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

Lemma valid_pointer_ren: forall f m m' b1 b2 ofs (Hmem_obs_eq: mem_obs_eq f m m') (Hf: f b1 = Some b2), Mem.valid_pointer m b1 ofs = Mem.valid_pointer m' b2 ofs.