#[local]
Hint Resolve lt_tree_not_in lt_tree_trans gt_tree_not_in gt_tree_trans : core.
(** * Empty map *)
Definition Empty m := forall (a:key)(e:elt) , ~ MapsTo a e m.

(** * Membership *)
Lemma mem_1 : forall m x, bst m -> In x m -> mem x m = true.