
theorem
  for a,b be odd Integer holds max ((a + b) mod 4, (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;
    ((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;
    hence thesis by A1,XXREAL_0:def 10,SDM;
  end;
