Definition join (j k:meminj):meminj := fun b =>
  match j b with
     Some (b1, delta) => Some (b1,delta)
   | None => k b
  end.Definition disjoint (j k:meminj):Prop :=
    forall b, j b = None \/ k b = None.

Lemma joinI_None: forall j k b (J:j b = None) (K:k b = None), join j k b = None.