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

Lemma proj_value_obs: forall f q vl1 vl2, (forall b1 b1' b2 : block, f b1 = Some b2 -> f b1' = Some b2 -> b1 = b1') -> Coqlib.list_forall2 (memval_obs_eq f) vl1 vl2 -> val_obs f (proj_value q vl1) (proj_value q vl2).