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 joinD_Some: forall j k b b' delta (J: join j k b = Some(b',delta)), j b = Some(b',delta) \/ (j b = None /\ k b = Some(b',delta)).