Let $M = (E,\mathcal I)$ be a matroid on a finite ground set $E$, and let $e \in E$ be a nonloop of $M$. Define the contraction $M/e$ to have ground set $E \setminus \{e\}$ and independent sets
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\begin{align*}
\mathcal I(M/e) := \{I \subset E \setminus \{e\} : I \cup \{e\} \in \mathcal I\}.
\end{align*}