TPTP Problem File: ITP013+5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP013+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Ewords_2En2w__sub.p, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Ewords_2En2w__sub.p [Gau20]
% : HL406001+5.p [TPAP]
% Status : Theorem
% Rating : 1.00 v8.1.0, 0.97 v7.5.0
% Syntax : Number of formulae : 11132 ( 627 unt; 0 def)
% Number of atoms : 77522 (12507 equ)
% Maximal formula atoms : 5765 ( 6 avg)
% Number of connectives : 67672 (1282 ~; 637 |;20988 &)
% (4329 <=>;40436 =>; 0 <=; 0 <~>)
% Maximal formula depth : 363 ( 9 avg)
% Maximal term depth : 34 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 3515 (3515 usr; 394 con; 0-11 aty)
% Number of variables : 53672 (40519 !;13153 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001+2.ax').
include('Axioms/ITP001/ITP002+5.ax').
include('Axioms/ITP001/ITP003+5.ax').
include('Axioms/ITP001/ITP004+5.ax').
include('Axioms/ITP001/ITP007+5.ax').
include('Axioms/ITP001/ITP006+5.ax').
include('Axioms/ITP001/ITP005+5.ax').
include('Axioms/ITP001/ITP008+5.ax').
include('Axioms/ITP001/ITP009+5.ax').
include('Axioms/ITP001/ITP010+5.ax').
include('Axioms/ITP001/ITP012+5.ax').
include('Axioms/ITP001/ITP011+5.ax').
include('Axioms/ITP001/ITP013+5.ax').
include('Axioms/ITP001/ITP014+5.ax').
include('Axioms/ITP001/ITP015+5.ax').
include('Axioms/ITP001/ITP017+5.ax').
include('Axioms/ITP001/ITP016+5.ax').
include('Axioms/ITP001/ITP019+5.ax').
include('Axioms/ITP001/ITP018+5.ax').
include('Axioms/ITP001/ITP021+5.ax').
include('Axioms/ITP001/ITP022+5.ax').
include('Axioms/ITP001/ITP020+5.ax').
include('Axioms/ITP001/ITP024+5.ax').
include('Axioms/ITP001/ITP023+5.ax').
include('Axioms/ITP001/ITP025+5.ax').
include('Axioms/ITP001/ITP026+5.ax').
include('Axioms/ITP001/ITP027+5.ax').
include('Axioms/ITP001/ITP028+5.ax').
include('Axioms/ITP001/ITP031+5.ax').
include('Axioms/ITP001/ITP029+5.ax').
include('Axioms/ITP001/ITP033+5.ax').
include('Axioms/ITP001/ITP030+5.ax').
include('Axioms/ITP001/ITP032+5.ax').
include('Axioms/ITP001/ITP038+5.ax').
include('Axioms/ITP001/ITP035+5.ax').
include('Axioms/ITP001/ITP034+5.ax').
include('Axioms/ITP001/ITP036+5.ax').
include('Axioms/ITP001/ITP037+5.ax').
include('Axioms/ITP001/ITP039+5.ax').
include('Axioms/ITP001/ITP041+5.ax').
include('Axioms/ITP001/ITP042+5.ax').
include('Axioms/ITP001/ITP040+5.ax').
include('Axioms/ITP001/ITP044+5.ax').
include('Axioms/ITP001/ITP051+5.ax').
include('Axioms/ITP001/ITP045+5.ax').
include('Axioms/ITP001/ITP056+5.ax').
include('Axioms/ITP001/ITP046+5.ax').
include('Axioms/ITP001/ITP043+5.ax').
include('Axioms/ITP001/ITP052+5.ax').
include('Axioms/ITP001/ITP057+5.ax').
include('Axioms/ITP001/ITP048+5.ax').
include('Axioms/ITP001/ITP047+5.ax').
include('Axioms/ITP001/ITP055+5.ax').
include('Axioms/ITP001/ITP053+5.ax').
include('Axioms/ITP001/ITP054+5.ax').
include('Axioms/ITP001/ITP058+5.ax').
include('Axioms/ITP001/ITP049+5.ax').
include('Axioms/ITP001/ITP050+5.ax').
include('Axioms/ITP001/ITP061+5.ax').
include('Axioms/ITP001/ITP069+5.ax').
include('Axioms/ITP001/ITP062+5.ax').
include('Axioms/ITP001/ITP068+5.ax').
include('Axioms/ITP001/ITP078+5.ax').
include('Axioms/ITP001/ITP064+5.ax').
include('Axioms/ITP001/ITP060+5.ax').
include('Axioms/ITP001/ITP067+5.ax').
include('Axioms/ITP001/ITP075+5.ax').
include('Axioms/ITP001/ITP074+5.ax').
include('Axioms/ITP001/ITP063+5.ax').
include('Axioms/ITP001/ITP059+5.ax').
include('Axioms/ITP001/ITP065+5.ax').
include('Axioms/ITP001/ITP076+5.ax').
include('Axioms/ITP001/ITP066+5.ax').
include('Axioms/ITP001/ITP077+5.ax').
include('Axioms/ITP001/ITP070+5.ax').
include('Axioms/ITP001/ITP071+5.ax').
include('Axioms/ITP001/ITP072+5.ax').
include('Axioms/ITP001/ITP073+5.ax').
include('Axioms/ITP001/ITP080+5.ax').
include('Axioms/ITP001/ITP083+5.ax').
include('Axioms/ITP001/ITP088+5.ax').
include('Axioms/ITP001/ITP082+5.ax').
include('Axioms/ITP001/ITP081+5.ax').
include('Axioms/ITP001/ITP079+5.ax').
include('Axioms/ITP001/ITP087+5.ax').
include('Axioms/ITP001/ITP085+5.ax').
include('Axioms/ITP001/ITP086+5.ax').
%------------------------------------------------------------------------------
fof(mem_c_2Ewords_2EBIT__SET,axiom,
mem(c_2Ewords_2EBIT__SET,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))) ).
fof(mem_c_2Ewords_2EINT__MAX,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2EINT__MAX(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Ewords_2EINT__MIN,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2EINT__MIN(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Ewords_2EUINT__MAX,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2EUINT__MAX(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Ewords_2Eadd__with__carry,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eadd__with__carry(A_27a),arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),bool)),ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(bool,bool)))) ) ).
fof(mem_c_2Ewords_2Ebit__count,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ebit__count(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Ewords_2Ebit__count__upto,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ebit__count__upto(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Enum_2Enum))) ) ).
fof(mem_c_2Ewords_2Ebit__field__insert,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewords_2Ebit__field__insert(A_27a,A_27b),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27b),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))))) ) ) ).
fof(mem_c_2Ewords_2Econcat__word__list,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewords_2Econcat__word__list(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,A_27a)),ty_2Efcp_2Ecart(bool,A_27b))) ) ) ).
fof(mem_c_2Ewords_2Edimword,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Edimword(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Ewords_2El2w,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2El2w(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2En2w,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2En2w(A_27a),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2En2w__itself,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2En2w__itself(A_27a),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Ebool_2Eitself(A_27a)),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Enzcv,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Enzcv(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)))))) ) ).
fof(mem_c_2Ewords_2Ereduce__and,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ereduce__and(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) ) ).
fof(mem_c_2Ewords_2Ereduce__nand,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ereduce__nand(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) ) ).
fof(mem_c_2Ewords_2Ereduce__nor,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ereduce__nor(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) ) ).
fof(mem_c_2Ewords_2Ereduce__or,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ereduce__or(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) ) ).
fof(mem_c_2Ewords_2Ereduce__xnor,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ereduce__xnor(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) ) ).
fof(mem_c_2Ewords_2Ereduce__xor,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ereduce__xor(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) ) ).
fof(mem_c_2Ewords_2Es2w,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Es2w(A_27a),arr(ty_2Enum_2Enum,arr(arr(ty_2Estring_2Echar,ty_2Enum_2Enum),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Efcp_2Ecart(bool,A_27a))))) ) ).
fof(mem_c_2Ewords_2Esaturate__add,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Esaturate__add(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Esaturate__mul,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Esaturate__mul(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Esaturate__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Esaturate__n2w(A_27a),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Esaturate__sub,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Esaturate__sub(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Esaturate__w2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewords_2Esaturate__w2w(A_27a,A_27b),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27b))) ) ) ).
fof(mem_c_2Ewords_2Esw2sw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewords_2Esw2sw(A_27a,A_27b),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27b))) ) ) ).
fof(mem_c_2Ewords_2Ew2l,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ew2l(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Enum_2Enum)))) ) ).
fof(mem_c_2Ewords_2Ew2n,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ew2n(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Ewords_2Ew2s,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Ew2s(A_27a),arr(ty_2Enum_2Enum,arr(arr(ty_2Enum_2Enum,ty_2Estring_2Echar),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Estring_2Echar))))) ) ).
fof(mem_c_2Ewords_2Ew2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewords_2Ew2w(A_27a,A_27b),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27b))) ) ) ).
fof(mem_c_2Ewords_2Eword__1comp,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__1comp(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__2comp,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__2comp(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__H,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__H(A_27a),ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(mem_c_2Ewords_2Eword__L,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__L(A_27a),ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(mem_c_2Ewords_2Eword__L2,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__L2(A_27a),ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(mem_c_2Ewords_2Eword__T,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__T(A_27a),ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(mem_c_2Ewords_2Eword__abs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__abs(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__add,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__add(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__and,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__and(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__asr,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__asr(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__asr__bv,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__asr__bv(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__bit,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__bit(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Ewords_2Eword__bits,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__bits(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))))) ) ).
fof(mem_c_2Ewords_2Eword__compare,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__compare(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)))) ) ).
fof(mem_c_2Ewords_2Eword__concat,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27c),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27b),ty_2Efcp_2Ecart(bool,A_27c)))) ) ) ) ).
fof(mem_c_2Ewords_2Eword__div,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__div(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__extract,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewords_2Eword__extract(A_27a,A_27b),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27b))))) ) ) ).
fof(mem_c_2Ewords_2Eword__from__bin__list,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__from__bin__list(A_27a),arr(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__from__bin__string,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__from__bin__string(A_27a),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__from__dec__list,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__from__dec__list(A_27a),arr(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__from__dec__string,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__from__dec__string(A_27a),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__from__hex__list,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__from__hex__list(A_27a),arr(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__from__hex__string,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__from__hex__string(A_27a),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__from__oct__list,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__from__oct__list(A_27a),arr(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__from__oct__string,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__from__oct__string(A_27a),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__ge,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__ge(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Ewords_2Eword__gt,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__gt(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Ewords_2Eword__hi,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__hi(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Ewords_2Eword__hs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__hs(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Ewords_2Eword__join,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewords_2Eword__join(A_27a,A_27b),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27b),ty_2Efcp_2Ecart(bool,ty_2Esum_2Esum(A_27a,A_27b))))) ) ) ).
fof(mem_c_2Ewords_2Eword__le,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__le(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Ewords_2Eword__len,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__len(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Ewords_2Eword__lo,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__lo(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Ewords_2Eword__log2,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__log2(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__ls,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__ls(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Ewords_2Eword__lsb,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__lsb(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool)) ) ).
fof(mem_c_2Ewords_2Eword__lsl,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__lsl(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__lsl__bv,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__lsl__bv(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__lsr,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__lsr(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__lsr__bv,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__lsr__bv(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__lt,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__lt(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) ).
fof(mem_c_2Ewords_2Eword__max,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__max(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__min,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__min(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__mod,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__mod(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__modify,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__modify(A_27a),arr(arr(ty_2Enum_2Enum,arr(bool,bool)),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__msb,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__msb(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool)) ) ).
fof(mem_c_2Ewords_2Eword__mul,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__mul(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__nand,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__nand(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__nor,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__nor(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__or,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__or(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__quot,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__quot(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__reduce,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__reduce(A_27a),arr(arr(bool,arr(bool,bool)),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)))) ) ).
fof(mem_c_2Ewords_2Eword__rem,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__rem(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__replicate,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ewords_2Eword__replicate(A_27a,A_27b),arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27b)))) ) ) ).
fof(mem_c_2Ewords_2Eword__reverse,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__reverse(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__rol,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__rol(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__rol__bv,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__rol__bv(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__ror,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__ror(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__ror__bv,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__ror__bv(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__rrx,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__rrx(A_27a),arr(ty_2Epair_2Eprod(bool,ty_2Efcp_2Ecart(bool,A_27a)),ty_2Epair_2Eprod(bool,ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__sign__extend,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__sign__extend(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__signed__bits,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__signed__bits(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))))) ) ).
fof(mem_c_2Ewords_2Eword__slice,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__slice(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))))) ) ).
fof(mem_c_2Ewords_2Eword__smax,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__smax(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__smin,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__smin(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__sub,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__sub(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__to__bin__list,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__to__bin__list(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Enum_2Enum))) ) ).
fof(mem_c_2Ewords_2Eword__to__bin__string,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__to__bin__string(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Estring_2Echar))) ) ).
fof(mem_c_2Ewords_2Eword__to__dec__list,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__to__dec__list(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Enum_2Enum))) ) ).
fof(mem_c_2Ewords_2Eword__to__dec__string,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__to__dec__string(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Estring_2Echar))) ) ).
fof(mem_c_2Ewords_2Eword__to__hex__list,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__to__hex__list(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Enum_2Enum))) ) ).
fof(mem_c_2Ewords_2Eword__to__hex__string,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__to__hex__string(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Estring_2Echar))) ) ).
fof(mem_c_2Ewords_2Eword__to__oct__list,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__to__oct__list(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Enum_2Enum))) ) ).
fof(mem_c_2Ewords_2Eword__to__oct__string,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__to__oct__string(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Estring_2Echar))) ) ).
fof(mem_c_2Ewords_2Eword__xnor,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__xnor(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(mem_c_2Ewords_2Eword__xor,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__xor(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(ax_thm_2Ewords_2Edimword__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ).
fof(ax_thm_2Ewords_2EINT__MIN__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ).
fof(ax_thm_2Ewords_2EUINT__MAX__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(ax_thm_2Ewords_2EINT__MAX__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(lameq_f2160,axiom,
! [A_27a,V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1i] : ap(f2160(A_27a,V0w),V1i) = ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1i)),V1i) ) ).
fof(ax_thm_2Ewords_2Ew2n__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ew2n(A_27a),V0w) = ap(ap(c_2Esum__num_2ESUM,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),f2160(A_27a,V0w)) ) ) ).
fof(ax_thm_2Ewords_2En2w__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2En2w(A_27a),V0n) = ap(c_2Efcp_2EFCP(bool,A_27a),f249(V0n)) ) ) ).
