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

Lemma check_value_obs: forall f n vl vl' v v' q (Hf: forall b1 b1' b2, f b1 = Some b2 -> f b1' = Some b2 -> b1 = b1'), Coqlib.list_forall2 (memval_obs_eq f) vl vl' -> val_obs f v v' -> check_value n v q vl = check_value n v' q vl'.