(* 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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(*                             Lib_Eq_Le_Lt.v                               *)
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Require Export Arith.
Require Export Compare.
red in |- *; intros.
apply H; auto with arith.
Qed.
Hint Resolve not_S_eq.
simple induction n; auto with arith.
Qed.
Hint Resolve neq_O_le.
intros m n H.
apply le_lt_trans with m; auto with arith.
Qed.
Hint Immediate lt_O.
intros.
elim H.
exists 0; try trivial with arith.
intros; exists m; try trivial with arith.
Qed.
Hint Resolve lt_Ex_n.

Lemma lt_m_neq : forall m n : nat, m < n -> n <> m.