fof(ax_thm_2Ewords_2Ew2w__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w) = ap(c_2Ewords_2En2w(A_27b),ap(c_2Ewords_2Ew2n(A_27a),V0w)) ) ) ) ).
fof(ax_thm_2Ewords_2Esw2sw__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Esw2sw(A_27a,A_27b),V0w) = ap(c_2Ewords_2En2w(A_27b),ap(ap(ap(c_2Ebit_2ESIGN__EXTEND,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Ewords_2Ew2n(A_27a),V0w))) ) ) ) ).
fof(ax_thm_2Ewords_2Ew2l__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Ew2l(A_27a),V0b),V1w) = ap(ap(c_2Enumposrep_2En2l,V0b),ap(c_2Ewords_2Ew2n(A_27a),V1w)) ) ) ) ).
fof(ax_thm_2Ewords_2El2w__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(ap(c_2Ewords_2El2w(A_27a),V0b),V1l) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Enumposrep_2El2n,V0b),V1l)) ) ) ) ).
fof(ax_thm_2Ewords_2Ew2s__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,ty_2Estring_2Echar))
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(ap(c_2Ewords_2Ew2s(A_27a),V0b),V1f),V2w) = ap(ap(ap(c_2EASCIInumbers_2En2s,V0b),V1f),ap(c_2Ewords_2Ew2n(A_27a),V2w)) ) ) ) ) ).
fof(ax_thm_2Ewords_2Es2w__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Estring_2Echar,ty_2Enum_2Enum))
=> ! [V2s] :
( mem(V2s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(ap(c_2Ewords_2Es2w(A_27a),V0b),V1f),V2s) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(c_2EASCIInumbers_2Es2n,V0b),V1f),V2s)) ) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__from__bin__list__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__from__bin__list(A_27a) = ap(c_2Ewords_2El2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) ).
fof(ax_thm_2Ewords_2Eword__from__oct__list__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__from__oct__list(A_27a) = ap(c_2Ewords_2El2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).
fof(ax_thm_2Ewords_2Eword__from__dec__list__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__from__dec__list(A_27a) = ap(c_2Ewords_2El2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).
fof(ax_thm_2Ewords_2Eword__from__hex__list__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__from__hex__list(A_27a) = ap(c_2Ewords_2El2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) ) ).
fof(ax_thm_2Ewords_2Eword__to__bin__list__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__to__bin__list(A_27a) = ap(c_2Ewords_2Ew2l(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) ).
fof(ax_thm_2Ewords_2Eword__to__oct__list__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__to__oct__list(A_27a) = ap(c_2Ewords_2Ew2l(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).
fof(ax_thm_2Ewords_2Eword__to__dec__list__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__to__dec__list(A_27a) = ap(c_2Ewords_2Ew2l(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).
fof(ax_thm_2Ewords_2Eword__to__hex__list__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__to__hex__list(A_27a) = ap(c_2Ewords_2Ew2l(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) ) ).
fof(ax_thm_2Ewords_2Eword__from__bin__string__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__from__bin__string(A_27a) = ap(ap(c_2Ewords_2Es2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),c_2EASCIInumbers_2EUNHEX) ) ).
fof(ax_thm_2Ewords_2Eword__from__oct__string__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__from__oct__string(A_27a) = ap(ap(c_2Ewords_2Es2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),c_2EASCIInumbers_2EUNHEX) ) ).
fof(ax_thm_2Ewords_2Eword__from__dec__string__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__from__dec__string(A_27a) = ap(ap(c_2Ewords_2Es2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),c_2EASCIInumbers_2EUNHEX) ) ).
fof(ax_thm_2Ewords_2Eword__from__hex__string__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__from__hex__string(A_27a) = ap(ap(c_2Ewords_2Es2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),c_2EASCIInumbers_2EUNHEX) ) ).
fof(ax_thm_2Ewords_2Eword__to__bin__string__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__to__bin__string(A_27a) = ap(ap(c_2Ewords_2Ew2s(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),c_2EASCIInumbers_2EHEX) ) ).
fof(ax_thm_2Ewords_2Eword__to__oct__string__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__to__oct__string(A_27a) = ap(ap(c_2Ewords_2Ew2s(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),c_2EASCIInumbers_2EHEX) ) ).
fof(ax_thm_2Ewords_2Eword__to__dec__string__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__to__dec__string(A_27a) = ap(ap(c_2Ewords_2Ew2s(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),c_2EASCIInumbers_2EHEX) ) ).
fof(ax_thm_2Ewords_2Eword__to__hex__string__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__to__hex__string(A_27a) = ap(ap(c_2Ewords_2Ew2s(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),c_2EASCIInumbers_2EHEX) ) ).
fof(ax_thm_2Ewords_2Eword__T__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__T(A_27a) = ap(c_2Ewords_2En2w(A_27a),ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ).
fof(ax_thm_2Ewords_2Eword__L__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__L(A_27a) = ap(c_2Ewords_2En2w(A_27a),ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ).
fof(ax_thm_2Ewords_2Eword__H__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__H(A_27a) = ap(c_2Ewords_2En2w(A_27a),ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ).
fof(lameq_f2161,axiom,
! [A_27a,V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1i] : ap(f2161(A_27a,V0w),V1i) = ap(c_2Ebool_2E_7E,ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1i)) ) ).
fof(ax_thm_2Ewords_2Eword__1comp__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__1comp(A_27a),V0w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2161(A_27a,V0w)) ) ) ).
fof(lameq_f2162,axiom,
! [A_27a,V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2162(A_27a,V0v,V1w),V2i) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0v),V2i)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V2i)) ) ) ).
fof(ax_thm_2Ewords_2Eword__and__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),V0v),V1w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2162(A_27a,V0v,V1w)) ) ) ) ).
fof(lameq_f2163,axiom,
! [A_27a,V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2163(A_27a,V0v,V1w),V2i) = ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0v),V2i)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V2i)) ) ) ).
fof(ax_thm_2Ewords_2Eword__or__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),V0v),V1w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2163(A_27a,V0v,V1w)) ) ) ) ).
fof(lameq_f2164,axiom,
! [A_27a,V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2164(A_27a,V1w,V0v),V2i) = ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0v),V2i)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V2i))) ) ) ).
fof(ax_thm_2Ewords_2Eword__xor__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),V0v),V1w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2164(A_27a,V1w,V0v)) ) ) ) ).
fof(lameq_f2165,axiom,
! [A_27a,V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2165(A_27a,V1w,V0v),V2i) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0v),V2i)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V2i))) ) ) ).
fof(ax_thm_2Ewords_2Eword__nand__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__nand(A_27a),V0v),V1w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2165(A_27a,V1w,V0v)) ) ) ) ).
fof(lameq_f2166,axiom,
! [A_27a,V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2166(A_27a,V1w,V0v),V2i) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0v),V2i)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V2i))) ) ) ).
fof(ax_thm_2Ewords_2Eword__nor__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__nor(A_27a),V0v),V1w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2166(A_27a,V1w,V0v)) ) ) ) ).
fof(lameq_f2167,axiom,
! [A_27a,V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2167(A_27a,V0v,V1w),V2i) = ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0v),V2i)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V2i)) ) ) ).
fof(ax_thm_2Ewords_2Eword__xnor__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xnor(A_27a),V0v),V1w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2167(A_27a,V0v,V1w)) ) ) ) ).
fof(lameq_f2168,axiom,
! [V0f] :
( mem(V0f,arr(bool,arr(bool,bool)))
=> ! [V2l] : ap(f2168(V0f),V2l) = ap(ap(ap(c_2Elist_2EFOLDL(bool,bool),V0f),ap(c_2Elist_2EHD(bool),V2l)),ap(c_2Elist_2ETL(bool),V2l)) ) ).
fof(lameq_f2169,axiom,
! [A_27a,V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3i] : ap(f2169(A_27a,V1w),V3i) = ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3i)) ) ).
fof(ax_thm_2Ewords_2Eword__reduce__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(bool,arr(bool,bool)))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__reduce(A_27a),V0f),V1w) = ap(c_2Efcp_2EFCP(bool,ty_2Eone_2Eone),ap(c_2Ecombin_2EK(bool,ty_2Enum_2Enum),ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(bool),bool),f2168(V0f)),ap(ap(c_2Elist_2EGENLIST(bool),f2169(A_27a,V1w)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))))) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__compare__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__compare(A_27a),V0a),V1b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),V0a),V1b)),ap(c_2Ewords_2En2w(ty_2Eone_2Eone),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Ewords_2En2w(ty_2Eone_2Eone),c_2Enum_2E0)) ) ) ) ).
fof(ax_thm_2Ewords_2Ereduce__and__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Ereduce__and(A_27a) = ap(c_2Ewords_2Eword__reduce(A_27a),c_2Ebool_2E_2F_5C) ) ).
fof(ax_thm_2Ewords_2Ereduce__or__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Ereduce__or(A_27a) = ap(c_2Ewords_2Eword__reduce(A_27a),c_2Ebool_2E_5C_2F) ) ).
fof(lameq_f2170,axiom,
! [V0x] :
( mem(V0x,bool)
=> ! [V1y] : ap(f2170(V0x),V1y) = ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),V0x),V1y)) ) ).
fof(lameq_f2171,axiom,
! [V0x] : ap(f2171,V0x) = f2170(V0x) ).
fof(ax_thm_2Ewords_2Ereduce__xor__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Ereduce__xor(A_27a) = ap(c_2Ewords_2Eword__reduce(A_27a),f2171) ) ).
fof(lameq_f2172,axiom,
! [V0a] :
( mem(V0a,bool)
=> ! [V1b] : ap(f2172(V0a),V1b) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2E_2F_5C,V0a),V1b)) ) ).
fof(lameq_f2173,axiom,
! [V0a] : ap(f2173,V0a) = f2172(V0a) ).
fof(ax_thm_2Ewords_2Ereduce__nand__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Ereduce__nand(A_27a) = ap(c_2Ewords_2Eword__reduce(A_27a),f2173) ) ).
fof(lameq_f2174,axiom,
! [V0a] :
( mem(V0a,bool)
=> ! [V1b] : ap(f2174(V0a),V1b) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2E_5C_2F,V0a),V1b)) ) ).
fof(lameq_f2175,axiom,
! [V0a] : ap(f2175,V0a) = f2174(V0a) ).
fof(ax_thm_2Ewords_2Ereduce__nor__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Ereduce__nor(A_27a) = ap(c_2Ewords_2Eword__reduce(A_27a),f2175) ) ).
fof(ax_thm_2Ewords_2Ereduce__xnor__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Ereduce__xnor(A_27a) = ap(c_2Ewords_2Eword__reduce(A_27a),c_2Emin_2E_3D(bool)) ) ).
fof(ax_thm_2Ewords_2Eword__lsb__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(c_2Ewords_2Eword__lsb(A_27a),V0w))
<=> p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),c_2Enum_2E0)) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__msb__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(c_2Ewords_2Eword__msb(A_27a),V0w))
<=> p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) ).
fof(lameq_f2176,axiom,
! [A_27a,V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V3i] : ap(f2176(A_27a,V2w,V0h,V1l),V3i) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,V1l),V3i)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,V3i),ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V2w),V3i))) ) ) ) ).
fof(lameq_f2177,axiom,
! [A_27a,V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V2w] : ap(f2177(A_27a,V1l,V0h),V2w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2176(A_27a,V2w,V0h,V1l)) ) ) ).
fof(ax_thm_2Ewords_2Eword__slice__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1l) = f2177(A_27a,V1l,V0h) ) ) ) ).
fof(lameq_f2178,axiom,
! [A_27a,V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3i] : ap(f2178(A_27a,V0h,V1l,V2w),V3i) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V3i),V1l)),ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V2w),ap(ap(c_2Earithmetic_2E_2B,V3i),V1l))) ) ) ) ).
fof(lameq_f2179,axiom,
! [A_27a,V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V2w] : ap(f2179(A_27a,V1l,V0h),V2w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2178(A_27a,V0h,V1l,V2w)) ) ) ).
fof(ax_thm_2Ewords_2Eword__bits__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l) = f2179(A_27a,V1l,V0h) ) ) ) ).
fof(lameq_f2180,axiom,
! [A_27a,V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V3i] : ap(f2180(A_27a,V2w,V0h,V1l),V3i) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,V1l),ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V2w),ap(ap(c_2Earithmetic_2EMIN,ap(ap(c_2Earithmetic_2E_2B,V3i),V1l)),ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) ) ) ) ).
fof(lameq_f2181,axiom,
! [A_27a,V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V2w] : ap(f2181(A_27a,V1l,V0h),V2w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2180(A_27a,V2w,V0h,V1l)) ) ) ).
fof(ax_thm_2Ewords_2Eword__signed__bits__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__signed__bits(A_27a),V0h),V1l) = f2181(A_27a,V1l,V0h) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__extract__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l) = ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27b),ty_2Efcp_2Ecart(bool,A_27a)),c_2Ewords_2Ew2w(A_27a,A_27b)),ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l)) ) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__bit__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__bit(A_27a),V0b),V1w))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0b),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
& p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V0b)) ) ) ) ) ) ).
fof(lameq_f2182,axiom,
! [A_27a,V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1i] : ap(f2182(A_27a,V0w),V1i) = ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1i)) ) ).
fof(ax_thm_2Ewords_2Eword__reverse__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__reverse(A_27a),V0w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2182(A_27a,V0w)) ) ) ).
fof(lameq_f2183,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool)))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2183(A_27a,V0f,V1w),V2i) = ap(ap(V0f,V2i),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V2i)) ) ) ).
fof(ax_thm_2Ewords_2Eword__modify__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool)))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__modify(A_27a),V0f),V1w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2183(A_27a,V0f,V1w)) ) ) ) ).
fof(conj_thm_2Ewords_2EBIT__SET__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ( ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( ( ( V2n != c_2Enum_2E0
& p(ap(c_2Earithmetic_2EODD,V2n)) )
=> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V1i)),ap(ap(c_2Earithmetic_2EDIV,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) )
& ( ( V2n != c_2Enum_2E0
& ~ p(ap(c_2Earithmetic_2EODD,V2n)) )
=> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V1i)),ap(ap(c_2Earithmetic_2EDIV,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) )
=> p(ap(ap(V0P,V1i),V2n)) ) ) )
=> ! [V3v] :
( mem(V3v,ty_2Enum_2Enum)
=> ! [V4v1] :
( mem(V4v1,ty_2Enum_2Enum)
=> p(ap(ap(V0P,V3v),V4v1)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EBIT__SET__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2EBIT__SET,V1i),V0n) = ap(ap(ap(c_2Ebool_2ECOND(arr(ty_2Enum_2Enum,bool)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0n),c_2Enum_2E0)),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)),ap(ap(ap(c_2Ebool_2ECOND(arr(ty_2Enum_2Enum,bool)),ap(c_2Earithmetic_2EODD,V0n)),ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V1i),ap(ap(c_2Ewords_2EBIT__SET,ap(c_2Enum_2ESUC,V1i)),ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Ewords_2EBIT__SET,ap(c_2Enum_2ESUC,V1i)),ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ) ).
