(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(****************************************************************)
(*           The Calculus of Inductive Constructions            *)
(*                       COQ v5.10                              *)
(*                                                              *)
(* Laurent Arditi.  Laboratoire I3S. CNRS ura 1376.             *)
(* Universite de Nice - Sophia Antipolis                        *)
(* arditi@unice.fr, http://wwwi3s.unice.fr/~arditi/lolo.html    *)
(*                                                              *)
(* date: october 1995                                           *)
(* file: IncrDecr.v                                             *)
(* contents: definnition of an incrementer and a decrementer    *)
(* on BVs     **** TO BE COMPLETED ****                         *)
(****************************************************************)
Require Export AdderProof.
Fixpoint BV_increment (l : list bool) : BV :=
match l with
| nil => nilbv
| false :: v => true :: v
| true :: v => false :: BV_increment v
end.
Fixpoint BV_increment_carry (l : list bool) : bool :=
match l with
| nil => true
| false :: v => false
| true :: v => BV_increment_carry v
end.
Fixpoint BV_decrement (l : list bool) : BV :=
match l with
| nil => nilbv
| false :: v => true :: BV_decrement v
| true :: v => false :: v
end.
Fixpoint BV_decrement_carry (l : list bool) : bool :=
match l with
| nil => true
| false :: v => BV_decrement_carry v
| true :: v => false
end.

(* Specifications: *)
Lemma length_BV_increment :
forall v : BV, lengthbv (BV_increment v) = lengthbv v.