diff --git a/ws2019/ana/lectures/analysis25.pdf b/ws2019/ana/lectures/analysis25.pdf
index 50a6c8f..adafaf1 100644
Binary files a/ws2019/ana/lectures/analysis25.pdf and b/ws2019/ana/lectures/analysis25.pdf differ
diff --git a/ws2019/ana/lectures/analysis25.tex b/ws2019/ana/lectures/analysis25.tex
index 6c50960..74d5b12 100644
--- a/ws2019/ana/lectures/analysis25.tex
+++ b/ws2019/ana/lectures/analysis25.tex
@@ -260,4 +260,7 @@
     .\end{align*}
 \end{lemma}
 
+\begin{proof}[Ende]
+\end{proof}
+
 \end{document}