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

(* Specifications: *)
Lemma empty_map_spec: forall b ofs, Maps.PMap.get b empty_map ofs = None.