
theorem Th28:
  for I being non degenerated domRing-like commutative Ring for u
  being Element of Quot.I holds (quotadd(I)).(u,(quotaddinv(I)).(u)) = q0.I & (
  quotadd(I)).((quotaddinv(I)).(u),u) = q0.I
proof
  let I be non degenerated domRing-like commutative Ring;
  let u be Element of Quot.I;
A1: (quotadd(I)).((quotaddinv(I)).(u),u) = (quotadd(I)).(qaddinv(u),u) by Def14
    .= qadd(qaddinv(u),u) by Def12
    .= q0.I by Th17;
  (quotadd(I)).(u,(quotaddinv(I)).(u)) = (quotadd(I)).(u,qaddinv(u)) by Def14
    .= qadd(u,qaddinv(u)) by Def12
    .= q0.I by Th17;
  hence thesis by A1;
end;
