weak{-}antecedent{-}function(${\it es}$;$P$;$Q$;$f$)
\\[0ex]$\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$$\forall$$e$:\{$e$:es{-}E(${\it es}$)$\mid$ $P$($e$)\} . es{-}causle(${\it es}$;$f$($e$);$e$) \& $Q$($f$($e$))