$\forall$$T$:Type\{j\}, $R$:($T$$\rightarrow$$T$$\rightarrow\mathbb{P}$\{i\}), $a$, $b$:$T$. Symmetrize($x$,$y$.$R$($x$,$y$);$a$;$b$) $\in$ $\mathbb{P}$\{i\}