(** Matching global environments *)

Inductive match_globalenvs (f: meminj) (bound: block): Prop :=
  | mk_match_globalenvs
      (DOMAIN: forall b, Plt b bound -> f b = Some(b, 0))
      (IMAGE: forall b1 b2 delta, f b1 = Some(b2, delta) -> Plt b2 bound -> b1 = b2)
      (SYMBOLS: forall id b, Genv.find_symbol ge id = Some b -> Plt b bound)
      (FUNCTIONS: forall b fd, Genv.find_funct_ptr ge b = Some fd -> Plt b bound)
      (VARINFOS: forall b gv, Genv.find_var_info ge b = Some gv -> Plt b bound).(** Matching global environments *)

Inductive match_globalenvs (f: meminj) (bound: block): Prop :=
  | mk_match_globalenvs
      (DOMAIN: forall b, Plt b bound -> f b = Some(b, 0))
      (IMAGE: forall b1 b2 delta, f b1 = Some(b2, delta) -> Plt b2 bound -> b1 = b2)
      (SYMBOLS: forall id b, Genv.find_symbol ge id = Some b -> Plt b bound)
      (FUNCTIONS: forall b fd, Genv.find_funct_ptr ge b = Some fd -> Plt b bound)
      (VARINFOS: forall b gv, Genv.find_var_info ge b = Some gv -> Plt b bound).

Lemma match_globalenvs_preserves_globals: forall f, (exists bound, match_globalenvs f bound) -> meminj_preserves_globals ge f.