 reserve n,s for Nat;

theorem Th55:
  Triangle (n) + Triangle (n + 1) = (n + 1) ^2
  proof
    Triangle n = n * (n + 1) / 2 by Th19; then
    Triangle n + Triangle (n + 1)
       = n * (n + 1) / 2 + (n + 1) * (n + 1 + 1) / 2 by Th19
      .= (n + 1) ^2;
    hence thesis;
  end;
