(* $Id$ *)

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(*                              Bruno Barras                                *)
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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.
    Induction 2;Intros.
    Apply Acc_intro;Auto with sets.
  Save.

  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.
  Save.

End WfInclusion.