$\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($\oplus$($L$))) $\Rightarrow$ ($\exists$$f$$\in$$L$.($\uparrow$$x$ $\in$ dom($f$)) \& $\oplus$($L$)($x$) = $f$($x$) $\in$ $B$($x$))