
theorem
  for I being non degenerated domRing-like commutative Ring for u,v
being Element of the_Field_of_Quotients(I) holds (quotmult(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 as Element of Quot.I;
  reconsider t = v as Element of Quot.I;
  (quotmult(I)).(u,v) = qmult(s,t) by Def13;
  hence thesis;
end;
