
theorem
  for R being up-complete /\-complete LATTICE, N being net of R,
  i being Element of N holds sup inf_net N = lim_inf (N|i)
proof
  let R be up-complete /\-complete LATTICE, N be net of R, i be Element of N;
  sup inf_net N = lim_inf N by Th24;
  hence thesis by WAYBEL21:41;
end;
