 reserve L for Lattice;
 reserve I,P for non empty ClosedSubset of L;

theorem Th2:
  for L being pseudocomplemented lower-bounded Lattice,
  a, b, x being Element of L st a is_a_pseudocomplement_of x &
    b is_a_pseudocomplement_of x holds a = b
  proof
    let L be pseudocomplemented lower-bounded Lattice;
    let a, b, x be Element of L;
    assume that
a1: a is_a_pseudocomplement_of x and
b1: b is_a_pseudocomplement_of x;
a2: a "/\" x = Bottom L by a1;
b2: b "/\" x = Bottom L by b1;
ab1:b [= a by a1,b2;
    a [= b by b1,a2;
    hence a = b by ab1,LATTICES:8;
  end;
