$\forall$$A$:Type, $B$:($A$$\rightarrow$Type), ${\it eq}$:EqDecider($A$), $f$,$h$,$g$:fpf($A$; $a$.$B$($a$)).
\\[0ex]fpf{-}sub($A$; $a$.$B$($a$); ${\it eq}$; $h$; $f$) $\Rightarrow$ fpf{-}sub($A$; $a$.$B$($a$); ${\it eq}$; $h$; fpf{-}join(${\it eq}$; $f$; $g$))