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@@ -633,6 +633,7 @@ This lets us use the same symbol for composition of functions.
\begin{proof}
%$x\in\dom{R}$ and $z\in\ran{S}$.
There exists $y$ such that $x\mathrel{R} y\mathrel{S} z$ by \cref{circ,pair_eq_iff}.
+ Follows by assumption.
\end{proof}
\begin{proposition}\label{circ_iff}