
theorem Th25:
  for I being non degenerated domRing-like commutative Ring for u
being Element of Quot.I holds (quotmult(I)).(u,q1.I) = u & (quotmult(I)).(q1.I,
  u) = u
proof
  let I be non degenerated domRing-like commutative Ring;
  let u be Element of Quot.I;
A1: (quotmult(I)).(q1.I,u) = qmult(q1.I,u) by Def13
    .= u by Th14;
  (quotmult(I)).(u,q1.I) = qmult(u,q1.I) by Def13
    .= u by Th14;
  hence thesis by A1;
end;
