ITP001 Axioms: ITP094+5.ax
%------------------------------------------------------------------------------
% File : ITP094+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, 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 : bitstring+2.ax [Gau20]
% : HL4094+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 167 ( 43 unt; 0 def)
% Number of atoms : 741 ( 165 equ)
% Maximal formula atoms : 127 ( 4 avg)
% Number of connectives : 576 ( 2 ~; 0 |; 70 &)
% ( 35 <=>; 469 =>; 0 <=; 0 <~>)
% Maximal formula depth : 67 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 165 ( 165 usr; 64 con; 0-3 aty)
% Number of variables : 472 ( 470 !; 2 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Ebitstring_2Eadd,axiom,
mem(c_2Ebitstring_2Eadd,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Eband,axiom,
mem(c_2Ebitstring_2Eband,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Ebitify,axiom,
mem(c_2Ebitstring_2Ebitify,arr(ty_2Elist_2Elist(ty_2Enum_2Enum),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(ty_2Enum_2Enum)))) ).
fof(mem_c_2Ebitstring_2Ebitwise,axiom,
mem(c_2Ebitstring_2Ebitwise,arr(arr(bool,arr(bool,bool)),arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool))))) ).
fof(mem_c_2Ebitstring_2Ebnand,axiom,
mem(c_2Ebitstring_2Ebnand,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Ebnor,axiom,
mem(c_2Ebitstring_2Ebnor,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Ebnot,axiom,
mem(c_2Ebitstring_2Ebnot,arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool))) ).
fof(mem_c_2Ebitstring_2Eboolify,axiom,
mem(c_2Ebitstring_2Eboolify,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Ebor,axiom,
mem(c_2Ebitstring_2Ebor,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Ebxnor,axiom,
mem(c_2Ebitstring_2Ebxnor,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Ebxor,axiom,
mem(c_2Ebitstring_2Ebxor,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Eextend,axiom,
mem(c_2Ebitstring_2Eextend,arr(bool,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool))))) ).
fof(mem_c_2Ebitstring_2Efield,axiom,
mem(c_2Ebitstring_2Efield,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool))))) ).
fof(mem_c_2Ebitstring_2Efield__insert,axiom,
mem(c_2Ebitstring_2Efield__insert,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(bool),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))))) ).
fof(mem_c_2Ebitstring_2Efixwidth,axiom,
mem(c_2Ebitstring_2Efixwidth,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Emodify,axiom,
mem(c_2Ebitstring_2Emodify,arr(arr(ty_2Enum_2Enum,arr(bool,bool)),arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2En2v,axiom,
mem(c_2Ebitstring_2En2v,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(bool))) ).
fof(mem_c_2Ebitstring_2Ereplicate,axiom,
mem(c_2Ebitstring_2Ereplicate,arr(ty_2Elist_2Elist(bool),arr(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Erev__count__list,axiom,
mem(c_2Ebitstring_2Erev__count__list,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Enum_2Enum))) ).
fof(mem_c_2Ebitstring_2Erotate,axiom,
mem(c_2Ebitstring_2Erotate,arr(ty_2Elist_2Elist(bool),arr(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Es2v,axiom,
mem(c_2Ebitstring_2Es2v,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(bool))) ).
fof(mem_c_2Ebitstring_2Eshiftl,axiom,
mem(c_2Ebitstring_2Eshiftl,arr(ty_2Elist_2Elist(bool),arr(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Eshiftr,axiom,
mem(c_2Ebitstring_2Eshiftr,arr(ty_2Elist_2Elist(bool),arr(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Esign__extend,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebitstring_2Esign__extend(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Ebitstring_2Etestbit,axiom,
mem(c_2Ebitstring_2Etestbit,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(bool),bool))) ).
fof(mem_c_2Ebitstring_2Ev2n,axiom,
mem(c_2Ebitstring_2Ev2n,arr(ty_2Elist_2Elist(bool),ty_2Enum_2Enum)) ).
fof(mem_c_2Ebitstring_2Ev2s,axiom,
mem(c_2Ebitstring_2Ev2s,arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(mem_c_2Ebitstring_2Ev2w,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebitstring_2Ev2w(A_27a),arr(ty_2Elist_2Elist(bool),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ebitstring_2Ew2v,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebitstring_2Ew2v(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Elist_2Elist(bool))) ) ).
fof(mem_c_2Ebitstring_2Ezero__extend,axiom,
mem(c_2Ebitstring_2Ezero__extend,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(ax_thm_2Ebitstring_2Eextend__def,axiom,
( ! [V0v0] :
( mem(V0v0,bool)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Eextend,V0v0),c_2Enum_2E0),V1l) = V1l ) )
& ! [V2c] :
( mem(V2c,bool)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Eextend,V2c),ap(c_2Enum_2ESUC,V3n)),V4l) = ap(ap(ap(c_2Ebitstring_2Eextend,V2c),V3n),ap(ap(c_2Elist_2ECONS(bool),V2c),V4l)) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eextend__def__compute,axiom,
( ! [V0v0] :
( mem(V0v0,bool)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Eextend,V0v0),c_2Enum_2E0),V1l) = V1l ) )
& ! [V2c] :
( mem(V2c,bool)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Eextend,V2c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),V4l) = ap(ap(ap(c_2Ebitstring_2Eextend,V2c),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Elist_2ECONS(bool),V2c),V4l)) ) ) )
& ! [V5c] :
( mem(V5c,bool)
=> ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Eextend,V5c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6n))),V7l) = ap(ap(ap(c_2Ebitstring_2Eextend,V5c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(ap(c_2Elist_2ECONS(bool),V5c),V7l)) ) ) ) ) ).
fof(ax_thm_2Ebitstring_2Eboolify__def,axiom,
( ! [V0a] :
( mem(V0a,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Eboolify,V0a),c_2Elist_2ENIL(ty_2Enum_2Enum)) = V0a )
& ! [V1a] :
( mem(V1a,ty_2Elist_2Elist(bool))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(ap(c_2Ebitstring_2Eboolify,V1a),ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V2n),V3l)) = ap(ap(c_2Ebitstring_2Eboolify,ap(ap(c_2Elist_2ECONS(bool),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0))),V1a)),V3l) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Ebitify__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(ty_2Enum_2Enum),arr(ty_2Elist_2Elist(bool),bool)))
=> ( ( ! [V1a] :
( mem(V1a,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> p(ap(ap(V0P,V1a),c_2Elist_2ENIL(bool))) )
& ! [V2a] :
( mem(V2a,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(V0P,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),c_2Enum_2E0),V2a)),V3l))
=> p(ap(ap(V0P,V2a),ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2EF),V3l))) ) ) )
& ! [V4a] :
( mem(V4a,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(V0P,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V4a)),V5l))
=> p(ap(ap(V0P,V4a),ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2ET),V5l))) ) ) ) )
=> ! [V6v] :
( mem(V6v,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V7v1] :
( mem(V7v1,ty_2Elist_2Elist(bool))
=> p(ap(ap(V0P,V6v),V7v1)) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Ebitify__def,axiom,
( ! [V0a] :
( mem(V0a,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(ap(c_2Ebitstring_2Ebitify,V0a),c_2Elist_2ENIL(bool)) = V0a )
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(bool))
=> ! [V2a] :
( mem(V2a,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(ap(c_2Ebitstring_2Ebitify,V2a),ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2EF),V1l)) = ap(ap(c_2Ebitstring_2Ebitify,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),c_2Enum_2E0),V2a)),V1l) ) )
& ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(bool))
=> ! [V4a] :
( mem(V4a,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(ap(c_2Ebitstring_2Ebitify,V4a),ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2ET),V3l)) = ap(ap(c_2Ebitstring_2Ebitify,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V4a)),V3l) ) ) ) ).
fof(ax_thm_2Ebitstring_2En2v__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ebitstring_2En2v,V0n) = ap(ap(c_2Ebitstring_2Eboolify,c_2Elist_2ENIL(bool)),ap(c_2Enumposrep_2Enum__to__bin__list,V0n)) ) ).
fof(ax_thm_2Ebitstring_2Ev2n__def,axiom,
! [V0l] :
( mem(V0l,ty_2Elist_2Elist(bool))
=> ap(c_2Ebitstring_2Ev2n,V0l) = ap(c_2Enumposrep_2Enum__from__bin__list,ap(ap(c_2Ebitstring_2Ebitify,c_2Elist_2ENIL(ty_2Enum_2Enum)),V0l)) ) ).
fof(lameq_f2288,axiom,
! [V0c] : ap(f2288,V0c) = ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Estring_2Echar),V0c),ap(c_2Estring_2ECHR,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))),ap(ap(c_2Emin_2E_3D(ty_2Estring_2Echar),V0c),ap(c_2Estring_2ECHR,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) ).
