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

Lemma alwA' A B s (p : proc A) scs (P : B -> state -> proc A -> Prop) : alwsafe_sc s p scs -> (always_sc s p scs (fun s' p' => forall x, P x s' p') <-> forall x, always_sc s p scs (fun s' p' => P x s' p')).