(* 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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(*                              Compare_Nat.v                               *)
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Require Export Arith.
Global Set Asymmetric Patterns.
Inductive Or3 (A B C : Prop) : Set :=
| First : A -> Or3 A B C
| Second : B -> Or3 A B C
| Third : C -> Or3 A B C.
Hint Resolve First Second Third.

Lemma Lt_eq_Gt : forall n m : nat, Or3 (n < m) (n = m) (n > m).
simple induction n; simple induction m.