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

theorem Th4:
  for L being Boolean Lattice holds L is satisfying_Stone_identity
  proof
    let L be Boolean Lattice, x be Element of L;
    x* "\/" ((x*)*) = Top L
    proof
      x* "\/" ((x*)*) = x` "\/" ((x*)*) by ThE .= x` "\/" ((x`)*) by ThE
      .= x` "\/" ((x`)`) by ThE .= Top L by LATTICES:21;
      hence thesis;
    end;
    hence thesis;
  end;
