simp [Nat.Ico_succ_succ]
case h
n : ℕ
hn : 2 < n
⊢ (∏ i in Finset.Ico 0 (Nat.succ (Nat.sqrt (2 * n))), i ^ ↑(Nat.factorization (Nat.centralBinom n)) i) *
      ∏ i in Finset.Ico (Nat.succ (Nat.sqrt (2 * n))) (Nat.succ (2 * n)),
        i ^ ↑(Nat.factorization (Nat.centralBinom n)) i ≤
    (2 * n) ^ Nat.sqrt (2 * n) * 4 ^ Nat.pred (2 * n / 3) * ∏ p in primes (Finset.Ioc n (2 * n)), p
case h
n : ℕ
hn : 2 < n
⊢ (∏ x in Finset.range (Nat.succ (Nat.sqrt (2 * n))), x ^ ↑(Nat.factorization (Nat.centralBinom n)) x) *
      ∏ x in Finset.Ioc (Nat.sqrt (2 * n)) (2 * n), x ^ ↑(Nat.factorization (Nat.centralBinom n)) x ≤
    (2 * n) ^ Nat.sqrt (2 * n) * 4 ^ Nat.pred (2 * n / 3) * ∏ p in primes (Finset.Ioc n (2 * n)), p