induction ls; intuition; simpl in *.
eapply IHls; eauto.
rewrite H0.
eapply ratAdd_eqRat_compat; eauto.
eapply eqRat_refl.
intuition.
Qed.

Lemma sumList_0 : forall (ls : list A) f,
(sumList ls f == 0) <-> (forall a, In a ls -> (f a) == 0).