theorem Th57:
  L is upper-bounded implies Top latt <.p.) = Top L
proof
  given q such that
A1: for r holds q"\/"r = q & r"\/"q = q;
  L is 1_Lattice by A1,LATTICES:def 14;
  then Top L in <.p.) by Th11;
  then reconsider q9 = Top L as Element of latt <.p.) by Th49;
A2: q = Top L by A1,RLSUB_2:65;
  now
    let r9 be Element of latt <.p.);
    reconsider r = r9 as Element of <.p.) by Th49;
    thus r9"\/"q9 = q"\/"r by A2,Th50
      .= q9 by A1,A2;
  end;
  hence thesis by RLSUB_2:65;
end;
