reserve p,q for Rational;
reserve g,m,m1,m2,n,n1,n2 for Nat;
reserve i,i1,i2,j,j1,j2 for Integer;

theorem
  m = denominator p & n = numerator p & n <> 0 implies
  denominator(p") = n / ( n gcd m ) &
  numerator(p") = m / ( n gcd m )
  proof
    assume
A1: m = denominator p & n = numerator p & n <> 0;
    hence denominator(p") = n div ( n gcd m ) by Th33
    .= n / ( n gcd m ) by Th8;
    thus numerator(p") = m div ( n gcd m ) by A1,Th33
    .= m / ( n gcd m ) by Th7;
end;
