The Stacks project

Lemma 31.13.14. Let $f : S' \to S$ be a morphism of schemes. Let $D_1$, $D_2$ be effective Cartier divisors on $S$. If the pullbacks of $D_1$ and $D_2$ are defined then the pullback of $D = D_1 + D_2$ is defined and $f^*D = f^*D_1 + f^*D_2$.

Proof. Omitted. $\square$

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