cr{-}fails{-}before(${\it es}$; ${\it Sys}$; ${\it chain}$; $x$; $y$) $\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$$\exists$$e$:E(${\it Sys}$). (($y$ $\in$ ${\it chain}$($e$)) \& ($\neg$($x$ $\in$ ${\it chain}$($e$))))