(** Valid values are the ones that have no pointers outside the domain of f*)
  Definition valid_val (f: memren) (v : val) : Prop :=
    match v with
    | Vptr b _ =>
      exists b', f b = Some b'
    | _ => True
    end.Definition valid_memval (f: memren) (mv : memval) : Prop :=
    match mv with
    | Fragment v _ _ =>
      valid_val f v
    | _ => True
    end.

Lemma valid_val_add: forall f v1 v2, valid_val f v1 -> valid_val f v2 -> valid_val f (Val.add v1 v2).