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

theorem Th7:
  for a being Element of L holds a* = a***
  proof
    let a be Element of L;
a1: a*** [= a* by Th6,Th5;
    a* [= a*** by Th5;
    hence thesis by a1,LATTICES:8;
  end;
