\documentclass[ngerman]{article}

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\providecommand{\proving}[2]{$#1 \implies #2$}

\usepackage{amsthm}
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\DeclarePairedDelimiter\norm{\lVert}{\rVert}

\begin{document}
\begin{satz}
  Sei $X$ ein Banachraum. Äquivalent sind:
  \begin{enumerate}
  \item \label{it:index-one_daugavet} $n(X) = 1$,
  \item \label{it:alternative-daugavet-all} $\max_{\omega \in \mathbb T}
    \norm{\operatorname{id} + \omega T} = 1 + \norm T$ für alle $T \in L(X)$.
  \end{enumerate}
  \begin{proof}
    \proving{\eqref{it:index-one_daugavet}}{\eqref{it:alternative-daugavet-all}}: %
    Sei $T \in L(X)$ beliebig. [..]
  \end{proof}
\end{satz}
\end{document}