Lemma 70.6.12. Let $S$ be a scheme. Let $f : X' \to X$ be a morphism of algebraic spaces over $S$. Let $D_1$, $D_2$ be effective Cartier divisors on $X$. 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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