
theorem Not3DividesTriangle:
  for n being Nat holds
    3 divides Triangle (3 * n + 1) - 1
  proof
    let n be Nat;
    Triangle (3 * n + 1) = (3 * n + 1) * (3 * n + 1 + 1) / 2
      by NUMPOLY1:19; then
    Triangle (3 * n + 1) - 1 = 3 * (3 * ((n + 1) * n) / 2);
    hence thesis;
  end;
