reserve T for non empty TopSpace,
  X,Z for Subset of T;
reserve x,y for Element of OpenClosedSet(T);
reserve x,y,X for set;
reserve BL for non trivial B_Lattice,
  a,b,c,p,q for Element of BL,
  UF,F,F0,F1,F2 for Filter of BL;

theorem
  UFilter BL.Top BL = ultraset BL
proof
  thus UFilter BL.Top BL = UFilter BL.(Bottom BL)` by LATTICE4:30
    .= ultraset BL \ UFilter BL.Bottom BL by Th25
    .= ultraset BL \ {} by Th30
    .= ultraset BL;
end;
