Corollary

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

Commutative Algebra, chapter VII, § 1. Krull domains

If $x, y$ and $x + y$ are in $K^*$ , then $\operatorname{div}(x + y) \geq \inf(\operatorname{div}(x), \operatorname{div}(y))$ .

$A(x + y) \subset Ax + Ay$ and hence $\operatorname{div}(x + y) \geq \operatorname{div}(Ax + Ay)$ .

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

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