fof(lameq_f2184,axiom,
! [A_27b,V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Efcp_2Ecart(bool,A_27b))
=> ! [V3i] : ap(f2184(A_27b,V0h,V1l,V2a),V3i) = ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,V1l),V3i)),ap(ap(c_2Earithmetic_2E_3C_3D,V3i),V0h))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27b),V2a),ap(ap(c_2Earithmetic_2E_2D,V3i),V1l))) ) ) ) ).
fof(ax_thm_2Ewords_2Ebit__field__insert__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Efcp_2Ecart(bool,A_27b))
=> ap(ap(ap(c_2Ewords_2Ebit__field__insert(A_27a,A_27b),V0h),V1l),V2a) = ap(c_2Ewords_2Eword__modify(A_27a),f2184(A_27b,V0h,V1l,V2a)) ) ) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__sign__extend__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sign__extend(A_27a),V0n),V1w) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(c_2Ebit_2ESIGN__EXTEND,V0n),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2Ew2n(A_27a),V1w))) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__len__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__len(A_27a),V0w) = ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)) ) ) ).
fof(lameq_f2185,axiom,
! [A_27a,V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2185(A_27a,V1w),V2i) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V2i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0) ) ).
fof(ax_thm_2Ewords_2Ebit__count__upto__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Ebit__count__upto(A_27a),V0n),V1w) = ap(ap(c_2Esum__num_2ESUM,V0n),f2185(A_27a,V1w)) ) ) ) ).
fof(ax_thm_2Ewords_2Ebit__count__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ebit__count(A_27a),V0w) = ap(ap(c_2Ewords_2Ebit__count__upto(A_27a),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0w) ) ) ).
fof(ax_thm_2Ewords_2Eword__2comp__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__2comp(A_27a),V0w) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2Ew2n(A_27a),V0w))) ) ) ).
fof(ax_thm_2Ewords_2Eword__add__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2Ew2n(A_27a),V0v)),ap(c_2Ewords_2Ew2n(A_27a),V1w))) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__mul__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V1w) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Ewords_2Ew2n(A_27a),V0v)),ap(c_2Ewords_2Ew2n(A_27a),V1w))) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__log2__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__log2(A_27a),V0w) = ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebit_2ELOG2,ap(c_2Ewords_2Ew2n(A_27a),V0w))) ) ) ).
fof(lameq_f2186,axiom,
! [A_27a,V5carry__out] :
( mem(V5carry__out,bool)
=> ! [V4result] :
( mem(V4result,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V6overflow] : ap(f2186(A_27a,V5carry__out,V4result),V6overflow) = ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(bool,bool)),V4result),ap(ap(c_2Epair_2E_2C(bool,bool),V5carry__out),V6overflow)) ) ) ).
fof(lameq_f2187,axiom,
! [A_27a,V4result] :
( mem(V4result,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V5carry__out] : ap(f2187(A_27a,V4result),V5carry__out) = f2186(A_27a,V5carry__out,V4result) ) ).
fof(lameq_f2188,axiom,
! [A_27a,V0x] :
( mem(V0x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1y] :
( mem(V1y,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3unsigned__sum] :
( mem(V3unsigned__sum,ty_2Enum_2Enum)
=> ! [V4result] : ap(f2188(A_27a,V0x,V1y,V3unsigned__sum),V4result) = ap(ap(c_2Ebool_2ELET(bool,ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(bool,bool))),ap(ap(c_2Ebool_2ELET(bool,arr(bool,ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(bool,bool)))),f2187(A_27a,V4result)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Ewords_2Ew2n(A_27a),V4result)),V3unsigned__sum)))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(bool),ap(c_2Ewords_2Eword__msb(A_27a),V0x)),ap(c_2Ewords_2Eword__msb(A_27a),V1y))),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),ap(c_2Ewords_2Eword__msb(A_27a),V0x)),ap(c_2Ewords_2Eword__msb(A_27a),V4result))))) ) ) ) ).
fof(lameq_f2189,axiom,
! [A_27a,V0x] :
( mem(V0x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1y] :
( mem(V1y,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3unsigned__sum] : ap(f2189(A_27a,V0x,V1y),V3unsigned__sum) = ap(ap(c_2Ebool_2ELET(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(bool,bool))),f2188(A_27a,V0x,V1y,V3unsigned__sum)),ap(c_2Ewords_2En2w(A_27a),V3unsigned__sum)) ) ) ).
fof(ax_thm_2Ewords_2Eadd__with__carry__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1y] :
( mem(V1y,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2carry__in] :
( mem(V2carry__in,bool)
=> ap(c_2Ewords_2Eadd__with__carry(A_27a),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),bool)),V0x),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27a),bool),V1y),V2carry__in))) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(bool,bool))),f2189(A_27a,V0x,V1y)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2Ew2n(A_27a),V0x)),ap(c_2Ewords_2Ew2n(A_27a),V1y))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V2carry__in),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0))) ) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__sub__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),ap(c_2Ewords_2Eword__2comp(A_27a),V1w)) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__div__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__div(A_27a),V0v),V1w) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2EDIV,ap(c_2Ewords_2Ew2n(A_27a),V0v)),ap(c_2Ewords_2Ew2n(A_27a),V1w))) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__mod__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__mod(A_27a),V0v),V1w) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Ewords_2Ew2n(A_27a),V0v)),ap(c_2Ewords_2Ew2n(A_27a),V1w))) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__quot__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__quot(A_27a),V0a),V1b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(c_2Ewords_2Eword__msb(A_27a),V0a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(c_2Ewords_2Eword__msb(A_27a),V1b)),ap(ap(c_2Ewords_2Eword__div(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0a)),ap(c_2Ewords_2Eword__2comp(A_27a),V1b))),ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__div(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0a)),V1b)))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(c_2Ewords_2Eword__msb(A_27a),V1b)),ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__div(A_27a),V0a),ap(c_2Ewords_2Eword__2comp(A_27a),V1b)))),ap(ap(c_2Ewords_2Eword__div(A_27a),V0a),V1b))) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__rem__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__rem(A_27a),V0a),V1b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(c_2Ewords_2Eword__msb(A_27a),V0a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(c_2Ewords_2Eword__msb(A_27a),V1b)),ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__mod(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0a)),ap(c_2Ewords_2Eword__2comp(A_27a),V1b)))),ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__mod(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0a)),V1b)))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(c_2Ewords_2Eword__msb(A_27a),V1b)),ap(ap(c_2Ewords_2Eword__mod(A_27a),V0a),ap(c_2Ewords_2Eword__2comp(A_27a),V1b))),ap(ap(c_2Ewords_2Eword__mod(A_27a),V0a),V1b))) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__L2__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__L2(A_27a) = ap(ap(c_2Ewords_2Eword__mul(A_27a),c_2Ewords_2Eword__L(A_27a)),c_2Ewords_2Eword__L(A_27a)) ) ).
fof(lameq_f2190,axiom,
! [A_27a,V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2q] :
( mem(V2q,ty_2Enum_2Enum)
=> ! [V3r] : ap(f2190(A_27a,V0a,V1b,V2q),V3r) = ap(ap(c_2Epair_2E_2C(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))),ap(c_2Ewords_2Eword__msb(A_27a),V3r)),ap(ap(c_2Epair_2E_2C(bool,ty_2Epair_2Eprod(bool,bool)),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),V3r),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0))),ap(ap(c_2Epair_2E_2C(bool,bool),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Ebit_2EBIT,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V2q)),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),V1b),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)))),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),ap(c_2Ewords_2Eword__msb(A_27a),V0a)),ap(c_2Ewords_2Eword__msb(A_27a),V1b)))),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),ap(c_2Ewords_2Eword__msb(A_27a),V3r)),ap(c_2Ewords_2Eword__msb(A_27a),V0a))))))) ) ) ) ).
fof(lameq_f2191,axiom,
! [A_27a,V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2q] : ap(f2191(A_27a,V0a,V1b),V2q) = ap(ap(c_2Ebool_2ELET(ty_2Efcp_2Ecart(bool,A_27a),ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)))),f2190(A_27a,V0a,V1b,V2q)),ap(c_2Ewords_2En2w(A_27a),V2q)) ) ) ).
fof(ax_thm_2Ewords_2Enzcv__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Enzcv(A_27a),V0a),V1b) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)))),f2191(A_27a,V0a,V1b)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2Ew2n(A_27a),V0a)),ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V1b)))) ) ) ) ).
fof(lameq_f2192,axiom,
! [V2n] :
( mem(V2n,bool)
=> ! [V5v] : ap(f2192(V2n),V5v) = ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),V2n),V5v)) ) ).
fof(lameq_f2193,axiom,
! [V2n] : ap(f2193,V2n) = ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,bool),bool),k(bool,ap(c_2Epair_2EUNCURRY(bool,bool,bool),k(bool,f2192(V2n))))) ).
fof(ax_thm_2Ewords_2Eword__lt__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__lt(A_27a),V0a),V1b))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))),bool),ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)),bool),f2193)),ap(ap(c_2Ewords_2Enzcv(A_27a),V0a),V1b))) ) ) ) ) ).
fof(lameq_f2194,axiom,
! [V2n] :
( mem(V2n,bool)
=> ! [V3z] :
( mem(V3z,bool)
=> ! [V5v] : ap(f2194(V2n,V3z),V5v) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,V3z)),ap(ap(c_2Emin_2E_3D(bool),V2n),V5v)) ) ) ).
fof(lameq_f2195,axiom,
! [V2n] :
( mem(V2n,bool)
=> ! [V3z] : ap(f2195(V2n),V3z) = ap(c_2Epair_2EUNCURRY(bool,bool,bool),k(bool,f2194(V2n,V3z))) ) ).
fof(lameq_f2196,axiom,
! [V2n] : ap(f2196,V2n) = ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,bool),bool),f2195(V2n)) ).
fof(ax_thm_2Ewords_2Eword__gt__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__gt(A_27a),V0a),V1b))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))),bool),ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)),bool),f2196)),ap(ap(c_2Ewords_2Enzcv(A_27a),V0a),V1b))) ) ) ) ) ).
fof(lameq_f2197,axiom,
! [V2n] :
( mem(V2n,bool)
=> ! [V3z] :
( mem(V3z,bool)
=> ! [V5v] : ap(f2197(V2n,V3z),V5v) = ap(ap(c_2Ebool_2E_5C_2F,V3z),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),V2n),V5v))) ) ) ).
fof(lameq_f2198,axiom,
! [V2n] :
( mem(V2n,bool)
=> ! [V3z] : ap(f2198(V2n),V3z) = ap(c_2Epair_2EUNCURRY(bool,bool,bool),k(bool,f2197(V2n,V3z))) ) ).
fof(lameq_f2199,axiom,
! [V2n] : ap(f2199,V2n) = ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,bool),bool),f2198(V2n)) ).
fof(ax_thm_2Ewords_2Eword__le__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__le(A_27a),V0a),V1b))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))),bool),ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)),bool),f2199)),ap(ap(c_2Ewords_2Enzcv(A_27a),V0a),V1b))) ) ) ) ) ).
fof(lameq_f2200,axiom,
! [V2n] :
( mem(V2n,bool)
=> ! [V5v] : ap(f2200(V2n),V5v) = ap(ap(c_2Emin_2E_3D(bool),V2n),V5v) ) ).
fof(lameq_f2201,axiom,
! [V2n] : ap(f2201,V2n) = ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,bool),bool),k(bool,ap(c_2Epair_2EUNCURRY(bool,bool,bool),k(bool,f2200(V2n))))) ).
fof(ax_thm_2Ewords_2Eword__ge__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__ge(A_27a),V0a),V1b))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))),bool),ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)),bool),f2201)),ap(ap(c_2Ewords_2Enzcv(A_27a),V0a),V1b))) ) ) ) ) ).
fof(lameq_f2202,axiom,
! [V3z] :
( mem(V3z,bool)
=> ! [V4c] : ap(f2202(V3z),V4c) = k(bool,ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_7E,V4c)),V3z)) ) ).
fof(lameq_f2203,axiom,
! [V3z] : ap(f2203,V3z) = ap(c_2Epair_2EUNCURRY(bool,bool,bool),f2202(V3z)) ).
fof(ax_thm_2Ewords_2Eword__ls__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__ls(A_27a),V0a),V1b))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))),bool),ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)),bool),k(bool,ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,bool),bool),f2203)))),ap(ap(c_2Ewords_2Enzcv(A_27a),V0a),V1b))) ) ) ) ) ).
fof(lameq_f2204,axiom,
! [V3z] :
( mem(V3z,bool)
=> ! [V4c] : ap(f2204(V3z),V4c) = k(bool,ap(ap(c_2Ebool_2E_2F_5C,V4c),ap(c_2Ebool_2E_7E,V3z))) ) ).
fof(lameq_f2205,axiom,
! [V3z] : ap(f2205,V3z) = ap(c_2Epair_2EUNCURRY(bool,bool,bool),f2204(V3z)) ).
fof(ax_thm_2Ewords_2Eword__hi__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__hi(A_27a),V0a),V1b))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))),bool),ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)),bool),k(bool,ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,bool),bool),f2205)))),ap(ap(c_2Ewords_2Enzcv(A_27a),V0a),V1b))) ) ) ) ) ).
fof(lameq_f2206,axiom,
! [V4c] : ap(f2206,V4c) = k(bool,ap(c_2Ebool_2E_7E,V4c)) ).
fof(ax_thm_2Ewords_2Eword__lo__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__lo(A_27a),V0a),V1b))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))),bool),ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)),bool),k(bool,ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,bool),bool),k(bool,ap(c_2Epair_2EUNCURRY(bool,bool,bool),f2206)))))),ap(ap(c_2Ewords_2Enzcv(A_27a),V0a),V1b))) ) ) ) ) ).
fof(lameq_f2207,axiom,
! [V4c] : ap(f2207,V4c) = k(bool,V4c) ).
