$\forall$$A$:Type, ${\it eq}$:EqDecider($A$), $B$:($A$$\rightarrow$Type), $L$:($a$:$A$ fp$\rightarrow$ $B$($a$) List), $x$:$A$.
\\[0ex]($x$ $\in$ fpf{-}domain($\oplus$($L$))) $\Leftarrow\!\Rightarrow$ ($\exists$$f$$\in$$L$.($x$ $\in$ fpf{-}domain($f$)))