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

Lemma load_None_obs: forall (mc mf : mem) (f:memren) (b1 b2 : block) chunk (ofs : Z) (Hload: Mem.load chunk mc b1 ofs = None) (Hf: f b1 = Some b2) (Hinjective: forall b0 b1' b3 : block, f b0 = Some b3 -> f b1' = Some b3 -> b0 = b1') (Hobs_eq: strong_mem_obs_eq f mc mf), Mem.load chunk mf b2 ofs = None.