(** ** 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.