 reserve n,s for Nat;

theorem Th21:
  Triangle (n -' 1) = n * (n - 1) / 2
  proof
    per cases;
    suppose n <> 0; then
A1:   1 <= 1 * n by Th1;
      Triangle (n -' 1) = (n -' 1) * (n -' 1 + 1) / 2 by Th19
        .= (n -' 1) * n / 2 by XREAL_1:235,A1;
      hence thesis by XREAL_1:233,A1;
    end;
    suppose
A2:   n = 0; then
      Triangle (n -' 1) = Triangle 0 by XREAL_0:def 2,Lm3
         .= n * (n - 1) / 2 by A2;
      hence thesis;
    end;
  end;
