reserve L for Lattice,
  p,q,r for Element of L,
  p9,q9,r9 for Element of L.:,
  x, y for set;
reserve I,J for Ideal of L,
  F for Filter of L;

theorem
  (ex r st p "\/" r <> p) implies (.p.> <> the carrier of L
proof
  given r such that
A1: p"\/"r <> p;
  p"\/"r = p.:"/\"r.:;
  then <.p.:.) <> carr(L.:) by A1,FILTER_0:19;
  hence thesis by Th29;
end;
