Proof using.
intros P s cnyP.
induction cnyP.
- destruct s as [e s].
intros ifP.
apply always_now in ifP.
induction ifP.
* destruct s0 as [e0 s0].
apply always_now in H.
unfold not_tl in H.
contradict H.
trivial.
* apply always_invar in H.
contradict IHifP.
trivial.
- intro ioP.
apply always_invar in ioP.
contradict IHcnyP.
trivial.
Qed.

Lemma inf_often_not_continuously :
forall (P : infseq T -> Prop) (s : infseq T),
inf_often (~_ P) s -> ~ continuously P s.