Lemma 42.48.2. In Lemma 42.48.1 let $X' \to X$ be a morphism which is locally of finite type. Denote $b' : W' \to \mathbf{P}^1_{X'}$ and $i'_\infty : W'_\infty \to W'$ the base changes of $b$ and $i_\infty $. Then the class $C' \in A^0(W'_\infty \to X')$ constructed as in Lemma 42.48.1 using $b'$ is the restriction (Remark 42.33.5) of $C$.

**Proof.**
Immediate from the construction and the fact that a similar statement holds for flat pullback and $i_\infty ^*$.
$\square$

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