reserve X for non empty TopSpace;
reserve Y for non empty TopStruct;

theorem
  for F being Subset-Family of Y st F is anti-discrete-set-family holds
  meet F is anti-discrete
proof
  let F be Subset-Family of Y;
  assume
A1: F is anti-discrete-set-family;
  hereby
    per cases;
    suppose
      meet F = {};
      hence thesis;
    end;
    suppose
   meet F <> {};
      meet F c= union F by SETFAM_1:2;
      hence thesis by A1,Th5,Th8;
    end;
  end;
end;
