induction l...
intros.
simpl.
apply Rplus_le_le_0_compat; intuition.
Qed.

(* Specifications: *)
Lemma Rsum_single x: Rsum (x :: nil) = x.
Lemma RsumOver_cons (X: Set) (x: X) (l: list X) (f: X -> R): RsumOver (x :: l) f = f x + RsumOver l f.
Lemma RsumOver_constant_le (X: Set) (l: list X) (f: X -> R) (c: R):
(forall x, List.In x l -> f x <= c) -> RsumOver l f <= INR (length l) * c.