fof(ax_thm_2Ewords_2Eword__hs__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__hs(A_27a),V0a),V1b))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))),bool),ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)),bool),k(bool,ap(c_2Epair_2EUNCURRY(bool,ty_2Epair_2Eprod(bool,bool),bool),k(bool,ap(c_2Epair_2EUNCURRY(bool,bool,bool),f2207)))))),ap(ap(c_2Ewords_2Enzcv(A_27a),V0a),V1b))) ) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__min__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__min(A_27a),V0a),V1b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Ewords_2Eword__lo(A_27a),V0a),V1b)),V0a),V1b) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__max__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__max(A_27a),V0a),V1b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Ewords_2Eword__lo(A_27a),V0a),V1b)),V1b),V0a) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__smin__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__smin(A_27a),V0a),V1b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Ewords_2Eword__lt(A_27a),V0a),V1b)),V0a),V1b) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__smax__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__smax(A_27a),V0a),V1b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Ewords_2Eword__lt(A_27a),V0a),V1b)),V1b),V0a) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__abs__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__abs(A_27a),V0w) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Ewords_2Eword__lt(A_27a),V0w),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0))),ap(c_2Ewords_2Eword__2comp(A_27a),V0w)),V0w) ) ) ).
fof(lameq_f2208,axiom,
! [A_27a,V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2208(A_27a,V1n,V0w),V2i) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,V2i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2i)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2E_2D,V2i),V1n)))) ) ) ).
fof(ax_thm_2Ewords_2Eword__lsl__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__lsl(A_27a),V0w),V1n) = ap(c_2Efcp_2EFCP(bool,A_27a),f2208(A_27a,V1n,V0w)) ) ) ) ).
fof(lameq_f2209,axiom,
! [A_27a,V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2i] : ap(f2209(A_27a,V0w,V1n),V2i) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2i),V1n)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2E_2B,V2i),V1n))) ) ) ).
fof(ax_thm_2Ewords_2Eword__lsr__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__lsr(A_27a),V0w),V1n) = ap(c_2Efcp_2EFCP(bool,A_27a),f2209(A_27a,V0w,V1n)) ) ) ) ).
fof(lameq_f2210,axiom,
! [A_27a,V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2210(A_27a,V1n,V0w),V2i) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(ap(c_2Earithmetic_2E_2B,V2i),V1n))),ap(c_2Ewords_2Eword__msb(A_27a),V0w)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2E_2B,V2i),V1n))) ) ) ).
fof(ax_thm_2Ewords_2Eword__asr__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__asr(A_27a),V0w),V1n) = ap(c_2Efcp_2EFCP(bool,A_27a),f2210(A_27a,V1n,V0w)) ) ) ) ).
fof(lameq_f2211,axiom,
! [A_27a,V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2211(A_27a,V1n,V0w),V2i) = ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2i),V1n)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(ax_thm_2Ewords_2Eword__ror__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__ror(A_27a),V0w),V1n) = ap(c_2Efcp_2EFCP(bool,A_27a),f2211(A_27a,V1n,V0w)) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__rol__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__rol(A_27a),V0w),V1n) = ap(ap(c_2Ewords_2Eword__ror(A_27a),V0w),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(ap(c_2Earithmetic_2EMOD,V1n),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))) ) ) ) ).
fof(lameq_f2212,axiom,
! [A_27a,V0c] :
( mem(V0c,bool)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2212(A_27a,V0c,V1w),V2i) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2i),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0c),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(ap(c_2Ewords_2Eword__lsr(A_27a),V1w),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2i)) ) ) ).
fof(ax_thm_2Ewords_2Eword__rrx__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0c] :
( mem(V0c,bool)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__rrx(A_27a),ap(ap(c_2Epair_2E_2C(bool,ty_2Efcp_2Ecart(bool,A_27a)),V0c),V1w)) = ap(ap(c_2Epair_2E_2C(bool,ty_2Efcp_2Ecart(bool,A_27a)),ap(c_2Ewords_2Eword__lsb(A_27a),V1w)),ap(c_2Efcp_2EFCP(bool,A_27a),f2212(A_27a,V0c,V1w))) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__lsl__bv__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__lsl__bv(A_27a),V0w),V1n) = ap(ap(c_2Ewords_2Eword__lsl(A_27a),V0w),ap(c_2Ewords_2Ew2n(A_27a),V1n)) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__lsr__bv__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__lsr__bv(A_27a),V0w),V1n) = ap(ap(c_2Ewords_2Eword__lsr(A_27a),V0w),ap(c_2Ewords_2Ew2n(A_27a),V1n)) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__asr__bv__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__asr__bv(A_27a),V0w),V1n) = ap(ap(c_2Ewords_2Eword__asr(A_27a),V0w),ap(c_2Ewords_2Ew2n(A_27a),V1n)) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__ror__bv__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__ror__bv(A_27a),V0w),V1n) = ap(ap(c_2Ewords_2Eword__ror(A_27a),V0w),ap(c_2Ewords_2Ew2n(A_27a),V1n)) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__rol__bv__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__rol__bv(A_27a),V0w),V1n) = ap(ap(c_2Ewords_2Eword__rol(A_27a),V0w),ap(c_2Ewords_2Ew2n(A_27a),V1n)) ) ) ) ).
fof(lameq_f2213,axiom,
! [A_27b,A_27a,V2cv] :
( mem(V2cv,ty_2Efcp_2Ecart(bool,ty_2Esum_2Esum(A_27a,A_27b)))
=> ! [V3cw] : ap(f2213(A_27b,A_27a,V2cv),V3cw) = ap(ap(c_2Ewords_2Eword__or(ty_2Esum_2Esum(A_27a,A_27b)),ap(ap(c_2Ewords_2Eword__lsl(ty_2Esum_2Esum(A_27a,A_27b)),V2cv),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))),V3cw) ) ).
fof(lameq_f2214,axiom,
! [A_27b,A_27a,V2cv] : ap(f2214(A_27b,A_27a),V2cv) = f2213(A_27b,A_27a,V2cv) ).
fof(ax_thm_2Ewords_2Eword__join__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27b))
=> ap(ap(c_2Ewords_2Eword__join(A_27a,A_27b),V0v),V1w) = ap(ap(c_2Ebool_2ELET(ty_2Efcp_2Ecart(bool,ty_2Esum_2Esum(A_27a,A_27b)),ty_2Efcp_2Ecart(bool,ty_2Esum_2Esum(A_27a,A_27b))),ap(ap(c_2Ebool_2ELET(ty_2Efcp_2Ecart(bool,ty_2Esum_2Esum(A_27a,A_27b)),arr(ty_2Efcp_2Ecart(bool,ty_2Esum_2Esum(A_27a,A_27b)),ty_2Efcp_2Ecart(bool,ty_2Esum_2Esum(A_27a,A_27b)))),f2214(A_27b,A_27a)),ap(c_2Ewords_2Ew2w(A_27a,ty_2Esum_2Esum(A_27a,A_27b)),V0v))),ap(c_2Ewords_2Ew2w(A_27b,ty_2Esum_2Esum(A_27a,A_27b)),V1w)) ) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__concat__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27b))
=> ap(ap(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27c),V0v),V1w) = ap(c_2Ewords_2Ew2w(ty_2Esum_2Esum(A_27a,A_27b),A_27c),ap(ap(c_2Ewords_2Eword__join(A_27a,A_27b),V0v),V1w)) ) ) ) ) ) ).
fof(lameq_f2215,axiom,
! [A_27a,V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2215(A_27a,V0n,V1w),V2i) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,V2i),ap(ap(c_2Earithmetic_2E_2A,V0n),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),ap(ap(c_2Earithmetic_2EMOD,V2i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))) ) ) ).
fof(ax_thm_2Ewords_2Eword__replicate__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__replicate(A_27a,A_27b),V0n),V1w) = ap(c_2Efcp_2EFCP(bool,A_27b),f2215(A_27a,V0n,V1w)) ) ) ) ) ).
fof(ax_thm_2Ewords_2Econcat__word__list__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ap(c_2Ewords_2Econcat__word__list(A_27a,A_27b),c_2Elist_2ENIL(ty_2Efcp_2Ecart(bool,A_27a))) = ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0)
& ! [V0h] :
( mem(V0h,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,A_27a)))
=> ap(c_2Ewords_2Econcat__word__list(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(ty_2Efcp_2Ecart(bool,A_27a)),V0h),V1t)) = ap(ap(c_2Ewords_2Eword__or(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0h)),ap(ap(c_2Ewords_2Eword__lsl(A_27b),ap(c_2Ewords_2Econcat__word__list(A_27a,A_27b),V1t)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ) ) ).
fof(ax_thm_2Ewords_2Esaturate__n2w__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2Esaturate__n2w(A_27a),V0n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0n)),c_2Ewords_2Eword__T(A_27a)),ap(c_2Ewords_2En2w(A_27a),V0n)) ) ) ).
fof(ax_thm_2Ewords_2Esaturate__w2w__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Esaturate__w2w(A_27a,A_27b),V0w) = ap(c_2Ewords_2Esaturate__n2w(A_27b),ap(c_2Ewords_2Ew2n(A_27a),V0w)) ) ) ) ).
fof(ax_thm_2Ewords_2Esaturate__add__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Esaturate__add(A_27a),V0a),V1b) = ap(c_2Ewords_2Esaturate__n2w(A_27a),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2Ew2n(A_27a),V0a)),ap(c_2Ewords_2Ew2n(A_27a),V1b))) ) ) ) ).
fof(ax_thm_2Ewords_2Esaturate__sub__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Esaturate__sub(A_27a),V0a),V1b) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2Ew2n(A_27a),V0a)),ap(c_2Ewords_2Ew2n(A_27a),V1b))) ) ) ) ).
fof(ax_thm_2Ewords_2Esaturate__mul__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Esaturate__mul(A_27a),V0a),V1b) = ap(c_2Ewords_2Esaturate__n2w(A_27a),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Ewords_2Ew2n(A_27a),V0a)),ap(c_2Ewords_2Ew2n(A_27a),V1b))) ) ) ) ).
fof(conj_thm_2Ewords_2EZERO__LT__dimword,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ewords_2EDIMINDEX__GT__0,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ewords_2Edimword__IS__TWICE__INT__MIN,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ).
fof(conj_thm_2Ewords_2Edimword__sub__int__min,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))) = ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a)) ) ).
fof(conj_thm_2Ewords_2EONE__LT__dimword,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ewords_2EEXISTS__HB,axiom,
! [A_27a] :
( ne(A_27a)
=> ? [V0m] :
( mem(V0m,ty_2Enum_2Enum)
& ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Enum_2ESUC,V0m) ) ) ).
fof(conj_thm_2Ewords_2EMOD__DIMINDEX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))) = ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),V0n) ) ) ).
fof(conj_thm_2Ewords_2EBITS__ZEROL__DIMINDEX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),V0n) = V0n ) ) ) ).
fof(conj_thm_2Ewords_2EMOD__2EXP__DIMINDEX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))) = ap(ap(c_2Ebit_2EMOD__2EXP,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0n) ) ) ).
fof(conj_thm_2Ewords_2EINT__MIN__SUM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(c_2Ewords_2EINT__MIN(ty_2Esum_2Esum(A_27a,A_27b)),c_2Ebool_2Ethe__value(ty_2Esum_2Esum(A_27a,A_27b))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))),ap(c_2Epred__set_2EFINITE(A_27b),c_2Epred__set_2EUNIV(A_27b)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EINT__MIN(A_27b),c_2Ebool_2Ethe__value(A_27b)))),ap(c_2Ewords_2EINT__MIN(ty_2Esum_2Esum(A_27a,A_27b)),c_2Ebool_2Ethe__value(ty_2Esum_2Esum(A_27a,A_27b)))) ) ) ).
fof(conj_thm_2Ewords_2EZERO__LT__INT__MIN,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ewords_2EZERO__LT__INT__MAX,axiom,
! [A_27a] :
( ne(A_27a)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(conj_thm_2Ewords_2EZERO__LE__INT__MAX,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ewords_2EZERO__LT__UINT__MAX,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ewords_2EINT__MIN__LT__DIMWORD,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ewords_2EINT__MAX__LT__DIMWORD,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ewords_2Edimindex__lt__dimword,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ewords_2EBOUND__ORDER,axiom,
! [A_27a] :
( ne(A_27a)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__dimword__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))
<=> ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Ewords_2Edimword(A_27b),c_2Ebool_2Ethe__value(A_27b)) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__dimword__le__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2Edimword(A_27b),c_2Ebool_2Ethe__value(A_27b)))) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__dimword__lt__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2Edimword(A_27b),c_2Ebool_2Ethe__value(A_27b)))) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__int__min__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))
<=> ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Ewords_2EINT__MIN(A_27b),c_2Ebool_2Ethe__value(A_27b)) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__int__min__le__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EINT__MIN(A_27b),c_2Ebool_2Ethe__value(A_27b)))) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__int__min__lt__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EINT__MIN(A_27b),c_2Ebool_2Ethe__value(A_27b)))) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__int__max__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))
<=> ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Ewords_2EINT__MAX(A_27b),c_2Ebool_2Ethe__value(A_27b)) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__int__max__le__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EINT__MAX(A_27b),c_2Ebool_2Ethe__value(A_27b)))) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__int__max__lt__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EINT__MAX(A_27b),c_2Ebool_2Ethe__value(A_27b)))) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__uint__max__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))
<=> ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Ewords_2EUINT__MAX(A_27b),c_2Ebool_2Ethe__value(A_27b)) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__uint__max__le__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EUINT__MAX(A_27b),c_2Ebool_2Ethe__value(A_27b)))) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__uint__max__lt__iso,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2EUINT__MAX(A_27b),c_2Ebool_2Ethe__value(A_27b)))) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2n__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)) = ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ) ).
fof(conj_thm_2Ewords_2En2w__w2n,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2En2w(A_27a),ap(c_2Ewords_2Ew2n(A_27a),V0w)) = V0w ) ) ).
fof(conj_thm_2Ewords_2Eword__nchotomy,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& V0w = ap(c_2Ewords_2En2w(A_27a),V1n) ) ) ) ).
fof(conj_thm_2Ewords_2En2w__mod,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) = ap(c_2Ewords_2En2w(A_27a),V0n) ) ) ).
fof(conj_thm_2Ewords_2En2w__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(c_2Ewords_2En2w(A_27a),V0m) = ap(c_2Ewords_2En2w(A_27a),V1n)
<=> ap(ap(c_2Earithmetic_2EMOD,V0m),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))) = ap(ap(c_2Earithmetic_2EMOD,V1n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eranged__word__nchotomy,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& V0w = ap(c_2Ewords_2En2w(A_27a),V1n)
& p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ).
fof(conj_thm_2Ewords_2Edimindex__1__cases,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
=> ( V0a = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
| V0a = ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ) ).
