Remark add_inject:
  forall v1 v1' v2 v2',
  inject f v1 v1' ->
  inject f v2 v2' ->
  inject f (Val.add v1 v2) (Val.add v1' v2').Remark sub_inject:
  forall v1 v1' v2 v2',
  inject f v1 v1' ->
  inject f v2 v2' ->
  inject f (Val.sub v1 v2) (Val.sub v1' v2').Remark addl_inject:
  forall v1 v1' v2 v2',
  inject f v1 v1' ->
  inject f v2 v2' ->
  inject f (Val.addl v1 v2) (Val.addl v1' v2').Remark subl_inject:
  forall v1 v1' v2 v2',
  inject f v1 v1' ->
  inject f v2 v2' ->
  inject f (Val.subl v1 v2) (Val.subl v1' v2').

Lemma offset_ptr_inject: forall v v' ofs, inject f v v' -> inject f (offset_ptr v ofs) (offset_ptr v' ofs).