Definition REACH_closed m (X: Values.block -> bool) : Prop :=
  (forall b, REACH m X b = true -> X b = true).Definition mapped (j:meminj) b : bool :=
  match j b with None => false | Some _ => true end.

Lemma mapped_charT: forall j b, (mapped j b = true) <-> (exists p, j b = Some p).