\begin{definition}[Definition:Euclidean Relation/Left-Euclidean]
Let $\RR \subseteq S \times S$ be a relation in $S$.
$\RR$ is '''left-Euclidean''' {{iff}}:
:$\tuple {x, z} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, y} \in \RR$
\end{definition}