ewords_2Eword__lt @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LESS__OR__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b )
<=> ( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
| ( V0a = V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__GREATER__OR__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ge @ A_27a @ V0a @ V1b )
<=> ( ( c_2Ewords_2Eword__gt @ A_27a @ V0a @ V1b )
| ( V0a = V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__LESS__TRANS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__lt @ A_27a @ V1b @ V2c ) )
=> ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V2c ) ) ).
thf(thm_2Ewords_2EWORD__LESS__EQ__TRANS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__le @ A_27a @ V1b @ V2c ) )
=> ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V2c ) ) ).
thf(thm_2Ewords_2EWORD__LESS__EQ__LESS__TRANS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__lt @ A_27a @ V1b @ V2c ) )
=> ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V2c ) ) ).
thf(thm_2Ewords_2EWORD__LESS__LESS__EQ__TRANS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__le @ A_27a @ V1b @ V2c ) )
=> ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V2c ) ) ).
thf(thm_2Ewords_2EWORD__LESS__EQ__CASES,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b )
| ( c_2Ewords_2Eword__le @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LESS__CASES,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
| ( c_2Ewords_2Eword__le @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LESS__CASES__IMP,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( (~) @ ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b ) )
& ( (~) @ ( V0a = V1b ) ) )
=> ( c_2Ewords_2Eword__lt @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LESS__ANTISYM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( (~)
@ ( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__lt @ A_27a @ V1b @ V0a ) ) ) ).
thf(thm_2Ewords_2EWORD__LESS__EQ__ANTISYM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( (~)
@ ( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__le @ A_27a @ V1b @ V0a ) ) ) ).
thf(thm_2Ewords_2EWORD__LESS__EQ__REFL,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V0a ) ).
thf(thm_2Ewords_2EWORD__LESS__EQUAL__ANTISYM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__le @ A_27a @ V1b @ V0a ) )
=> ( V0a = V1b ) ) ).
thf(thm_2Ewords_2EWORD__LESS__IMP__LESS__OR__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
=> ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b ) ) ).
thf(thm_2Ewords_2EWORD__LESS__REFL,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( (~) @ ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LESS__LESS__CASES,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( V0a = V1b )
| ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
| ( c_2Ewords_2Eword__lt @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__NOT__GREATER,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~) @ ( c_2Ewords_2Eword__gt @ A_27a @ V0a @ V1b ) )
<=> ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b ) ) ).
thf(thm_2Ewords_2EWORD__LESS__NOT__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
=> ( (~) @ ( V0a = V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__NOT__LESS__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( V0a = V1b )
=> ( (~) @ ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__HIGHER,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hi @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__HIGHER__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hs @ A_27a @ V0a @ V1b )
= ( c_2Ewords_2Eword__ls @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__NOT__LOWER,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~) @ ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b ) )
<=> ( c_2Ewords_2Eword__ls @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__NOT__LOWER__EQUAL,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~) @ ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b ) )
<=> ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__OR__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b )
<=> ( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
| ( V0a = V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__HIGHER__OR__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__hs @ A_27a @ V0a @ V1b )
<=> ( ( c_2Ewords_2Eword__hi @ A_27a @ V0a @ V1b )
| ( V0a = V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__TRANS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ V2c ) )
=> ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V2c ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__EQ__TRANS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__ls @ A_27a @ V1b @ V2c ) )
=> ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V2c ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__EQ__LOWER__TRANS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ V2c ) )
=> ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V2c ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__LOWER__EQ__TRANS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a,V2c: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__ls @ A_27a @ V1b @ V2c ) )
=> ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V2c ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__EQ__CASES,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b )
| ( c_2Ewords_2Eword__ls @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__CASES,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
| ( c_2Ewords_2Eword__ls @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__CASES__IMP,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( (~) @ ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b ) )
& ( (~) @ ( V0a = V1b ) ) )
=> ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__ANTISYM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( (~)
@ ( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ V0a ) ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__EQ__ANTISYM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( (~)
@ ( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__ls @ A_27a @ V1b @ V0a ) ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__EQ__REFL,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V0a ) ).
thf(thm_2Ewords_2EWORD__LOWER__EQUAL__ANTISYM,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b )
& ( c_2Ewords_2Eword__ls @ A_27a @ V1b @ V0a ) )
=> ( V0a = V1b ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__IMP__LOWER__OR__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
=> ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__REFL,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( (~) @ ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__LOWER__CASES,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( V0a = V1b )
| ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
| ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__NOT__HIGHER,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~) @ ( c_2Ewords_2Eword__hi @ A_27a @ V0a @ V1b ) )
<=> ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b ) ) ).
thf(thm_2Ewords_2EWORD__LOWER__NOT__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b )
=> ( (~) @ ( V0a = V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__NOT__LOWER__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( V0a = V1b )
=> ( (~) @ ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__L__PLUS__H,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) @ ( c_2Ewords_2Eword__H @ A_27a ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(thm_2Ewords_2EWORD__L__LESS__EQ,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) @ V0a ) ).
