\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$$x$, $y$:$T$. $R$($x$,$y$) $\Leftarrow\!\Rightarrow$ ${\it R'}$($x$,$y$)
\\[0ex]$\vdash$  \=($\forall$$a$, $b$, $c$:$T$. ${\it R'}$($b$,$a$) $\Rightarrow$ ${\it R'}$($c$,$b$) $\Rightarrow$ ${\it R'}$($c$,$a$))\+
\\[0ex]$\Leftarrow\!\Rightarrow$ ($\forall$$a$, $b$, $c$:$T$. ${\it R'}$($b$,$a$) $\Rightarrow$ ${\it R'}$($c$,$b$) $\Rightarrow$ ${\it R'}$($c$,$a$))
\-
\end{tabbing}