Proof with auto.
intros.
replace b with ((b + 0)%nat)...
rewrite nats_plusb.
unfold RsumOver.
rewrite map_map...
f_equal.
unfold compose.
apply map_ext...
Qed.

Lemma RsumOver_le (X: Set) (f g: X -> R) (l: list X):
(forall x, In x l -> f x <= g x) -> RsumOver l f <= RsumOver l g.