(* RsumOver *)

Definition RsumOver (X: Set) (l: list X) (f: X -> R): R := Rsum (map f l).

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.