Sunflower bound for minimal members of a Razborov-closed family (source code)

= Sunflower bound for minimal members of a Razborov-closed family
{title2=$a_s\leq s!(r-1)^s$}

An inclusion-minimal $s$-set in an upward-closed family cannot belong to an $r$-member <delta-system> of such minimal sets: its proper core would be adjoined by <Razborov closure>, violating minimality. The <Erdős–Rado sunflower lemma> therefore bounds the number $a_s$ of minimal $s$-sets. This weaker factorial bound is sufficient for the <superpolynomial monotone clique lower bound>.