Definition 3

Tag 04WD, permanent. Cite it as [Bourbaki, Tag 04WD].

Commutative Algebra, chapter VI, § 8. Extensions of a valuation to an algebraic extension

Let $K$ be afield, $v$ a valuation on $K$ and $L$ an extension of $K$ . A family $(v'_i)_{i \in I}$ of valuations on $L$ which extend $v$ and such that every valuation on $L$ extending $v$ is equivalent to a unique $v'_i$ is called a complete system of extensions of $v$ to $L$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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