Example (3)
Tag 04TC, permanent. Cite it as [Bourbaki, Tag 04TC].
Commutative Algebra, chapter VI, § 3. Valuations
Let k be a field and K = k((T)). The mapping v which maps every non-zero formal power series to its order (Algebra, Chapter IV, § 5, no. 7) is a valuation on K whose order group is Z and whose ring is k[[T]]. The associated place is the canonical homomorphism f: k[[T]] → k extended to k((T)) by setting f(u) = ∞ if u ∉ k[[T]].
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.