Abort.  (* Not true *)
(** In fact, [naive_lookup_relateX] is provably false, as long as the type [V] contains at least two different values. *)

(* Specifications: *)
Theorem not_naive_lookup_relateX:
forall v, default <> v ->
~ (forall k t cts , AbsX t cts -> lookup k t =  cts k).
(** **** Exercise: 4 stars, optional (lookup_relateX)  *)
Theorem lookup_relateX:
forall k t cts ,
SearchTree t -> AbsX t cts -> lookup k t =  cts k.