reserve T for non empty TopSpace,
  X,Z for Subset of T;
reserve x,y for Element of OpenClosedSet(T);
reserve x,y,X for set;
reserve BL for non trivial B_Lattice,
  a,b,c,p,q for Element of BL,
  UF,F,F0,F1,F2 for Filter of BL;

theorem Th34:
  rng UFilter BL = the carrier of StoneBLattice BL
proof
  thus rng UFilter BL= StoneR BL .= the carrier of StoneBLattice BL by Th33;
end;
