reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;
reserve B for Element of Fin A;
reserve L for non empty LattStr,
  a,b,c for Element of L;
reserve L for Lattice;
reserve a,b,c,u,v for Element of L;
reserve A for non empty set,
  x for Element of A,
  B for Element of Fin A,
  f,g for Function of A, the carrier of L;
reserve L for 0_Lattice,
  f,g for Function of A, the carrier of L,
  u for Element of L;
reserve L for 1_Lattice,
  f,g for Function of A, the carrier of L,
  u for Element of L;

theorem
  for L being 0_Lattice holds Bottom L = Top (L.:)
proof
  let L be 0_Lattice;
  reconsider u = Bottom L as Element of L.:;
  now
    let v be Element of L.:;
    reconsider v9 = v as Element of L;
    thus v "\/" u = Bottom L "/\" v9 by Th37
      .= u;
  end;
  hence thesis by RLSUB_2:65;
end;