thf(thm_2Ewords_2EWORD__LESS__EQ__H,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ewords_2Eword__le @ A_27a @ V0a @ ( c_2Ewords_2Eword__H @ A_27a ) ) ).
thf(thm_2Ewords_2EWORD__L__LESS__H,axiom,
! [A_27a: $tType] : ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) ).
thf(thm_2Ewords_2ENOT__INT__MIN__ZERO,axiom,
! [A_27a: $tType] :
( (~)
@ ( ( c_2Ewords_2Eword__L @ A_27a )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EZERO__LO__INT__MIN,axiom,
! [A_27a: $tType] : ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ).
thf(thm_2Ewords_2EWORD__0__LS,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0w ) ).
thf(thm_2Ewords_2EWORD__LS__T,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ewords_2Eword__ls @ A_27a @ V0w @ ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(thm_2Ewords_2EWORD__ADD__LEFT__LO,axiom,
! [A_27a: $tType,V0b: tyop_2Efcp_2Ecart @ $o @ A_27a,V1c: tyop_2Efcp_2Ecart @ $o @ A_27a,V2a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V2a @ V0b ) @ V1c )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Ewords_2Eword__ls @ A_27a @ V0b @ V1c )
@ ( c_2Ebool_2ELET @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o
@ ^ [V3x: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ebool_2E_5C_2F @ ( c_2Ewords_2Eword__lo @ A_27a @ V2a @ V3x ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0b @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) @ ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1c ) @ V3x ) @ V2a ) ) )
@ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ A_27a @ V1c ) @ ( c_2Ewords_2Ew2n @ A_27a @ V0b ) ) ) )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0b ) @ V2a ) @ ( c_2Ewords_2Eword__lo @ A_27a @ V2a @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0b ) @ V1c ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__LEFT__LS,axiom,
! [A_27a: $tType,V0b: tyop_2Efcp_2Ecart @ $o @ A_27a,V1c: tyop_2Efcp_2Ecart @ $o @ A_27a,V2a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V2a @ V0b ) @ V1c )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Ewords_2Eword__ls @ A_27a @ V0b @ V1c )
@ ( c_2Ebool_2ELET @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o
@ ^ [V3x: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ebool_2E_5C_2F @ ( c_2Ewords_2Eword__ls @ A_27a @ V2a @ V3x ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0b @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) @ ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1c ) @ V3x ) @ V2a ) ) )
@ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ A_27a @ V1c ) @ ( c_2Ewords_2Ew2n @ A_27a @ V0b ) ) ) )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0b ) @ V2a ) @ ( c_2Ewords_2Eword__ls @ A_27a @ V2a @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0b ) @ V1c ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__RIGHT__LS,axiom,
! [A_27a: $tType,V0c: tyop_2Efcp_2Ecart @ $o @ A_27a,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a,V2b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ V1a @ ( c_2Ewords_2Eword__add @ A_27a @ V2b @ V0c ) )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Ewords_2Eword__ls @ A_27a @ V0c @ V1a )
@ ( c_2Ebool_2ELET @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o
@ ^ [V3x: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ebool_2E_2F_5C @ ( c_2Ewords_2Eword__ls @ A_27a @ V3x @ V2b ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__lo @ A_27a @ V2b @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1a ) @ V3x ) ) ) )
@ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ A_27a @ V1a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V0c ) ) ) )
@ ( c_2Ebool_2E_5C_2F @ ( c_2Ewords_2Eword__lo @ A_27a @ V2b @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) ) @ ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) @ V1a ) @ V2b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__RIGHT__LO,axiom,
! [A_27a: $tType,V0c: tyop_2Efcp_2Ecart @ $o @ A_27a,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a,V2b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V1a @ ( c_2Ewords_2Eword__add @ A_27a @ V2b @ V0c ) )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Ewords_2Eword__ls @ A_27a @ V0c @ V1a )
@ ( c_2Ebool_2ELET @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o
@ ^ [V3x: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( c_2Ebool_2E_2F_5C @ ( c_2Ewords_2Eword__lo @ A_27a @ V3x @ V2b ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Emin_2E_3D @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__lo @ A_27a @ V2b @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1a ) @ V3x ) ) ) )
@ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ A_27a @ V1a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V0c ) ) ) )
@ ( c_2Ebool_2E_5C_2F @ ( c_2Ewords_2Eword__lo @ A_27a @ V2b @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) ) @ ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) @ V1a ) @ V2b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__MSB__INT__MIN__LS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__msb @ A_27a @ V0a )
= ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) @ V0a ) ) ).
