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

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