On the structure of p-adic subanalytic functions and sets

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.