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 Th27:
  for X being non empty set ex Y being Element of Fin X st Y is non empty
proof
  let X be non empty set;
  set a = the Element of X;
  {. a .} is Element of Fin X;
  hence thesis;
end;
