
theorem
  for a be positive-yielding NAT-valued Real_Sequence,
  b be non trivial Nat,n be non zero Nat
  holds Liouville_seq (a,b).n > 0
  proof
    let a be positive-yielding NAT-valued Real_Sequence,b be non trivial Nat,
    n be non zero Nat;
A1: Liouville_seq (a,b).n = (a.n) / (b to_power (n!)) by DefLio;
    n in NAT by ORDINAL1:def 12; then
    n in dom a by FUNCT_2:def 1; then
    a.n in rng a by FUNCT_1:3; then
    a.n > 0 by PARTFUN3:def 1;
    hence thesis by A1;
  end;
