Can someone help me solve the following question please?

Let v be a vertex of a d-polytope P such that .

Prove that is a facet of .

The definitions are:

and a face of P is the empty set, P itself, or an intersection of P with a supporting hyperplane (i.e.- a hyperplane, such that P is located in one of the halfspaces it determines).

A facet is a face of maximal degree

Thanks