Proof using.
induction 1; firstorder using E0, E_next.
Qed.
(* until facts *)

(* Specifications: *)
Lemma until_Cons :
forall (x: T) (s: infseq T) J P,
until J P (Cons x s) -> P (Cons x s) \/ (J (Cons x s) /\ until J P s).