
theorem Th39:
  for m,n be non zero Nat holds
  (Liouville_seq (seq_const 1, m)).n = m to_power - n!
  proof
    let m,n be non zero Nat;
    thus (Liouville_seq (seq_const 1, m)).n
       = ((seq_const 1).n) / (m to_power (n!)) by DefLio
      .= 1/(m to_power (n!)) by SEQ_1:57
      .= (1/m) to_power (n!) by PREPOWER:7
      .= m to_power -n! by POWER:32;
  end;
