
theorem Th22:
  for I being non degenerated domRing-like commutative Ring for u
being Element of Quot.I holds (quotadd(I)).(u,q0.I) = u & (quotadd(I)).(q0.I,u)
  = u
proof
  let I be non degenerated domRing-like commutative Ring;
  let u be Element of Quot.I;
A1: (quotadd(I)).(q0.I,u) = qadd(q0.I,u) by Def12
    .= u by Th12;
  (quotadd(I)).(u,q0.I) = qadd(u,q0.I) by Def12
    .= u by Th12;
  hence thesis by A1;
end;
