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

Lemma val_obs_equal: forall f v1 v1' v2 v2' (Hinjective: forall b1 b1' b2, f b1 = Some b2 -> f b1' = Some b2 -> b1 = b1') (Hval1: val_obs f v1 v1') (Hval2: val_obs f v2 v2'), Val.eq v1 v2 <-> Val.eq v1' v2'.