Program Definition weak_exclusive_mpred (P: mpred): mpred :=
fun w => exclusive_mpred (approx (S (level w)) P).
Next Obligation.
intros; hnf; intros.
unfold exclusive_mpred in *.
apply age_level in H.
eapply derives_trans, H0.
apply sepcon_derives; apply approx_derives_ge; omega.
Defined.

Lemma exclusive_mpred_nonexpansive:
nonexpansive weak_exclusive_mpred.