fof(ax_thm_2Ebitstring_2Es2v__def,axiom,
c_2Ebitstring_2Es2v = ap(c_2Elist_2EMAP(ty_2Estring_2Echar,bool),f2288) ).
fof(lameq_f2289,axiom,
! [V0b] : ap(f2289,V0b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Estring_2Echar),V0b),ap(c_2Estring_2ECHR,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))),ap(c_2Estring_2ECHR,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))) ).
fof(ax_thm_2Ebitstring_2Ev2s__def,axiom,
c_2Ebitstring_2Ev2s = ap(c_2Elist_2EMAP(bool,ty_2Estring_2Echar),f2289) ).
fof(ax_thm_2Ebitstring_2Ezero__extend__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Ezero__extend,V0n),V1v) = ap(ap(ap(c_2Elist_2EPAD__LEFT(bool),c_2Ebool_2EF),V0n),V1v) ) ) ).
fof(ax_thm_2Ebitstring_2Esign__extend__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Ebitstring_2Esign__extend(A_27a),V0n),V1v) = ap(ap(ap(c_2Elist_2EPAD__LEFT(A_27a),ap(c_2Elist_2EHD(A_27a),V1v)),V0n),V1v) ) ) ) ).
fof(lameq_f2290,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ! [V2l] : ap(f2290(V0n,V1v),V2l) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(bool)),ap(ap(c_2Eprim__rec_2E_3C,V2l),V0n)),ap(ap(c_2Ebitstring_2Ezero__extend,V0n),V1v)),ap(ap(c_2Elist_2EDROP(bool),ap(ap(c_2Earithmetic_2E_2D,V2l),V0n)),V1v)) ) ) ).
fof(ax_thm_2Ebitstring_2Efixwidth__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Efixwidth,V0n),V1v) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)),f2290(V0n,V1v)),ap(c_2Elist_2ELENGTH(bool),V1v)) ) ) ).
fof(ax_thm_2Ebitstring_2Eshiftl__def,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ebitstring_2Eshiftl,V0v),V1m) = ap(ap(ap(c_2Elist_2EPAD__RIGHT(bool),c_2Ebool_2EF),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(bool),V0v)),V1m)),V0v) ) ) ).
fof(ax_thm_2Ebitstring_2Eshiftr__def,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ebitstring_2Eshiftr,V0v),V1m) = ap(ap(c_2Elist_2ETAKE(bool),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(bool),V0v)),V1m)),V0v) ) ) ).
fof(ax_thm_2Ebitstring_2Efield__def,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Efield,V0h),V1l),V2v) = ap(ap(c_2Ebitstring_2Efixwidth,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)),ap(ap(c_2Ebitstring_2Eshiftr,V2v),V1l)) ) ) ) ).
fof(lameq_f2291,axiom,
! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V3x] : ap(f2291(V2l,V0v),V3x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(bool)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2l),c_2Enum_2E0)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3x),c_2Enum_2E0))),V0v),ap(ap(c_2Elist_2EAPPEND(bool),ap(ap(ap(c_2Ebitstring_2Efield,ap(ap(c_2Earithmetic_2E_2D,V3x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),V0v)),ap(ap(ap(c_2Ebitstring_2Efield,ap(ap(c_2Earithmetic_2E_2D,V2l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3x),V0v))) ) ) ).
fof(lameq_f2292,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2l] : ap(f2292(V0v,V1m),V2l) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)),f2291(V2l,V0v)),ap(ap(c_2Earithmetic_2EMOD,V1m),V2l)) ) ) ).
fof(ax_thm_2Ebitstring_2Erotate__def,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ap(ap(c_2Ebitstring_2Erotate,V0v),V1m) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)),f2292(V0v,V1m)),ap(c_2Elist_2ELENGTH(bool),V0v)) ) ) ).
fof(ax_thm_2Ebitstring_2Etestbit__def,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(c_2Ebitstring_2Etestbit,V0b),V1v))
<=> ap(ap(ap(c_2Ebitstring_2Efield,V0b),V0b),V1v) = ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2ET),c_2Elist_2ENIL(bool)) ) ) ) ).
fof(ax_thm_2Ebitstring_2Ew2v__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ebitstring_2Ew2v(A_27a),V0w) = ap(ap(c_2Elist_2EGENLIST(bool),f2182(A_27a,V0w)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ) ).
fof(lameq_f2293,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1i] : ap(f2293(V0v),V1i) = ap(ap(c_2Ebitstring_2Etestbit,V1i),V0v) ) ).
fof(ax_thm_2Ebitstring_2Ev2w__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ebitstring_2Ev2w(A_27a),V0v) = ap(c_2Efcp_2EFCP(bool,A_27a),f2293(V0v)) ) ) ).
fof(lameq_f2294,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] : ap(f2294(V0n),V1i) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1i) ) ).
fof(ax_thm_2Ebitstring_2Erev__count__list__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ebitstring_2Erev__count__list,V0n) = ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),f2294(V0n)),V0n) ) ).
fof(ax_thm_2Ebitstring_2Emodify__def,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool)))
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Emodify,V0f),V1v) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,bool),bool),ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,bool,bool),V0f)),ap(c_2Elist_2EZIP(ty_2Enum_2Enum,bool),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Elist_2Elist(bool)),ap(c_2Ebitstring_2Erev__count__list,ap(c_2Elist_2ELENGTH(bool),V1v))),V1v))) ) ) ).
fof(lameq_f2295,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2s] :
( mem(V2s,ty_2Elist_2Elist(bool))
=> ! [V3i] : ap(f2295(V0h,V1l,V2s),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_2Ebitstring_2Etestbit,ap(ap(c_2Earithmetic_2E_2D,V3i),V1l)),V2s)) ) ) ) ).
fof(ax_thm_2Ebitstring_2Efield__insert__def,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2s] :
( mem(V2s,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Efield__insert,V0h),V1l),V2s) = ap(c_2Ebitstring_2Emodify,f2295(V0h,V1l,V2s)) ) ) ) ).
fof(lameq_f2296,axiom,
! [V0a] :
( mem(V0a,ty_2Elist_2Elist(bool))
=> ! [V1b] :
( mem(V1b,ty_2Elist_2Elist(bool))
=> ! [V2m] : ap(f2296(V0a,V1b),V2m) = ap(ap(c_2Ebitstring_2Ezero__extend,V2m),ap(c_2Ebitstring_2En2v,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ebitstring_2Ev2n,V0a)),ap(c_2Ebitstring_2Ev2n,V1b)))) ) ) ).
fof(ax_thm_2Ebitstring_2Eadd__def,axiom,
! [V0a] :
( mem(V0a,ty_2Elist_2Elist(bool))
=> ! [V1b] :
( mem(V1b,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Eadd,V0a),V1b) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)),f2296(V0a,V1b)),ap(ap(c_2Earithmetic_2EMAX,ap(c_2Elist_2ELENGTH(bool),V0a)),ap(c_2Elist_2ELENGTH(bool),V1b))) ) ) ).
fof(lameq_f2297,axiom,
! [V1v1] :
( mem(V1v1,ty_2Elist_2Elist(bool))
=> ! [V2v2] :
( mem(V2v2,ty_2Elist_2Elist(bool))
=> ! [V0f] :
( mem(V0f,arr(bool,arr(bool,bool)))
=> ! [V3m] : ap(f2297(V1v1,V2v2,V0f),V3m) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(bool,bool),bool),ap(c_2Epair_2EUNCURRY(bool,bool,bool),V0f)),ap(c_2Elist_2EZIP(bool,bool),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)),ap(ap(c_2Ebitstring_2Efixwidth,V3m),V1v1)),ap(ap(c_2Ebitstring_2Efixwidth,V3m),V2v2)))) ) ) ) ).
fof(ax_thm_2Ebitstring_2Ebitwise__def,axiom,
! [V0f] :
( mem(V0f,arr(bool,arr(bool,bool)))
=> ! [V1v1] :
( mem(V1v1,ty_2Elist_2Elist(bool))
=> ! [V2v2] :
( mem(V2v2,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Ebitwise,V0f),V1v1),V2v2) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)),f2297(V1v1,V2v2,V0f)),ap(ap(c_2Earithmetic_2EMAX,ap(c_2Elist_2ELENGTH(bool),V1v1)),ap(c_2Elist_2ELENGTH(bool),V2v2))) ) ) ) ).
fof(ax_thm_2Ebitstring_2Ebnot__def,axiom,
c_2Ebitstring_2Ebnot = ap(c_2Elist_2EMAP(bool,bool),c_2Ebool_2E_7E) ).
