
theorem Th16:
  for L being Lattice,
      a being Element of L holds
    { F where F is Filter of L : F is prime & a in F } c= PFilters L
  proof
    let L be Lattice,
        a be Element of L;
    let x be object;
    assume x in { F where F is Filter of L : F is prime & a in F };
    then ex UF being Filter of L st UF = x & UF is prime & a in UF;
    hence thesis;
  end;
