Proposition 1

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

Commutative Algebra, chapter VIII, § 7. Multiplicités

Let $\hat{A}$ and $\hat{M}$ be the completions of A and M for their q-adic topologies; then $e_q^A(M) = e_{q\hat{A}}(\hat{M})$ .

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

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