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

Lemma mem_free_obs: forall f m m' lo hi b1 b2 m2 (Hmem_obs_eq: mem_obs_eq f m m') (Hf: f b1 = Some b2) (Hfree: Mem.free m b1 lo hi = Some m2), exists m2', Mem.free m' b2 lo hi = Some m2' /\ mem_obs_eq f m2 m2'.