Proposition 5

Tag 04U9, permanent. Cite it as [Bourbaki, Tag 04U9].

Commutative Algebra, chapter VI, § 4. The height of a valuation

The height of a valuation is equal to the number of non-zero prime ideals in its ring.

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

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Nothing.