cofix subsub.
intros si s su. case su; clear su si s.
intros (s1, si) s0. simpl. intros su sb. constructor.
- assumption.
- apply subsub. assumption.
Qed.

(* Specifications: *)
Lemma subseqs'_subseqs : forall si s, subseqs' si s -> subseqs si s.
cofix subsub.