(* Hint Rewrite move_prop_from_SEP move_local_from_SEP : norm. *)

Lemma lower_PROP_LOCAL_SEP:
forall P Q R rho, PROPx P (LOCALx Q (SEPx R)) rho =
(!!fold_right and True P && (local (fold_right (`and) (`True) (map locald_denote Q)) && `(fold_right sepcon emp R))) rho.