induction n; intuition; simpl in *.
destruct ls1; simpl in *.
omega.
f_equal.
eapply IHn.
omega.
Qed.

Lemma sumList_rel_func : forall (A : Set)(f : A -> Rat -> Prop) ls r1,
sumList_rel f ls r1 ->
forall r2,
sumList_rel f ls r2 ->
(forall a v1 v2, f a v1 -> f a v2 -> v1 == v2) ->
r1 == r2.