(** ** A few results about [mindepth] and [maxdepth] *)

(* Specifications: *)
Lemma mindepth_maxdepth s : mindepth s <= maxdepth s.
Lemma maxdepth_cardinal s : cardinal s < 2^(maxdepth s).
Lemma mindepth_cardinal s : 2^(mindepth s) <= S (cardinal s).
Lemma maxdepth_log_cardinal s : s <> Leaf ->
Nat.log2 (cardinal s) < maxdepth s.
Lemma mindepth_log_cardinal s : mindepth s <= Nat.log2 (S (cardinal s)).
End Props.