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Diffstat (limited to 'theories/Wellfounded/Inclusion.v')
| -rw-r--r-- | theories/Wellfounded/Inclusion.v | 21 |
1 files changed, 10 insertions, 11 deletions
diff --git a/theories/Wellfounded/Inclusion.v b/theories/Wellfounded/Inclusion.v index 2038b34bf..2508011dc 100644 --- a/theories/Wellfounded/Inclusion.v +++ b/theories/Wellfounded/Inclusion.v @@ -10,24 +10,23 @@ (** Author: Bruno Barras *) -Require Relation_Definitions. +Require Import Relation_Definitions. Section WfInclusion. - Variable A:Set. - Variable R1,R2:A->A->Prop. + Variable A : Set. + Variables R1 R2 : A -> A -> Prop. - Lemma Acc_incl: (inclusion A R1 R2)->(z:A)(Acc A R2 z)->(Acc A R1 z). + Lemma Acc_incl : inclusion A R1 R2 -> forall z:A, Acc R2 z -> Acc R1 z. Proof. - NewInduction 2. - Apply Acc_intro;Auto with sets. + induction 2. + apply Acc_intro; auto with sets. Qed. - Hints Resolve Acc_incl. + Hint Resolve Acc_incl. - Theorem wf_incl: - (inclusion A R1 R2)->(well_founded A R2)->(well_founded A R1). + Theorem wf_incl : inclusion A R1 R2 -> well_founded R2 -> well_founded R1. Proof. - Unfold well_founded ;Auto with sets. + unfold well_founded in |- *; auto with sets. Qed. -End WfInclusion. +End WfInclusion.
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