theorem Th39:
  m = denominator p & n = denominator q &
  i = numerator p & j = numerator q implies
  denominator(p*q) = (m*n) div ( (i*j) gcd (m*n) ) &
  numerator(p*q) = (i*j) div ( (i*j) gcd (m*n) )
  proof
    p = numerator p / denominator p & q = numerator q / denominator q
    by RAT_1:15;
    hence thesis by Th25;
  end;
