Proof using.
intros x s P cny.
apply eventually_Cons in cny.
case cny; trivial.
intro alP.
apply E0.
apply always_invar in alP; assumption.
Qed.

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