= Erdős–Rado sunflower lemma
{c}
{title2=$|\mathcal F|>s!(r-1)^s\Longrightarrow\text{an }r\text{-member sunflower}$}
= Sunflower lemma
{synonym}
A sunflower is a <delta-system>: its pairwise <intersections> all equal one core, and its petals outside the core are pairwise disjoint. For an $s$-<uniform set family>, prove the displayed bound by <induction> on $s$. If a maximal disjoint subfamily has $r$ members, their core is empty. Otherwise its union has at most $s(r-1)$ points and meets every member. Some point belongs to more than $(s-1)!(r-1)^{s-1}$ members. Remove it and apply the induction hypothesis; putting it back enlarges the common core. The case $s=0$ is immediate.
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