Proof with auto.
unfold RsumOver.
intros.
rewrite <- (map_length f l).
apply Rsum_le...
intros.
destruct (In_map_inv H0).
destruct H1.
subst...
Qed.

Lemma nats_plusb b b' w: nats (b + b') w = map (plus b) (nats b' w).
Proof with auto.