induction ls; intuition.
inversion H; clear H; subst.
econstructor.
rewrite H3.
apply ratMult_0_r.
inversion H; clear H; subst.
econstructor.
eauto.
unfold ratMult_rel.
intuition.
eapply ratMult_eqRat_compat; eauto.
rewrite H8.
eapply ratMult_distrib.
Qed.

(* Specifications: *)
Lemma series_le : forall n (f1 f2 : nat -> Rat -> Prop) r1 r2,
(forall i v1 v2, f1 i v1 -> f2 i v2 -> v2 <= v1) ->
sumList_rel f1 (getNats O n) r1 ->
sumList_rel f2 (getNats O n) r2 ->
r2 <= r1.