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 Th10:
  F in F_primeSet(L) iff F <> the carrier of L & F is prime
proof
  F in F_primeSet(L) iff ex F0 being Filter of L st F0=F & F0 <> the
  carrier of L & F0 is prime;
  hence thesis;
end;
