$\forall$$T$:Type, $R$:($T$$\rightarrow$$T$$\rightarrow\mathbb{P}$), $x$:$T$, $L$:($T$ List).
\\[0ex]sorted{-}by($R$;[$x$ / $L$]) $\Leftarrow\!\Rightarrow$ (sorted{-}by($R$;$L$) \& ($\forall$$z$$\in$$L$. $R$($x$,$z$)))