reserve T for TopSpace;
reserve A,B for Subset of T;
reserve T for non empty TopSpace;
reserve P,Q for Element of Topology_of T;
reserve p,q for Element of Open_setLatt(T);
reserve L for D_Lattice;
reserve F for Filter of L;
reserve a,b for Element of L;
reserve x,X,X1,X2,Y,Z for set;

theorem Th11:
  F in StoneH(L).a iff F in F_primeSet(L) & a in F
proof
  StoneH(L).a = {F0 where F0 is Filter of L: F0 in F_primeSet(L) & a in F0
  } by Def6;
  then
  F in StoneH(L).a iff ex F0 being Filter of L st F=F0 & F0 in F_primeSet(
  L) & a in F0;
  hence thesis;
end;
