#[local]
Hint Resolve lt_left lt_right gt_left gt_right : core.

(* Specifications: *)
Lemma lt_tree_not_in :
forall x m, lt_tree x m -> ~ In x m.
Lemma lt_tree_trans :
forall x y, X.lt x y -> forall m, lt_tree x m -> lt_tree y m.
Lemma gt_tree_not_in :
forall x m, gt_tree x m -> ~ In x m.
Lemma gt_tree_trans :
forall x y, X.lt y x -> forall m, gt_tree x m -> gt_tree y m.