thf(thm_2Ewords_2EWORD__LT__LO,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lt @ A_27a @ V0a @ V1b )
<=> ( ( ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) @ V0a )
& ( ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ ( c_2Ewords_2Eword__L @ A_27a ) )
| ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b ) ) )
| ( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ ( c_2Ewords_2Eword__L @ A_27a ) )
& ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ ( c_2Ewords_2Eword__L @ A_27a ) )
& ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LE__LS,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__le @ A_27a @ V0a @ V1b )
<=> ( ( ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__L @ A_27a ) @ V0a )
& ( ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ ( c_2Ewords_2Eword__L @ A_27a ) )
| ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b ) ) )
| ( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ ( c_2Ewords_2Eword__L @ A_27a ) )
& ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ ( c_2Ewords_2Eword__L @ A_27a ) )
& ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LESS__NEG__LEFT,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) @ V1b )
<=> ( ( (~)
@ ( V1b
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( ( V0a
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1b ) @ V0a ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LESS__NEG__RIGHT,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V0a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1b ) )
<=> ( ( (~)
@ ( V1b
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( ( V0a
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ A_27a @ V1b @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0a ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LS__word__0,axiom,
! [A_27a: $tType,V0n: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ V0n @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
<=> ( V0n
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__LO__word__0,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0n: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0n )
<=> ( (~)
@ ( V0n
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) )
& ! [V1n: tyop_2Efcp_2Ecart @ $o @ A_27b] : ( (~) @ ( c_2Ewords_2Eword__lo @ A_27b @ V1n @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__LEFT__LO2,axiom,
! [A_27a: $tType,V0c: tyop_2Efcp_2Ecart @ $o @ A_27a,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0c @ V1a ) @ V1a )
<=> ( ( (~)
@ ( V1a
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( ( ( (~)
@ ( V0c
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) @ V1a ) )
| ( V1a
= ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__LEFT__LS2,axiom,
! [A_27a: $tType,V0c: tyop_2Efcp_2Ecart @ $o @ A_27a,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0c @ V1a ) @ V1a )
<=> ( ( V0c
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
| ( ( (~)
@ ( V1a
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) @ V1a )
| ( V1a
= ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__RIGHT__LO2,axiom,
! [A_27a: $tType,V0c: tyop_2Efcp_2Ecart @ $o @ A_27a,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V1a @ ( c_2Ewords_2Eword__add @ A_27a @ V0c @ V1a ) )
<=> ( ( (~)
@ ( V0c
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( ( V1a
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ A_27a @ V1a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__ADD__RIGHT__LS2,axiom,
! [A_27a: $tType,V0c: tyop_2Efcp_2Ecart @ $o @ A_27a,V1a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ V1a @ ( c_2Ewords_2Eword__add @ A_27a @ V0c @ V1a ) )
<=> ( ( V1a
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
| ( V0c
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ A_27a @ V1a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0c ) ) ) ) ).
thf(thm_2Ewords_2Eword__msb__neg,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__msb @ A_27a @ V0w )
= ( c_2Ewords_2Eword__lt @ A_27a @ V0w @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Eword__abs,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__abs @ A_27a @ V0w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Ewords_2Eword__msb @ A_27a @ V0w ) ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ewords_2Eword__msb @ A_27a @ V0w ) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) @ V1i ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__abs__word__abs,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__abs @ A_27a @ ( c_2Ewords_2Eword__abs @ A_27a @ V0w ) )
= ( c_2Ewords_2Eword__abs @ A_27a @ V0w ) ) ).
thf(thm_2Ewords_2Eword__abs__neg,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__abs @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ V0w ) )
= ( c_2Ewords_2Eword__abs @ A_27a @ V0w ) ) ).
thf(thm_2Ewords_2Eword__abs__diff,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__abs @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0a @ V1b ) )
= ( c_2Ewords_2Eword__abs @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V1b @ V0a ) ) ) ).
thf(thm_2Ewords_2EFST__ADD__WITH__CARRY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
( ! [V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Epair_2EFST @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ ( c_2Ewords_2Eadd__with__carry @ A_27a @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o ) @ V0a @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o @ V1b @ c_2Ebool_2EF ) ) ) )
= ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b ) )
& ! [V2a: tyop_2Efcp_2Ecart @ $o @ A_27b,V3b: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Epair_2EFST @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ ( c_2Ewords_2Eadd__with__carry @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ $o ) @ V2a @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ $o @ ( c_2Ewords_2Eword__1comp @ A_27b @ V3b ) @ c_2Ebool_2ET ) ) ) )
= ( c_2Ewords_2Eword__sub @ A_27b @ V2a @ V3b ) )
& ! [V4a: tyop_2Efcp_2Ecart @ $o @ A_27c,V5b: tyop_2Efcp_2Ecart @ $o @ A_27c] :
( ( c_2Epair_2EFST @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ ( c_2Ewords_2Eadd__with__carry @ A_27c @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ $o ) @ ( c_2Ewords_2Eword__1comp @ A_27c @ V4a ) @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ $o @ V5b @ c_2Ebool_2ET ) ) ) )
= ( c_2Ewords_2Eword__sub @ A_27c @ V5b @ V4a ) )
& ! [V6n: tyop_2Enum_2Enum,V7a: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Epair_2EFST @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ ( c_2Ewords_2Eadd__with__carry @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ $o ) @ V7a @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ $o @ ( c_2Ewords_2En2w @ A_27b @ V6n ) @ c_2Ebool_2ET ) ) ) )
= ( c_2Ewords_2Eword__sub @ A_27b @ V7a @ ( c_2Ewords_2Eword__1comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ V6n ) ) ) )
& ! [V8n: tyop_2Enum_2Enum,V9b: tyop_2Efcp_2Ecart @ $o @ A_27c] :
( ( c_2Epair_2EFST @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ ( c_2Ewords_2Eadd__with__carry @ A_27c @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ $o ) @ ( c_2Ewords_2En2w @ A_27c @ V8n ) @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27c ) @ $o @ V9b @ c_2Ebool_2ET ) ) ) )
= ( c_2Ewords_2Eword__sub @ A_27c @ V9b @ ( c_2Ewords_2Eword__1comp @ A_27c @ ( c_2Ewords_2En2w @ A_27c @ V8n ) ) ) ) ) ).
