theorem
  m <> 0 & n <> 0 implies
  denominator((i/m)*(j/n)) = (m*n) / ( (i*j) gcd (m*n) ) &
  numerator((i/m)*(j/n)) = (i*j) / ( (i*j) gcd (m*n) )
  proof
    assume
A1: m <> 0 & n <> 0;
    hence denominator((i/m)*(j/n)) = (m*n) div ( (i*j) gcd (m*n) ) by Th25
    .= (m*n) / ( (i*j) gcd (m*n) ) by Th8;
    thus numerator((i/m)*(j/n)) = (i*j) div ( (i*j) gcd (m*n) ) by A1,Th25
    .= (i*j) / ( (i*j) gcd (m*n) ) by Th7;
  end;
