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diff --git a/test/phase5/exact-local-function-failure.tex b/test/phase5/exact-local-function-failure.tex
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+\begin{proposition}\label{phase5_local_function_failure}
+    For all $A$ we have $A = A$.
+\end{proposition}
+\begin{proof}
+    Fix $A$.
+    Let $f(x) = f$ for $x\in A$.
+    Follows by assumption.
+\end{proof}