
theorem SDM:
  for a,b be odd Integer holds (a + b) mod 4 = 2 or (a - b) mod 4 = 2
  proof
    let a,b be odd Integer;
    A1: a + b mod (2*2) is even & (a - b) mod (2*2) is even;
    A2: ((a + b) mod (3 + 1) = 0 or ... or (a + b) mod (3 + 1) = 3) &
    ((a - b) mod (3 + 1) = 0 or ... or (a - b) mod (3 + 1) = 3)
      by NUMBER03:11;
    per cases by A1,A2;
    suppose
      (a + b) mod 4 = 0; then
      4 divides (a + b) by INT_1:62; then
      not 4 divides (a - b) by NEWTON03:73;
      hence thesis by A1,A2,INT_1:62;
    end;
    suppose
      (a + b) mod 4 = 2;
      hence thesis;
    end;
  end;
