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_foreign_pub: forall mu (WD: SM_wd mu),
disjoint (foreign_of mu) (pub_of mu).