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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