On the differentiability properties of the infimal regularisation of a prox-regular function

A short proof of the fact that the infimal convolution of a prox-regular function possesses the C-1,C-1 property is provided. The approach here is based on techniques from generalised convexity and thus avoids the use of maximal monotone operator theory as Used is in (Prox-regular functions in varitional analysis. Transactions of the Amercian Mathematical Society, 348(5), 1805-1838).