Program Definition bupd (P: pred rmap): pred rmap :=
fun m => forall c, joins (ghost_of m) (ghost_approx m c) ->
exists b, joins b (ghost_approx m c) /\
exists m', level m' = level m /\ resource_at m' = resource_at m /\ ghost_of m' = b /\ P m'.
Next Obligation.

Lemma bupd_frame_r: forall P Q, bupd P * Q |-- bupd (P * Q).