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 <> 0 implies
  denominator((m/i)") = m / ( m gcd i ) &
  numerator((m/i)") = i / ( m gcd i )
  proof
    assume
A1: m <> 0;
    hence denominator((m/i)") = m div ( m gcd i ) by Th19
    .= m / ( m gcd i ) by Th8;
    thus numerator((m/i)") = i div ( m gcd i ) by A1,Th19
    .= i / ( m gcd i ) by Th7;
  end;
