
theorem SCP: ::: NEWTON02:48
  for a be even Integer, b be Integer st a,b are_coprime holds
    (a + b),(a - b) are_coprime
  proof
    let a be even Integer, b be Integer such that
    A1: a,b are_coprime;
    a gcd b is odd by A1; then
    reconsider b as odd Integer;
    A2: a + b, 2 are_coprime by NEWTON03:def 5;
    (1*b + a) gcd b = a gcd b by NEWTON02:5; then
    a + b, b are_coprime by A1; then
    A3: (a + b),2*b are_coprime by A2,INT_2:26;
    (a + b) gcd (a - b) = (a + b) gcd ((a - b) - 1*(a + b)) by NEWTON02:5
    .= (a + b) gcd (-2*b)
    .= (a + b) gcd (2*b) by NEWTON02:1;
    hence thesis by A3;
  end;
