Remark 1

Tag 0D2U, permanent. Cite it as [Bourbaki, Tag 0D2U].

Commutative Algebra, chapter X, § 2. Modules et anneaux macaulayens

Every finite subset S of A such that SM = M is strongly secant for M. When SM ≠ M, it follows from lemma 2 that, for S to be strongly secant for M, it is necessary and sufficient that one have Card(S) = codim(Supp(M/SM), Supp(M)), or again ht( $\overline{\mathscr{G}}$ ) = Card(S).

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

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