Hint Resolve closed_wrt_PROPx closed_wrtl_PROPx: closed.

(* Specifications: *)
Lemma closed_wrt_LOCALx:
forall S Q R, Forall (closed_wrt_vars S) (map locald_denote Q) ->
closed_wrt_vars S R ->
closed_wrt_vars S (LOCALx Q R).
Lemma closed_wrtl_LOCALx:
forall S Q R, Forall (closed_wrt_lvars S) (map locald_denote Q) ->
closed_wrt_lvars S R ->
closed_wrt_lvars S (LOCALx Q R).