reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T;
reserve x for Point of T;

theorem
  for T being set, A being SetSequence of T holds
  rng A is countable non empty Subset-Family of T
proof
  let T be set, A be SetSequence of T;
  A.1 in rng A by FUNCT_2:4;
  then reconsider AA = rng A as non empty Subset-Family of T;
  card rng A c= card dom A & dom A is countable by CARD_2:61,FUNCT_2:def 1;
  then AA is countable by WAYBEL12:1;
  hence thesis;
end;
