reserve x,X,X2,Y,Y2 for set;
reserve GX for non empty TopSpace;
reserve A2,B2 for Subset of GX;
reserve B for Subset of GX;

theorem
  for B being Subset of GX, V being Subset of GX|B st V c= B holds Down(
  Up(V),B)=V by XBOOLE_1:28;
