Author: Bruno Barras |
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.