induction ls1; intuition; simpl in *.
unfold sumList; simpl in *.
rewrite <- ratAdd_0_l.
intuition.
repeat rewrite sumList_cons.
rewrite IHls1.
rewrite ratAdd_assoc.
intuition.
Qed.

(* Specifications: *)
Lemma filter_all_true :
forall (A : Set)(ls : list A)(P : A -> bool),
(forall a, In a ls -> P a = true) ->
filter P ls = ls.