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

Lemma mem_obs_eq_storeF: forall f mc mf mf' chunk b ofs v pmap pmap2 (Hlt: permMapLt pmap (getMaxPerm mf)) (Hlt': permMapLt pmap (getMaxPerm mf')) (Hlt2: permMapLt pmap2 (getMaxPerm mf)) (Hstore: Mem.store chunk (restrPermMap Hlt2) b ofs v = Some mf') (Hdisjoint: permMapCoherence pmap pmap2 \/ permMapsDisjoint pmap pmap2) (Hobs_eq: mem_obs_eq f mc (restrPermMap Hlt)), mem_obs_eq f mc (restrPermMap Hlt').