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 disjoint_sub: forall j k (D: disjoint j k) j' k' (J: inject_incr j' j) (K:inject_incr k' k), disjoint j' k'.