(* 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                  *)
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(*                                                                          *)
(*              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_Prog.v                               *)
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Require Export Factorization.
Section Factorization_for_Realizer.
Variable A : Set.
Variable BASE : BT.
Let b := base BASE.
Let Num := num BASE.
Let Val_bound := val_bound BASE.
Let Digit := digit BASE.
Let Tl := tl Digit.
Variable FR : forall n : nat, A -> inf n -> inf n -> A.
Let R (n : nat) (a : A) (x y : inf n) (a' : A) : Prop := a' = FR n a x y.
Notation Factorizable := (factorizable _) (only parsing).
Notation Proper := (proper _) (only parsing).

(* Specifications: *)
Theorem factorization_for_realizer :
factorizable _ R ->
proper _ BASE R ->
forall (n : nat) (a : A) (X Y : Num n),
{a' : A | R (exp b n) a (Val_bound n X) (Val_bound n Y) a'}.