Proof using.
intros P.
cofix c.
intros [x s] cnyP.
apply Always.
- unfold continuously in cnyP.
apply not_eventually_always_not in cnyP.
apply always_now in cnyP.
unfold not_tl in cnyP.
apply not_always_eventually_not in cnyP.
assumption.
- apply c.
intros cnynP.
contradict cnyP.
apply E_next.
assumption.
Qed.

Lemma not_tl_and_tl_or_tl :
forall (P Q : infseq T -> Prop) (s : infseq T),
(~_ (P /\_ Q)) s -> ((~_ P) \/_ (~_ Q)) s.