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