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

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

Lemma split_nontrivial : forall x1 x2 x, split x = (x1, x2) -> (x1 = bot \/ x2 = bot) -> x = bot.