  In his beautiful paper on the central set from 1981, Y. Yomdin makes use of a
Lipschitz Inverse Function Theorem that seemingly has been unproved until now.
After a brief discussion of a natural and straightforward Lipschitz counterpart
of an implicit function theorem, based on a geometric condition we finally
provide a proof of Yomdin's version holds by proving the geometric condition is
in fact equivalent to the one given by Yomdin. Therefore, Yomdin's Generic
Structure Theorem, whose updated version is also presented here, concerning the
medial axis (central set) of a subset of in ${\Rz}^n$ is now flawless. We also
note that Yomdin's Lipschitz Implicit Function Theorem is equivalent to
Clarke's Lipschitz Inverse Function Theorem. The paper ends with some
additional properties of Lipschitz germs satisfying the Yomdin condition (e.g.
a Lipschitz triviality result).
