
theorem Th32:
  for L being distributive well-complemented preOrthoLattice, x
  being Element of L holds x`` = x
proof
  let L be distributive well-complemented preOrthoLattice;
  let x be Element of L;
  x`` is_a_complement_of x` by Def10;
  then
A1: x`` + x` = Top L & x`` "/\" x` = Bottom L;
  x` is_a_complement_of x by Def10;
  then x` "\/" x = Top L & x` "/\" x = Bottom L;
  hence thesis by A1,LATTICES:12;
end;