thf(thm_2Ewords_2EADD__WITH__CARRY__SUB,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eadd__with__carry @ A_27a @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o ) @ V0x @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ $o @ ( c_2Ewords_2Eword__1comp @ A_27a @ V1y ) @ c_2Ebool_2ET ) ) )
= ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( tyop_2Epair_2Eprod @ $o @ $o ) @ ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ V1y ) @ ( c_2Epair_2E_2C @ $o @ $o @ ( c_2Ewords_2Eword__ls @ A_27a @ V1y @ V0x ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ ( c_2Ewords_2Eword__msb @ A_27a @ V0x ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1y ) ) ) @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ $o @ ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ V1y ) ) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0x ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__eq__n2w,axiom,
! [A_27a: $tType] :
( ! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( ( c_2Ewords_2En2w @ A_27a @ V0m )
= ( c_2Ewords_2En2w @ A_27a @ V1n ) )
<=> ( c_2Ebit_2EMOD__2EXP__EQ @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0m @ V1n ) )
& ! [V2n: tyop_2Enum_2Enum] :
( ( ( c_2Ewords_2En2w @ A_27a @ V2n )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
<=> ( c_2Ebit_2EMOD__2EXP__MAX @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V2n ) )
& ! [V3n: tyop_2Enum_2Enum] :
( ( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Ewords_2En2w @ A_27a @ V3n ) )
<=> ( c_2Ebit_2EMOD__2EXP__MAX @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V3n ) ) ) ).
thf(thm_2Ewords_2Eword__lt__n2w,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) )
= ( c_2Ebool_2ELET @ $o @ $o
@ ( c_2Ebool_2ELET @ $o @ ( $o > $o )
@ ^ [V2sa: $o,V3sb: $o] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Emin_2E_3D @ $o @ V2sa @ V3sb ) @ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EMOD @ V0a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Earithmetic_2EMOD @ V1b @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) @ ( c_2Ebool_2E_2F_5C @ V2sa @ ( c_2Ebool_2E_7E @ V3sb ) ) )
@ ( c_2Ebit_2EBIT @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0a ) )
@ ( c_2Ebit_2EBIT @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__gt__n2w,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__gt @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) )
= ( c_2Ebool_2ELET @ $o @ $o
@ ( c_2Ebool_2ELET @ $o @ ( $o > $o )
@ ^ [V2sa: $o,V3sb: $o] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Emin_2E_3D @ $o @ V2sa @ V3sb ) @ ( c_2Earithmetic_2E_3E @ ( c_2Earithmetic_2EMOD @ V0a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Earithmetic_2EMOD @ V1b @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ V2sa ) @ V3sb ) )
@ ( c_2Ebit_2EBIT @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0a ) )
@ ( c_2Ebit_2EBIT @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__le__n2w,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) )
= ( c_2Ebool_2ELET @ $o @ $o
@ ( c_2Ebool_2ELET @ $o @ ( $o > $o )
@ ^ [V2sa: $o,V3sb: $o] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Emin_2E_3D @ $o @ V2sa @ V3sb ) @ ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ V0a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Earithmetic_2EMOD @ V1b @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) @ ( c_2Ebool_2E_2F_5C @ V2sa @ ( c_2Ebool_2E_7E @ V3sb ) ) )
@ ( c_2Ebit_2EBIT @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0a ) )
@ ( c_2Ebit_2EBIT @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__ge__n2w,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ge @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) )
= ( c_2Ebool_2ELET @ $o @ $o
@ ( c_2Ebool_2ELET @ $o @ ( $o > $o )
@ ^ [V2sa: $o,V3sb: $o] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Emin_2E_3D @ $o @ V2sa @ V3sb ) @ ( c_2Earithmetic_2E_3E_3D @ ( c_2Earithmetic_2EMOD @ V0a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Earithmetic_2EMOD @ V1b @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ V2sa ) @ V3sb ) )
@ ( c_2Ebit_2EBIT @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0a ) )
@ ( c_2Ebit_2EBIT @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1b ) ) ) ).
