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_lowerbound s : s<>Leaf ->
Nat.log2 (cardinal s) < maxdepth s.