fof(ax_thm_2Ebitstring_2Ebor__def,axiom,
c_2Ebitstring_2Ebor = ap(c_2Ebitstring_2Ebitwise,c_2Ebool_2E_5C_2F) ).
fof(ax_thm_2Ebitstring_2Eband__def,axiom,
c_2Ebitstring_2Eband = ap(c_2Ebitstring_2Ebitwise,c_2Ebool_2E_2F_5C) ).
fof(ax_thm_2Ebitstring_2Ebxor__def,axiom,
c_2Ebitstring_2Ebxor = ap(c_2Ebitstring_2Ebitwise,f2171) ).
fof(lameq_f2298,axiom,
! [V0x] :
( mem(V0x,bool)
=> ! [V1y] : ap(f2298(V0x),V1y) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2E_5C_2F,V0x),V1y)) ) ).
fof(lameq_f2299,axiom,
! [V0x] : ap(f2299,V0x) = f2298(V0x) ).
fof(ax_thm_2Ebitstring_2Ebnor__def,axiom,
c_2Ebitstring_2Ebnor = ap(c_2Ebitstring_2Ebitwise,f2299) ).
fof(ax_thm_2Ebitstring_2Ebxnor__def,axiom,
c_2Ebitstring_2Ebxnor = ap(c_2Ebitstring_2Ebitwise,c_2Emin_2E_3D(bool)) ).
fof(lameq_f2300,axiom,
! [V0x] :
( mem(V0x,bool)
=> ! [V1y] : ap(f2300(V0x),V1y) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2E_2F_5C,V0x),V1y)) ) ).
fof(lameq_f2301,axiom,
! [V0x] : ap(f2301,V0x) = f2300(V0x) ).
fof(ax_thm_2Ebitstring_2Ebnand__def,axiom,
c_2Ebitstring_2Ebnand = ap(c_2Ebitstring_2Ebitwise,f2301) ).
fof(ax_thm_2Ebitstring_2Ereplicate__def,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebitstring_2Ereplicate,V0v),V1n) = ap(c_2Elist_2EFLAT(bool),ap(ap(c_2Elist_2EGENLIST(ty_2Elist_2Elist(bool)),ap(c_2Ecombin_2EK(ty_2Elist_2Elist(bool),ty_2Enum_2Enum),V0v)),V1n)) ) ) ).
fof(conj_thm_2Ebitstring_2Eextend__cons,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1c] :
( mem(V1c,bool)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Eextend,V1c),ap(c_2Enum_2ESUC,V0n)),V2l) = ap(ap(c_2Elist_2ECONS(bool),V1c),ap(ap(ap(c_2Ebitstring_2Eextend,V1c),V0n),V2l)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Epad__left__extend,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(bool))
=> ! [V2c] :
( mem(V2c,bool)
=> ap(ap(ap(c_2Elist_2EPAD__LEFT(bool),V2c),V0n),V1l) = ap(ap(ap(c_2Ebitstring_2Eextend,V2c),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Elist_2ELENGTH(bool),V1l))),V1l) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eextend,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Ezero__extend,V0n),V1v) = ap(ap(ap(c_2Ebitstring_2Eextend,c_2Ebool_2EF),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Elist_2ELENGTH(bool),V1v))),V1v) ) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3v] :
( mem(V3v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Esign__extend(bool),V2n),V3v) = ap(ap(ap(c_2Ebitstring_2Eextend,ap(c_2Elist_2EHD(bool),V3v)),ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Elist_2ELENGTH(bool),V3v))),V3v) ) ) ) ).
fof(lameq_f2302,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ! [V2l] : ap(f2302(V0n,V1v),V2l) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(bool)),ap(ap(c_2Eprim__rec_2E_3C,V2l),V0n)),ap(ap(ap(c_2Ebitstring_2Eextend,c_2Ebool_2EF),ap(ap(c_2Earithmetic_2E_2D,V0n),V2l)),V1v)),ap(ap(c_2Elist_2EDROP(bool),ap(ap(c_2Earithmetic_2E_2D,V2l),V0n)),V1v)) ) ) ).
fof(conj_thm_2Ebitstring_2Efixwidth,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Efixwidth,V0n),V1v) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(bool)),f2302(V0n,V1v)),ap(c_2Elist_2ELENGTH(bool),V1v)) ) ) ).
fof(conj_thm_2Ebitstring_2Efixwidth__id,axiom,
! [V0w] :
( mem(V0w,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Elist_2ELENGTH(bool),V0w)),V0w) = V0w ) ).
fof(conj_thm_2Ebitstring_2Efixwidth__id__imp,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(bool))
=> ( V0n = ap(c_2Elist_2ELENGTH(bool),V1w)
=> ap(ap(c_2Ebitstring_2Efixwidth,V0n),V1w) = V1w ) ) ) ).
fof(lameq_f2303,axiom,
! [V2n] : ap(f2303,V2n) = ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)) ).
fof(conj_thm_2Ebitstring_2Eboolify__reverse__map,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Eboolify,V1a),V0v) = ap(ap(c_2Elist_2EAPPEND(bool),ap(c_2Elist_2EREVERSE(bool),ap(ap(c_2Elist_2EMAP(ty_2Enum_2Enum,bool),f2303),V0v))),V1a) ) ) ).
fof(lameq_f2304,axiom,
! [V2b] : ap(f2304,V2b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V2b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0) ).
fof(conj_thm_2Ebitstring_2Ebitify__reverse__map,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1a] :
( mem(V1a,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(ap(c_2Ebitstring_2Ebitify,V1a),V0v) = ap(ap(c_2Elist_2EAPPEND(ty_2Enum_2Enum),ap(c_2Elist_2EREVERSE(ty_2Enum_2Enum),ap(ap(c_2Elist_2EMAP(bool,ty_2Enum_2Enum),f2304),V0v))),V1a) ) ) ).
fof(conj_thm_2Ebitstring_2Eevery__bit__bitify,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> p(ap(ap(c_2Elist_2EEVERY(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ebitstring_2Ebitify,c_2Elist_2ENIL(ty_2Enum_2Enum)),V0v))) ) ).
fof(conj_thm_2Ebitstring_2Elength__pad__left,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(ap(c_2Elist_2EPAD__LEFT(A_27a),V0x),V1n),V2a)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V2a)),V1n)),V1n),ap(c_2Elist_2ELENGTH(A_27a),V2a)) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Elength__pad__right,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(ap(c_2Elist_2EPAD__RIGHT(A_27a),V0x),V1n),V2a)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V2a)),V1n)),V1n),ap(c_2Elist_2ELENGTH(A_27a),V2a)) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Elength__zero__extend,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(bool),V1v)),V0n))
=> ap(c_2Elist_2ELENGTH(bool),ap(ap(c_2Ebitstring_2Ezero__extend,V0n),V1v)) = V0n ) ) ) ).
fof(conj_thm_2Ebitstring_2Elength__sign__extend,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V1v)),V0n))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Ebitstring_2Esign__extend(A_27a),V0n),V1v)) = V0n ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Elength__fixwidth,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(c_2Elist_2ELENGTH(bool),ap(ap(c_2Ebitstring_2Efixwidth,V0n),V1v)) = V0n ) ) ).
fof(conj_thm_2Ebitstring_2Elength__field,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(bool))
=> ap(c_2Elist_2ELENGTH(bool),ap(ap(ap(c_2Ebitstring_2Efield,V0h),V1l),V2v)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l) ) ) ) ).
fof(conj_thm_2Ebitstring_2Elength__bitify,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),ap(ap(c_2Ebitstring_2Ebitify,V1l),V0v)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),V1l)),ap(c_2Elist_2ELENGTH(bool),V0v)) ) ) ).
fof(conj_thm_2Ebitstring_2Elength__bitify__null,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1l] :
( mem(V1l,A_27a)
=> ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),ap(ap(c_2Ebitstring_2Ebitify,c_2Elist_2ENIL(ty_2Enum_2Enum)),V0v)) = ap(c_2Elist_2ELENGTH(bool),V0v) ) ) ) ).
fof(conj_thm_2Ebitstring_2Elength__shiftr,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Elist_2ELENGTH(bool),ap(ap(c_2Ebitstring_2Eshiftr,V0v),V1n)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(bool),V0v)),V1n) ) ) ).
fof(conj_thm_2Ebitstring_2Elength__rev__count__list,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),ap(c_2Ebitstring_2Erev__count__list,V0n)) = V0n ) ).
fof(conj_thm_2Ebitstring_2Elength__w2v,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Elist_2ELENGTH(bool),ap(c_2Ebitstring_2Ew2v(A_27a),V0w)) = ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)) ) ) ).
