Corollary

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

Commutative Algebra, chapter VIII, § 7. Multiplicités

If $[B/m_i : A/\rho^{-1}(m_i)] = 1$ for every i, one has $e_q^A(N) = e_{qB}^B(N)$ .

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

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