\qed vertical alignment in Beamer

Question

I am using beamer for some presentation and when I end the proof with a multi-line equation, I cannot set the positition the \qed symbol at the end of the last equation line.

\documentclass[10pt]{beamer}

\usetheme{Warsaw}
\usecolortheme{seahorse}

\renewcommand{\qedsymbol}{{\usebeamercolor[fg]{structure}$\blacksquare$}}

\begin{document}

\begin{frame}

\begin{block}{\proofname}
Some text here
\begin{equation}
\begin{cases}
1\\
2\\
3\\
4.
\end{cases}\notag
\end{equation}
\hfill\qedsymbol
\end{block}

\end{frame}

\end{document} 

This gives me the following output

but I need the following.

Answer 1

Here is an quick and dirty way of doing it:

\documentclass[10pt]{beamer}
\usetheme{Warsaw}
\usecolortheme{seahorse}

\renewcommand{\qedsymbol}{\raisebox{\dimexpr\belowdisplayskip+\lineskip\relax}[0pt]{\usebeamercolor[fg]{structure}$\blacksquare$}\vspace{-\belowdisplayskip}}

\begin{document}

\begin{frame}
    \begin{block}{\proofname}
        Some text here
        \begin{equation}
        \begin{cases}
        1\\
        2\\
        3\\
        4.
        \end{cases}\notag
        \end{equation}
        \hfill\qedsymbol
    \end{block}
\end{frame}

\end{document} 

An extra space (seems 5pt, not sure why) will be inserted when the equation is too long so further adjustment is needed.

Answer 2

You might do like this, but I'm not sure you really need an end of proof symbol.

\documentclass[10pt]{beamer}

\usetheme{Warsaw}
\usecolortheme{seahorse}

\renewcommand{\qedsymbol}{{\usebeamercolor[fg]{structure}$\blacksquare$}}

\begin{document}

\begin{frame}

\begin{block}{\proofname}\pushQED{\qed}
Some text here
\begin{equation*}
\begin{gathered}[b]
\begin{cases}
1\\
2\\
3\\
4.
\end{cases}\\[-1.2\normalbaselineskip]
\mathstrut
\end{gathered}\qedhere
\end{equation*}
\popQED\end{block}

\end{frame}