fof(conj_thm_2Ebitstring_2Elength__rotate,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Elist_2ELENGTH(bool),ap(ap(c_2Ebitstring_2Erotate,V0v),V1n)) = ap(c_2Elist_2ELENGTH(bool),V0v) ) ) ).
fof(conj_thm_2Ebitstring_2Eel__rev__count__list,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),V0n))
=> ap(ap(c_2Elist_2EEL(ty_2Enum_2Enum),V1i),ap(c_2Ebitstring_2Erev__count__list,V0n)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1i) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eel__zero__extend,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(c_2Elist_2EEL(bool),V1i),ap(ap(c_2Ebitstring_2Ezero__extend,V0n),V2v)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Elist_2ELENGTH(bool),V2v))),V1i))
& p(ap(ap(c_2Elist_2EEL(bool),ap(ap(c_2Earithmetic_2E_2D,V1i),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Elist_2ELENGTH(bool),V2v)))),V2v)) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eel__sign__extend,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EEL(A_27a),V1i),ap(ap(c_2Ebitstring_2Esign__extend(A_27a),V0n),V2v)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Elist_2ELENGTH(A_27a),V2v)))),ap(ap(c_2Elist_2EEL(A_27a),c_2Enum_2E0),V2v)),ap(ap(c_2Elist_2EEL(A_27a),ap(ap(c_2Earithmetic_2E_2D,V1i),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Elist_2ELENGTH(A_27a),V2v)))),V2v)) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eel__fixwidth,axiom,
! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0i),V1n))
=> ( p(ap(ap(c_2Elist_2EEL(bool),V0i),ap(ap(c_2Ebitstring_2Efixwidth,V1n),V2w)))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(bool),V2w)),V1n)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Elist_2ELENGTH(bool),V2w))),V0i)),ap(ap(c_2Elist_2EEL(bool),ap(ap(c_2Earithmetic_2E_2D,V0i),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Elist_2ELENGTH(bool),V2w)))),V2w))),ap(ap(c_2Elist_2EEL(bool),ap(ap(c_2Earithmetic_2E_2B,V0i),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(bool),V2w)),V1n))),V2w))) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eel__field,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Enum_2Enum)
=> ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3i),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V1h)),V2l)))
=> ( p(ap(ap(c_2Elist_2EEL(bool),V3i),ap(ap(ap(c_2Ebitstring_2Efield,V1h),V2l),V0v)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1h)),ap(ap(c_2Earithmetic_2E_2B,V3i),ap(c_2Elist_2ELENGTH(bool),V0v))))
& p(ap(ap(c_2Elist_2EEL(bool),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V3i),ap(c_2Elist_2ELENGTH(bool),V0v))),ap(c_2Enum_2ESUC,V1h))),V0v)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eel__w2v,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))
=> ( p(ap(ap(c_2Elist_2EEL(bool),V1n),ap(c_2Ebitstring_2Ew2v(A_27a),V0w)))
<=> p(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)))),V1n))) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eel__shiftr,axiom,
! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3d] :
( mem(V3d,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V3d))
& p(ap(ap(c_2Eprim__rec_2E_3C,V0i),ap(ap(c_2Earithmetic_2E_2D,V3d),V2n)))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3d)) )
=> ( p(ap(ap(c_2Elist_2EEL(bool),V0i),ap(ap(c_2Ebitstring_2Eshiftr,ap(ap(c_2Ebitstring_2Efixwidth,V3d),V1v)),V2n)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V3d),ap(ap(c_2Earithmetic_2E_2B,V0i),ap(c_2Elist_2ELENGTH(bool),V1v))))
& p(ap(ap(c_2Elist_2EEL(bool),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0i),ap(c_2Elist_2ELENGTH(bool),V1v))),V3d)),V1v)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eshiftr__0,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Eshiftr,V0v),c_2Enum_2E0) = V0v ) ).
fof(conj_thm_2Ebitstring_2Efield__fixwidth,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ebitstring_2Efield,V0h),c_2Enum_2E0),V1v) = ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Enum_2ESUC,V0h)),V1v) ) ) ).
fof(lameq_f2305,axiom,
! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V2n] : ap(f2305(V1v,V0b),V2n) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,V0b),V2n)),ap(ap(c_2Elist_2EEL(bool),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0b)),V1v)) ) ) ).
fof(conj_thm_2Ebitstring_2Etestbit,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(c_2Ebitstring_2Etestbit,V0b),V1v))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,bool),f2305(V1v,V0b)),ap(c_2Elist_2ELENGTH(bool),V1v))) ) ) ) ).
fof(conj_thm_2Ebitstring_2Etestbit__geq__len,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(bool),V0v)),V1i))
=> ~ p(ap(ap(c_2Ebitstring_2Etestbit,V1i),V0v)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Etestbit__el,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Elist_2ELENGTH(bool),V0v)))
=> ( p(ap(ap(c_2Ebitstring_2Etestbit,V1i),V0v))
<=> p(ap(ap(c_2Elist_2EEL(bool),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(bool),V0v)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1i)),V0v)) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Ebit__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(c_2Ewords_2Eword__bit(A_27a),V0n),ap(c_2Ebitstring_2Ev2w(A_27a),V1v)))
<=> ( 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_2Ebitstring_2Etestbit,V0n),V1v)) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__index__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0index_20too_20large] :
( mem(V0index_20too_20large,bool)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V1v)),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_2Ebitstring_2Etestbit,V2i),V1v)),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_2Ebitstring_2Ev2w(A_27a),V1v)),V2i))) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Etestbit__w2v,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ebitstring_2Etestbit,V0n),ap(c_2Ebitstring_2Ew2v(A_27a),V1w)))
<=> p(ap(ap(c_2Ewords_2Eword__bit(A_27a),V0n),V1w)) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Ew2v__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ebitstring_2Ew2v(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) = ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v) ) ) ).
fof(conj_thm_2Ebitstring_2Ev2w__w2v,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ebitstring_2Ev2w(A_27a),ap(c_2Ebitstring_2Ew2v(A_27a),V0w)) = V0w ) ) ).
fof(conj_thm_2Ebitstring_2Ev2w__fixwidth,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v)) = ap(c_2Ebitstring_2Ev2w(A_27a),V0v) ) ) ).
fof(conj_thm_2Ebitstring_2Efixwidth__fixwidth,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ebitstring_2Efixwidth,V0n),ap(ap(c_2Ebitstring_2Efixwidth,V0n),V1v)) = ap(ap(c_2Ebitstring_2Efixwidth,V0n),V1v) ) ) ).
fof(conj_thm_2Ebitstring_2Ebitstring__nchotomy,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ? [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
& V0w = ap(c_2Ebitstring_2Ev2w(A_27a),V1v) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eranged__bitstring__nchotomy,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ? [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
& V0w = ap(c_2Ebitstring_2Ev2w(A_27a),V1v)
& p(ap(c_2Emarker_2EAbbrev,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Elist_2ELENGTH(bool),V1v)),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))) ) ) ) ).
fof(conj_thm_2Ebitstring_2Efixwidth__eq,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ! [V2w] :
( mem(V2w,ty_2Elist_2Elist(bool))
=> ( ap(ap(c_2Ebitstring_2Efixwidth,V0n),V1v) = ap(ap(c_2Ebitstring_2Efixwidth,V0n),V2w)
<=> ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V0n))
=> ( p(ap(ap(c_2Ebitstring_2Etestbit,V3i),V1v))
<=> p(ap(ap(c_2Ebitstring_2Etestbit,V3i),V2w)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Ev2w__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(bool))
=> ( ap(c_2Ebitstring_2Ev2w(A_27a),V0v) = ap(c_2Ebitstring_2Ev2w(A_27a),V1w)
<=> ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v) = ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1w) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Efield__concat__right,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1a] :
( mem(V1a,ty_2Elist_2Elist(bool))
=> ! [V2b] :
( mem(V2b,ty_2Elist_2Elist(bool))
=> ( ap(c_2Elist_2ELENGTH(bool),V2b) = ap(c_2Enum_2ESUC,V0h)
=> ap(ap(ap(c_2Ebitstring_2Efield,V0h),c_2Enum_2E0),ap(ap(c_2Elist_2EAPPEND(bool),V1a),V2b)) = V2b ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Efield__concat__left,axiom,
! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Elist_2Elist(bool))
=> ! [V3b] :
( mem(V3b,ty_2Elist_2Elist(bool))
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),V0h))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(bool),V3b)),V1l)) )
=> ap(ap(ap(c_2Ebitstring_2Efield,V0h),V1l),ap(ap(c_2Elist_2EAPPEND(bool),V2a),V3b)) = ap(ap(ap(c_2Ebitstring_2Efield,ap(ap(c_2Earithmetic_2E_2D,V0h),ap(c_2Elist_2ELENGTH(bool),V3b))),ap(ap(c_2Earithmetic_2E_2D,V1l),ap(c_2Elist_2ELENGTH(bool),V3b))),V2a) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Efield__id__imp,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ( ap(c_2Enum_2ESUC,V0n) = ap(c_2Elist_2ELENGTH(bool),V1v)
=> ap(ap(ap(c_2Ebitstring_2Efield,V0n),c_2Enum_2E0),V1v) = V1v ) ) ) ).
