(* This code is copyrighted by its authors; it is distributed under  *)
(* the terms of the LGPL license (see LICENSE and description files) *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(*                   Solange Coupet-Grimal & Line Jakubiec                  *)
(*                                                                          *)
(*                                                                          *)
(*              Laboratoire d'Informatique de Marseille                     *)
(*               CMI-Technopole de Chateau-Gombert                          *)
(*                   39, Rue F. Joliot Curie                                *)
(*                   13453 MARSEILLE Cedex 13                               *)
(*           e-mail:{Solange.Coupet,Line.Jakubiec}@lim.univ-mrs.fr          *)
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(*                                Coq V5.10                                 *)
(*                              May 30th 1996                               *)
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(*                           Factorization_Verif.v                          *)
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Require Export Linear_Structures.
Require Export Factorization.
Section Factorization_for_Verification.
Variable A : Set.
Variable BASE : BT.
Let b := base BASE.
Let Num := num BASE.
Let Digit := digit BASE.
Let Val_bound := val_bound BASE.
Variable R : forall n : nat, A -> inf n -> inf n -> A -> Prop.
Definition Connection := connection A Digit Digit (R b).
Notation Factorizable := (factorizable _) (only parsing).
Notation Proper := (proper _) (only parsing).

Theorem factorization_for_verification :
factorizable _ R ->
proper _ BASE R ->
forall (n : nat) (X Y : Num n) (a a' : A),
Connection n a X Y a' -> R (exp b n) a (Val_bound n X) (Val_bound n Y) a'.