
theorem Th7:
  for L being lower-bounded Lattice holds not(ex b being Element of
  L st b is-lower-neighbour-of Bottom L)
proof
  let L be lower-bounded Lattice;
  given b being Element of L such that
A1: b is-lower-neighbour-of Bottom L;
A2: Bottom L [= b by LATTICES:16;
  b [= Bottom L & b <> Bottom L by A1;
  hence thesis by A2,LATTICES:8;
end;
