$r${-}Prime($u$)
\\[0ex]$\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$($\neg$$u$ $\mid$ 1$r$ in $r$) \& ($\forall$$v$:$\mid$$r$$\mid$, $w$:$\mid$$r$$\mid$. $u$ $\mid$ $v$ ($\ast$$r$) $w$ in $r$ $\Rightarrow$ ($u$ $\mid$ $v$ in $r$ $\vee$ $u$ $\mid$ $w$ in $r$))