
theorem
  for a be odd Integer, b be even Integer st a,b are_coprime holds
  (a - b)*(a + b) gcd 2*a*b = 1
  proof
    let a be odd Integer, b be even Integer such that
    A1: a,b are_coprime;
    reconsider d = a - b as odd Integer;
    reconsider s = a + b as odd Integer;
    A2: s*d,a*b are_coprime by A1,SDC;
    s*d,2 are_coprime by NEWTON03:def 5; then
    (s*d), 2*(a*b) are_coprime by A2,INT_2:26;
    hence thesis;
  end;
