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+\begin{proposition}\label{phase5_formula_quantified_set_induction}
+    $\forall x. x = x$.
+\end{proposition}
+\begin{proof}[Proof by \in-induction]
+    Show $x = x$.
+    \begin{subproof}
+        Follows.
+    \end{subproof}
+    Follows by assumption.
+\end{proof}