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