Definition genvs_domain_eq {F1 F2 V1 V2: Type}
  (ge1: Genv.t F1 V1) (ge2: Genv.t F2 V2) :=
    (forall b, fst (genv2blocks ge1) b <-> fst (genv2blocks ge2) b) /\
    (forall b, snd (genv2blocks ge1) b <-> snd (genv2blocks ge2) b) /\
    (forall b, (exists f, Genv.find_funct_ptr ge1 b = Some f)
           <-> (exists f, Genv.find_funct_ptr ge2 b = Some f)).

Lemma genvs_domain_eq_preserves: forall {F1 F2 V1 V2: Type} (ge1: Genv.t F1 V1) (ge2: Genv.t F2 V2) j, genvs_domain_eq ge1 ge2 -> (meminj_preserves_globals_ind (genv2blocks ge1) j <-> meminj_preserves_globals_ind (genv2blocks ge2) j).