Lemma 54.63.7. Let $X$ be a scheme. Let $\Lambda $ be a ring. The tensor product of two locally constant sheaves of $\Lambda $-modules on $X_{\acute{e}tale}$ is a locally constant sheaf of $\Lambda $-modules.

**Proof.**
This holds on any site, see Modules on Sites, Lemma 18.42.6.
$\square$

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