(** * Relating the memory states *)
(** The [magree] predicate is a variant of [Mem.extends] where we allow the contents of the two memory states to differ arbitrarily on some locations.  The predicate [P] is true on the locations whose contents must be in the [lessdef] relation. *)
Definition locset := block -> Z -> Prop.
Record magree (m1 m2: mem) (P: locset) : Prop := mk_magree {
ma_perm:
forall b ofs k p,
Mem.perm m1 b ofs k p -> Mem.perm m2 b ofs k p;
ma_perm_inv:
forall b ofs k p,
Mem.perm m2 b ofs k p -> Mem.perm m1 b ofs k p \/ ~Mem.perm m1 b ofs Max Nonempty;
ma_memval:
forall b ofs,
Mem.perm m1 b ofs Cur Readable ->
P b ofs ->
memval_lessdef (ZMap.get ofs (PMap.get b (Mem.mem_contents m1)))
(ZMap.get ofs (PMap.get b (Mem.mem_contents m2)));
ma_nextblock:
Mem.nextblock m2 = Mem.nextblock m1
}.

Lemma magree_free:
forall m1 m2 (P Q: locset) b lo hi m1',
magree m1 m2 P ->
Mem.free m1 b lo hi = Some m1' ->
(forall b' i, Q b' i ->
b' <> b \/ ~(lo <= i < hi) ->
P b' i) ->
exists m2', Mem.free m2 b lo hi = Some m2' /\ magree m1' m2' Q.