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)).