Corollary mem_obs_eq_domain_ren:
    forall f m m',
      mem_obs_eq f m m' ->
      domain_memren f m.

Lemma mem_free_obs_perm: forall f m m' m2 m2' lo hi b1 b2 (Hmem_obs_eq: mem_obs_eq f m m') (Hf: f b1 = Some b2) (Hfree: Mem.free m b1 lo hi = Some m2) (Hfree': Mem.free m' b2 lo hi = Some m2') b0 b3 ofs (Hf0: f b0 = Some b3), permissions.permission_at m2 b0 ofs Cur = permissions.permission_at m2' b3 ofs Cur.