thf(thm_2Ewords_2Eword__ls__n2w,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ V0a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Earithmetic_2EMOD @ V1b @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__hi__n2w,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__hi @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) )
= ( c_2Earithmetic_2E_3E @ ( c_2Earithmetic_2EMOD @ V0a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Earithmetic_2EMOD @ V1b @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__lo__n2w,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EMOD @ V0a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Earithmetic_2EMOD @ V1b @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__hs__n2w,axiom,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__hs @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) )
= ( c_2Earithmetic_2E_3E_3D @ ( c_2Earithmetic_2EMOD @ V0a @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Earithmetic_2EMOD @ V1b @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Ew2n__add,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V0a ) )
& ( (~) @ ( c_2Ewords_2Eword__msb @ A_27a @ V1b ) ) )
=> ( ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Ewords_2Ew2n @ A_27a @ V0a ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1b ) ) ) ) ).
thf(thm_2Ewords_2Esaturate__w2w__n2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Esaturate__w2w @ A_27a @ A_27b @ ( c_2Ewords_2En2w @ A_27a @ V0n ) )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ A_27b )
@ ^ [V1m: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( c_2Ebool_2E_2F_5C @ ( 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_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ V1m ) ) @ ( c_2Ewords_2Eword__T @ A_27b ) @ ( c_2Ewords_2En2w @ A_27b @ V1m ) )
@ ( c_2Earithmetic_2EMOD @ V0n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2Esaturate__w2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esaturate__w2w @ A_27a @ A_27b @ V0w )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( c_2Ebool_2E_2F_5C @ ( 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__ls @ A_27a @ ( c_2Ewords_2Ew2w @ A_27b @ A_27a @ ( c_2Ewords_2Eword__T @ A_27b ) ) @ V0w ) ) @ ( c_2Ewords_2Eword__T @ A_27b ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0w ) ) ) ).
thf(thm_2Ewords_2Esaturate__sub,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esaturate__sub @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__ls @ A_27a @ V0a @ V1b ) @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2Esaturate__add,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esaturate__add @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2Eword__T @ A_27a ) @ V0a ) @ V1b ) @ ( c_2Ewords_2Eword__T @ A_27a ) @ ( c_2Ewords_2Eword__add @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2ENOT__FINITE__IMP__dimword__2,axiom,
! [A_27a: $tType] :
( ( (~) @ ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
=> ( ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Esaturate__mul,axiom,
! [A_27a: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Esaturate__mul @ A_27a @ V0a @ V1b )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ ( c_2Ewords_2Eword__ls @ ( tyop_2Esum_2Esum @ A_27a @ A_27a ) @ ( c_2Ewords_2Ew2w @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( c_2Ewords_2Eword__mul @ ( tyop_2Esum_2Esum @ A_27a @ A_27a ) @ ( c_2Ewords_2Ew2w @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27a ) @ V0a ) @ ( c_2Ewords_2Ew2w @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27a ) @ V1b ) ) ) ) @ ( c_2Ewords_2Eword__T @ A_27a ) @ ( c_2Ewords_2Eword__mul @ A_27a @ V0a @ V1b ) ) ) ).
thf(thm_2Ewords_2EWORD__DIVISION,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~)
@ ( V0w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
=> ! [V1v: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( V1v
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__mul @ A_27a @ ( c_2Ewords_2Eword__div @ A_27a @ V1v @ V0w ) @ V0w ) @ ( c_2Ewords_2Eword__mod @ A_27a @ V1v @ V0w ) ) )
& ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2Eword__mod @ A_27a @ V1v @ V0w ) @ V0w ) ) ) ).
thf(thm_2Ewords_2Eword__reverse__0,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2Eword__reverse__word__T,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Esw2sw__0,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( c_2Ewords_2Esw2sw @ A_27a @ A_27b @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2Esw2sw__word__T,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( c_2Ewords_2Esw2sw @ A_27b @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__div__1,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__div @ A_27a @ V0v @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= V0v ) ).
thf(thm_2Ewords_2Eword__bit__0,axiom,
! [A_27a: $tType,V0h: tyop_2Enum_2Enum] : ( (~) @ ( c_2Ewords_2Eword__bit @ A_27a @ V0h @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Eword__lsb__word__T,axiom,
! [A_27a: $tType] : ( c_2Ewords_2Eword__lsb @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__msb__word__T,axiom,
! [A_27a: $tType] : ( c_2Ewords_2Eword__msb @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__bit__0__word__T,axiom,
! [A_27a: $tType] : ( c_2Ewords_2Eword__bit @ A_27a @ c_2Enum_2E0 @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__log2__1,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__log2 @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2Eword__join__0,axiom,
! [A_27a: $tType,A_27b: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__join @ A_27b @ A_27a @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) @ V0a )
= ( c_2Ewords_2Ew2w @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ V0a ) ) ).
