
theorem Th33:
  for a be NAT-valued Real_Sequence, b be non trivial Nat,n be Nat
  holds Liouville_seq (a,b).n >= 0
  proof
    let a be NAT-valued Real_Sequence, b be non trivial Nat, n be Nat;
    per cases;
    suppose n = 0;
      hence thesis by DefLio;
    end;
    suppose n <> 0; then
      Liouville_seq (a,b).n = (a.n) / (b to_power (n!)) by DefLio;
      hence thesis;
    end;
  end;
