$\forall$$A$, $B$:Type, $a$:EqDecider($A$), $b$:EqDecider($B$).
\\[0ex]prod{-}deq($A$;$B$;$a$;$b$) $\in$ ($\forall$$p$, $q$:($A$$\times$$B$). $p$ $=$ $q$ $\Leftrightarrow$ proddeq($a$;$b$)($p$,$q$))