Local Hint Resolve lt_leaf gt_leaf lt_tree_node gt_tree_node : core.

(* Specifications: *)
Lemma lt_tree_not_in :
forall (x : elt) (t : tree), lt_tree x t -> ~ InT x t.
Lemma lt_tree_trans :
forall x y, X.lt x y -> forall t, lt_tree x t -> lt_tree y t.
Lemma gt_tree_not_in :
forall (x : elt) (t : tree), gt_tree x t -> ~ InT x t.
Lemma gt_tree_trans :
forall x y, X.lt y x -> forall t, gt_tree x t -> gt_tree y t.