(* 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 pmap_inj_incr:
forall f f' pmap pmap'
(Hincr: ren_incr f f')
(Hinjective: forall b1 b1' b2,
f' b1 = Some b2 ->
f' b1' = Some b2 ->
b1 = b1')
(Hinj: pmap_inj f pmap pmap'),
pmap_inj f' pmap pmap'.