IsIntegDom($r$) $\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$0 $\neq$ 1 $\in$ $\mid$$r$$\mid$  \& ($\forall$$u$, $v$:$\mid$$r$$\mid$. ($\neg$($v$ = 0)) $\Rightarrow$ (($u$ $\ast$ $v$) = 0) $\Rightarrow$ ($u$ = 0))