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\label{eq:cons_lemma}  R(a_l) \xrightarrow[l \rightarrow \infty]{P} \inf_{a \in \Lambda}R(a)  \end{equation}  \textit{proof} \textit{Proof.}  Denote \begin{equation}  \label{eq:T}  T \triangleq \inf_{a \in \Lambda}R(a)