
theorem
  for a,b be non zero Nat holds (a - b)|^2 mod (4*a*b) = (a + b)|^2 mod (4*a*b)
  proof
    let a,b be non zero Nat;
    A1: (a - b)|^2 = (a-b)*(a - b) & (a + b)|^2 = (a+b)*(a+b) by NEWTON:81;
    ((a - b)|^2 + (4*a*b)) mod (4*a*b) =
      (((a - b)|^2 mod (4*a*b)) + ((4*a*b) mod (4*a*b))) mod (4*a*b)
        by NAT_D:66;
    hence thesis by A1;
  end;
