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 Th34:
  card Domin_0(2*n,n) = Catalan(n+1)
proof
A1: Catalan(n+1)=((2*(n+1) -' 2) choose ((n+1) -' 1))/(n+1) by CATALAN1:def 1;
  2*n+2 -' 2=2*n+2-2 & n+1 -'1 =n+1-1 by XREAL_0:def 2;
  hence thesis by A1,Th33;
end;