fof(conj_thm_2Ebitstring_2Eshiftl__replicate__F,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ebitstring_2Eshiftl,V0v),V1n) = ap(ap(c_2Elist_2EAPPEND(bool),V0v),ap(ap(c_2Ebitstring_2Ereplicate,ap(ap(c_2Elist_2ECONS(bool),c_2Ebool_2EF),c_2Elist_2ENIL(bool))),V1n)) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__lsb__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ( p(ap(c_2Ewords_2Eword__lsb(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)))
<=> ( V0v != c_2Elist_2ENIL(bool)
& p(ap(c_2Elist_2ELAST(bool),V0v)) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__msb__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ( p(ap(c_2Ewords_2Eword__msb(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)))
<=> p(ap(ap(c_2Ebitstring_2Etestbit,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)))),V0v)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Ew2w__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Ew2w(A_27a,A_27b),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) = ap(c_2Ebitstring_2Ev2w(A_27b),ap(ap(c_2Ebitstring_2Efixwidth,ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),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(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),V0v)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Esw2sw__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Esw2sw(A_27a,A_27b),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27b)),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)))),ap(c_2Ebitstring_2Ev2w(A_27b),ap(ap(c_2Ebitstring_2Esign__extend(bool),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v)))),ap(c_2Ebitstring_2Ev2w(A_27b),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V0v))) ) ) ) ).
fof(conj_thm_2Ebitstring_2En2w__v2n,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V0v)) = ap(c_2Ebitstring_2Ev2w(A_27a),V0v) ) ) ).
fof(conj_thm_2Ebitstring_2Ev2n__n2v,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ebitstring_2Ev2n,ap(c_2Ebitstring_2En2v,V0n)) = V0n ) ).
fof(conj_thm_2Ebitstring_2Ev2w__n2v,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Ebitstring_2Ev2w(A_27a),ap(c_2Ebitstring_2En2v,V0n)) = ap(c_2Ewords_2En2w(A_27a),V0n) ) ) ).
fof(conj_thm_2Ebitstring_2Ew2n__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) = ap(ap(c_2Ebit_2EMOD__2EXP,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Ebitstring_2Ev2n,V0v)) ) ) ).
fof(conj_thm_2Ebitstring_2Ev2n__lt,axiom,
! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ebitstring_2Ev2n,V0v)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(bool),V0v)))) ) ).
fof(conj_thm_2Ebitstring_2Eword__and__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__and(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)),ap(c_2Ebitstring_2Ev2w(A_27a),V1w)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Eband,V0v),V1w)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__or__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__or(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)),ap(c_2Ebitstring_2Ev2w(A_27a),V1w)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Ebor,V0v),V1w)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__xor__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__xor(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)),ap(c_2Ebitstring_2Ev2w(A_27a),V1w)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Ebxor,V0v),V1w)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__nand__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__nand(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)),ap(c_2Ebitstring_2Ev2w(A_27a),V1w)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Ebnand,ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v)),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1w))) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__nor__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__nor(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)),ap(c_2Ebitstring_2Ev2w(A_27a),V1w)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Ebnor,ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v)),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1w))) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__xnor__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1w] :
( mem(V1w,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__xnor(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)),ap(c_2Ebitstring_2Ev2w(A_27a),V1w)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Ebxnor,ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v)),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1w))) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__1comp__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(c_2Ebitstring_2Ebnot,ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v))) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__lsl__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__lsl(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V1v)),V0n) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Eshiftl,V1v),V0n)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__lsr__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__lsr(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V1v)),V0n) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Eshiftr,ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1v)),V0n)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__modify__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool)))
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__modify(A_27a),V0f),ap(c_2Ebitstring_2Ev2w(A_27a),V1v)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Emodify,V0f),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1v))) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__bits__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),ap(c_2Ebitstring_2Ev2w(A_27a),V2v)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(ap(c_2Ebitstring_2Efield,V0h),V1l),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V2v))) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__extract__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l),ap(c_2Ebitstring_2Ev2w(A_27a),V2v)) = ap(c_2Ewords_2Ew2w(A_27a,A_27b),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l),ap(c_2Ebitstring_2Ev2w(A_27a),V2v))) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__slice__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Ewords_2Eword__slice(A_27a),V0h),V1l),ap(c_2Ebitstring_2Ev2w(A_27a),V2v)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Eshiftl,ap(ap(ap(c_2Ebitstring_2Efield,V0h),V1l),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V2v))),V1l)) ) ) ) ) ).
fof(lameq_f2306,axiom,
! [A_27a,V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V2l] : ap(f2306(A_27a,V0n),V2l) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Esign__extend(bool),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(bool)),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0n)),ap(ap(c_2Elist_2ECONS(bool),ap(c_2Elist_2EHD(bool),V2l)),c_2Elist_2ENIL(bool))),ap(ap(c_2Ebitstring_2Eshiftr,V2l),V0n)))) ) ).
fof(conj_thm_2Ebitstring_2Eword__asr__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__asr(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V1v)),V0n) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(bool),ty_2Efcp_2Ecart(bool,A_27a)),f2306(A_27a,V0n)),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1v)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__ror__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__ror(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V1v)),V0n) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(ap(c_2Ebitstring_2Erotate,ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1v)),V0n)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__reverse__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Eword__reverse(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(c_2Elist_2EREVERSE(bool),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v))) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__join__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0v1] :
( mem(V0v1,ty_2Elist_2Elist(bool))
=> ! [V1v2] :
( mem(V1v2,ty_2Elist_2Elist(bool))
=> ( ( 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))) )
=> ap(ap(c_2Ewords_2Eword__join(A_27a,A_27b),ap(c_2Ebitstring_2Ev2w(A_27a),V0v1)),ap(c_2Ebitstring_2Ev2w(A_27b),V1v2)) = ap(c_2Ebitstring_2Ev2w(ty_2Esum_2Esum(A_27a,A_27b)),ap(ap(c_2Elist_2EAPPEND(bool),V0v1),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V1v2))) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__concat__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0v1] :
( mem(V0v1,ty_2Elist_2Elist(bool))
=> ! [V1v2] :
( mem(V1v2,ty_2Elist_2Elist(bool))
=> ( ( 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))) )
=> ap(ap(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27c),ap(c_2Ebitstring_2Ev2w(A_27a),V0v1)),ap(c_2Ebitstring_2Ev2w(A_27b),V1v2)) = ap(c_2Ebitstring_2Ev2w(A_27c),ap(ap(c_2Ebitstring_2Efixwidth,ap(ap(c_2Earithmetic_2EMIN,ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c))),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(ap(c_2Elist_2EAPPEND(bool),V0v1),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V1v2)))) ) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__join__v2w__rwt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0bad_20domain] :
( mem(V0bad_20domain,bool)
=> ! [V1v1] :
( mem(V1v1,ty_2Elist_2Elist(bool))
=> ! [V2v2] :
( mem(V2v2,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__join(A_27a,A_27b),ap(c_2Ebitstring_2Ev2w(A_27a),V1v1)),ap(c_2Ebitstring_2Ev2w(A_27b),V2v2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,ty_2Esum_2Esum(A_27a,A_27b))),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(c_2Ebitstring_2Ev2w(ty_2Esum_2Esum(A_27a,A_27b)),ap(ap(c_2Elist_2EAPPEND(bool),V1v1),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V2v2)))),ap(ap(ap(ap(c_2Ecombin_2EFAIL(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)))),bool),c_2Ewords_2Eword__join(A_27a,A_27b)),V0bad_20domain),ap(c_2Ebitstring_2Ev2w(A_27a),V1v1)),ap(c_2Ebitstring_2Ev2w(A_27b),V2v2))) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eword__concat__v2w__rwt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0bad_20domain] :
( mem(V0bad_20domain,bool)
=> ! [V1v1] :
( mem(V1v1,ty_2Elist_2Elist(bool))
=> ! [V2v2] :
( mem(V2v2,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27c),ap(c_2Ebitstring_2Ev2w(A_27a),V1v1)),ap(c_2Ebitstring_2Ev2w(A_27b),V2v2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27c)),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(c_2Ebitstring_2Ev2w(A_27c),ap(ap(c_2Ebitstring_2Efixwidth,ap(ap(c_2Earithmetic_2EMIN,ap(c_2Efcp_2Edimindex(A_27c),c_2Ebool_2Ethe__value(A_27c))),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(ap(c_2Elist_2EAPPEND(bool),V1v1),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))),V2v2))))),ap(ap(ap(ap(c_2Ecombin_2EFAIL(arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27b),ty_2Efcp_2Ecart(bool,A_27c))),bool),c_2Ewords_2Eword__concat(A_27a,A_27b,A_27c)),V0bad_20domain),ap(c_2Ebitstring_2Ev2w(A_27a),V1v1)),ap(c_2Ebitstring_2Ev2w(A_27b),V2v2))) ) ) ) ) ) ) ).
