theorem Th33:
  m = denominator p & n = numerator p & n <> 0 implies
  denominator(p") = n div ( n gcd m ) &
  numerator(p") = m div ( n gcd m )
  proof
    assume m = denominator p & n = numerator p;
    then p = n/m by RAT_1:15;
    hence thesis by Th19;
  end;
