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 Th21:
  Domin_0(n,m) c= Choose(n,m,1,0)
proof
  let x be object;
  assume x in Domin_0(n,m);
  then consider p such that
A1: p = x and
A2: p is dominated_by_0 and
A3: dom p = n & Sum p = m by Def2;
  rng p c= {0,1} by A2;
  hence thesis by A1,A3,CARD_FIN:40;
end;
