$\Pi$$g$ ${\it lb}$ $\leq$ $i$ $<$ ${\it ub}$. $E$($i$) $\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$$\Pi$($\ast$$g$,e$g$) ${\it lb}$ $\leq$ $i$ $<$ ${\it ub}$. $E$($i$)