 reserve L for Lattice;
 reserve I,P for non empty ClosedSubset of L;

theorem ThD:
  for L being pseudocomplemented lower-bounded Lattice, x being Element of L
  holds x* "/\" x = Bottom L
  proof
    let L be pseudocomplemented lower-bounded Lattice, x be Element of L;
    x* is_a_pseudocomplement_of x by def3;
    hence thesis;
  end;
