induction y...
intros.
simpl.
rewrite IHy.
rewrite <- plus_n_Sm...
Qed.

(* Specifications: *)
Lemma nats_Sw b w: nats b (S w) = b :: nats (S b) w.
Lemma nats_Sw' w b: nats b (S w) = nats b w ++ (w + b :: nil).
Proof with auto.