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

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.