The Stacks project

Lemma 62.14.2. Let $f : X \to Y$ and $g : Y \to S$ be a morphisms of schemes. Assume $S$ locally Noetherian, $g$ locally of finite type and flat of relative dimension $e \ge 0$, and $f$ locally of finite type and flat of relative dimension $r \geq 0$. Then $[X/X/Y]_ r \circ [Y/Y/S]_ e = [X/X/S]_{r + e}$ in $z(X/S, r + e)$.

Proof. Special case of Lemma 62.13.5. $\square$

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