reserve x,y,X for set;

theorem Th16:
  for T being non empty TopSpace for F being proper Filter of
  BoolePoset [#]T for x being Point of T holds x is_a_cluster_point_of a_net F
  iff x is_a_cluster_point_of F, T
proof
  let T be non empty TopSpace;
  let F be proper Filter of BoolePoset [#]T;
  F = a_filter a_net F by Th14;
  hence thesis by Th11;
end;
