
theorem TopBot:
  for L being non trivial bounded Lattice holds
    Top L <> Bottom L
  proof
    let L be non trivial bounded Lattice;
    set p = Top L;
    assume
A0: Top L = Bottom L;
    consider p being Element of L such that
A2: p <> Top L by SUBSET_1:50;
    Bottom L [= p;
    hence thesis by A2,A0;
  end;
