Example 4

Tag 0D4V, permanent. Cite it as [Bourbaki, Tag 0D4V].

Commutative Algebra, chapter X, § 3. Profondeur et dimension homologique

Let $A$ be a regular local noetherian ring; then $A$ is a Gorenstein ring. In fact, let $x$ be a system of coordinates of $A$ (VIII, § 5, No. 1, Def. 1). The sequence $x$ is $A$ -regular (loc. cit., No. 2, Theorem 1) and generates the ideal $m_A$ ; one can therefore apply Example 3.

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

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