(*D11*)
 Definition sub (x y : canonTree) : option canonTree :=
  match eq_dec (glb x y) y with
  | left _ => Some (glb x (comp y))
  | right _ => None
  end.

Lemma sub_join : forall t1 t2 t3, sub t1 t2 = Some t3 <-> join t2 t3 t1.