 reserve L for Lattice;
 reserve I,P for non empty ClosedSubset of L;
reserve L for lower-bounded pseudocomplemented Lattice;

theorem Th11a:
  for L being pseudocomplemented bounded Lattice holds (Top L)* = Bottom L
  proof
    let L be pseudocomplemented bounded Lattice;
    for x be Element of L st Top L "/\" x = Bottom L holds x [= Bottom L; then
    Bottom L is_a_pseudocomplement_of Top L;
    hence (Top L)* = Bottom L by def3;
  end;
