From 442d732696ad431b84f6e5c72b6ee785be4fd968 Mon Sep 17 00:00:00 2001
From: adelon <22380201+adelon@users.noreply.github.com>
Date: Sat, 10 Feb 2024 02:22:14 +0100
Subject: Initial commit

---
 test/examples/proofdefinefunction.tex | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 test/examples/proofdefinefunction.tex

(limited to 'test/examples/proofdefinefunction.tex')

diff --git a/test/examples/proofdefinefunction.tex b/test/examples/proofdefinefunction.tex
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+++ b/test/examples/proofdefinefunction.tex
@@ -0,0 +1,27 @@
+% The builtin "-(-)" notation desugars to "\apply{-}{-}".
+% This is just a dummy definition.
+\begin{definition}\label{apply}
+    $\apply{f}{x} = x$.
+\end{definition}
+
+% Dummy definition for the domain
+\begin{definition}\label{dom}
+    $\dom{f} = f$.
+\end{definition}
+
+% Dummy definition for right-uniqueness
+\begin{definition}\label{rightunique}
+    $f$ is right-unique iff $f=f$.
+\end{definition}
+
+% Dummy definition for relations
+\begin{definition}\label{relation}
+    $f$ is a relation iff $f=f$.
+\end{definition}
+
+\begin{proposition}\label{definefunctiontest}
+    If $x\in y$, then $x\in y$.
+\end{proposition}
+\begin{proof}
+    Let $f(z) = z$ for $z\in x$.
+\end{proof}
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