  Establishing explicit formulas of coderivatives with respect to a set of the
normal cone mapping to a polyhedron, the solution set of a variational
inequalities system, is one of the main goals of this paper. By using our
coderivative formulas, we provide a characteristic of the Aubin property with
respect to a set of that normal cone mapping and thereby give necessary
optimality conditions for simple bilevel optimization problems under weak
qualification conditions.
