intros.
unfold Ravg.
rewrite (@Rsum_constant v)...
unfold Rdiv.
rewrite (Rmult_comm (INR (length l))).
rewrite Rmult_assoc.
rewrite Rinv_r.
apply Rmult_1_r.
apply not_0_INR...
destruct l...
discriminate.
Qed.
Instance elemsR_le_Ravg: Proper (elemsR Rle ==> Rle) Ravg.
Proof with auto with real.
repeat intro.
unfold Ravg.
destruct x; inversion_clear H...
simpl @length.
rewrite (elemsR_length H1).
unfold Rdiv.
apply Rmult_le_compat_r...
apply elemsR_le_Rsum...
Qed.

(* Specifications: *)
Lemma Ravg_map_le X (f g: X -> R) (l: list X): (forall x, In x l -> f x <= g x) -> Ravg (map f l) <= Ravg (map g l).