$\forall$$A$:Type, ${\it eq}$:EqDecider($A$), $B$:($A$$\rightarrow$Type), $L$:($a$:$A$ fp$\rightarrow$ $B$($a$) List), $x$:$A$.
\\[0ex]($\uparrow$$x$ $\in$ dom($\oplus$($L$)))
\\[0ex]$\Rightarrow$ ($\forall$$f$,$g$$\in$$L$.  $\forall$$x$:$A$. $\neg$(($\uparrow$$x$ $\in$ dom($f$)) \& ($\uparrow$$x$ $\in$ dom($g$))))
\\[0ex]$\Rightarrow$ ($\forall$$f$:$a$:$A$ fp$\rightarrow$ $B$($a$). ($f$ $\in$ $L$) $\Rightarrow$ ($\uparrow$$x$ $\in$ dom($f$)) $\Rightarrow$ ($\oplus$($L$)($x$) = $f$($x$) $\in$ $B$($x$)))