Proof using.
intros x s J P ul.
change (P (Cons x s) \/ (J (Cons x s) /\ until J P (tl (Cons x s)))). case ul; auto.
Qed.

(* Specifications: *)
Lemma until_eventually :
forall (J P : infseq T -> Prop),
forall s, until J P s -> eventually P s.