Lemma 93.6.2. Example 93.6.1 satisfies the Rim-Schlessinger condition (RS). In particular, $\mathcal{D}\! \mathit{ef}_{V, \rho _0}$ is a deformation category for any finite dimensional continuous representation $\rho _0 : \Gamma \to \text{GL}_ k(V)$.

**Proof.**
The proof is exactly the same as the proof of Lemma 93.5.2.
$\square$

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