
theorem Th19:
  for I being non degenerated domRing-like commutative Ring holds q1.I <> q0.I
proof
  let I be non degenerated domRing-like commutative Ring;
  reconsider t = [0.I,1_I] as Element of Q.I by Def1;
  assume
A1: q1.I = q0.I;
 t`1 = 0.I;
  then t in q0.I by Def8;
  then t`1 = t`2 by A1,Def9;
  hence contradiction;
end;
