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diff --git a/test/phase5/exact-separation.tex b/test/phase5/exact-separation.tex
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\end{definition}
\begin{proposition}\label{phase5_separation_theorem}
- For all $A, x$ we have if $x \in \{ y \in A \mid y = y \}$, then $x \in A$.
+ For all $A, x$ we have if $x \in \phasefiveseparation{A}$, then $x \in A$.
\end{proposition}
\begin{proof}
Fix $A, x$.
- Assume $x \in \{ y \in A \mid y = y \}$.
- Follows by assumption.
+ Assume $x \in \phasefiveseparation{A}$.
\end{proof}