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 p st p in I
proof
  set i = the Element of I qua non empty Subset of L;
  i is Element of L;
  hence thesis;
end;
