Remark 1
Tag 0D6V, permanent. Cite it as [Bourbaki, Tag 0D6V].
Commutative Algebra, chapter X, § 5. Intersections complètes
When the ring is noetherian, one may replace in conditions (ii) and (ii') "completely secant" by "regular" (A, X, p. 160, cor. 1).
It should be noted that this is not so in condition (i): a sequence completely secant for A is not necessarily A-regular (exerc. 1).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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