We prove a p-adic version of the Lion-Rolin preparation theorem. As a consequence, we obtain a cell decomposition theorem, which can be viewed as an extension of Denef's cell decomposition theorem to the p-adic analytic case. Using these theorems, we give shorter and more explicit proofs of some of the results by Denef and van den Dries on p-adic subanalytic sets.
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机译：我们证明了Lion-Rolin准备定理的p-adic版本。结果，我们获得了细胞分解定理，它可以看作是Denef细胞分解定理到p-adic分析案例的扩展。使用这些定理，我们给出了Denef和van den Dries在p-adic亚分析集上得到的一些结果的更短和更明确的证明。
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