Global Notation "a # b" := (Maps.PMap.get b a) (at level 1).

Lemma permission_at_free_2 : forall m m' (lo hi : Z) b b' ofs' (Hfree: Mem.free m b lo hi = Some m') (Hb: b <> b'), forall k : perm_kind, permission_at m b' ofs' k = permission_at m' b' ofs' k.