Definition:Order-Preserving

Let $$\left({S, \preceq_1}\right)$$ and $$\left({T \preceq_2}\right)$$ be posets.

Let $$\phi: S \to T$$ be an injection.

Then $$\phi$$ is order-preserving iff:


 * $$\forall x, y \in S: x \preceq_1 y \implies \phi \left({x}\right) \preceq_2 \phi \left({y}\right)$$