$\forall$$k$:$\mathbb{N}$, $A$:((:($\mathbb{Q}$ List) $\times$ (:$\mathbb{Z}$ $\times$ ($\mathbb{Q}$ List))) List), $y$:($\mathbb{Q}$ List). q{-}sat{-}constraints($k$;$A$;$y$) $\in$ $\mathbb{P}$