reserve x,y,X for set;

theorem Th14:
  for T being non empty 1-sorted for F being proper Filter of
  BoolePoset [#]T holds F = a_filter a_net F
proof
  let T be non empty 1-sorted;
  let F be proper Filter of BoolePoset [#]T;
  not {} in F by Th1;
  then F \ {{}} = F by ZFMISC_1:57;
  hence thesis by Th13;
end;
