Lemma 60.12.3. In Situation 60.7.5. For $(U, T, \delta )$ in $\text{Cris}(X/S)$ the restriction $(\Omega _{X/S})_ T$ to $T$ is $\Omega _{T/S, \delta }$ and the restriction $\text{d}_{X/S}|_ T$ is equal to $\text{d}_{T/S, \delta }$.

Proof. Omitted. $\square$

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