induction ls; intuition.
unfold sumList; simpl.
reflexivity.
rewrite sumList_cons.
simpl.
rewrite IHls.
rewrite ratS_num.
intuition.
Qed.

Theorem fold_left_orb_true_init :
forall (A : Type)(f : A -> bool)(ls : list A),
fold_left (fun b x => orb b (f x)) ls true = true.