Section Elt.
Variable elt:Type.
Implicit Types m r : t elt.
(** * Basic results about [MapsTo], [In], [lt_tree], [gt_tree], [height] *)
(** Facts about [MapsTo] and [In]. *)
Hint Resolve MapsTo_In : core.
Hint Immediate MapsTo_1 : core.
(** Results about [lt_tree] and [gt_tree] *)
Hint Resolve lt_leaf gt_leaf lt_tree_node gt_tree_node : core.
Hint Resolve lt_left lt_right gt_left gt_right : core.

Lemma lt_tree_not_in :
forall x m, lt_tree x m -> ~ In x m.