$\forall$$T$:Type, $r$:($T$$\rightarrow$$T$$\rightarrow\mathbb{P}$).
\\[0ex]dec\_binrel($T$;$x$,$y$:$T$. $x$ = $y$ $\in$ $T$) $\Rightarrow$ refl($T$;$r$) $\Rightarrow$ anti\_sym($T$;$r$) $\Rightarrow$ ((($r$$\backslash$)$^{\circ}$) $\Lleftarrow\!\Rrightarrow$\{$T$\} $r$)