Corollary 1
Tag 04W9, permanent. Cite it as [Bourbaki, Tag 04W9].
Commutative Algebra, chapter VI, § 8. Extensions of a valuation to an algebraic extension
The height of is equal to that of .
This follows from Proposition 1 and the following lemma:
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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