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

Lemma setPermBlock_weak_obs_eq: forall (f : block -> option block) (bl1 bl2 : block) (ofsl : Z) (pmap pmapF : access_map) (mc mf : mem) (p : option permission) (Hlt : permMapLt pmap (getMaxPerm mc)) (HltF : permMapLt pmapF (getMaxPerm mf)) (Hfl: f bl1 = Some bl2) (Hweak_obs_eq: weak_mem_obs_eq f (restrPermMap Hlt) (restrPermMap HltF)) (Hlt' : permMapLt (setPermBlock p bl1 ofsl pmap lksize.LKSIZE_nat) (getMaxPerm mc)) (HltF' : permMapLt (setPermBlock p bl2 ofsl pmapF lksize.LKSIZE_nat) (getMaxPerm mf)), weak_mem_obs_eq f (restrPermMap Hlt') (restrPermMap HltF').