$\forall$$T$:Type, $E$:($T$$\rightarrow$$T$$\rightarrow\mathbb{P}$).
\\[0ex]($\forall$$x$, $y$:$T$. Dec($E$($x$,$y$))) $\Leftarrow\!\Rightarrow$ ($\exists$$f$:$T$$\rightarrow$$T$$\rightarrow\mathbb{B}$. ($\forall$$x$, $y$:$T$. ($\uparrow$($x$ $f$ $y$)) $\Leftarrow\!\Rightarrow$ $E$($x$,$y$)))