Module MemErasure.
(** The values of the erased memory may be more defined and its permissions are top.*)
(** In retrospect setting the permissions to top was a bad choice. It should have been that the permissions of the erased memory are above the permissions of the other memory. This would make it more reusable and it wouldn't need a second definition for free. *)
Local Notation "a # b" := (PMap.get b a) (at level 1).
Record mem_erasure (m m': mem) :=
{ perm_le:
forall b ofs k,
Mem.valid_block m' b ->
(Mem.mem_access m')#b ofs k = Some Freeable;
erased_contents: forall b ofs,
memval_erasure (ZMap.get ofs ((Mem.mem_contents m) # b))
(ZMap.get ofs ((Mem.mem_contents m') # b));
erased_nb: Mem.nextblock m = Mem.nextblock m'
}.

Lemma setN_erasure :
forall (vl1 vl2 : seq.seq memval),
memval_erasure_list vl1 vl2 ->
forall (p : Z) (c1 c2 : ZMap.t memval),
(forall q : Z,
memval_erasure (ZMap.get q c1) (ZMap.get q c2)) ->
forall q : Z,
memval_erasure (ZMap.get q (Mem.setN vl1 p c1))
(ZMap.get q (Mem.setN vl2 p c2)).