(** [] *)

Remark omega_on_keys:
   forall i j : key, ~ (i > j) -> ~ (i < j) -> i=j.

(* Specifications: *)
Theorem insert_SearchTree: forall k v t, SearchTree t -> SearchTree (insert k v t).
Lemma lookup_relate': forall (k : key) (t : tree) (cts : total_map V), SearchTree t -> Abs t cts -> lookup k t = cts k.
Theorem insert_relate': forall k v t cts, SearchTree t -> Abs t cts -> Abs (insert k v t) (t_update cts k v).