Notation alwsafe_sc s p scs := (always_sc s p scs (fun _ _ => True)).Notation alwsafe s p := (always s p (fun _ _ => True)).

Lemma alwI A s (p : proc A) (P : Prop) (Q : state -> proc A -> Prop) : alwsafe s p -> always s p (fun s' p' => P -> Q s' p') <-> (P -> always s p (fun s' p' => Q s' p')).