Proof using.
intros P.
cofix c.
intros s evP.
destruct s as [e s].
apply Always.
* unfold not_tl.
intro Pn.
case evP.
apply E0.
assumption.
* apply c.
intro evPn.
contradict evP.
apply E_next.
assumption.
Qed.

(* Specifications: *)
Lemma always_not_eventually :
forall (P : infseq T -> Prop) (s : infseq T),
always (~_ P) s -> ~ eventually P s.