
theorem Divides3Triangle:
  for n being Nat holds
    3 divides Triangle (3 * n)
  proof
    let n be Nat;
A0: 2 * 1 + 1 is odd;
a1: n * (3 * n + 1) is even
    proof
      per cases;
      suppose n is even;
        hence thesis;
      end;
      suppose
        n is odd;
        hence thesis by A0;
      end;
    end;
    Triangle (3 * n) = (3 * n) * (3 * n + 1) / 2
      by NUMPOLY1:19; then
    Triangle (3 * n) = 3 * (n * (3 * n + 1) / 2);
    hence thesis by a1;
  end;
