\begin{definition}[Definition:Order-Reflecting Mapping]
Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be ordered sets.
Let $\phi: S \to T$ be a mapping.
Then $\phi$ is an '''order-reflecting mapping''' or '''reflects order''' {{iff}}:
: $\forall x, y \in S: \phi \left({x}\right) \preceq_2 \phi\left({y}\right) \implies x \preceq_1 y$
\end{definition}