Coq.Wellfounded.Inclusion

# Module Coq.Wellfounded.Inclusion

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Author: 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.

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Index