diff --git a/ITP/related-work.tex b/ITP/related-work.tex index 8e7448c..c8f1301 100644 --- a/ITP/related-work.tex +++ b/ITP/related-work.tex @@ -13,7 +13,7 @@ Rather than devise a new SAT encoding, we use essentially the same encoding presented by Heule and Scheucher~\cite{emptyHexagonNumber}. Interestingly, -a (verified) proof of $g(6) \leq 17$ can be obtained +a formal proof of $g(6) \leq 17$ can be obtained as a corollary of our development. We can assert the hole variables $\hvar_{a,b,c}$ as true while leaving the remainder of the encoding in~\Cref{fig:full-encoding} unchanged, @@ -29,8 +29,8 @@ We checked this formula to be unsatisfiable for $n = 17$, giving the same result as Marić: \begin{lstlisting} -theorem gon_6_theorem (pts : List Point) (gp : ListInGenPos pts) - (h : pts.length ≥ 17) : HasConvexKGon 6 pts.toFinset +theorem gon_6_theorem : ∀ (pts : Finset Point), + SetInGenPos pts → pts.card = 17 → HasConvexKGon 6 pts \end{lstlisting} Since both formalizations can be executed,