
theorem
  for L being complete LATTICE holds lim_inf-Convergence L is (CONSTANTS)
proof
  let L be complete LATTICE;
  let N be constant net of L;
A1: for M being subnet of N holds the_value_of N = lim_inf M
  proof
    let M be subnet of N;
A2: M is constant by Th16;
    thus the_value_of N = the_value_of M by Th16
      .= lim_inf M by A2,WAYBEL11:23;
  end;
  assume N in NetUniv L;
  hence thesis by A1,Def3;
end;
