Proof using.
intros J P.
cofix c.
intros [x s] al.
apply R_tl.
- apply always_now in al.
assumption.
- simpl.
apply c.
apply always_invar in al.
assumption.
Qed.

(* Specifications: *)
Lemma always_inf_often :
forall (P: infseq T -> Prop) (s : infseq T), always P s -> inf_often P s.