Module BAF := BA_Facts BA.(* Now, we prove the axioms about relativization.
     Again, this mostly involves packing and unpacking
     the canonTree type and pushing around mkCanon.
   *)

    Definition rel (a x:t) : t.

Lemma rel_classification : forall a x, { x = bot /\ rel a x = bot } + { x <> bot /\ proj1_sig (rel a x) = relativ_tree (proj1_sig a) (proj1_sig x) /\ (a = bot <-> rel a x = bot) }.