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

theorem
  for L being lower-bounded pseudocomplemented Lattice holds
    Skeleton L = { a where a is Element of L : a** = a }
  proof
    let L be lower-bounded pseudocomplemented Lattice;
    thus Skeleton L c= { a where a is Element of L : a** = a }
    proof
      let x be object;
      assume x in Skeleton L; then
      consider a being Element of L such that
a1:   x = a*;
      a*** = a* by Th7;
      hence thesis by a1;
    end;
    let x be object;
    assume x in { a where a is Element of L : a** = a };
    then consider a being Element of L such that
a3: x = a & a** = a;
    thus thesis by a3;
  end;
