#[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.

(** * Emptyness test *)
Lemma is_empty_1 : forall m, Empty m -> is_empty m = true.