Proof using.
intros P s alP.
apply E0.
assumption.
Qed.
(* weak_until and eventually facts *)

Lemma weak_until_Cons :
forall (x: T) (s: infseq T) J P,
weak_until J P (Cons x s) -> P (Cons x s) \/ (J (Cons x s) /\ weak_until J P s).