Notation coherent := (Coh W).Definition always A s (p : proc A) P := forall scs, always_sc s p scs P.

Lemma alwp_envsq A s1 (p1 : proc A) scs (P : _ -> _ -> Prop) : always_sc s1 p1 scs P -> always_sc s1 p1 scs (fun s2 p2 => forall s3, network_rely W this s2 s3 -> P s3 p2).