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
  for BL being non trivial B_Lattice ex T being non empty TopSpace st
  BL, OpenClosedSetLatt(T) are_isomorphic
proof
  let BL be non trivial B_Lattice;
  reconsider T = StoneSpace BL as non empty TopSpace;
  take T;
  OpenClosedSetLatt(T) = StoneBLattice BL;
  hence thesis by Th35;
end;
