\begin{tabbing}
$g$ glues ${\it Ia}$:${\it Qa}$ $--$$f$$\rightarrow$ ${\it Ib}$:${\it Rb}$
\\[0ex]$\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$\=\{${\it Ia}$\} $\leftarrow\leftarrow$= $g$== \{${\it Ib}$\} \& $g$ is ${\it Qa}${-}${\it Rb}${-}pre{-}preserving on \{${\it Ib}$\}\+
\\[0ex]\& Inj(\{$e$:E$\mid$ $\uparrow$($e$ $\in_{b}$ ${\it Ib}$)\} ;E;$g$)
\\[0ex]\& ($\forall$$e$:E(${\it Ib}$). $f$($g$($e$)) = ${\it Ib}$($e$))
\-
\end{tabbing}