(* Blocks that are not mapped by f are set to empty permission. This makes the invariant preservation easier. *)
Definition projectMap (f : memren) (pmap : access_map) : access_map :=
(pmap#1, Maps.PTree.fold (fun acc b bperm =>
match f b with
| Some b' =>
Maps.PTree.set b' bperm acc
| None =>
acc end)
pmap.2 (Maps.PTree.empty _)).

Lemma projectMap_tree_2:
forall (f:memren) pmap b'
(Hf: ~ exists b, f b = Some b'),
Maps.PTree.get b' (projectMap f pmap).2 = None.