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

Lemma proj_bytes_obs: forall (f : memren) (vl vl' : seq memval), Coqlib.list_forall2 (memval_obs_eq f) vl vl' -> forall bl : seq byte, proj_bytes vl = Some bl -> proj_bytes vl' = Some bl.