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diff --git a/library/subfinite.tex b/library/subfinite.tex
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+\import{function.tex}
+\import{nat.tex}
+
+\begin{definition}\label{subfinite}
+    $X$ is subfinite iff
+        there exists a natural number $k$ such that
+        there exists an injective function $f$ from $k$ to $X$.
+\end{definition}
+
+\begin{proposition}\label{emptyset_subfinite}
+    $\emptyset$ is subfinite.
+\end{proposition}