fof(lameq_f2307,axiom,
! [V0f] :
( mem(V0f,arr(bool,arr(bool,bool)))
=> ! [V2l] : ap(f2307(V0f),V2l) = ap(c_2Ebitstring_2Ev2w(ty_2Eone_2Eone),ap(ap(c_2Elist_2ECONS(bool),ap(ap(ap(c_2Elist_2EFOLDL(bool,bool),V0f),ap(c_2Elist_2EHD(bool),V2l)),ap(c_2Elist_2ETL(bool),V2l))),c_2Elist_2ENIL(bool))) ) ).
fof(conj_thm_2Ebitstring_2Eword__reduce__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(bool,arr(bool,bool)))
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(ap(c_2Ewords_2Eword__reduce(A_27a),V0f),ap(c_2Ebitstring_2Ev2w(A_27a),V1v)) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(bool),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),f2307(V0f)),ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V1v)) ) ) ) ).
fof(conj_thm_2Ebitstring_2Ereduce__and__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Ereduce__and(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) = ap(ap(c_2Ewords_2Eword__reduce(A_27a),c_2Ebool_2E_2F_5C),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) ) ) ).
fof(conj_thm_2Ebitstring_2Ereduce__or__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Ereduce__or(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) = ap(ap(c_2Ewords_2Eword__reduce(A_27a),c_2Ebool_2E_5C_2F),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) ) ) ).
fof(conj_thm_2Ebitstring_2Eextract__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(bool))
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(bool),V2v)),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(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)
& 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),V0h),V1l),ap(c_2Ebitstring_2Ev2w(A_27a),V2v)) = ap(c_2Ebitstring_2Ev2w(A_27b),ap(ap(ap(c_2Ebitstring_2Efield,V0h),V1l),V2v)) ) ) ) ) ) ) ).
fof(lameq_f2308,axiom,
! [V2l] : ap(f2308,V2l) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(c_2Elist_2ENULL(bool),V2l))),ap(c_2Elist_2ELAST(bool),V2l)) ).
fof(conj_thm_2Ebitstring_2Eword__bit__last__shiftr,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ( 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_2Ewords_2Eword__bit(A_27a),V0i),ap(c_2Ebitstring_2Ev2w(A_27a),V1v)))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(bool),bool),f2308),ap(ap(c_2Ebitstring_2Eshiftr,V1v),V0i))) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eops__to__v2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [A_27g] :
( ne(A_27g)
=> ! [A_27h] :
( ne(A_27h)
=> ! [A_27i] :
( ne(A_27i)
=> ! [A_27j] :
( ne(A_27j)
=> ! [A_27k] :
( ne(A_27k)
=> ! [A_27l] :
( ne(A_27l)
=> ! [A_27m] :
( ne(A_27m)
=> ! [A_27n] :
( ne(A_27n)
=> ! [A_27o] :
( ne(A_27o)
=> ! [A_27p] :
( ne(A_27p)
=> ! [A_27q] :
( ne(A_27q)
=> ! [A_27r] :
( ne(A_27r)
=> ! [A_27s] :
( ne(A_27s)
=> ! [A_27t] :
( ne(A_27t)
=> ( ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__or(A_27c),ap(c_2Ebitstring_2Ev2w(A_27c),V0v)),ap(c_2Ewords_2En2w(A_27c),V1n)) = ap(ap(c_2Ewords_2Eword__or(A_27c),ap(c_2Ebitstring_2Ev2w(A_27c),V0v)),ap(c_2Ebitstring_2Ev2w(A_27c),ap(c_2Ebitstring_2En2v,V1n))) ) )
& ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(bool))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__or(A_27d),ap(c_2Ewords_2En2w(A_27d),V3n)),ap(c_2Ebitstring_2Ev2w(A_27d),V2v)) = ap(ap(c_2Ewords_2Eword__or(A_27d),ap(c_2Ebitstring_2Ev2w(A_27d),ap(c_2Ebitstring_2En2v,V3n))),ap(c_2Ebitstring_2Ev2w(A_27d),V2v)) ) )
& ! [V4v] :
( mem(V4v,ty_2Elist_2Elist(bool))
=> ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__and(A_27e),ap(c_2Ebitstring_2Ev2w(A_27e),V4v)),ap(c_2Ewords_2En2w(A_27e),V5n)) = ap(ap(c_2Ewords_2Eword__and(A_27e),ap(c_2Ebitstring_2Ev2w(A_27e),V4v)),ap(c_2Ebitstring_2Ev2w(A_27e),ap(c_2Ebitstring_2En2v,V5n))) ) )
& ! [V6v] :
( mem(V6v,ty_2Elist_2Elist(bool))
=> ! [V7n] :
( mem(V7n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__and(A_27f),ap(c_2Ewords_2En2w(A_27f),V7n)),ap(c_2Ebitstring_2Ev2w(A_27f),V6v)) = ap(ap(c_2Ewords_2Eword__and(A_27f),ap(c_2Ebitstring_2Ev2w(A_27f),ap(c_2Ebitstring_2En2v,V7n))),ap(c_2Ebitstring_2Ev2w(A_27f),V6v)) ) )
& ! [V8v] :
( mem(V8v,ty_2Elist_2Elist(bool))
=> ! [V9n] :
( mem(V9n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__xor(A_27g),ap(c_2Ebitstring_2Ev2w(A_27g),V8v)),ap(c_2Ewords_2En2w(A_27g),V9n)) = ap(ap(c_2Ewords_2Eword__xor(A_27g),ap(c_2Ebitstring_2Ev2w(A_27g),V8v)),ap(c_2Ebitstring_2Ev2w(A_27g),ap(c_2Ebitstring_2En2v,V9n))) ) )
& ! [V10v] :
( mem(V10v,ty_2Elist_2Elist(bool))
=> ! [V11n] :
( mem(V11n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__xor(A_27h),ap(c_2Ewords_2En2w(A_27h),V11n)),ap(c_2Ebitstring_2Ev2w(A_27h),V10v)) = ap(ap(c_2Ewords_2Eword__xor(A_27h),ap(c_2Ebitstring_2Ev2w(A_27h),ap(c_2Ebitstring_2En2v,V11n))),ap(c_2Ebitstring_2Ev2w(A_27h),V10v)) ) )
& ! [V12v] :
( mem(V12v,ty_2Elist_2Elist(bool))
=> ! [V13n] :
( mem(V13n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__nor(A_27i),ap(c_2Ebitstring_2Ev2w(A_27i),V12v)),ap(c_2Ewords_2En2w(A_27i),V13n)) = ap(ap(c_2Ewords_2Eword__nor(A_27i),ap(c_2Ebitstring_2Ev2w(A_27i),V12v)),ap(c_2Ebitstring_2Ev2w(A_27i),ap(c_2Ebitstring_2En2v,V13n))) ) )
& ! [V14v] :
( mem(V14v,ty_2Elist_2Elist(bool))
=> ! [V15n] :
( mem(V15n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__nor(A_27j),ap(c_2Ewords_2En2w(A_27j),V15n)),ap(c_2Ebitstring_2Ev2w(A_27j),V14v)) = ap(ap(c_2Ewords_2Eword__nor(A_27j),ap(c_2Ebitstring_2Ev2w(A_27j),ap(c_2Ebitstring_2En2v,V15n))),ap(c_2Ebitstring_2Ev2w(A_27j),V14v)) ) )
& ! [V16v] :
( mem(V16v,ty_2Elist_2Elist(bool))
=> ! [V17n] :
( mem(V17n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__nand(A_27k),ap(c_2Ebitstring_2Ev2w(A_27k),V16v)),ap(c_2Ewords_2En2w(A_27k),V17n)) = ap(ap(c_2Ewords_2Eword__nand(A_27k),ap(c_2Ebitstring_2Ev2w(A_27k),V16v)),ap(c_2Ebitstring_2Ev2w(A_27k),ap(c_2Ebitstring_2En2v,V17n))) ) )
& ! [V18v] :
( mem(V18v,ty_2Elist_2Elist(bool))
=> ! [V19n] :
