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(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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(*         *       GNU Lesser General Public License Version 2.1        *)
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(*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.