Remark 4

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

Let $(Y_i)_{i \in I}$ be a finite family of closed subsets of $X$ and $Y = \bigcup_{i \in I} Y_i$ ; one has

\operatorname{codim}(Y, X) = \inf_{i \in I} \operatorname{codim}(Y_i, X).

In fact, every irreducible component of $Y$ is contained in one of the $Y_i$ .

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

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