reserve x, x1, x2, y, z, X9 for set,
  X, Y for finite set,
  n, k, m for Nat,
  f for Function;

theorem Th9:
 for x1,x2 being object holds
  card X < k implies Choose(X,k,x1,x2) is empty
proof let x1,x2 be object;
  assume
A1: card X < k;
  assume Choose(X,k,x1,x2) is non empty;
  then consider z being object such that
A2: z in Choose(X,k,x1,x2);
  ex f be Function of X,{x1,x2} st f = z & card (f"{x1}) = k by A2,Def1;
  hence thesis by A1,NAT_1:43;
end;
