induction ls; intuition; simpl in *.
intuition.
eapply eqRat_trans.
eapply fold_add_body_eq.
eapply eqRat_symm.
eapply ratMult_distrib_r.
intuition.
eapply eqRat_refl.
eapply IHls.
Qed.

Lemma sumList_factor_constant_r : forall (A : Set)(ls : list A)(f : A -> Rat) c,
sumList ls (fun a => (f a) * c) == (sumList ls f) * c.