thf(thm_2Ewords_2Eword__concat__0__0,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27c @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2Ew2w__eq__n2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
& ( c_2Eprim__rec_2E_3C @ V1y @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ V0x )
= ( c_2Ewords_2En2w @ A_27b @ V1y ) )
<=> ( V0x
= ( c_2Ewords_2En2w @ A_27a @ V1y ) ) ) ) ).
thf(thm_2Ewords_2Eword__extract__eq__n2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1h: tyop_2Enum_2Enum,V2y: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( 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_3C_3D @ ( c_2Earithmetic_2E_2D @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1h )
& ( c_2Eprim__rec_2E_3C @ V2y @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ( c_2Ewords_2Eword__extract @ A_27a @ A_27b @ V1h @ c_2Enum_2E0 @ V0x )
= ( c_2Ewords_2En2w @ A_27b @ V2y ) )
<=> ( V0x
= ( c_2Ewords_2En2w @ A_27a @ V2y ) ) ) ) ).
thf(thm_2Ewords_2Eword__concat__0,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x: tyop_2Enum_2Enum] :
( ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
& ( c_2Eprim__rec_2E_3C @ V0x @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
=> ( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ A_27b @ V0x ) )
= ( c_2Ewords_2En2w @ A_27c @ V0x ) ) ) ).
thf(thm_2Ewords_2Eword__concat__0__eq,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27b,V1y: tyop_2Enum_2Enum] :
( ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
& ( c_2Eprim__rec_2E_3C @ V1y @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
=> ( ( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0x )
= ( c_2Ewords_2En2w @ A_27c @ V1y ) )
<=> ( V0x
= ( c_2Ewords_2En2w @ A_27b @ V1y ) ) ) ) ).
thf(thm_2Ewords_2Eword__concat__assoc,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,V0a: tyop_2Efcp_2Ecart @ $o @ A_27a,V1b: tyop_2Efcp_2Ecart @ $o @ A_27b,V2c: tyop_2Efcp_2Ecart @ $o @ A_27c] :
( ( ( 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_2Epred__set_2EFINITE @ A_27c @ ( c_2Epred__set_2EUNIV @ A_27c ) )
& ( ( c_2Efcp_2Edimindex @ A_27d @ ( c_2Ebool_2Ethe__value @ A_27d ) )
= ( 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_2Efcp_2Edimindex @ A_27e @ ( c_2Ebool_2Ethe__value @ A_27e ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
& ( ( c_2Efcp_2Edimindex @ A_27f @ ( c_2Ebool_2Ethe__value @ A_27f ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Efcp_2Edimindex @ A_27d @ ( c_2Ebool_2Ethe__value @ A_27d ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) ) )
=> ( ( c_2Ewords_2Eword__concat @ A_27d @ A_27c @ A_27f @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27d @ V0a @ V1b ) @ V2c )
= ( c_2Ewords_2Eword__concat @ A_27a @ A_27e @ A_27f @ V0a @ ( c_2Ewords_2Eword__concat @ A_27b @ A_27c @ A_27e @ V1b @ V2c ) ) ) ) ).
thf(thm_2Ewords_2Eword__join__word__T,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( c_2Ewords_2Eword__join @ A_27a @ A_27b @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ewords_2Eword__2comp @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ewords_2En2w @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__concat__word__T,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType] :
( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ewords_2Ew2w @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c @ ( c_2Ewords_2Eword__2comp @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Ewords_2En2w @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Elsr__1__word__T,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ewords_2Eword__H @ A_27a ) ) ).
thf(thm_2Ewords_2Eword__rrx__0,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( ( c_2Ewords_2Eword__rrx @ A_27a @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ c_2Ebool_2EF @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
= ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ c_2Ebool_2EF @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( ( c_2Ewords_2Eword__rrx @ A_27b @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ c_2Ebool_2ET @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) ) )
= ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ c_2Ebool_2EF @ ( c_2Ewords_2Eword__L @ A_27b ) ) ) ) ).
