 reserve n,s for Nat;

theorem Th67:
  1 + 9 * Triangle n = Triangle (3 * n + 1)
  proof
A1: Triangle n = n * (n + 1) / 2 by Th19;
    Triangle (3 * n + 1) = (3 * n + 1) * (3 * n + 1 + 1) / 2 by Th19
      .= 1 + 9 * Triangle n by A1;
    hence thesis;
  end;
