induction ls; intuition.
unfold sumList.
simpl.
econstructor.
intuition.
unfold sumList in *. simpl in *.
econstructor.
eapply IHls.
eauto.
rewrite fold_add_body_eq.
2:{
eapply ratAdd_comm.
}
rewrite fold_add_init.
eapply eqRat_refl.
intuition.
Qed.

(* Specifications: *)
Lemma sumList_cons : forall (A : Set)(ls : list A) a f,
sumList (a :: ls) f == f a + (sumList ls f).