intuition.
eapply fold_add_subset'; eauto.
intuition.
Qed.

(* Specifications: *)
Lemma sumList_exactly_one : forall (A : Set) a (ls : list A) f,
NoDup ls ->
In a ls ->
(forall b, In b ls -> a <> b -> f b == 0) ->
sumList ls f == f a.