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(* 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: july 1995                                              *)
(* file: MultSeq.v                                              *)
(* contents: VERIFICATION OF A SEQUENTIAL MULTIPLIER.           *)
(* Proofs of the invariant and the final theorem                *)
(****************************************************************)
(* L'invariant est : si t<= size alors nat(R1(t)[size-t:size-1]@R2(t))=nat(V2)*nat(V1[0:t-1]) *)
(****************************************************************)
(* D'abord on prouve l'invariant pour t=O: *)

Lemma Invariant_t_O :
BV_to_nat (appbv (stripbv (R1 0) size) (R2 0)) =
BV_to_nat V2 * BV_to_nat (truncbv V1 0).