
theorem
  for a,b be Integer st a,b are_coprime holds min
    (Parity(a-b),Parity(a+b)) <= 2
  proof
    let a,b be Integer such that
    A1: a,b are_coprime;
    per cases;
    suppose
      B1: a is even; then
      b is odd by A1,PYTHTRIP10; then
      Parity (a + b) = 1 & Parity (a - b) = 1 by B1,NAT_2:def 1;
      hence thesis;
    end;
    suppose
      B1: b is even; then
      a is odd by A1,PYTHTRIP10; then
      Parity (a + b) = 1 & Parity (a - b) = 1 by B1,NAT_2:def 1;
      hence thesis;
    end;
    suppose a is odd & b is odd;
      hence thesis by ODP;
    end;
  end;
