The Stacks project

Lemma 62.11.1. The construction above is bilinear, i.e., we have $(\alpha _1 + \alpha _2) \cap \beta = \alpha _1 \cap \beta + \alpha _2 \cap \beta $ and $\alpha \cap (\beta _1 + \beta _2) = \alpha \cap \beta _1 + \alpha \cap \beta _2$.

Proof. Omitted. $\square$

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