Proof using.
intros P.
cofix c.
intros s cnyP.
induction cnyP.
- apply always_inf_often. assumption.
- apply Always.
* apply E_next. destruct s as [s x']. apply always_now in IHcnyP. assumption.
* apply IHcnyP.
Qed.
(* monotony *)

(* Specifications: *)
Lemma now_monotonic :
forall (P Q: T -> Prop),
(forall x, P x -> Q x) -> forall s, now P s -> now Q s.