Example 2

Tag 0D7P, permanent. Cite it as [Bourbaki, Tag 0D7P].

Commutative Algebra, chapter X, § 6. Extension des scalaires dans les algèbres régulières

In order that a local $k$ -algebra be essentially of finite type, it is necessary and sufficient that it be isomorphic to a $k$ -algebra of the form $A_p$ , where $A$ is a $k$ -algebra of finite type and $p$ a prime ideal of $A$ (cf. II, § 2, No. 5, Prop. 11 (iii)).

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

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