induction l...
simpl.
rewrite Rsum_app.
congruence.
Qed.
(* Things like the three lemmas above are more elegantly stated as extensional equalities on function compositions, but stated that way they cannot be easily rewritten with.. *)

Lemma Rsum_nonneg l: (forall x, In x l -> 0 <= x) -> 0 <= Rsum l.
Proof with auto with real.