reserve x for set;

theorem Th9:
  for L1, L2 being /\-complete up-complete Semilattice st the
  RelStr of L1 = the RelStr of L2 holds xi L1 = xi L2
proof
  let L1, L2 be /\-complete up-complete Semilattice;
  assume
A1: the RelStr of L1 = the RelStr of L2;
  xi L1 = the topology of ConvergenceSpace lim_inf-Convergence L1 & xi L2
  = the topology of ConvergenceSpace lim_inf-Convergence L2 by WAYBEL28:def 4;
  hence xi L1 c= xi L2 & xi L2 c= xi L1 by A1,Lm3;
end;
