
theorem
  for S being non void TopStruct holds [#]S is closed_under_lines
proof
  let S be non void TopStruct;
  thus [#]S is closed_under_lines
  proof
    let K be Block of S;
    assume 2 c= card (K /\ [#]S);
    K in the topology of S;
    hence thesis;
  end;
end;
