reserve X for non empty set;

theorem
  for B,Y being Subset-Family of X st Y c= UniCl B holds union Y in UniCl B
  proof
    let B,Y be Subset-Family of X;
    assume Y c= UniCl B;
    then union Y in UniCl UniCl B by CANTOR_1:def 1;
    hence thesis by YELLOW_9:15;
  end;
