
theorem SDO:
  for a,b be odd Integer holds (a + b) mod 4 = 0 or (a - b) mod 4 = 0
  proof
    let a,b be odd Integer;
    per cases by SDM;
    suppose
      (a + b) mod 4 = 2; then
      not 4 divides (a + b) by INT162; then
      4 divides (a - b) by NEWTON03:73;
      hence thesis by INT162;
    end;
    suppose
      (a - b) mod 4 = 2; then
      not 4 divides (a - b) by INT162; then
      4 divides (a + b) by NEWTON03:73;
      hence thesis by INT162;
    end;
  end;
