induction ls; intuition; simpl in *.
eapply eqRat_trans.
eapply ratAdd_0_l.
eapply ratAdd_eqRat_compat.
eapply eqRat_symm.
apply ratMult_0_r.
intuition.
rewrite IHls.
eapply eqRat_trans.
eapply ratAdd_eqRat_compat.
apply eqRat_refl.
apply ratAdd_comm.
rewrite <- (ratAdd_assoc).
apply ratAdd_eqRat_compat; intuition.
eapply eqRat_symm.
eapply eqRat_trans.
eapply ratMult_eqRat_compat.
apply eqRat_refl.
apply ratS_num.
rewrite ratMult_distrib.
rewrite ratAdd_comm.
apply ratAdd_eqRat_compat; intuition.
apply ratMult_1_r.
Qed.

Lemma sumList_body_const : forall (A : Set)(ls : list A) c,
sumList ls (fun a => c) == c * (length ls / 1).