theorem Th71:
  lim_inf S = (lim_sup Complement S)`
proof
  Union inferior_setsequence(B) = (Intersection superior_setsequence(
  Complement B))`
  proof
    lim_inf B = Union inferior_setsequence(B) & (lim_sup Complement B)` =
    ( Intersection superior_setsequence(Complement B))`;
    hence thesis by KURATO_0:9;
  end;
  hence thesis;
end;
