
theorem Th21:
  for I being non degenerated domRing-like commutative Ring for u,
  v being Element of Quot.I holds (quotadd(I)).(u,v) = (quotadd(I)).(v,u)
proof
  let I be non degenerated domRing-like commutative Ring;
  let u,v be Element of Quot.I;
  (quotadd(I)).(u,v) = qadd(u,v) by Def12
    .= qadd(v,u) by Th11
    .= (quotadd(I)).(v,u) by Def12;
  hence thesis;
end;
