$\forall$${\it ds}$:$x$:Id fp$\rightarrow$ Type, ${\it da}$:$k$:Knd fp$\rightarrow$ Type, ${\it upd}$:update{-}spec(${\it ds}$;${\it da}$).
\\[0ex]update{-}spec{-}decl(${\it upd}$;${\it ds}$) $\in$ Prop