
theorem Th45:
  for I being non degenerated domRing-like commutative Ring for u
being Element of the_Field_of_Quotients(I) st u <> 0.the_Field_of_Quotients(I)
  ex v being Element of the_Field_of_Quotients(I) st u * v = 1.
  the_Field_of_Quotients(I)
proof
  let I be non degenerated domRing-like commutative Ring;
  let u be Element of the_Field_of_Quotients(I);
  assume
A1: u <> 0.the_Field_of_Quotients(I);
  reconsider u as Element of Quot.I;
  reconsider v = (quotmultinv(I)).(u) as Element of the_Field_of_Quotients(I);
  reconsider u as Element of the_Field_of_Quotients(I);
  u * v = 1.the_Field_of_Quotients(I) by A1,Th29;
  hence thesis;
end;
