(** ** Memory invariants *)
(** A stack location is private if it is not the image of a valid location and we have full rights on it. *)
Definition loc_private (F: meminj) (m m': mem) (sp: block) (ofs: Z) : Prop :=
Mem.perm m' sp ofs Cur Freeable /\
(forall b delta, F b = Some(sp, delta) -> ~Mem.perm m b (ofs - delta) Max Nonempty).
(** Likewise, for a range of locations. *)
Definition range_private (F: meminj) (m m': mem) (sp: block) (lo hi: Z) : Prop :=
forall ofs, lo <= ofs < hi -> loc_private F m m' sp ofs.

Lemma range_private_free_left:
forall F m m' sp base sz hi b m1,
range_private F m m' sp (base + Z.max sz 0) hi ->
Mem.free m b 0 sz = Some m1 ->
F b = Some(sp, base) ->
Mem.inject F m m' ->
range_private F m1 m' sp base hi.