apply le_trans FactorizationCentralBinom.prodIocSqrtPowLeProdPrimes
case h.h₂.h₁
n : ℕ
hn : 2 < n
⊢ ∏ x in Finset.Ioc (Nat.sqrt (2 * n)) (2 * n / 3), x ^ ↑(Nat.factorization (Nat.centralBinom n)) x ≤
    4 ^ Nat.pred (2 * n / 3)
case h.h₂.h₁
n : ℕ
hn : 2 < n
⊢ ∏ p in primes (Finset.Ioc (Nat.sqrt (2 * n)) (2 * n / 3)), p ≤ 4 ^ Nat.pred (2 * n / 3)