
theorem Th3:
  for L being complemented' join-commutative meet-commutative
  distributive upper-bounded' distributive' non empty LattStr for x being
  Element of L holds x "/\" x `# = Bot' L
proof
  let L be complemented' join-commutative meet-commutative distributive
  upper-bounded' distributive' non empty LattStr;
  let x be Element of L;
  x `# is_a_complement'_of x by Def8;
  hence thesis;
end;
