Definition tail_filter_basis : Family (point_set X) :=
  Im Full_set net_tail.Definition tail_filter : Filter (point_set X).

(* Specifications: *)
Lemma net_limit_impl_tail_filter_limit: forall x0:point_set X, net_limit x x0 -> filter_limit tail_filter x0.
Lemma tail_filter_limit_impl_net_limit: forall x0:point_set X, filter_limit tail_filter x0 -> net_limit x x0.
Lemma net_cluster_point_impl_tail_filter_cluster_point: forall x0:point_set X, net_cluster_point x x0 -> filter_cluster_point tail_filter x0.
Lemma tail_filter_cluster_point_impl_net_cluster_point: forall x0:point_set X, filter_cluster_point tail_filter x0 -> net_cluster_point x x0.