$\forall$$p$, $q$:($\mathbb{Q}$ List), $F$:(\{0..$\parallel$$p$ @ $q$$\parallel^{-}$\}$\rightarrow\mathbb{Q}$).
\\[0ex]weighted{-}sum($p$ @ $q$;$F$) = (weighted{-}sum($p$;$F$) + weighted{-}sum($q$;$\lambda$$i$.$F$($i$+$\parallel$$p$$\parallel$))) $\in$ $\mathbb{Q}$