(*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.

(*L9*)
Lemma sub_join : forall t1 t2 t3,
sub t1 t2 = Some t3 <-> join t2 t3 t1.