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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(*i $Id: Inclusion.v,v 1.1.2.1 2004/07/16 19:31:41 herbelin Exp $ i*)
+
+(** Author: Bruno Barras *)
+
+Require Relation_Definitions.
+
+Section WfInclusion.
+  Variable A:Set.
+  Variable R1,R2:A->A->Prop.
+
+  Lemma Acc_incl: (inclusion A R1 R2)->(z:A)(Acc A R2 z)->(Acc A R1 z).
+  Proof.
+    NewInduction 2.
+    Apply Acc_intro;Auto with sets.
+  Qed.
+
+  Hints Resolve Acc_incl.
+
+  Theorem wf_incl: 
+         (inclusion A R1 R2)->(well_founded A R2)->(well_founded A R1).
+  Proof.
+    Unfold well_founded ;Auto with sets.
+  Qed.
+
+End WfInclusion.