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@@ -613,6 +613,9 @@ Laws of the order on the reals
\subsection{Order on the reals}
+\begin{axiom}\label{reals_order_is_transitive}
+ For all $x,y,z \in \reals$ such that $x < y$ and $y < z$ we have $x < z$.
+\end{axiom}
\begin{lemma}\label{plus_one_order}