Proof using.
intros until 1.
intro H_eventually.
induction H_eventually.
- apply E0.
destruct s.
firstorder using always_Cons.
- eauto using E_next, always_invar.
Qed.

Lemma cumul_inf_often_always :
forall (P Q : infseq T -> Prop) s,
always P s ->
inf_often Q s ->
inf_often (P /\_ Q) s.