
theorem
  for L being non trivial bounded Semilattice for x being Element of L
  st x is dense holds x <> Bottom L
proof
  let L be non trivial bounded Semilattice, x be Element of L such that
A1: x is dense;
  Top L <> Bottom L by WAYBEL_7:3;
  then x "/\" Top L <> Bottom L by A1;
  hence thesis by WAYBEL_1:4;
end;
