theorem Th36:
  (inferior_realsequence seq).n = lower_bound (seq ^\n)
proof
  reconsider Y = {seq.k: n <= k} as Subset of REAL by Th29;
  (inferior_realsequence seq).n = lower_bound Y by Def4
    .= lower_bound rng (seq ^\ n) by Th30;
  hence thesis;
end;
