Definition val_inject_opt (j: meminj) (v1 v2: option val) :=
  match v1, v2 with Some v1', Some v2' => val_inject j v1' v2'
  | None, None => True
  | _, _ => False
  end.

Lemma forall_valinject_lessdef: forall vals1 vals2 j (VInj12 : Forall2 (val_inject j) vals1 vals2) vals3 (LD23 : Forall2 Val.lessdef vals2 vals3), Forall2 (val_inject j) vals1 vals3.