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 inject_mapped: forall j m1 m2 (Inj12: Mem.inject j m1 m2) k (RC: REACH_closed m1 (mapped k)) (INC: inject_incr k j), Mem.inject k m1 m2.