# Derivation for Value Iteration of CVaR

I am reading a paper named Risk-sensitive and Robust Decision-making: a CVaR Optimization Approach.

In appendix A.3 they provide a proof for their Theorem $$4$$. The $$n=1$$ case for equation (11) is said to be held by definition. However, I cannot see why it is true from their definition of operator $$T$$.