Upper bound on l-intersecting families

[YaelDillies]

Let $1 \le \ell < r$ be fixed. If $n$ is large enough and $\mathcal A \subseteq X^{(r)}$ is an $\ell$-intersecting family, then $|\mathcal A| \le \binom{n - \ell}{r - \ell}$.

This is Theorem 1.17 in the lecture notes.