Monotonically increasing function

Function

 context $X,Y$ context $\le_X,\le_Y$ … non-strict partial order
 definiendum $f\in\mathrm{it}$
 inclusion $f:X\to Y$
 for all $x,y\in X$
 postulate $x\le_X y \implies f(x)\le_Y f(y)$