(* Axioms about splittability. These follow easily from relativization.
   *)

    Definition leftTree : canonTree.Definition rightTree : canonTree.Definition split (x:canonTree) := (rel x leftTree, rel x rightTree).

(* Specifications: *)
Lemma split_disjoint : forall x1 x2 x, split x = (x1, x2) -> glb x1 x2 = bot.
Lemma split_together : forall x1 x2 x, split x = (x1, x2) -> lub x1 x2 = x.
Lemma split_nontrivial : forall x1 x2 x, split x = (x1, x2) -> (x1 = bot \/ x2 = bot) -> x = bot.