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

Lemma weak_mem_obs_eq_store: forall mc mf mc' mf' rmap rmapF bl1 bl2 f (Hlt: permMapLt rmap (getMaxPerm mc)) (HltF: permMapLt rmapF (getMaxPerm mf)) (Hlt2: permMapLt rmap (getMaxPerm mc')) (Hlt2F: permMapLt rmapF (getMaxPerm mf')) (Hf: f bl1 = Some bl2) (Hinjective: forall b1 b1' b2 : block, f b1 = Some b2 -> f b1' = Some b2 -> b1 = b1') (Hobs_eq: weak_mem_obs_eq f (restrPermMap Hlt) (restrPermMap HltF)) (Hvb: forall b, Mem.valid_block mc b <-> Mem.valid_block mc' b) (HvbF: forall b, Mem.valid_block mf b <-> Mem.valid_block mf' b), weak_mem_obs_eq f (restrPermMap Hlt2) (restrPermMap Hlt2F).