Proof with auto.
induction l...
simpl.
intros.
rewrite plus_INR.
rewrite H...
rewrite IHl...
Qed.
Instance Rsum_Permutation: Proper (Permutation ==> eq) Rsum.
Proof with auto.
intros x y p.
induction p...
simpl.
rewrite IHp...
simpl.
do 2 rewrite <- Rplus_assoc.
rewrite (Rplus_comm y)...
rewrite IHp1...
Qed.

(* Specifications: *)
Lemma Rsum_app (x y: list R): Rsum (x ++ y) = Rsum x + Rsum y.
Proof with auto with real.