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Final stub. No more white bubbles!
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teorth committed Jul 1, 2024
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Expand Up @@ -104,7 +104,7 @@ \section{Rho functionals}
To get the equality, let $t^*:=\arg\max_t |A \cap (H+t)|$ and observe that $$\rho^-(U_H)\le D_{KL}(U_H \Vert U_A+(U_H-t^*))= \log |A| - \log \max_t|A \cap (H+t)|.$$
\end{proof}

\begin{corollary}[Rho plus of subgroup]\label{rhoplus-subgroup}\lean{rho_plus_of_subgroup}\uses{rhoplus-def} If $H$ is a finite subgroup of $G$, then $\rho^+(U_H) = \log |H| - \log \max_t |A \cap (H+t)|$.
\begin{corollary}[Rho plus of subgroup]\label{rhoplus-subgroup}\lean{rho_plus_of_subgroup}\uses{rhoplus-def}\leanok If $H$ is a finite subgroup of $G$, then $\rho^+(U_H) = \log |H| - \log \max_t |A \cap (H+t)|$.
\end{corollary}

\begin{proof}\uses{rhominus-subgroup} Straightforward by definition and \Cref{rhominus-subgroup}.
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