Example 5

Tag 0CK1, permanent. Cite it as [Bourbaki, Tag 0CK1].

Commutative Algebra, chapter VIII, § 1. Dimension de Krull d’un anneau

Let $X$ be a complex analytic variety. If $X$ is of complex dimension $n$ at a point $x$ of $X$ , the local ring of germs at $x$ of analytic functions on $X$ is of dimension $n$ . \*

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

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