Exercise 4.7 in SLP (dynamic programming)
It follows from Assumption 4.10.
Let $\lambda y \in \Gamma(\lambda x)$ be the solution.
Let $\delta = \frac{1}{\lambda}$.
By Assumption 4.10,
$$
\lambda y \in\Gamma(\lambda x) 
$$
implies
$$
\delta \lambda y \in \Gamma(\delta\lambda x)
$$
in other words
$$
 y \in \Gamma(x)
$$