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;
