(* Rsum *)
Definition Rsum: list R -> R := fold_right Rplus 0.

(* Specifications: *)
Lemma Rsum_sum_map (T: Set) (fi: T -> nat) (fr: T -> R) (l: list T):
(forall x, In x l -> fr x = INR (fi x)) -> Rsum (map fr l) = INR (sum (map fi l)).