intros si s su. case su; clear su si s.
intros si s0 s1 su sb. constructor; simpl.
- assumption.
- apply subsub. assumption.
Qed.
(* Relating inf subseq to infinitely often *)

(* Specifications: *)
(* In the next lemma, always1 is bit overkill, but is just what is needed below *)
Lemma subseqs_eventually :
forall P si s, subseqs si s -> always1 P si -> eventually P s.