  We propose a level proximal subdifferential for a proper lower semicontinuous
function. Level proximal subdifferential is a uniform refinement of the
well-known proximal subdifferential, and has the pleasant feature that its
resolvent always coincides with the proximal mapping of a function. It turns
out that the resolvent representation of proximal mapping in terms of
Mordukhovich limiting subdifferential is only valid for hypoconvex functions.
We also provide properties of level proximal subdifferential and numerous
examples to illustrate our results.
