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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i $Id: Inclusion.v 13323 2010-07-24 15:57:30Z herbelin $ i*)
(** Author: Bruno Barras *)
Require Import Relation_Definitions.
Section WfInclusion.
Variable A : Type.
Variables R1 R2 : A -> A -> Prop.
Lemma Acc_incl : inclusion A R1 R2 -> forall z:A, Acc R2 z -> Acc R1 z.
Proof.
induction 2.
apply Acc_intro; auto with sets.
Qed.
Hint Resolve Acc_incl.
Theorem wf_incl : inclusion A R1 R2 -> well_founded R2 -> well_founded R1.
Proof.
unfold well_founded in |- *; auto with sets.
Qed.
End WfInclusion.
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