Local Hint Resolve arb_nrr_rb arb_nr_rb : core.
(** ** A Red-Black tree has indeed a logarithmic depth *)
Definition redcarac s := rcase (fun _ _ _ => 1) (fun _ => 0) s.

Lemma maxdepth_upperbound s : Rbt s ->
maxdepth s <= 2 * Nat.log2 (S (cardinal s)).