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Diffstat (limited to 'theories/Wellfounded/Inclusion.v')
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diff --git a/theories/Wellfounded/Inclusion.v b/theories/Wellfounded/Inclusion.v new file mode 100644 index 00000000..1677659c --- /dev/null +++ b/theories/Wellfounded/Inclusion.v @@ -0,0 +1,32 @@ +(************************************************************************) +(* 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 1.7.2.1 2004/07/16 19:31:19 herbelin Exp $ i*) + +(** Author: Bruno Barras *) + +Require Import Relation_Definitions. + +Section WfInclusion. + Variable A : Set. + 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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