fof(conj_thm_2Ewords_2Emod__dimindex,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(conj_thm_2Ewords_2EWORD__INDUCT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Efcp_2Ecart(bool,A_27a),bool))
=> ( ( p(ap(V0P,ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)))
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V1n)),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ( p(ap(V0P,ap(c_2Ewords_2En2w(A_27a),V1n)))
=> p(ap(V0P,ap(c_2Ewords_2En2w(A_27a),ap(c_2Enum_2ESUC,V1n)))) ) ) ) )
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> p(ap(V0P,V2x)) ) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2n__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(c_2Ewords_2Ew2n(A_27a),V0v) = ap(c_2Ewords_2Ew2n(A_27a),V1w)
<=> V0v = V1w ) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2n__lt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2Ew2n(A_27a),V0w)),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(conj_thm_2Ewords_2Eword__0__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = c_2Enum_2E0 ) ).
fof(conj_thm_2Ewords_2Eword__1__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ).
fof(conj_thm_2Ewords_2Ew2n__eq__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(c_2Ewords_2Ew2n(A_27a),V0w) = c_2Enum_2E0
<=> V0w = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ).
fof(conj_thm_2Ewords_2En2w__dimword,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2En2w(A_27a),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ).
fof(conj_thm_2Ewords_2Eword__2comp__dimindex__1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
=> ap(c_2Ewords_2Eword__2comp(A_27a),V0w) = V0w ) ) ) ).
fof(conj_thm_2Ewords_2Eword__add__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2En2w(A_27a),V0m)),ap(c_2Ewords_2En2w(A_27a),V1n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__mul__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2En2w(A_27a),V0m)),ap(c_2Ewords_2En2w(A_27a),V1n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__log2__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2Eword__log2(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)) = ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebit_2ELOG2,ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))))) ) ) ).
fof(conj_thm_2Ewords_2Eword__1comp__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))))) ) ) ).
fof(conj_thm_2Ewords_2Eword__2comp__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))))) ) ) ).
fof(conj_thm_2Ewords_2Eword__lsb,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__lsb(A_27a) = ap(c_2Ewords_2Eword__bit(A_27a),c_2Enum_2E0) ) ).
fof(conj_thm_2Ewords_2Eword__msb,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__msb(A_27a) = ap(c_2Ewords_2Eword__bit(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ).
fof(conj_thm_2Ewords_2Eword__lsb__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Ewords_2Eword__lsb(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)))
<=> p(ap(c_2Earithmetic_2EODD,V0n)) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__msb__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Ewords_2Eword__msb(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)))
<=> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n)) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__msb__n2w__numeric,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(c_2Ewords_2Eword__msb(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))))) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__and__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),V1m)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),c_2Ebool_2E_2F_5C),V0n),V1m)) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__or__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),V1m)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),c_2Ebool_2E_5C_2F),V0n),V1m)) ) ) ) ).
fof(lameq_f2216,axiom,
! [V2x] :
( mem(V2x,bool)
=> ! [V3y] : ap(f2216(V2x),V3y) = ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),V2x),V3y)) ) ).
fof(lameq_f2217,axiom,
! [V2x] : ap(f2217,V2x) = f2216(V2x) ).
fof(conj_thm_2Ewords_2Eword__xor__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),V1m)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),f2217),V0n),V1m)) ) ) ) ).
fof(lameq_f2218,axiom,
! [V2x] :
( mem(V2x,bool)
=> ! [V3y] : ap(f2218(V2x),V3y) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2E_2F_5C,V2x),V3y)) ) ).
fof(lameq_f2219,axiom,
! [V2x] : ap(f2219,V2x) = f2218(V2x) ).
fof(conj_thm_2Ewords_2Eword__nand__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__nand(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),V1m)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),f2219),V0n),V1m)) ) ) ) ).
fof(lameq_f2220,axiom,
! [V2x] :
( mem(V2x,bool)
=> ! [V3y] : ap(f2220(V2x),V3y) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2E_5C_2F,V2x),V3y)) ) ).
fof(lameq_f2221,axiom,
! [V2x] : ap(f2221,V2x) = f2220(V2x) ).
fof(conj_thm_2Ewords_2Eword__nor__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__nor(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),V1m)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),f2221),V0n),V1m)) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__xnor__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__xnor(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),V1m)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),c_2Emin_2E_3D(bool)),V0n),V1m)) ) ) ) ).
fof(conj_thm_2Ewords_2El2w__w2l,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b))
=> ap(ap(c_2Ewords_2El2w(A_27a),V0b),ap(ap(c_2Ewords_2Ew2l(A_27a),V0b),V1w)) = V1w ) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2l__l2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(ap(c_2Ewords_2Ew2l(A_27a),V0b),ap(ap(c_2Ewords_2El2w(A_27a),V0b),V1l)) = ap(ap(c_2Enumposrep_2En2l,V0b),ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Enumposrep_2El2n,V0b),V1l)),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ).
fof(conj_thm_2Ewords_2Es2w__w2s,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0c2n] :
( mem(V0c2n,arr(ty_2Estring_2Echar,ty_2Enum_2Enum))
=> ! [V1n2c] :
( mem(V1n2c,arr(ty_2Enum_2Enum,ty_2Estring_2Echar))
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ! [V3w] :
( mem(V3w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V2b))
& ! [V4x] :
( mem(V4x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V4x),V2b))
=> ap(V0c2n,ap(V1n2c,V4x)) = V4x ) ) )
=> ap(ap(ap(c_2Ewords_2Es2w(A_27a),V2b),V0c2n),ap(ap(ap(c_2Ewords_2Ew2s(A_27a),V2b),V1n2c),V3w)) = V3w ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2s__s2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1c2n] :
( mem(V1c2n,arr(ty_2Estring_2Echar,ty_2Enum_2Enum))
=> ! [V2n2c] :
( mem(V2n2c,arr(ty_2Enum_2Enum,ty_2Estring_2Echar))
=> ! [V3s] :
( mem(V3s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(ap(ap(c_2Ewords_2Ew2s(A_27a),V0b),V2n2c),ap(ap(ap(c_2Ewords_2Es2w(A_27a),V0b),V1c2n),V3s)) = ap(ap(ap(c_2EASCIInumbers_2En2s,V0b),V2n2c),ap(ap(c_2Earithmetic_2EMOD,ap(ap(ap(c_2EASCIInumbers_2Es2n,V0b),V1c2n),V3s)),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2ENUMERAL__LESS__THM,axiom,
( ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))))
<=> ( V0m = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))
| p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) )
& ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V3n))))
<=> ( V2m = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))
| p(ap(ap(c_2Eprim__rec_2E_3C,V2m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n)))) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__bin__list,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Enum_2Enum)),c_2Ewords_2Eword__from__bin__list(A_27a)),c_2Ewords_2Eword__to__bin__list(A_27a)) = c_2Ecombin_2EI(ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(conj_thm_2Ewords_2Eword__oct__list,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Enum_2Enum)),c_2Ewords_2Eword__from__oct__list(A_27a)),c_2Ewords_2Eword__to__oct__list(A_27a)) = c_2Ecombin_2EI(ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(conj_thm_2Ewords_2Eword__dec__list,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Enum_2Enum)),c_2Ewords_2Eword__from__dec__list(A_27a)),c_2Ewords_2Eword__to__dec__list(A_27a)) = c_2Ecombin_2EI(ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(conj_thm_2Ewords_2Eword__hex__list,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Enum_2Enum)),c_2Ewords_2Eword__from__hex__list(A_27a)),c_2Ewords_2Eword__to__hex__list(A_27a)) = c_2Ecombin_2EI(ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(conj_thm_2Ewords_2Eword__bin__string,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Ewords_2Eword__from__bin__string(A_27a)),c_2Ewords_2Eword__to__bin__string(A_27a)) = c_2Ecombin_2EI(ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(conj_thm_2Ewords_2Eword__oct__string,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Ewords_2Eword__from__oct__string(A_27a)),c_2Ewords_2Eword__to__oct__string(A_27a)) = c_2Ecombin_2EI(ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(conj_thm_2Ewords_2Eword__dec__string,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Ewords_2Eword__from__dec__string(A_27a)),c_2Ewords_2Eword__to__dec__string(A_27a)) = c_2Ecombin_2EI(ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(conj_thm_2Ewords_2Eword__hex__string,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Ewords_2Eword__from__hex__string(A_27a)),c_2Ewords_2Eword__to__hex__string(A_27a)) = c_2Ecombin_2EI(ty_2Efcp_2Ecart(bool,A_27a)) ) ).
fof(conj_thm_2Ewords_2Eword__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ~ p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),V0i)) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__eq__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( V0w = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
<=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ~ p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1i)) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__T,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),c_2Ewords_2Eword__T(A_27a)),V0i)) ) ) ) ).
fof(conj_thm_2Ewords_2EFCP__T__F,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ap(c_2Efcp_2EFCP(bool,A_27a),ap(c_2Ecombin_2EK(bool,ty_2Enum_2Enum),c_2Ebool_2ET)) = c_2Ewords_2Eword__T(A_27a)
& ap(c_2Efcp_2EFCP(bool,A_27b),ap(c_2Ecombin_2EK(bool,ty_2Enum_2Enum),c_2Ebool_2EF)) = ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__L,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),c_2Ewords_2Eword__L(A_27a)),V0n))
<=> V0n = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__H,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),c_2Ewords_2Eword__H(A_27a)),V0n))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__L2,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ewords_2Eword__L2(A_27a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),c_2Ewords_2Eword__L(A_27a)) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__1,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = c_2Ewords_2Eword__T(A_27a) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__1__T,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0i)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__MSB__1COMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(c_2Ewords_2Eword__msb(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),V0w)))
<=> ~ p(ap(c_2Ewords_2Eword__msb(A_27a),V0w)) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2n__minus1,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Ewords_2Ew2n__plus1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2Ew2n(A_27a),V0a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),V0a),c_2Ewords_2Eword__T(A_27a))),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ewords_2Ew2n(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NOT__NOT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),V0a)) = V0a ) ) ).
fof(conj_thm_2Ewords_2EWORD__DE__MORGAN__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(c_2Ewords_2Eword__1comp(A_27a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b)) = ap(ap(c_2Ewords_2Eword__or(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),V0a)),ap(c_2Ewords_2Eword__1comp(A_27a),V1b))
& ap(c_2Ewords_2Eword__1comp(A_27a),ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V1b)) = ap(ap(c_2Ewords_2Eword__and(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),V0a)),ap(c_2Ewords_2Eword__1comp(A_27a),V1b)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NOT__XOR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),V0a)),ap(c_2Ewords_2Eword__1comp(A_27a),V1b)) = ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V1b)
& ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),ap(c_2Ewords_2Eword__1comp(A_27a),V1b)) = ap(c_2Ewords_2Eword__1comp(A_27a),ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V1b))
& ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),V0a)),V1b) = ap(c_2Ewords_2Eword__1comp(A_27a),ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V1b)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__AND__CLAUSES,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__and(A_27a),c_2Ewords_2Eword__T(A_27a)),V0a) = V0a
& ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),c_2Ewords_2Eword__T(A_27a)) = V0a
& ap(ap(c_2Ewords_2Eword__and(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),V0a) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
& ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
& ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V0a) = V0a ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__OR__CLAUSES,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__or(A_27a),c_2Ewords_2Eword__T(A_27a)),V0a) = c_2Ewords_2Eword__T(A_27a)
& ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),c_2Ewords_2Eword__T(A_27a)) = c_2Ewords_2Eword__T(A_27a)
& ap(ap(c_2Ewords_2Eword__or(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),V0a) = V0a
& ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = V0a
& ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V0a) = V0a ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__XOR__CLAUSES,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__xor(A_27a),c_2Ewords_2Eword__T(A_27a)),V0a) = ap(c_2Ewords_2Eword__1comp(A_27a),V0a)
& ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),c_2Ewords_2Eword__T(A_27a)) = ap(c_2Ewords_2Eword__1comp(A_27a),V0a)
& ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),V0a) = V0a
& ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = V0a
& ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V0a) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__AND__ASSOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b)),V2c) = ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),ap(ap(c_2Ewords_2Eword__and(A_27a),V1b),V2c)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__OR__ASSOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V1b)),V2c) = ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),ap(ap(c_2Ewords_2Eword__or(A_27a),V1b),V2c)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__XOR__ASSOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V1b)),V2c) = ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),ap(ap(c_2Ewords_2Eword__xor(A_27a),V1b),V2c)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__AND__COMM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b) = ap(ap(c_2Ewords_2Eword__and(A_27a),V1b),V0a) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__OR__COMM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V1b) = ap(ap(c_2Ewords_2Eword__or(A_27a),V1b),V0a) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__XOR__COMM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V1b) = ap(ap(c_2Ewords_2Eword__xor(A_27a),V1b),V0a) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__AND__IDEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V0a) = V0a ) ) ).
fof(conj_thm_2Ewords_2EWORD__OR__IDEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V0a) = V0a ) ) ).
fof(conj_thm_2Ewords_2EWORD__AND__ABSORD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b)) = V0a ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__OR__ABSORB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V1b)) = V0a ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__AND__COMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),ap(c_2Ewords_2Eword__1comp(A_27a),V0a)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ).
fof(conj_thm_2Ewords_2EWORD__OR__COMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),ap(c_2Ewords_2Eword__1comp(A_27a),V0a)) = c_2Ewords_2Eword__T(A_27a) ) ) ).
fof(conj_thm_2Ewords_2EWORD__XOR__COMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),ap(c_2Ewords_2Eword__1comp(A_27a),V0a)) = c_2Ewords_2Eword__T(A_27a) ) ) ).
