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

theorem DenseIsBot:
  for L being Stone Lattice, x being Element of L st x in DenseElements L holds
    x* = Bottom L
  proof
    let L be Stone Lattice, x be Element of L;
    assume x in DenseElements L; then
    consider aa being Element of L such that
A1: x = aa & aa* = Bottom L;
    thus thesis by A1;
  end;
