 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 SquaredCarrier:
  the carrier of (B squared-latt) = B squared
  proof
    set L = [:B,B:];
    set P = B squared;
    consider o1,o2 being BinOp of P such that
A1: o1 = (the L_join of L)||P & o2 = (the L_meet of L)||P &
    latt ([:B,B:], P) = LattStr (#P, o1, o2#) by FILTER_2:def 14;
    thus thesis by A1;
  end;