fof(conj_thm_2Ewords_2EWORD__RIGHT__AND__OVER__OR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V1b)),V2c) = ap(ap(c_2Ewords_2Eword__or(A_27a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V2c)),ap(ap(c_2Ewords_2Eword__and(A_27a),V1b),V2c)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__RIGHT__OR__OVER__AND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b)),V2c) = ap(ap(c_2Ewords_2Eword__and(A_27a),ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V2c)),ap(ap(c_2Ewords_2Eword__or(A_27a),V1b),V2c)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__RIGHT__AND__OVER__XOR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V1b)),V2c) = ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V2c)),ap(ap(c_2Ewords_2Eword__and(A_27a),V1b),V2c)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LEFT__AND__OVER__OR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),ap(ap(c_2Ewords_2Eword__or(A_27a),V1b),V2c)) = ap(ap(c_2Ewords_2Eword__or(A_27a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b)),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V2c)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LEFT__OR__OVER__AND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),ap(ap(c_2Ewords_2Eword__and(A_27a),V1b),V2c)) = ap(ap(c_2Ewords_2Eword__and(A_27a),ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V1b)),ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V2c)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LEFT__AND__OVER__XOR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),ap(ap(c_2Ewords_2Eword__xor(A_27a),V1b),V2c)) = ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b)),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V2c)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__XOR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V1b) = ap(ap(c_2Ewords_2Eword__or(A_27a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),ap(c_2Ewords_2Eword__1comp(A_27a),V1b))),ap(ap(c_2Ewords_2Eword__and(A_27a),V1b),ap(c_2Ewords_2Eword__1comp(A_27a),V0a))) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NAND__NOT__AND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__nand(A_27a),V0a),V1b) = ap(c_2Ewords_2Eword__1comp(A_27a),ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NOR__NOT__OR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__nor(A_27a),V0a),V1b) = ap(c_2Ewords_2Eword__1comp(A_27a),ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V1b)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__XNOR__NOT__XOR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xnor(A_27a),V0a),V1b) = ap(c_2Ewords_2Eword__1comp(A_27a),ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V1b)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__OR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V0a),V1b) = ap(ap(c_2Ewords_2Eword__or(A_27a),V0a),V1b) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__XOR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__and(A_27a),V0a),V1b) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V0a),V1b) = ap(ap(c_2Ewords_2Eword__xor(A_27a),V0a),V1b) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__AND__EXP__SUB1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(c_2Ewords_2En2w(A_27a),V1n)),ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0m))) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__msb__add__word__L,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(c_2Ewords_2Eword__msb(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0a),c_2Ewords_2Eword__L(A_27a))))
<=> ~ p(ap(c_2Ewords_2Eword__msb(A_27a),V0a)) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w)),V1i))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
& p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1i)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Esw2sw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27b),ap(c_2Ewords_2Esw2sw(A_27a,A_27b),V0w)),V1i))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1i)),ap(c_2Ewords_2Eword__msb(A_27a),V0w))) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2w__id,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ew2w(A_27a,A_27a),V0w) = V0w ) ) ).
fof(conj_thm_2Ewords_2Esw2sw__id,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Esw2sw(A_27a,A_27a),V0w) = V0w ) ) ).
fof(conj_thm_2Ewords_2Ew2w__w2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ew2w(A_27b,A_27c),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w)) = ap(c_2Ewords_2Ew2w(A_27a,A_27c),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),V0w)) ) ) ) ) ).
fof(conj_thm_2Ewords_2Esw2sw__sw2sw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Esw2sw(A_27b,A_27c),ap(c_2Ewords_2Esw2sw(A_27a,A_27b),V0w)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27c)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c))))),ap(c_2Ewords_2Esw2sw(A_27b,A_27c),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w))),ap(c_2Ewords_2Esw2sw(A_27a,A_27c),V0w)) ) ) ) ) ).
fof(conj_thm_2Ewords_2Esw2sw__w2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Esw2sw(A_27a,A_27b),V0w) = ap(ap(c_2Ewords_2Eword__or(A_27b),ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27b)),ap(c_2Ewords_2Eword__msb(A_27a),V0w)),ap(ap(c_2Ewords_2Eword__lsl(A_27b),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0))),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w)) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__bit,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1b),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1b))
<=> p(ap(ap(c_2Ewords_2Eword__bit(A_27a),V1b),V0w)) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__slice__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1l),ap(c_2Ewords_2En2w(A_27a),V2n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(c_2Ebit_2ESLICE,ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V1l),V2n)) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__bits__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),ap(c_2Ewords_2En2w(A_27a),V2n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V1l),V2n)) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__bit__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ewords_2Eword__bit(A_27a),V0b),ap(c_2Ewords_2En2w(A_27a),V1n)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0b),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
& p(ap(ap(c_2Ebit_2EBIT,V0b),V1n)) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__signed__bits__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__signed__bits(A_27a),V0h),V1l),ap(c_2Ewords_2En2w(A_27a),V2n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(c_2Ebit_2ESIGN__EXTEND,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EMIN,ap(c_2Enum_2ESUC,V0h)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),V1l)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V1l),V2n))) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__sign__extend__bits,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(ap(c_2Ewords_2Eword__signed__bits(A_27a),V0h),V1l),V2w) = ap(ap(c_2Ewords_2Eword__sign__extend(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EMIN,ap(c_2Enum_2ESUC,V0h)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),V1l)),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V2w)) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__index__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0index_20too_20large] :
( mem(V0index_20too_20large,bool)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(c_2Ewords_2En2w(A_27a),V1n)),V2i))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Eprim__rec_2E_3C,V2i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(ap(c_2Ebit_2EBIT,V2i),V1n)),ap(ap(ap(ap(c_2Ecombin_2EFAIL(arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Enum_2Enum,bool)),bool),c_2Efcp_2Efcp__index(bool,A_27a)),V0index_20too_20large),ap(c_2Ewords_2En2w(A_27a),V1n)),V2i))) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__index,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),V1i))
<=> p(ap(ap(c_2Ebit_2EBIT,V1i),V0n)) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__bits__w2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27b),V1h),V2l),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w)) = ap(c_2Ewords_2Ew2w(A_27a,A_27b),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(ap(c_2Earithmetic_2EMIN,V1h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V2l),V0w)) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__reverse__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2Eword__reverse(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Ebit_2EBIT__REVERSE,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0n)) ) ) ).
fof(conj_thm_2Ewords_2Eword__modify__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool)))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__modify(A_27a),V0f),ap(c_2Ewords_2En2w(A_27a),V1n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(c_2Ebit_2EBIT__MODIFY,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0f),V1n)) ) ) ) ).
fof(lameq_f2222,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,bool))
=> ! [V1i] : ap(f2222(V0f),V1i) = k(bool,ap(V0f,V1i)) ) ).
fof(conj_thm_2Ewords_2Efcp__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,bool))
=> ap(c_2Efcp_2EFCP(bool,A_27a),V0f) = ap(ap(c_2Ewords_2Eword__modify(A_27a),f2222(V0f)),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) ) ) ).
fof(conj_thm_2Ewords_2Ew2n__w2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ew2n(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))),ap(c_2Ewords_2Ew2n(A_27a),V0w)),ap(c_2Ewords_2Ew2n(A_27a),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),V0w))) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2n__w2w__le,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewords_2Ew2n(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w))),ap(c_2Ewords_2Ew2n(A_27a),V0w))) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2w__lt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2Ew2n(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w))),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2w__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2Ew2w(A_27a,A_27b),ap(c_2Ewords_2En2w(A_27a),V0n)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27b)),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Ewords_2En2w(A_27b),V0n)),ap(c_2Ewords_2En2w(A_27b),ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),V0n))) ) ) ) ).
fof(conj_thm_2Ewords_2Ew2w__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(c_2Ewords_2Ew2w(A_27b,A_27a),ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ).
fof(conj_thm_2Ewords_2Ew2n__11__lift,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27b))
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c))))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c)))) )
=> ( ap(c_2Ewords_2Ew2n(A_27a),V0a) = ap(c_2Ewords_2Ew2n(A_27b),V1b)
<=> ap(c_2Ewords_2Ew2w(A_27a,A_27c),V0a) = ap(c_2Ewords_2Ew2w(A_27b,A_27c),V1b) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__extract__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),ap(c_2Ewords_2En2w(A_27a),V2n)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27b)),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Ewords_2En2w(A_27b),ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V1l),V2n))),ap(c_2Ewords_2En2w(A_27b),ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2EMIN,ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1l))),V1l),V2n))) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2En2w__BITS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0h),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),ap(c_2Ewords_2En2w(A_27a),V2n)) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__extract__w2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27b,A_27c),V1h),V2l),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w)) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27c),V1h),V2l),V0w) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__w2w__EXTRACT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),V0w) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2x),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ( p(ap(ap(c_2Ewords_2Eword__bit(A_27a),V2x),V0v))
<=> p(ap(ap(c_2Ewords_2Eword__bit(A_27a),V2x),V1w)) ) ) )
<=> V0v = V1w ) ) ) ) ).
fof(lameq_f2223,axiom,
! [V1x] :
( mem(V1x,bool)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ! [V3b] : ap(f2223(V1x,V0n,V2i),V3b) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2i),V0n)),V1x),V3b) ) ) ) ).
fof(lameq_f2224,axiom,
! [V1x] :
( mem(V1x,bool)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V2i] : ap(f2224(V1x,V0n),V2i) = f2223(V1x,V0n,V2i) ) ) ).
fof(conj_thm_2Ewords_2EBIT__UPDATE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,bool)
=> ap(ap(c_2Efcp_2E_3A_2B(bool,A_27a),V0n),V1x) = ap(c_2Ewords_2Eword__modify(A_27a),f2224(V1x,V0n)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__MODIFY__BIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool)))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(ap(c_2Ewords_2Eword__modify(A_27a),V0f),V1w)),V2i))
<=> p(ap(ap(V0f,V2i),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1w),V2i))) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BIT__BITS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__bit(A_27a),V0b),V1w))
<=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0b),V0b),V1w) = ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__COMP__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h1] :
( mem(V0h1,ty_2Enum_2Enum)
=> ! [V1l1] :
( mem(V1l1,ty_2Enum_2Enum)
=> ! [V2h2] :
( mem(V2h2,ty_2Enum_2Enum)
=> ! [V3l2] :
( mem(V3l2,ty_2Enum_2Enum)
=> ! [V4w] :
( mem(V4w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V2h2),V3l2),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h1),V1l1),V4w)) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(ap(c_2Earithmetic_2EMIN,V0h1),ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1))),ap(ap(c_2Earithmetic_2E_2B,V3l2),V1l1)),V4w) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__EXTRACT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V2w) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27a),V0h),V1l),V2w) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__LSR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__lsr(A_27a),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V2w)),V3n) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),ap(ap(c_2Earithmetic_2E_2B,V1l),V3n)),V2w) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__ZERO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0h),V1l))
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V2w) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__ZERO2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__ZERO3,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1l))
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V2w) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__LT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2Ew2n(A_27a),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V2w))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)))) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__LT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2Ew2n(A_27b),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),V2w))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)))) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__ZERO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0h),V1l))
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),V2w) = ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__ZERO2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27b,A_27a),V0h),V1l),ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__ZERO3,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1l))
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),V2w) = ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SLICE__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1l),V2w) = ap(ap(c_2Ewords_2Eword__lsl(A_27a),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V2w)),V1l) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SLICE__ZERO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0h),V1l))
=> ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1l),V2w) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SLICE__ZERO2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Enum_2Enum)
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V1h),V0l),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SLICE__BITS__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),c_2Enum_2E0),V1w) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),c_2Enum_2E0),V1w) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__SLICE__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1l),V2w)) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V2w) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SLICE__COMP__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1m_27] :
( mem(V1m_27,ty_2Enum_2Enum)
=> ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3l] :
( mem(V3l,ty_2Enum_2Enum)
=> ! [V4w] :
( mem(V4w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V3l),V2m))
& V1m_27 = ap(ap(c_2Earithmetic_2E_2B,V2m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V0h)) )
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1m_27),V4w)),ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V2m),V3l),V4w)) = ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V3l),V4w) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__COMP__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27c))
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27b,A_27a),V1h),V2l),ap(ap(ap(c_2Ewords_2Eword__extract(A_27c,A_27b),V3m),V4n),V0w)) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27c,A_27a),ap(ap(c_2Earithmetic_2EMIN,V3m),ap(ap(c_2Earithmetic_2EMIN,ap(ap(c_2Earithmetic_2E_2B,V1h),V4n)),ap(ap(c_2Earithmetic_2EMIN,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V4n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))),ap(ap(c_2Earithmetic_2E_2B,V2l),V4n)),V0w) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__BITS__COMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0n] :
( mem(V0n,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2k] :
( mem(V2k,ty_2Enum_2Enum)
=> ! [V3j] :
( mem(V3j,ty_2Enum_2Enum)
=> ! [V4h] :
( mem(V4h,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V3j),V2k),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V4h),V1l),V0n)) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),ap(ap(c_2Earithmetic_2EMIN,V4h),ap(ap(c_2Earithmetic_2E_2B,V3j),V1l))),ap(ap(c_2Earithmetic_2E_2B,V2k),V1l)),V0n) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ALL__BITS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1h))
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V1h),c_2Enum_2E0),V0w) = V0w ) ) ) ) ).
