尝试拆分帧而不重复标题

Question

下面我尝试在特定位置拆分一个框架而不重复标题，但似乎没有发生。

\begin{frame}[allowframebreaks]{A result about multiples}
        \large

    \begin{Theorem}
        Let $\textit{n} \in \mathbb{Z}^{+}$. There is a multiple of n that only contains 0's and 1's (expressed base 10)
    \end{Theorem}

    \begin{Proof}
            \begin{itemize}

                \setbeamertemplate{itemize items}[ball]
                \item Write a list $1,11,111,1111,....$
                \item Each of these numbers on a division by n gives a remainder, one of $\{0,1,2,....,n-1\}$
                \item n possible remainders
                \framebreak
                \item more than \sout{one} \textit{n} (in fact infinity) numbers in list
                \item by Pigeonhole principle there are \textit{a,b} in list, $\textit{a}<\textit{b}$, same remainder \textit{r}
                \item \textit{b-a} is divisible by \textit{r}
                \item \textit{b-a} $=$
                \item \textit{b-a} is the required multiple.
            \end{itemize}   
        \end{Proof}
\end{frame}

我想要的是：

我得到的是：

Answer 1

    \begin{frame}{A result about multiples}
        \Large

    \begin{Theorem}
        Let $\textit{n} \in \mathbb{Z}^{+}$. There is a multiple of n that only contains 0's and 1's (expressed base 10)
    \end{Theorem}

    \begin{block}{Proof}
            \begin{itemize}
                \setlength{\itemsep}{4mm}
                \setbeamertemplate{itemize items}[ball]
                \item Write a list $1,11,111,1111,\dots$
                \item Each of these numbers on a division by n gives a remainder, one of $\{0,1,2,\dots,n-1\}$
                \item n possible remainders
            \end{itemize}
    \end{block}
    \end{frame}

    \begin{frame}
        \Large
        \vspace{-0.9cm}
        \begin{block}{Proof(cont.)}
        %\setbeamercolor{block title}{bg=white}
        %\setbeamercolor{block body}{bg=white}  
                \begin{itemize}
                \setlength{\itemsep}{7mm}
                \setbeamertemplate{itemize items}[ball]
                \item more than \xout{one} \textit{n} (in fact infinity) numbers in list
                \item by Pigeonhole principle there are \textit{a,b} in list, $\textit{a}<\textit{b}$, same remainder \textit{r}.
                \item \textit{b-a} is divisible by \textit{r}
                \item
                    $
                    \!
                    \begin{aligned}[t]
                    b-a &= 111\cdots \: 111 \text{ -- } 11 \cdots\cdots \: 111\\
                    &= 11 \: 11 \cdots\cdots 1100 \cdots 0
                    \end{aligned}
                    $
                \item \textit{b-a} is the required multiple.
                \qed
            \end{itemize}   
        \end{block}
\end{frame}