induction ls; intuition; simpl in *;
intuition; subst.
assert (init + f a <= r).
eapply IHls.
apply H.
eapply ratAdd_any_le; eauto.
assert (init + f a0 <= r).
eapply IHls.
eauto.
eapply ratAdd_any_le.
eapply leRat_trans.
apply eqRat_impl_leRat.
apply ratAdd_comm.
eauto.
edestruct IHls; eauto.
Qed.

(* Specifications: *)
Lemma sumList_iter_le : forall (A : Set)(ls : list A) f r a,
sumList ls f <= r ->
In a ls ->
f a <= r.