theorem Th34:
  PrimeIdeals(A,S) = PrimeIdeals(A,S-Ideal)
  proof
    PrimeIdeals(A,S) = Ideals(A,S) /\ Spectrum A by Th33
     .= Ideals(A,S-Ideal) /\ Spectrum A by Th2
     .= PrimeIdeals(A,S-Ideal) by Th33;
    hence thesis;
  end;
