Proof using.
intros e P ev. induction ev as [(x, s) Ps | x s ev induc_hyp].
- constructor 2; constructor 1; exact Ps.
- constructor 2. apply induc_hyp.
Qed.

Lemma eventually_always_cumul :
forall (s: infseq T) P Q,
eventually P s -> always Q s -> eventually (P /\_ always Q) s.