( mem(V19n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__nand(A_27l),ap(c_2Ewords_2En2w(A_27l),V19n)),ap(c_2Ebitstring_2Ev2w(A_27l),V18v)) = ap(ap(c_2Ewords_2Eword__nand(A_27l),ap(c_2Ebitstring_2Ev2w(A_27l),ap(c_2Ebitstring_2En2v,V19n))),ap(c_2Ebitstring_2Ev2w(A_27l),V18v)) ) )
& ! [V20v] :
( mem(V20v,ty_2Elist_2Elist(bool))
=> ! [V21n] :
( mem(V21n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__xnor(A_27m),ap(c_2Ebitstring_2Ev2w(A_27m),V20v)),ap(c_2Ewords_2En2w(A_27m),V21n)) = ap(ap(c_2Ewords_2Eword__xnor(A_27m),ap(c_2Ebitstring_2Ev2w(A_27m),V20v)),ap(c_2Ebitstring_2Ev2w(A_27m),ap(c_2Ebitstring_2En2v,V21n))) ) )
& ! [V22v] :
( mem(V22v,ty_2Elist_2Elist(bool))
=> ! [V23n] :
( mem(V23n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__xnor(A_27n),ap(c_2Ewords_2En2w(A_27n),V23n)),ap(c_2Ebitstring_2Ev2w(A_27n),V22v)) = ap(ap(c_2Ewords_2Eword__xnor(A_27n),ap(c_2Ebitstring_2Ev2w(A_27n),ap(c_2Ebitstring_2En2v,V23n))),ap(c_2Ebitstring_2Ev2w(A_27n),V22v)) ) )
& ! [V24v] :
( mem(V24v,ty_2Elist_2Elist(bool))
=> ! [V25n] :
( mem(V25n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27o),ap(c_2Ebitstring_2Ev2w(A_27a),V24v)),ap(c_2Ewords_2En2w(A_27b),V25n)) = ap(ap(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27o),ap(c_2Ebitstring_2Ev2w(A_27a),V24v)),ap(c_2Ebitstring_2Ev2w(A_27b),ap(c_2Ebitstring_2En2v,V25n))) ) )
& ! [V26v] :
( mem(V26v,ty_2Elist_2Elist(bool))
=> ! [V27n] :
( mem(V27n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27p),ap(c_2Ewords_2En2w(A_27a),V27n)),ap(c_2Ebitstring_2Ev2w(A_27b),V26v)) = ap(ap(c_2Ewords_2Eword__concat(A_27a,A_27b,A_27p),ap(c_2Ebitstring_2Ev2w(A_27a),ap(c_2Ebitstring_2En2v,V27n))),ap(c_2Ebitstring_2Ev2w(A_27b),V26v)) ) )
& ! [V28v] :
( mem(V28v,ty_2Elist_2Elist(bool))
=> ! [V29n] :
( mem(V29n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__join(A_27q,A_27r),ap(c_2Ebitstring_2Ev2w(A_27q),V28v)),ap(c_2Ewords_2En2w(A_27r),V29n)) = ap(ap(c_2Ewords_2Eword__join(A_27q,A_27r),ap(c_2Ebitstring_2Ev2w(A_27q),V28v)),ap(c_2Ebitstring_2Ev2w(A_27r),ap(c_2Ebitstring_2En2v,V29n))) ) )
& ! [V30v] :
( mem(V30v,ty_2Elist_2Elist(bool))
=> ! [V31n] :
( mem(V31n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__join(A_27s,A_27t),ap(c_2Ewords_2En2w(A_27s),V31n)),ap(c_2Ebitstring_2Ev2w(A_27t),V30v)) = ap(ap(c_2Ewords_2Eword__join(A_27s,A_27t),ap(c_2Ebitstring_2Ev2w(A_27s),ap(c_2Ebitstring_2En2v,V31n))),ap(c_2Ebitstring_2Ev2w(A_27t),V30v)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Eops__to__n2w,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [A_27g] :
( ne(A_27g)
=> ! [A_27h] :
( ne(A_27h)
=> ! [A_27i] :
( ne(A_27i)
=> ! [A_27j] :
( ne(A_27j)
=> ! [A_27k] :
( ne(A_27k)
=> ! [A_27l] :
( ne(A_27l)
=> ! [A_27m] :
( ne(A_27m)
=> ! [A_27n] :
( ne(A_27n)
=> ! [A_27o] :
( ne(A_27o)
=> ( ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ebitstring_2Ev2w(A_27b),V0v)) = ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),ap(c_2Ebitstring_2Ev2n,V0v))) )
& ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Eword__log2(A_27c),ap(c_2Ebitstring_2Ev2w(A_27c),V1v)) = ap(c_2Ewords_2Eword__log2(A_27c),ap(c_2Ewords_2En2w(A_27c),ap(c_2Ebitstring_2Ev2n,V1v))) )
& ! [V2v] :
( mem(V2v,ty_2Elist_2Elist(bool))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( ap(c_2Ebitstring_2Ev2w(A_27a),V2v) = ap(c_2Ewords_2En2w(A_27a),V3n)
<=> ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V2v)) = ap(c_2Ewords_2En2w(A_27a),V3n) ) ) )
& ! [V4v] :
( mem(V4v,ty_2Elist_2Elist(bool))
=> ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ( ap(c_2Ewords_2En2w(A_27a),V5n) = ap(c_2Ebitstring_2Ev2w(A_27a),V4v)
<=> ap(c_2Ewords_2En2w(A_27a),V5n) = ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V4v)) ) ) )
& ! [V6v] :
( mem(V6v,ty_2Elist_2Elist(bool))
=> ! [V7w] :
( mem(V7w,ty_2Efcp_2Ecart(bool,A_27d))
=> ap(ap(c_2Ewords_2Eword__add(A_27d),ap(c_2Ebitstring_2Ev2w(A_27d),V6v)),V7w) = ap(ap(c_2Ewords_2Eword__add(A_27d),ap(c_2Ewords_2En2w(A_27d),ap(c_2Ebitstring_2Ev2n,V6v))),V7w) ) )
& ! [V8v] :
( mem(V8v,ty_2Elist_2Elist(bool))
=> ! [V9w] :
( mem(V9w,ty_2Efcp_2Ecart(bool,A_27e))
=> ap(ap(c_2Ewords_2Eword__add(A_27e),V9w),ap(c_2Ebitstring_2Ev2w(A_27e),V8v)) = ap(ap(c_2Ewords_2Eword__add(A_27e),V9w),ap(c_2Ewords_2En2w(A_27e),ap(c_2Ebitstring_2Ev2n,V8v))) ) )
& ! [V10v] :
( mem(V10v,ty_2Elist_2Elist(bool))
=> ! [V11w] :
( mem(V11w,ty_2Efcp_2Ecart(bool,A_27f))
=> ap(ap(c_2Ewords_2Eword__sub(A_27f),ap(c_2Ebitstring_2Ev2w(A_27f),V10v)),V11w) = ap(ap(c_2Ewords_2Eword__sub(A_27f),ap(c_2Ewords_2En2w(A_27f),ap(c_2Ebitstring_2Ev2n,V10v))),V11w) ) )
& ! [V12v] :
( mem(V12v,ty_2Elist_2Elist(bool))
=> ! [V13w] :
( mem(V13w,ty_2Efcp_2Ecart(bool,A_27g))
=> ap(ap(c_2Ewords_2Eword__sub(A_27g),V13w),ap(c_2Ebitstring_2Ev2w(A_27g),V12v)) = ap(ap(c_2Ewords_2Eword__sub(A_27g),V13w),ap(c_2Ewords_2En2w(A_27g),ap(c_2Ebitstring_2Ev2n,V12v))) ) )
& ! [V14v] :
( mem(V14v,ty_2Elist_2Elist(bool))
=> ! [V15w] :
( mem(V15w,ty_2Efcp_2Ecart(bool,A_27h))
=> ap(ap(c_2Ewords_2Eword__mul(A_27h),ap(c_2Ebitstring_2Ev2w(A_27h),V14v)),V15w) = ap(ap(c_2Ewords_2Eword__mul(A_27h),ap(c_2Ewords_2En2w(A_27h),ap(c_2Ebitstring_2Ev2n,V14v))),V15w) ) )
& ! [V16v] :
( mem(V16v,ty_2Elist_2Elist(bool))
=> ! [V17w] :
( mem(V17w,ty_2Efcp_2Ecart(bool,A_27i))
=> ap(ap(c_2Ewords_2Eword__mul(A_27i),V17w),ap(c_2Ebitstring_2Ev2w(A_27i),V16v)) = ap(ap(c_2Ewords_2Eword__mul(A_27i),V17w),ap(c_2Ewords_2En2w(A_27i),ap(c_2Ebitstring_2Ev2n,V16v))) ) )
& ! [V18v] :
( mem(V18v,ty_2Elist_2Elist(bool))
=> ! [V19w] :
( mem(V19w,ty_2Efcp_2Ecart(bool,A_27j))
=> ap(ap(c_2Ewords_2Eword__quot(A_27j),ap(c_2Ebitstring_2Ev2w(A_27j),V18v)),V19w) = ap(ap(c_2Ewords_2Eword__quot(A_27j),ap(c_2Ewords_2En2w(A_27j),ap(c_2Ebitstring_2Ev2n,V18v))),V19w) ) )
& ! [V20v] :
( mem(V20v,ty_2Elist_2Elist(bool))
=> ! [V21w] :
( mem(V21w,ty_2Efcp_2Ecart(bool,A_27k))
=> ap(ap(c_2Ewords_2Eword__quot(A_27k),V21w),ap(c_2Ebitstring_2Ev2w(A_27k),V20v)) = ap(ap(c_2Ewords_2Eword__quot(A_27k),V21w),ap(c_2Ewords_2En2w(A_27k),ap(c_2Ebitstring_2Ev2n,V20v))) ) )
& ! [V22v] :
( mem(V22v,ty_2Elist_2Elist(bool))
=> ! [V23w] :
