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 REACH_closed_union: forall m X Y (HX: REACH_closed m X) (HY: REACH_closed m Y), REACH_closed m (fun b => X b || Y b).