(* 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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(*                             Compare_Num.v                                *)
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Require Export Numerals.
Require Export Compare_Nat.
Section compare_num.
Variable BASE : BT.
Let Digit := digit BASE.
Let valB := val BASE.
Let ValB := Val BASE.
Let Num := num BASE.
Let Val_bound := val_bound BASE.
Let Cons := cons Digit.
Let Nil := nil Digit.

(* Specifications: *)
Lemma Comp_dif :
forall (n : nat) (x y : Digit) (X Y : Num n),
valB x < valB y ->
Compare_Nat.comparison (ValB (S n) (Cons n x X)) (ValB (S n) (Cons n y Y)) =
L.