fof(conj_thm_2Ewords_2EEXTRACT__ALL__BITS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0h))
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),c_2Enum_2E0),V1w) = ap(c_2Ewords_2Ew2w(A_27a,A_27b),V1w) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__MIN__HIGH,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1h))
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V1h),V2l),V0w) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2l),V0w) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__MIN__HIGH,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V1l)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0h)) )
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),V2w) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1l),V2w) ) ) ) )
& ! [V3h] :
( mem(V3h,ty_2Enum_2Enum)
=> ! [V4l] :
( mem(V4l,ty_2Enum_2Enum)
=> ! [V5w] :
( mem(V5w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V4l)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V4l)),V3h)) )
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V3h),V4l),V5w) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V4l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V4l),V5w) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2ECONCAT__EXTRACT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ! [V3w] :
( mem(V3w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ( ap(ap(c_2Earithmetic_2E_2D,V0h),V1m) = ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))
& ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V1m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2l) = ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c))
& ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0h),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2l) = ap(c_2Efcp_2Edimindex(A_27d),c_2Ebool_2Ethe__value(A_27d))
& ap(c_2Efcp_2Edimindex(ty_2Esum_2Esum(A_27b,A_27c)),c_2Ebool_2Ethe__value(ty_2Esum_2Esum(A_27b,A_27c))) != ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) )
=> ap(ap(c_2Ewords_2Eword__concat(A_27b,A_27c,A_27d),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),ap(ap(c_2Earithmetic_2E_2B,V1m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3w)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27c),V1m),V2l),V3w)) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27d),V0h),V2l),V3w) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EEXTRACT__CONCAT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27b))
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a)))
& p(ap(c_2Epred__set_2EFINITE(A_27b),c_2Epred__set_2EUNIV(A_27b)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))),ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c)))) )
=> ( ap(ap(ap(c_2Ewords_2Eword__extract(A_27c,A_27b),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),ap(ap(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27c),V0v),V1w)) = V1w
& ap(ap(ap(c_2Ewords_2Eword__extract(A_27c,A_27a),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(ap(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27c),V0v),V1w)) = V0v ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EEXTRACT__JOIN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2m_27] :
( mem(V2m_27,ty_2Enum_2Enum)
=> ! [V3l] :
( mem(V3l,ty_2Enum_2Enum)
=> ! [V4s] :
( mem(V4s,ty_2Enum_2Enum)
=> ! [V5w] :
( mem(V5w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V3l),V1m))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m_27),V0h))
& V2m_27 = ap(ap(c_2Earithmetic_2E_2B,V1m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))
& V4s = ap(ap(c_2Earithmetic_2E_2D,V2m_27),V3l) )
=> ap(ap(c_2Ewords_2Eword__or(A_27b),ap(ap(c_2Ewords_2Eword__lsl(A_27b),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V2m_27),V5w)),V4s)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V1m),V3l),V5w)) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2EMIN,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V3l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),V3l),V5w) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EEXTRACT__JOIN__ADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2m_27] :
( mem(V2m_27,ty_2Enum_2Enum)
=> ! [V3l] :
( mem(V3l,ty_2Enum_2Enum)
=> ! [V4s] :
( mem(V4s,ty_2Enum_2Enum)
=> ! [V5w] :
( mem(V5w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V3l),V1m))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m_27),V0h))
& V2m_27 = ap(ap(c_2Earithmetic_2E_2B,V1m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))
& V4s = ap(ap(c_2Earithmetic_2E_2D,V2m_27),V3l) )
=> ap(ap(c_2Ewords_2Eword__add(A_27b),ap(ap(c_2Ewords_2Eword__lsl(A_27b),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V2m_27),V5w)),V4s)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V1m),V3l),V5w)) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),ap(ap(c_2Earithmetic_2EMIN,V0h),ap(ap(c_2Earithmetic_2EMIN,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V3l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),V3l),V5w) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EEXTEND__EXTRACT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0h),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1l)
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),V2w) = ap(c_2Ewords_2Ew2w(A_27c,A_27b),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27c),V0h),V1l),V2w)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SLICE__OVER__BITWISE,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3w] :
( mem(V3w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1l),V2v)),ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1l),V3w)) = ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1l),ap(ap(c_2Ewords_2Eword__and(A_27a),V2v),V3w)) ) ) ) )
& ! [V4h] :
( mem(V4h,ty_2Enum_2Enum)
=> ! [V5l] :
( mem(V5l,ty_2Enum_2Enum)
=> ! [V6v] :
( mem(V6v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V7w] :
( mem(V7w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V4h),V5l),V6v)),ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V4h),V5l),V7w)) = ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V4h),V5l),ap(ap(c_2Ewords_2Eword__or(A_27a),V6v),V7w)) ) ) ) )
& ! [V8h] :
( mem(V8h,ty_2Enum_2Enum)
=> ! [V9l] :
( mem(V9l,ty_2Enum_2Enum)
=> ! [V10v] :
( mem(V10v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V11w] :
( mem(V11w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V8h),V9l),V10v)),ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V8h),V9l),V11w)) = ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V8h),V9l),ap(ap(c_2Ewords_2Eword__xor(A_27a),V10v),V11w)) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__BITS__OVER__BITWISE,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3w] :
( mem(V3w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V2v)),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),V3w)) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),ap(ap(c_2Ewords_2Eword__and(A_27a),V2v),V3w)) ) ) ) )
& ! [V4h] :
( mem(V4h,ty_2Enum_2Enum)
=> ! [V5l] :
( mem(V5l,ty_2Enum_2Enum)
=> ! [V6v] :
( mem(V6v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V7w] :
( mem(V7w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V4h),V5l),V6v)),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V4h),V5l),V7w)) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V4h),V5l),ap(ap(c_2Ewords_2Eword__or(A_27a),V6v),V7w)) ) ) ) )
& ! [V8h] :
( mem(V8h,ty_2Enum_2Enum)
=> ! [V9l] :
( mem(V9l,ty_2Enum_2Enum)
=> ! [V10v] :
( mem(V10v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V11w] :
( mem(V11w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V8h),V9l),V10v)),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V8h),V9l),V11w)) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V8h),V9l),ap(ap(c_2Ewords_2Eword__xor(A_27a),V10v),V11w)) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__w2w__OVER__BITWISE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0v)),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V1w)) = ap(c_2Ewords_2Ew2w(A_27a,A_27b),ap(ap(c_2Ewords_2Eword__and(A_27a),V0v),V1w)) ) )
& ! [V2v] :
( mem(V2v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3w] :
( mem(V3w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V2v)),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V3w)) = ap(c_2Ewords_2Ew2w(A_27a,A_27b),ap(ap(c_2Ewords_2Eword__or(A_27a),V2v),V3w)) ) )
& ! [V4v] :
( mem(V4v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V5w] :
( mem(V5w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xor(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V4v)),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V5w)) = ap(c_2Ewords_2Ew2w(A_27a,A_27b),ap(ap(c_2Ewords_2Eword__xor(A_27a),V4v),V5w)) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__BITWISE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ( ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3w] :
( mem(V3w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__and(A_27b),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),V2v)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),V3w)) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),ap(ap(c_2Ewords_2Eword__and(A_27a),V2v),V3w)) ) ) ) )
& ! [V4h] :
( mem(V4h,ty_2Enum_2Enum)
=> ! [V5l] :
( mem(V5l,ty_2Enum_2Enum)
=> ! [V6v] :
( mem(V6v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V7w] :
( mem(V7w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__or(A_27c),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27c),V4h),V5l),V6v)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27c),V4h),V5l),V7w)) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27c),V4h),V5l),ap(ap(c_2Ewords_2Eword__or(A_27a),V6v),V7w)) ) ) ) )
& ! [V8h] :
( mem(V8h,ty_2Enum_2Enum)
=> ! [V9l] :
( mem(V9l,ty_2Enum_2Enum)
=> ! [V10v] :
( mem(V10v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V11w] :
( mem(V11w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__xor(A_27d),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27d),V8h),V9l),V10v)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27d),V8h),V9l),V11w)) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27d),V8h),V9l),ap(ap(c_2Ewords_2Eword__xor(A_27a),V10v),V11w)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__w2w__OVER__ADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ew2w(A_27a,A_27b),ap(ap(c_2Ewords_2Eword__add(A_27a),V0a),V1b)) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27b),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),ap(ap(c_2Ewords_2Eword__add(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0a)),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V1b))) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__w2w__OVER__MUL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ew2w(A_27a,A_27b),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0a),V1b)) = ap(ap(ap(c_2Ewords_2Eword__bits(A_27b),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),ap(ap(c_2Ewords_2Eword__mul(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0a)),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V1b))) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__ADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2h] :
( mem(V2h,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2h))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) )
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),ap(ap(c_2Ewords_2Eword__add(A_27a),V0a),V1b)) = ap(ap(c_2Ewords_2Eword__add(A_27b),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),V0a)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),V1b)) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__MUL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2h] :
( mem(V2h,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2h))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) )
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0a),V1b)) = ap(ap(c_2Ewords_2Eword__mul(A_27b),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),V0a)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),V1b)) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__ADD2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2h] :
( mem(V2h,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2h),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27b,A_27b),V2h),c_2Enum_2E0),ap(ap(c_2Ewords_2Eword__add(A_27b),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),V0a)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),V1b))) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),ap(ap(c_2Ewords_2Eword__add(A_27a),V0a),V1b)) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__MUL2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2h] :
( mem(V2h,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2h),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27b,A_27b),V2h),c_2Enum_2E0),ap(ap(c_2Ewords_2Eword__mul(A_27b),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),V0a)),ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),V1b))) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V2h),c_2Enum_2E0),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0a),V1b)) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EXTRACT__ID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2Ew2n(A_27a),V0w)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V1h))))
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27a),V1h),c_2Enum_2E0),V0w) = V0w ) ) ) ) ).
fof(conj_thm_2Ewords_2EBIT__SET,axiom,
! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebit_2EBIT,V0i),V1n))
<=> p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0i),ap(ap(c_2Ewords_2EBIT__SET,c_2Enum_2E0),V1n))) ) ) ) ).
fof(lameq_f2225,axiom,
! [V4a] :
( mem(V4a,bool)
=> ! [V5b] : ap(f2225(V4a),V5b) = ap(ap(c_2Ebool_2E_2F_5C,V4a),ap(c_2Ebool_2E_7E,V5b)) ) ).
fof(lameq_f2226,axiom,
! [V4a] : ap(f2226,V4a) = f2225(V4a) ).
fof(lameq_f2227,axiom,
! [V8a] :
( mem(V8a,bool)
=> ! [V9b] : ap(f2227(V8a),V9b) = ap(ap(c_2Ebool_2E_2F_5C,V8a),ap(c_2Ebool_2E_7E,V9b)) ) ).
fof(lameq_f2228,axiom,
! [V8a] : ap(f2228,V8a) = f2227(V8a) ).
fof(conj_thm_2Ewords_2EWORD__LITERAL__AND,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),V1m)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMIN,ap(c_2Ebit_2ELOG2,V0n)),ap(c_2Ebit_2ELOG2,V1m)))),c_2Ebool_2E_2F_5C),V0n),V1m)) ) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(c_2Ewords_2En2w(A_27a),V2n)),ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V3m))) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,ap(c_2Ebit_2ELOG2,V2n))),f2226),V2n),V3m)) ) )
& ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V7m] :
( mem(V7m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V7m))),ap(c_2Ewords_2En2w(A_27a),V6n)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,ap(c_2Ebit_2ELOG2,V6n))),f2228),V6n),V7m)) ) )
& ! [V10n] :
( mem(V10n,ty_2Enum_2Enum)
=> ! [V11m] :
( mem(V11m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V10n))),ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V11m))) = ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMAX,ap(c_2Ebit_2ELOG2,V10n)),ap(c_2Ebit_2ELOG2,V11m)))),c_2Ebool_2E_5C_2F),V10n),V11m))) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LITERAL__OR,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),V1m)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMAX,ap(c_2Ebit_2ELOG2,V0n)),ap(c_2Ebit_2ELOG2,V1m)))),c_2Ebool_2E_5C_2F),V0n),V1m)) ) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(c_2Ewords_2En2w(A_27a),V2n)),ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V3m))) = ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,ap(c_2Ebit_2ELOG2,V3m))),f2226),V3m),V2n))) ) )
& ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V7m] :
( mem(V7m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V7m))),ap(c_2Ewords_2En2w(A_27a),V6n)) = ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,ap(c_2Ebit_2ELOG2,V7m))),f2228),V7m),V6n))) ) )
& ! [V10n] :
( mem(V10n,ty_2Enum_2Enum)
=> ! [V11m] :
( mem(V11m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V10n))),ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V11m))) = ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMIN,ap(c_2Ebit_2ELOG2,V10n)),ap(c_2Ebit_2ELOG2,V11m)))),c_2Ebool_2E_2F_5C),V10n),V11m))) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LITERAL__XOR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),V1m)) = ap(c_2Ewords_2En2w(A_27a),ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMAX,ap(c_2Ebit_2ELOG2,V0n)),ap(c_2Ebit_2ELOG2,V1m)))),f2217),V0n),V1m)) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__replicate__concat__word__list,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__replicate(A_27a,A_27b),V0n),V1w) = ap(c_2Ewords_2Econcat__word__list(A_27a,A_27b),ap(ap(c_2Elist_2EGENLIST(ty_2Efcp_2Ecart(bool,A_27a)),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27a),ty_2Enum_2Enum),V1w)),V0n)) ) ) ) ) ).
fof(lameq_f2229,axiom,
! [A_27a,A_27b,V2a] :
( mem(V2a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V3b] :
( mem(V3b,ty_2Efcp_2Ecart(bool,A_27b))
=> ! [V4mask] : ap(f2229(A_27a,A_27b,V2a,V1l,V3b),V4mask) = ap(ap(c_2Ewords_2Eword__or(A_27b),ap(ap(c_2Ewords_2Eword__and(A_27b),ap(ap(c_2Ewords_2Eword__lsl(A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V2a)),V1l)),V4mask)),ap(ap(c_2Ewords_2Eword__and(A_27b),V3b),ap(c_2Ewords_2Eword__1comp(A_27b),V4mask))) ) ) ) ).
fof(conj_thm_2Ewords_2Ebit__field__insert,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3b] :
( mem(V3b,ty_2Efcp_2Ecart(bool,A_27b))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0h),ap(ap(c_2Earithmetic_2E_2B,V1l),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))))
=> ap(ap(ap(ap(c_2Ewords_2Ebit__field__insert(A_27b,A_27a),V0h),V1l),V2a),V3b) = ap(ap(c_2Ebool_2ELET(ty_2Efcp_2Ecart(bool,A_27b),ty_2Efcp_2Ecart(bool,A_27b)),f2229(A_27a,A_27b,V2a,V1l,V3b)),ap(ap(ap(c_2Ewords_2Eword__slice(A_27b),V0h),V1l),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2Eword__join__index,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2b] :
( mem(V2b,ty_2Efcp_2Ecart(bool,A_27b))
=> ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a)))
& p(ap(c_2Epred__set_2EFINITE(A_27b),c_2Epred__set_2EUNIV(A_27b)))
& p(ap(ap(c_2Eprim__rec_2E_3C,V0i),ap(c_2Efcp_2Edimindex(ty_2Esum_2Esum(A_27a,A_27b)),c_2Ebool_2Ethe__value(ty_2Esum_2Esum(A_27a,A_27b))))) )
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,ty_2Esum_2Esum(A_27a,A_27b)),ap(ap(c_2Ewords_2Eword__join(A_27a,A_27b),V1a),V2b)),V0i))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Eprim__rec_2E_3C,V0i),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27b),V2b),V0i)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1a),ap(ap(c_2Earithmetic_2E_2D,V0i),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))))) ) ) ) ) ) ) ) ).
fof(lameq_f2230,axiom,
! [V1l] : ap(f2230,V1l) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),c_2Ewords_2Eword__and(ty_2Eone_2Eone)),ap(c_2Elist_2EHD(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)),ap(c_2Elist_2ETL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)) ).
fof(lameq_f2231,axiom,
! [A_27a,V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3n] : ap(f2231(A_27a,V0w),V3n) = ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,ty_2Eone_2Eone),V3n),V3n),V0w) ) ).
fof(lameq_f2232,axiom,
! [A_27a,V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i] : ap(f2232(A_27a,V0w),V2i) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2231(A_27a,V0w)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2i)) ) ).
fof(conj_thm_2Ewords_2Efoldl__reduce__and,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ereduce__and(A_27a),V0w) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2230),ap(ap(c_2Elist_2EGENLIST(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2232(A_27a,V0w)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(lameq_f2233,axiom,
! [V1l] : ap(f2233,V1l) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),c_2Ewords_2Eword__or(ty_2Eone_2Eone)),ap(c_2Elist_2EHD(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)),ap(c_2Elist_2ETL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)) ).
fof(conj_thm_2Ewords_2Efoldl__reduce__or,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ereduce__or(A_27a),V0w) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2233),ap(ap(c_2Elist_2EGENLIST(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2232(A_27a,V0w)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(lameq_f2234,axiom,
! [V1l] : ap(f2234,V1l) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),c_2Ewords_2Eword__xor(ty_2Eone_2Eone)),ap(c_2Elist_2EHD(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)),ap(c_2Elist_2ETL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)) ).
