Definition PMap_eq {A} (m m' : PMap.t (Z -> A)) := forall b' ofs', m !! b' ofs' = m' !! b' ofs'.

Lemma PMap_eq_trans {A} : transitive _ (@PMap_eq A). intros ? ? ? E E' ? ?. rewrite E, E'. auto. Qed.
Definition A2P {A} :=
(fun (pmap : access_map) (a : address * A) =>
let (a0, _) := a in let (b0, ofs0) := a0 in setPermBlock (Some Writable) b0 ofs0 pmap LKSIZE_nat).