 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 SquaredBottom:
  Bottom (B squared-latt) = [Bottom B, Bottom B]
  proof
    [Bottom B, Bottom B] in B squared; then
    Bottom [:B,B:] in B squared by FILTER_1:42; then
    Bottom latt ([:B,B:], B squared) = Bottom [:B,B:] by ThB;
    hence thesis by FILTER_1:42;
  end;
