  In this paper we study the properties of the normal cone to the proximally
smooth set. We give the complete characterization of the proximally smooth set
through the monotony properties of its normal cone in an arbitrary uniformly
convex and uniformly smooth Banach space. We give the exact bounds for
right-hand side in the monotonicity inequality for normal cone in terms of the
moduli of smoothness and convexity of a Banach space.

Functional Analysis