 reserve L for Lattice;
 reserve I,P for non empty ClosedSubset of L;
reserve L for lower-bounded pseudocomplemented Lattice;

theorem ThF:
  for L being pseudocomplemented bounded Lattice, x, y being Element of L st
    y is_a_pseudocomplement_of x holds y in PseudoComplements x
  proof
    let L be pseudocomplemented bounded Lattice, x, y be Element of L;
    assume y is_a_pseudocomplement_of x; then
    x "/\" y = Bottom L; then
    y in { xx where xx is Element of L : x "/\" xx = Bottom L };
    hence thesis by LATTICEA:def 8;
  end;
