Definition Qabs (q:Q):Q:= 
  match q with 
  | Zero => Zero
  | Qpos qp => Qpos qp
  | Qneg qp => Qpos qp
  end.

Lemma Qabs_Qminus_bound:forall low up q1 q2, low <= q1 -> q1 <= up -> low <= q2 -> q2 <= up -> Qabs (q1-q2) <= up-low.