reserve x, x1, x2, y, X, D for set,
  i, j, k, l, m, n, N for Nat,
  p, q for XFinSequence of NAT,
  q9 for XFinSequence,
  pd, qd for XFinSequence of D;

theorem
  card Domin_0(6+k,3) = (k+1)*(k+5)*(k+6)/6
proof
  card Domin_0(6+k,3)=(6+k+1-2*3)/(6+k+1-3)*((6+k) choose 3) by Th29,NAT_1:11
    .=(k+1)/(k+4)*((6+k)*(6+k-1)*(6+k-2)/6) by STIRL2_1:51
    .=((k+1)/(k+4)*(4+k))*(5+k)*(6+k)/6
    .=(k+1)*(5+k)*(6+k)/6 by XCMPLX_1:87;
  hence thesis;
end;
