Example 2

Tag 0D5Y, permanent. Cite it as [Bourbaki, Tag 0D5Y].

Commutative Algebra, chapter X, § 4. Anneaux réguliers

In order that a ring be regular, it is necessary and sufficient that it be isomorphic to the product of a finite family of integral regular rings; this follows in fact from the fact that every regular ring is locally integral ( $§ 1$ , No. 8), since regular local rings are integral.

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

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