(*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 tree_avg_nonzero: forall sL sR s n, avg n sL sR = Some s -> (s <> bot <-> sL <> bot \/ sR <> bot).