Proof with auto.
unfold Ravg. intros. repeat rewrite map_length.
rewrite Rsum_map_plus.
unfold Rdiv.
rewrite Rmult_plus_distr_r...
Qed.

Lemma Ravg_constant l: l <> nil -> forall v, (forall x, In x l -> x = v) -> Ravg l = v.
Proof with auto.