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 Th29:
  for L being 0_Lattice holds
  not ex F being Filter of L st F is being_ultrafilter & Bottom L in F
proof
  let L be 0_Lattice;
  given F being Filter of L such that
A1: F is being_ultrafilter and
A2: Bottom L in F;
  F = the carrier of L by A2,FILTER_0:26;
  hence contradiction by A1,FILTER_0:def 3;
end;
