
theorem
  for I being non degenerated domRing-like commutative Ring for u,v
being Element of the_Field_of_Quotients(I) holds (quotadd(I)).(u,v) is Element
  of the_Field_of_Quotients(I)
proof
  let I be non degenerated domRing-like commutative Ring;
  let u,v be Element of the_Field_of_Quotients(I);
  reconsider s = u, t = v as Element of Quot.I;
  (quotadd(I)).(u,v) = qadd(s,t) by Def12;
  hence thesis;
end;
