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 cmplu_bool_inject: forall c v1 v2 v1' v2' b, inject f v1 v1' -> inject f v2 v2' -> Val.cmplu_bool valid_ptr1 c v1 v2 = Some b -> Val.cmplu_bool valid_ptr2 c v1' v2' = Some b.