Corollary 2
Tag 04WB, permanent. Cite it as [Bourbaki, Tag 04WB].
Commutative Algebra, chapter VI, § 8. Extensions of a valuation to an algebraic extension
For to be improper (resp. of height 1), it is necessary and sufficient that be improper (resp. of height 1).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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