thf(thm_2Ewords_2Eword__rrx__word__T,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ( ( c_2Ewords_2Eword__rrx @ A_27a @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ c_2Ebool_2EF @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ c_2Ebool_2ET @ ( c_2Ewords_2Eword__H @ A_27a ) ) )
& ( ( c_2Ewords_2Eword__rrx @ A_27b @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ c_2Ebool_2ET @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( c_2Epair_2E_2C @ $o @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ c_2Ebool_2ET @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Eword__T__not__zero,axiom,
! [A_27a: $tType] :
( (~)
@ ( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__LS__word__T,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0n: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0n )
<=> ( V0n
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V1n: tyop_2Efcp_2Ecart @ $o @ A_27b] : ( c_2Ewords_2Eword__ls @ A_27b @ V1n @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LO__word__T,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0n: tyop_2Efcp_2Ecart @ $o @ A_27a] : ( (~) @ ( c_2Ewords_2Eword__lo @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0n ) )
& ! [V1n: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Ewords_2Eword__lo @ A_27b @ V1n @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
<=> ( (~)
@ ( V1n
= ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LESS__0__word__T,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
( ( (~) @ ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( (~) @ ( c_2Ewords_2Eword__le @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( c_2Ewords_2Eword__lt @ A_27c @ ( c_2Ewords_2Eword__2comp @ A_27c @ ( c_2Ewords_2En2w @ A_27c @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ewords_2En2w @ A_27c @ c_2Enum_2E0 ) )
& ( c_2Ewords_2Eword__le @ A_27d @ ( c_2Ewords_2Eword__2comp @ A_27d @ ( c_2Ewords_2En2w @ A_27d @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ewords_2En2w @ A_27d @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2Eword__reverse__thm,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1v: tyop_2Efcp_2Ecart @ $o @ A_27a,V2n: tyop_2Enum_2Enum] :
( ( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2Eword__reverse @ A_27a @ V0w ) )
= V0w )
& ( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2Eword__lsl @ A_27a @ V0w @ V2n ) )
= ( c_2Ewords_2Eword__lsr @ A_27a @ ( c_2Ewords_2Eword__reverse @ A_27a @ V0w ) @ V2n ) )
& ( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V0w @ V2n ) )
= ( c_2Ewords_2Eword__lsl @ A_27a @ ( c_2Ewords_2Eword__reverse @ A_27a @ V0w ) @ V2n ) )
& ( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2Eword__or @ A_27a @ V0w @ V1v ) )
= ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2Eword__reverse @ A_27a @ V0w ) @ ( c_2Ewords_2Eword__reverse @ A_27a @ V1v ) ) )
& ( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V0w @ V1v ) )
= ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__reverse @ A_27a @ V0w ) @ ( c_2Ewords_2Eword__reverse @ A_27a @ V1v ) ) )
& ( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2Eword__xor @ A_27a @ V0w @ V1v ) )
= ( c_2Ewords_2Eword__xor @ A_27a @ ( c_2Ewords_2Eword__reverse @ A_27a @ V0w ) @ ( c_2Ewords_2Eword__reverse @ A_27a @ V1v ) ) )
& ( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2Eword__1comp @ A_27a @ V0w ) )
= ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ewords_2Eword__reverse @ A_27a @ V0w ) ) )
& ( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
& ( ( c_2Ewords_2Eword__reverse @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( ( ( c_2Ewords_2Eword__reverse @ A_27a @ V0w )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
<=> ( V0w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( ( ( c_2Ewords_2Eword__reverse @ A_27a @ V0w )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
<=> ( V0w
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Ebit__count__upto__0,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Ebit__count__upto @ A_27a @ c_2Enum_2E0 @ V0w )
= c_2Enum_2E0 ) ).
thf(thm_2Ewords_2Ebit__count__upto__SUC,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Ebit__count__upto @ A_27a @ ( c_2Enum_2ESUC @ V1n ) @ V0w )
= ( c_2Earithmetic_2E_2B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1n ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) @ ( c_2Ewords_2Ebit__count__upto @ A_27a @ V1n @ V0w ) ) ) ).
thf(thm_2Ewords_2Ebit__count__upto__is__zero,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Ebit__count__upto @ A_27a @ V0n @ V1w )
= c_2Enum_2E0 )
<=> ! [V2i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V2i @ V0n )
=> ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1w @ V2i ) ) ) ) ).
thf(thm_2Ewords_2Ebit__count__is__zero,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Ebit__count @ A_27a @ V0w )
= c_2Enum_2E0 )
<=> ( V0w
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Ewords_2EWORD__FINITE,axiom,
! [A_27a: $tType,V0s: ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o] : ( c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V0s ) ).
thf(thm_2Ewords_2EWORD__SET__INDUCT,axiom,
! [A_27a: $tType,V0P: ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) > $o] :
( ( ( V0P @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) )
& ! [V1s: ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o] :
( ( V0P @ V1s )
=> ! [V2e: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~) @ ( c_2Ebool_2EIN @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V2e @ V1s ) )
=> ( V0P @ ( c_2Epred__set_2EINSERT @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ V2e @ V1s ) ) ) ) )
=> ! [V3s: ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o] : ( V0P @ V3s ) ) ).
thf(thm_2Ewords_2ESUC__WORD__PRED,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~)
@ ( V0x
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
=> ( ( c_2Enum_2ESUC @ ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( c_2Ewords_2Ew2n @ A_27a @ V0x ) ) ) ).
thf(thm_2Ewords_2EWORD__PRED__THM,axiom,
! [A_27a: $tType,V0m: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( (~)
@ ( V0m
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0m @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Ewords_2Ew2n @ A_27a @ V0m ) ) ) ).