fof(conj_thm_2Ewords_2Efoldl__reduce__xor,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ereduce__xor(A_27a),V0w) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2234),ap(ap(c_2Elist_2EGENLIST(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2232(A_27a,V0w)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(lameq_f2235,axiom,
! [V1l] : ap(f2235,V1l) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),c_2Ewords_2Eword__nand(ty_2Eone_2Eone)),ap(c_2Elist_2EHD(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)),ap(c_2Elist_2ETL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)) ).
fof(conj_thm_2Ewords_2Efoldl__reduce__nand,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ereduce__nand(A_27a),V0w) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2235),ap(ap(c_2Elist_2EGENLIST(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2232(A_27a,V0w)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(lameq_f2236,axiom,
! [V1l] : ap(f2236,V1l) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),c_2Ewords_2Eword__nor(ty_2Eone_2Eone)),ap(c_2Elist_2EHD(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)),ap(c_2Elist_2ETL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)) ).
fof(conj_thm_2Ewords_2Efoldl__reduce__nor,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ereduce__nor(A_27a),V0w) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2236),ap(ap(c_2Elist_2EGENLIST(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2232(A_27a,V0w)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(lameq_f2237,axiom,
! [V1l] : ap(f2237,V1l) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),c_2Ewords_2Eword__xnor(ty_2Eone_2Eone)),ap(c_2Elist_2EHD(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)),ap(c_2Elist_2ETL(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V1l)) ).
fof(conj_thm_2Ewords_2Efoldl__reduce__xnor,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ereduce__xnor(A_27a),V0w) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2237),ap(ap(c_2Elist_2EGENLIST(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2232(A_27a,V0w)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ).
fof(conj_thm_2Ewords_2ELOG2__w2n__lt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( V0w != ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ebit_2ELOG2,ap(c_2Ewords_2Ew2n(A_27a),V0w))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ).
fof(conj_thm_2Ewords_2ELOG2__w2n,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( V0w != ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
=> ap(c_2Ebit_2ELOG2,ap(c_2Ewords_2Ew2n(A_27a),V0w)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Ewhile_2ELEAST,f2182(A_27a,V0w))) ) ) ) ).
fof(lameq_f2238,axiom,
! [A_27a,V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1i] : ap(f2238(A_27a,V0w),V1i) = ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1i) ) ).
fof(conj_thm_2Ewords_2ELEAST__BIT__LT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( V0w != ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewhile_2ELEAST,f2238(A_27a,V0w))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ).
fof(lameq_f2239,axiom,
! [V1f] :
( mem(V1f,arr(bool,arr(bool,bool)))
=> ! [V2l] : ap(f2239(V1f),V2l) = ap(ap(ap(c_2Elist_2EFOLDL(bool,bool),V1f),ap(c_2Elist_2EHD(bool),V2l)),ap(c_2Elist_2ETL(bool),V2l)) ) ).
fof(conj_thm_2Ewords_2Eword__reduce__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(bool,arr(bool,bool)))
=> ap(ap(c_2Ewords_2Eword__reduce(A_27a),V1f),ap(c_2Ewords_2En2w(A_27a),V0n)) = ap(c_2Efcp_2EFCP(bool,ty_2Eone_2Eone),ap(c_2Ecombin_2EK(bool,ty_2Enum_2Enum),ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(bool),bool),f2239(V1f)),ap(ap(ap(c_2Enumposrep_2EBOOLIFY,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0n),c_2Elist_2ENIL(bool))))) ) ) ) ).
fof(conj_thm_2Ewords_2ENOT__UINTMAXw,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( V0w != c_2Ewords_2Eword__T(A_27a)
=> ? [V1i] :
( mem(V1i,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
& ~ p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1i)) ) ) ) ) ).
fof(conj_thm_2Ewords_2ENOT__0w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( V0w != ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
=> ? [V1i] :
( mem(V1i,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
& p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1i)) ) ) ) ) ).
fof(conj_thm_2Ewords_2Ereduce__and,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ereduce__and(A_27a),V0w) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),V0w),c_2Ewords_2Eword__T(A_27a))),ap(c_2Ewords_2En2w(ty_2Eone_2Eone),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Ewords_2En2w(ty_2Eone_2Eone),c_2Enum_2E0)) ) ) ).
fof(conj_thm_2Ewords_2Ereduce__or,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Ereduce__or(A_27a),V0w) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),V0w),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0))),ap(c_2Ewords_2En2w(ty_2Eone_2Eone),c_2Enum_2E0)),ap(c_2Ewords_2En2w(ty_2Eone_2Eone),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V0w),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = V0w )
& ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),V1w) = V1w ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__ASSOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),ap(ap(c_2Ewords_2Eword__add(A_27a),V1w),V2x)) = ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w)),V2x) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__MULT__ASSOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),ap(ap(c_2Ewords_2Eword__mul(A_27a),V1w),V2x)) = ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V1w)),V2x) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__COMM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a),V1w),V0v) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__MULT__COMM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V1w) = ap(ap(c_2Ewords_2Eword__mul(A_27a),V1w),V0v) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__MULT__CLAUSES,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),V0v) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
& ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
& ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0v) = V0v
& ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0v
& ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V1w)),V1w)
& ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),ap(ap(c_2Ewords_2Eword__add(A_27a),V1w),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V1w)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LEFT__ADD__DISTRIB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),ap(ap(c_2Ewords_2Eword__add(A_27a),V1w),V2x)) = ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V1w)),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V2x)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__RIGHT__ADD__DISTRIB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w)),V2x) = ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V2x)),ap(ap(c_2Ewords_2Eword__mul(A_27a),V1w),V2x)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__SUB__ASSOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w)),V2x) = ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),ap(ap(c_2Ewords_2Eword__sub(A_27a),V1w),V2x)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__SUB__SYM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w)),V2x) = ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V2x)),V1w) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__LINV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0w)),V0w) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__RINV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V0w),ap(c_2Ewords_2Eword__2comp(A_27a),V0w)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__REFL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V0w),V0w) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__ADD2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),ap(ap(c_2Ewords_2Eword__sub(A_27a),V1w),V0v)) = V1w ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__SUB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w)),V1w) = V0v ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__ADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w)),V1w) = V0v ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__EQ__SUB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w) = V2x
<=> V0v = ap(ap(c_2Ewords_2Eword__sub(A_27a),V2x),V1w) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__INV__0__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w) = V0v
<=> V1w = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EQ__ADD__LCANCEL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V2x)
<=> V1w = V2x ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EQ__ADD__RCANCEL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a),V2x),V1w)
<=> V0v = V2x ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__2comp(A_27a),V0w) = ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2Eword__1comp(A_27a),V0w)),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NOT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__1comp(A_27a),V0w) = ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0w)),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__ADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w)) = ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0v)),ap(c_2Ewords_2Eword__2comp(A_27a),V1w)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__NEG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0w)) = V0w ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__LNEG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0v)),V1w) = ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__RNEG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),ap(c_2Ewords_2Eword__2comp(A_27a),V1w)) = ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__SUB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),ap(ap(c_2Ewords_2Eword__sub(A_27a),V1w),V2x)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V2x)),V1w) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__SUB2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w)) = V1w ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EQ__SUB__LADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ( V0v = ap(ap(c_2Ewords_2Eword__sub(A_27a),V1w),V2x)
<=> ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V2x) = V1w ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EQ__SUB__RADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w) = V2x
<=> V0v = ap(ap(c_2Ewords_2Eword__add(A_27a),V2x),V1w) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EQ__SUB__ZERO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1v] :
( mem(V1v,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__sub(A_27a),V1v),V0w) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
<=> V1v = V0w ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LCANCEL__SUB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V2x),V1w)
<=> V0v = V2x ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__RCANCEL__SUB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V2x)
<=> V1w = V2x ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__PLUS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),ap(ap(c_2Ewords_2Eword__add(A_27a),V1w),V2x)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w)),V2x) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__LZERO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),V0w) = ap(c_2Ewords_2Eword__2comp(A_27a),V0w) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__RZERO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V0w),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = V0w ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__LID__UNIQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w) = V1w
<=> V0v = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__RID__UNIQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1w) = V0v
<=> V1w = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUM__ZERO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__add(A_27a),V0a),V1b) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
<=> V0a = ap(c_2Ewords_2Eword__2comp(A_27a),V1b) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__SUB2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V1w),V0v)),V1w) = V0v ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__SUB3,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1x] :
( mem(V1x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),V1x)) = ap(c_2Ewords_2Eword__2comp(A_27a),V1x) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__SUB3,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1v] :
( mem(V1v,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__sub(A_27a),V1v),V0w)),V1v) = ap(c_2Ewords_2Eword__2comp(A_27a),V0w) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__EQ__NEG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(c_2Ewords_2Eword__2comp(A_27a),V0v) = ap(c_2Ewords_2Eword__2comp(A_27a),V1w)
<=> V0v = V1w ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1v] :
( mem(V1v,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(c_2Ewords_2Eword__2comp(A_27a),V1v) = V0w
<=> V1v = ap(c_2Ewords_2Eword__2comp(A_27a),V0w) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__EQ__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(c_2Ewords_2Eword__2comp(A_27a),V0v) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)
<=> V0v = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V1w)),V0v) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__NEG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0v)),ap(c_2Ewords_2Eword__2comp(A_27a),V1w)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V1w),V0v) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__SUB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1v] :
( mem(V1v,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__sub(A_27a),V1v),V0w)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V0w),V1v) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__TRIANGLE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w)),ap(ap(c_2Ewords_2Eword__sub(A_27a),V1w),V2x)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V2x) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NOT__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = c_2Ewords_2Eword__T(A_27a) ) ).
fof(conj_thm_2Ewords_2EWORD__NOT__T,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Eword__1comp(A_27a),c_2Ewords_2Eword__T(A_27a)) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__T,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Ewords_2Eword__2comp(A_27a),c_2Ewords_2Eword__T(A_27a)) = ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Ewords_2EWORD__MULT__SUC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2B,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),ap(c_2Ewords_2En2w(A_27a),V1n))),V0v) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__LMUL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V1w)) = ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V0v)),V1w) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__RMUL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V1w)) = ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),ap(c_2Ewords_2Eword__2comp(A_27a),V1w)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__NEG__MUL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__2comp(A_27a),V0w) = ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0w) ) ) ).
fof(conj_thm_2Ewords_2Esw2sw__w2w__add,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Esw2sw(A_27a,A_27b),V0w) = ap(ap(c_2Ewords_2Eword__add(A_27b),ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27b)),ap(c_2Ewords_2Eword__msb(A_27a),V0w)),ap(ap(c_2Ewords_2Eword__lsl(A_27b),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0))),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__BIT0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V0a),V1b)),c_2Enum_2E0))
<=> ~ ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0a),c_2Enum_2E0))
<=> p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1b),c_2Enum_2E0)) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__ADD__BIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2b] :
( mem(V2b,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),V1a),V2b)),V0n))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0n),c_2Enum_2E0)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1a),c_2Enum_2E0)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V2b),c_2Enum_2E0)))),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),V2b))),V0n)),ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1a),V0n)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V2b),V0n))),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1a),V0n)),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V2b),V0n)))))) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LEFT__SUB__DISTRIB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),ap(ap(c_2Ewords_2Eword__sub(A_27a),V1w),V2x)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V1w)),ap(ap(c_2Ewords_2Eword__mul(A_27a),V0v),V2x)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__RIGHT__SUB__DISTRIB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(ap(c_2Ewords_2Eword__sub(A_27a),V1w),V2x)),V0v) = ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V1w),V0v)),ap(ap(c_2Ewords_2Eword__mul(A_27a),V2x),V0v)) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LITERAL__MULT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2En2w(A_27a),V0m)),ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V1n))) = ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))) ) )
& ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__mul(A_27b),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),V2m))),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),V3n))) = ap(c_2Ewords_2En2w(A_27b),ap(ap(c_2Earithmetic_2E_2A,V2m),V3n)) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V0m))),ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V1n))) = ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) ) )
& ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__add(A_27b),ap(c_2Ewords_2En2w(A_27b),V2m)),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),V3n))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27b)),ap(ap(c_2Earithmetic_2E_3C_3D,V3n),V2m)),ap(c_2Ewords_2En2w(A_27b),ap(ap(c_2Earithmetic_2E_2D,V2m),V3n))),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),ap(ap(c_2Earithmetic_2E_2D,V3n),V2m)))) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__SUB__INTRO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0x] :
( mem(V0x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1y] :
( mem(V1y,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V1y)),V0x) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V0x),V1y) ) )
& ! [V2x] :
( mem(V2x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3y] :
( mem(V3y,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V2x),ap(c_2Ewords_2Eword__2comp(A_27a),V3y)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V2x),V3y) ) )
& ! [V4x] :
( mem(V4x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V5y] :
( mem(V5y,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V6z] :
( mem(V6z,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V4x)),V5y)),V6z) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V6z),ap(ap(c_2Ewords_2Eword__mul(A_27a),V4x),V5y)) ) ) )
& ! [V7x] :
( mem(V7x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V8y] :
( mem(V8y,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V9z] :
( mem(V9z,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__add(A_27a),V9z),ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V7x)),V8y)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),V9z),ap(ap(c_2Ewords_2Eword__mul(A_27a),V7x),V8y)) ) ) )
& ! [V10x] :
( mem(V10x,ty_2Efcp_2Ecart(bool,A_27b))
=> ap(ap(c_2Ewords_2Eword__mul(A_27b),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V10x) = ap(c_2Ewords_2Eword__2comp(A_27b),V10x) )
& ! [V11x] :
( mem(V11x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V12y] :
( mem(V12y,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V13z] :
( mem(V13z,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V13z),ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V11x)),V12y)) = ap(ap(c_2Ewords_2Eword__add(A_27a),V13z),ap(ap(c_2Ewords_2Eword__mul(A_27a),V11x),V12y)) ) ) )
& ! [V14x] :
( mem(V14x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V15y] :
( mem(V15y,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V16z] :
( mem(V16z,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),V14x)),V15y)),V16z) = ap(c_2Ewords_2Eword__2comp(A_27a),ap(ap(c_2Ewords_2Eword__add(A_27a),ap(ap(c_2Ewords_2Eword__mul(A_27a),V14x),V15y)),V16z)) ) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2En2w__SUC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ewords_2En2w(A_27a),ap(c_2Enum_2ESUC,V0n)) = ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ) ).
fof(conj_thm_2Ewords_2En2w__sub,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a))
=> ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(c_2Ewords_2En2w(A_27a),V0a)),ap(c_2Ewords_2En2w(A_27a),V1b)) ) ) ) ) ).
%------------------------------------------------------------------------------