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