thf(thm_2Ewords_2ELSR__LESS,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( (~)
@ ( V1y
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0m ) )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__lsr @ A_27a @ V1y @ V0m ) ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1y ) ) ) ).
thf(thm_2Ewords_2Eword__sub__w2n,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__ls @ A_27a @ V1y @ V0x )
=> ( ( c_2Ewords_2Ew2n @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ V1y ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ A_27a @ V0x ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1y ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LE__EQ__LS,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0x )
& ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1y ) )
=> ( ( c_2Ewords_2Eword__le @ A_27a @ V0x @ V1y )
= ( c_2Ewords_2Eword__ls @ A_27a @ V0x @ V1y ) ) ) ).
thf(thm_2Ewords_2EWORD__LT__EQ__LO,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0x )
& ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1y ) )
=> ( ( c_2Ewords_2Eword__lt @ A_27a @ V0x @ V1y )
= ( c_2Ewords_2Eword__lo @ A_27a @ V0x @ V1y ) ) ) ).
thf(thm_2Ewords_2EWORD__ZERO__LE,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0w )
= ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) @ ( c_2Ewords_2EINT__MIN @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(thm_2Ewords_2EWORD__LT__SUB__UPPER,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1y )
& ( c_2Ewords_2Eword__lt @ A_27a @ V1y @ V0x ) )
=> ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ V1y ) @ V0x ) ) ).
thf(thm_2Ewords_2EWORD__SUB__LT,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1y )
& ( c_2Ewords_2Eword__lt @ A_27a @ V1y @ V0x ) )
=> ( ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ V1y ) )
& ( c_2Ewords_2Eword__lt @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ V1y ) @ V0x ) ) ) ).
thf(thm_2Ewords_2EWORD__SUB__LE,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1y )
& ( c_2Ewords_2Eword__le @ A_27a @ V1y @ V0x ) )
=> ( ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ V1y ) )
& ( c_2Ewords_2Eword__le @ A_27a @ ( c_2Ewords_2Eword__sub @ A_27a @ V0x @ V1y ) @ V0x ) ) ) ).
thf(thm_2Ewords_2Edimindex__1,axiom,
( ( c_2Efcp_2Edimindex @ tyop_2Eone_2Eone @ ( c_2Ebool_2Ethe__value @ tyop_2Eone_2Eone ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Ewords_2Efinite__1,axiom,
c_2Epred__set_2EFINITE @ tyop_2Eone_2Eone @ ( c_2Epred__set_2EUNIV @ tyop_2Eone_2Eone ) ).
thf(thm_2Ewords_2EINT__MIN__1,axiom,
( ( c_2Ewords_2EINT__MIN @ tyop_2Eone_2Eone @ ( c_2Ebool_2Ethe__value @ tyop_2Eone_2Eone ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Ewords_2Edimword__1,axiom,
( ( c_2Ewords_2Edimword @ tyop_2Eone_2Eone @ ( c_2Ebool_2Ethe__value @ tyop_2Eone_2Eone ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Ewords_2Edimindex__2,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Ewords_2Efinite__2,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ).
thf(thm_2Ewords_2EINT__MIN__2,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Ewords_2Edimword__2,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__3,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Efinite__3,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ).
thf(thm_2Ewords_2EINT__MIN__3,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Edimword__3,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__4,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Efinite__4,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__4,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__4,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__5,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Efinite__5,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__5,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__5,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__6,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Ewords_2Efinite__6,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__6,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__6,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__7,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__7,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__7,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__7,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__8,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__8,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__8,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__8,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__9,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__9,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__9,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__9,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__10,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__10,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__10,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__10,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__11,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__11,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__11,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__11,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__12,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__12,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__12,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__12,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__16,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__16,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__16,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__16,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__20,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__20,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__20,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__20,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__24,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__24,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__24,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__24,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__28,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__28,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__28,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__28,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__30,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__30,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__30,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__30,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__32,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__32,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__32,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__32,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__48,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__48,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__48,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__48,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__64,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__64,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__64,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__64,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__96,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__96,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__96,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__96,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimindex__128,axiom,
( ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Efinite__128,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2EINT__MIN__128,axiom,
( ( c_2Ewords_2EINT__MIN @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2Edimword__128,axiom,
( ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ewords_2En2w__itself__ind,axiom,
! [A_27a: $tType,V0P: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) ) > $o] :
( ! [V1n: tyop_2Enum_2Enum] : ( V0P @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) @ V1n @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ! [V2v: tyop_2Enum_2Enum,V3v1: tyop_2Ebool_2Eitself @ A_27a] : ( V0P @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) @ V2v @ V3v1 ) ) ) ).
thf(thm_2Ewords_2En2w__itself__def,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2En2w__itself @ A_27a @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Ebool_2Eitself @ A_27a ) @ V0n @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Ewords_2En2w @ A_27a @ V0n ) ) ).
%------------------------------------------------------------------------------