(* Demonstrate that intersection distributes over union and vice-versa. *)

(* Specifications: *)
Lemma intersect_distrib : forall x y z,
intersect_tree x (union_tree y z) =
union_tree (intersect_tree x y) (intersect_tree x z).
Lemma union_distrib : forall x y z,
union_tree x (intersect_tree y z) =
intersect_tree (union_tree x y) (union_tree x z).