\begin{tabbing}
1. $T$ : Type
\\[0ex]2. $R$ : $T$$\rightarrow$$T$$\rightarrow\mathbb{P}$
\\[0ex]3. ${\it R'}$ : $T$$\rightarrow$$T$$\rightarrow\mathbb{P}$
\\[0ex]4. $\forall$$x$, $y$:$T$. $R$($x$,$y$) $\Leftarrow\!\Rightarrow$ ${\it R'}$($x$,$y$)
\\[0ex]$\vdash$  \=(Refl($T$;$x$,$y$.$R$($x$,$y$)) \& Trans($T$;$x$,$y$.$R$($x$,$y$)) \& AntiSym($T$;$x$,$y$.$R$($x$,$y$)))\+
\\[0ex]$\Leftarrow\!\Rightarrow$ (Refl($T$;$x$,$y$.${\it R'}$($x$,$y$)) \& Trans($T$;$x$,$y$.${\it R'}$($x$,$y$)) \& AntiSym($T$;$x$,$y$.${\it R'}$($x$,$y$)))
\-
\end{tabbing}