
theorem Th18:
  for L being complemented' join-commutative meet-commutative
  lower-bounded' upper-bounded' join-idempotent distributive distributive' non
  empty LattStr holds Top L = Top' L
proof
  let L be complemented' join-commutative meet-commutative lower-bounded'
upper-bounded' join-idempotent distributive distributive' non empty LattStr;
  set Y = Top' L;
  L is upper-bounded & for a being Element of L holds Y "\/" a = Y & a
  "\/" Y = Y by Th4,Th12;
  hence thesis by LATTICES:def 17;
end;
