(* 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)                    *)
(****************************************************************************)
(*                                                                          *)
(*                                                                          *)
(*                   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          *)
(*                                                                          *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              May 30th 1996                               *)
(*                                                                          *)
(****************************************************************************)
(*                               Lib_Minus.v                                *)
(****************************************************************************)
Require Export Lib_Pred.
intros n.
elim minus_Sn_m.
apply eq_S.
elim minus_Sn_m.
apply eq_S.
elim minus_n_n; auto with arith.
auto with arith.
auto with arith.
Qed.
Hint Resolve minus_SS_n.
intros; simpl in |- *; auto with arith.
Qed.
Hint Resolve minus_S.

Lemma pred_minus_minus : forall n m : nat, pred (n - m) = n - S m.