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\begin{proposition}\label{assumetest} If $x\in y$, then $x\in y$. \end{proposition} \begin{proof} Assume $x\in y$. Then $x\in y$. \end{proof} \begin{proposition}\label{assumetesttwo} If $x\in y$ and $a\in b$, then $x\in y$. \end{proposition} \begin{proof} Assume $a\in b$. Assume $x\in y$. Then $x\in y$. \end{proof}