The following form of Hensel's Lemma in Algebraic Geometry is well-documented in the literature:



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> $\textbf{Theorem 1}$: Let $R$ be an Henselian local ring with maximal ideal $\mathfrak{m}$, and let $X$ be a smooth $R$-scheme. Then $X(R)\to X(R/\mathfrak{m})$ is surjective.
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One can for example refer to $[EGA\_{IV}]$, Théorème $18.5.17$.


Now I would like to use the following variation:



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> $\textbf{Theorem 2}$: Let $R$ be a Henselian local ring with maximal ideal $\mathfrak{m}$, and let $X$ be a smooth $R$-scheme. Then $X(R/\mathfrak{m}^l)\to X(R/\mathfrak{m}^k)$ is surjective, for any integers $l\geq k>0$ (where $l=\infty$ is allowed, in which case $\mathfrak{m}^l = (0)$).
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And I would really prefer to avoid saying that the proof is a straightforward adaptation of the proof of Theorem 1 (or to write it). Is there a reference for Theorem 2 ?



Reference for Hensel's Lemma in Algebraic Geometry
The question has been answered in the comments


