 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;
 reserve L1, L2 for Lattice;
 reserve p1, q1 for Element of L1;
 reserve p2, q2 for Element of L2;
 reserve L1, L2 for non empty Lattice;
reserve B for Boolean Lattice;

theorem
  Skeleton (B squared-latt) = the set of all [a,a] where a is Element of B
  proof
    set L = B squared-latt;
    Skeleton (B squared-latt) = the set of all [a,a] where a is Element of B
    proof
      thus Skeleton (B squared-latt)
      c= the set of all [a,a] where a is Element of B
      proof
        let x be object;
        assume x in Skeleton L; then
        consider a being Element of L such that
A1:     x = a*;
        a in the carrier of L; then
        a in B squared by SquaredCarrier; then
        consider a1,a2 being Element of B such that
A2:     a = [a1,a2] & a1 [= a2;
        a* = [a2`,a2`] by A2,PseudoInSquared;
        hence thesis by A1;
      end;
      let x be object;
      assume x in the set of all [a,a] where a is Element of B; then
      consider a being Element of B such that
B1:   x = [a,a];
      set b = [a`,a`];
      b in B squared; then
      reconsider b as Element of L by FILTER_2:72;
      reconsider a1 = b* as Element of L;
      b* = [a``,a``] by PseudoInSquared .= [a,a];
      hence thesis by B1;
    end;
    hence thesis;
  end;
