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 Th37:
  m = denominator p & n = denominator q &
  i = numerator p & j = numerator q implies
  denominator(p-q) = (m*n) div ( (i*n-j*m) gcd (m*n) ) &
  numerator(p-q) = (i*n-j*m) div ( (i*n-j*m) gcd (m*n) )
  proof
    p = numerator p / denominator p & q = numerator q / denominator q
    by RAT_1:15;
    hence thesis by Th23;
  end;
