(* Some basic facts about the relativization operation: It is injective when a is nonempty; a number of facts about nonemptyness, nonfullness and canonical trees; it commutes with union, intersection, mkCanon; and it is an associative operation. *)

Lemma relativ_empty : forall a x,
nonEmptyTree a -> nonEmptyTree x ->
nonEmptyTree (relativ_tree a x).