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

theorem
  for L being pseudocomplemented bounded Lattice, x being Element of L holds
    x* in PseudoComplements x
  proof
    let L be pseudocomplemented bounded Lattice, a be Element of L;
    a* is_a_pseudocomplement_of a by def3;
    hence thesis by ThF;
  end;
