induction l.
rewrite Ravg_nil...
intros.
rewrite Ravg_cons.
rewrite IHl.
rewrite Rmult_0_l.
rewrite (H a).
rewrite Rplus_0_l.
unfold Rdiv.
rewrite Rmult_0_l...
left...
intros.
apply H.
right...
Qed.
(* Ravg_0 and Ravg_0_le cannot be generalized to arbitrary constant resp. lower bound, because Ravg nil = 0 *)

(* Specifications: *)
Lemma Ravg_app x y:
Ravg (x ++ y) = / INR (length x + length y) * (Ravg x * INR (length x) + Ravg y * INR (length y)).