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 Th18:
  F in UFilter BL.a iff F is being_ultrafilter & a in F
proof
  hereby
    assume F in UFilter BL.a;
    then ex F0 st ( F0=F)&( F0 is being_ultrafilter)&( a in F0) by Th17;
    hence F is being_ultrafilter & a in F;
  end;
  thus thesis by Th17;
end;
