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.