
theorem Th19:
  for L being complemented' join-commutative meet-commutative
  lower-bounded' upper-bounded' join-idempotent distributive distributive' non
  empty LattStr holds Bottom L = Bot' L
proof
  let L be complemented' join-commutative meet-commutative lower-bounded'
upper-bounded' join-idempotent distributive distributive' non empty LattStr;
  set Y = Bot' L;
  L is lower-bounded & for a being Element of L holds Y "/\" a = Y & a
  "/\" Y = Y by Th5,Th14;
  hence thesis by LATTICES:def 16;
end;