( mem(V23w,ty_2Efcp_2Ecart(bool,A_27l))
=> ap(ap(c_2Ewords_2Eword__div(A_27l),ap(c_2Ebitstring_2Ev2w(A_27l),V22v)),V23w) = ap(ap(c_2Ewords_2Eword__div(A_27l),ap(c_2Ewords_2En2w(A_27l),ap(c_2Ebitstring_2Ev2n,V22v))),V23w) ) )
& ! [V24v] :
( mem(V24v,ty_2Elist_2Elist(bool))
=> ! [V25w] :
( mem(V25w,ty_2Efcp_2Ecart(bool,A_27m))
=> ap(ap(c_2Ewords_2Eword__div(A_27m),V25w),ap(c_2Ebitstring_2Ev2w(A_27m),V24v)) = ap(ap(c_2Ewords_2Eword__div(A_27m),V25w),ap(c_2Ewords_2En2w(A_27m),ap(c_2Ebitstring_2Ev2n,V24v))) ) )
& ! [V26v] :
( mem(V26v,ty_2Elist_2Elist(bool))
=> ! [V27w] :
( mem(V27w,ty_2Efcp_2Ecart(bool,A_27n))
=> ap(ap(c_2Ewords_2Eword__mod(A_27n),ap(c_2Ebitstring_2Ev2w(A_27n),V26v)),V27w) = ap(ap(c_2Ewords_2Eword__mod(A_27n),ap(c_2Ewords_2En2w(A_27n),ap(c_2Ebitstring_2Ev2n,V26v))),V27w) ) )
& ! [V28v] :
( mem(V28v,ty_2Elist_2Elist(bool))
=> ! [V29w] :
( mem(V29w,ty_2Efcp_2Ecart(bool,A_27o))
=> ap(ap(c_2Ewords_2Eword__mod(A_27o),V29w),ap(c_2Ebitstring_2Ev2w(A_27o),V28v)) = ap(ap(c_2Ewords_2Eword__mod(A_27o),V29w),ap(c_2Ewords_2En2w(A_27o),ap(c_2Ebitstring_2Ev2n,V28v))) ) )
& ! [V30v] :
( mem(V30v,ty_2Elist_2Elist(bool))
=> ! [V31w] :
( mem(V31w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__lt(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V30v)),V31w))
<=> p(ap(ap(c_2Ewords_2Eword__lt(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V30v))),V31w)) ) ) )
& ! [V32v] :
( mem(V32v,ty_2Elist_2Elist(bool))
=> ! [V33w] :
( mem(V33w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__lt(A_27a),V33w),ap(c_2Ebitstring_2Ev2w(A_27a),V32v)))
<=> p(ap(ap(c_2Ewords_2Eword__lt(A_27a),V33w),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V32v)))) ) ) )
& ! [V34v] :
( mem(V34v,ty_2Elist_2Elist(bool))
=> ! [V35w] :
( mem(V35w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__gt(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V34v)),V35w))
<=> p(ap(ap(c_2Ewords_2Eword__gt(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V34v))),V35w)) ) ) )
& ! [V36v] :
( mem(V36v,ty_2Elist_2Elist(bool))
=> ! [V37w] :
( mem(V37w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__gt(A_27a),V37w),ap(c_2Ebitstring_2Ev2w(A_27a),V36v)))
<=> p(ap(ap(c_2Ewords_2Eword__gt(A_27a),V37w),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V36v)))) ) ) )
& ! [V38v] :
( mem(V38v,ty_2Elist_2Elist(bool))
=> ! [V39w] :
( mem(V39w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__le(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V38v)),V39w))
<=> p(ap(ap(c_2Ewords_2Eword__le(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V38v))),V39w)) ) ) )
& ! [V40v] :
( mem(V40v,ty_2Elist_2Elist(bool))
=> ! [V41w] :
( mem(V41w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__le(A_27a),V41w),ap(c_2Ebitstring_2Ev2w(A_27a),V40v)))
<=> p(ap(ap(c_2Ewords_2Eword__le(A_27a),V41w),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V40v)))) ) ) )
& ! [V42v] :
( mem(V42v,ty_2Elist_2Elist(bool))
=> ! [V43w] :
( mem(V43w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__ge(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V42v)),V43w))
<=> p(ap(ap(c_2Ewords_2Eword__ge(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V42v))),V43w)) ) ) )
& ! [V44v] :
( mem(V44v,ty_2Elist_2Elist(bool))
=> ! [V45w] :
( mem(V45w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__ge(A_27a),V45w),ap(c_2Ebitstring_2Ev2w(A_27a),V44v)))
<=> p(ap(ap(c_2Ewords_2Eword__ge(A_27a),V45w),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V44v)))) ) ) )
& ! [V46v] :
( mem(V46v,ty_2Elist_2Elist(bool))
=> ! [V47w] :
( mem(V47w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__lo(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V46v)),V47w))
<=> p(ap(ap(c_2Ewords_2Eword__lo(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V46v))),V47w)) ) ) )
& ! [V48v] :
( mem(V48v,ty_2Elist_2Elist(bool))
=> ! [V49w] :
( mem(V49w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__lo(A_27a),V49w),ap(c_2Ebitstring_2Ev2w(A_27a),V48v)))
<=> p(ap(ap(c_2Ewords_2Eword__lo(A_27a),V49w),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V48v)))) ) ) )
& ! [V50v] :
( mem(V50v,ty_2Elist_2Elist(bool))
=> ! [V51w] :
( mem(V51w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__hi(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V50v)),V51w))
<=> p(ap(ap(c_2Ewords_2Eword__hi(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V50v))),V51w)) ) ) )
& ! [V52v] :
( mem(V52v,ty_2Elist_2Elist(bool))
=> ! [V53w] :
( mem(V53w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__hi(A_27a),V53w),ap(c_2Ebitstring_2Ev2w(A_27a),V52v)))
<=> p(ap(ap(c_2Ewords_2Eword__hi(A_27a),V53w),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V52v)))) ) ) )
& ! [V54v] :
( mem(V54v,ty_2Elist_2Elist(bool))
=> ! [V55w] :
( mem(V55w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__ls(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V54v)),V55w))
<=> p(ap(ap(c_2Ewords_2Eword__ls(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V54v))),V55w)) ) ) )
& ! [V56v] :
( mem(V56v,ty_2Elist_2Elist(bool))
=> ! [V57w] :
( mem(V57w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__ls(A_27a),V57w),ap(c_2Ebitstring_2Ev2w(A_27a),V56v)))
<=> p(ap(ap(c_2Ewords_2Eword__ls(A_27a),V57w),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V56v)))) ) ) )
& ! [V58v] :
( mem(V58v,ty_2Elist_2Elist(bool))
=> ! [V59w] :
( mem(V59w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__hs(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V58v)),V59w))
<=> p(ap(ap(c_2Ewords_2Eword__hs(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V58v))),V59w)) ) ) )
& ! [V60v] :
( mem(V60v,ty_2Elist_2Elist(bool))
=> ! [V61w] :
( mem(V61w,ty_2Efcp_2Ecart(bool,A_27a))
=> ( p(ap(ap(c_2Ewords_2Eword__hs(A_27a),V61w),ap(c_2Ebitstring_2Ev2w(A_27a),V60v)))
<=> p(ap(ap(c_2Ewords_2Eword__hs(A_27a),V61w),ap(c_2Ewords_2En2w(A_27a),ap(c_2Ebitstring_2Ev2n,V60v)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------