intuition.
unfold sumList. simpl.
rewrite fold_add_body_eq.
2:{
eapply ratAdd_comm.
}
rewrite fold_add_init.
eapply eqRat_refl.
intuition.
Qed.

Lemma sumList_sum : forall (A : Set)(ls : list A)(f1 f2 : A -> Rat),
sumList ls (fun a => f1 a + f2 a) ==
sumList ls f1 + sumList ls f2.