reserve            x for object,
               X,Y,Z for set,
         i,j,k,l,m,n for Nat,
                 r,s for Real,
                  no for Element of OrderedNAT,
                   A for Subset of [:NAT,NAT:];

theorem Th17:
  for X being non empty set, cF being Filter of X holds
    cF is proper Filter of BoolePoset X
  proof
    let X be non empty set,cF be Filter of X;
    reconsider cF as non empty Subset of BooleLatt X by LATTICE3:def 1;
    reconsider cF as Filter of BoolePoset X by CARDFIL2:73,CARDFIL2:75;
    not {} in cF by CARD_FIL:def 1;
    then not Bottom BoolePoset X in cF by YELLOW_1:18;
    hence thesis by WAYBEL_7:4;
  end;
