$\forall$$A$:Type, ${\it eq}$:EqDecider($A$), $B$:($A$$\rightarrow$Type), $g$:$x$:$A$ fp$\rightarrow$ $B$($x$), $x$:$A$.
\\[0ex]$x$ $\in$ dom($g$) $\Rightarrow$ fpf{-}normalize(${\it eq}$;$g$)($x$) $=$ $g$($x$) $\in$ $B$($x$)