#[local]
Hint Resolve lt_leaf gt_leaf lt_tree_node gt_tree_node : core.

(* Specifications: *)
Lemma lt_left : forall x y l r e h,
lt_tree x (Node l y e r h) -> lt_tree x l.
Lemma lt_right : forall x y l r e h,
lt_tree x (Node l y e r h) -> lt_tree x r.
Lemma gt_left : forall x y l r e h,
gt_tree x (Node l y e r h) -> gt_tree x l.
Lemma gt_right : forall x y l r e h,
gt_tree x (Node l y e r h) -> gt_tree x r.