Proof using.
induction 1; firstorder using E0, E_next.
Qed.

(* Specifications: *)
Lemma eventually_or_tl_introl :
forall (P Q : infseq T -> Prop) s,
eventually P s ->
eventually (P \/_ Q) s.
Lemma eventually_or_tl_or :
forall (P Q : infseq T -> Prop) s,
eventually (P \/_ Q) s ->
eventually P s \/ eventually Q s.