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

Lemma Qabs_Zero_Qminus_eq:forall q1 q2, q1=q2 -> Qabs (q1-q2) = Zero.