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

Lemma mem_obs_eq_of_weak_strong: forall m m' f pmap1 pmap1' pmap2 pmap2' (Hlt1: permMapLt pmap1 (getMaxPerm m)) (Hlt2: permMapLt pmap2 (getMaxPerm m')) (Hlt1': permMapLt pmap1' (getMaxPerm m)) (Hlt2': permMapLt pmap2' (getMaxPerm m')) (Hstrong_obs: strong_mem_obs_eq f (restrPermMap Hlt1) (restrPermMap Hlt2)) (Hweak: weak_mem_obs_eq f (restrPermMap Hlt1') (restrPermMap Hlt2')), mem_obs_eq f (restrPermMap Hlt1) (restrPermMap Hlt2).