\begin{definition}[Definition:Extension of Relation]
Let:
:$\RR_1 \subseteq X \times Y$ be a relation on $X \times Y$
:$\RR_2 \subseteq S \times T$ be a relation on $S \times T$
:$X \subseteq S$
:$Y \subseteq T$
:$\RR_2 \restriction_{X \times Y}$ be the restriction of $\RR_2$ to $X \times Y$.
Let $\RR_2 \restriction_{X \times Y} = \RR_1$.
Then $\RR_2$ '''extends''' or '''is an extension of''' $\RR_1$.
\end{definition}