Proof using.
intros P Q.
cofix c.
intros s alP alQ.
destruct alP.
destruct alQ.
apply Always.
- split; assumption.
- apply c; assumption.
Qed.

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