theorem
  Top lattice G = (Omega).G
proof
  set L = lattice G;
  reconsider E = (Omega). G as Element of L by GROUP_3:def 1;
  now
    let A be Element of L;
    reconsider H = A as strict Subgroup of G by GROUP_3:def 1;
    thus A "\/" E = SubJoin(G).(A,E) by LATTICES:def 1
      .= H "\/" (Omega).G by Def10
      .= E by Th59;
  end;
  hence thesis by RLSUB_2:65;
end;
