Hint Resolve closed_wrt_exp closed_wrtl_exp : closed.

(* Specifications: *)
Lemma closed_wrt_imp: forall S (P Q: environ->mpred),
closed_wrt_vars S P -> closed_wrt_vars S Q ->
closed_wrt_vars S (P --> Q).
Lemma closed_wrtl_imp: forall S (P Q: environ->mpred),
closed_wrt_lvars S P -> closed_wrt_lvars S Q ->
closed_wrt_lvars S (P --> Q).