reserve x,y,X for set;

theorem Th10:
  for T being non empty 1-sorted for N being non empty NetStr over
T for A being set holds A in a_filter N iff N is_eventually_in A & A is Subset
  of T
proof
  let T be non empty 1-sorted;
  let N be non empty NetStr over T;
  let B be set;
  B in a_filter N iff ex A being Subset of T st B = A & N is_eventually_in A;
  hence thesis;
end;
