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 join_left_agree: forall j k b b1 d1 (JK: join j k b = Some(b1,d1)) b2 d2 (J: j b = Some(b2,d2)), b1=b2 /\ d1=d2.