(*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 decompose_lub: forall t1 t11 t12 t2 t21 t22 t3 t31 t32, decompose t1 = (t11,t12) -> decompose t2 = (t21,t22) -> decompose t3 = (t31,t32) -> (lub t1 t2 = t3 <-> (lub t11 t21 = t31 /\ lub t12 t22 = t32)).