Definition access_map := Maps.PMap.t (Z -> option permission).
Definition delta_map := Maps.PTree.t (Z -> option (option permission)).
Section permMapDefs.
Definition empty_map : access_map :=
(fun z => None, Maps.PTree.empty (Z -> option permission)).

Lemma empty_map_spec: forall b ofs,
Maps.PMap.get b empty_map ofs = None.