apply Finset.prod_le_pow_card
n : ℕ
s : Finset ℕ
hn : 0 < n
⊢ ∏ p in s, p ^ ↑(Nat.factorization (Nat.centralBinom n)) p ≤ (2 * n) ^ Finset.card s
case h
n : ℕ
s : Finset ℕ
hn : 0 < n
⊢ ∀ (x : ℕ), x ∈ s → x ^ ↑(Nat.factorization (Nat.centralBinom n)) x ≤ 2 * n