Remark 4
Tag 0CN1, permanent. Cite it as [Bourbaki, Tag 0CN1].
Commutative Algebra, chapter VIII, § 3. Dimension des anneaux noethériens
It is not true in general that a sequence secant for M is completely secant for M (p. 87, Exercise 6). We shall study later the modules over a noetherian local ring for which every secant sequence is completely secant.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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