Definition total_Qdiv_lazy (x y : Q) :=
  match Q_zerop y with
  | left _ => Zero
  | right h => Qdiv_lazy x y h
  end.

Lemma second_QField : field_theory Zero Qone Qplus_lazy Qmult_lazy Qminus_lazy Qopp_lazy total_Qdiv_lazy total_Qinv_lazy (eq(A:=Q)).