Proof with try field.
induction l; simpl...
rewrite IHl...
Qed.

(* Specifications: *)
Lemma Rsum_map_app_map X Y f g (h: X -> Y) (l: list X):
Rsum (map f (map g l ++ map h l)) = Rsum (map (fun x => f (g x) + f (h x)) l).