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

theorem Th5:
  for a being Element of L holds a [= a**
  proof
    let a be Element of L;
a1: a** is_a_pseudocomplement_of a* by def3;
    a* is_a_pseudocomplement_of a by def3;
    hence thesis by a1;
  end;
