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;
