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'.