induction b; simpl; intros.
induction (nats b' w)...
simpl.
rewrite <- IHl...
rewrite nats_Sb.
rewrite IHb.
rewrite map_map...
Qed.

(* Specifications: *)
Lemma RsumOver_nats b w f:
RsumOver (nats b w) f =
RsumOver (nats 0 w) (f ∘ plus b).