rw [prodPrimesSplit (by linarith : n.succ ≤ (2*n).succ)]
case odd_prime
n : ℕ
hp : Nat.Prime (Nat.succ (2 * n))
hi : prodPrimes (Nat.succ n) ≤ 4 ^ n
⊢ prodPrimes (Nat.succ (2 * n)) ≤ 4 ^ n * 4 ^ n
case odd_prime
n : ℕ
hp : Nat.Prime (Nat.succ (2 * n))
hi : prodPrimes (Nat.succ n) ≤ 4 ^ n
⊢ prodPrimes (Nat.succ n) * ∏ p in primes (Finset.Ioc (Nat.succ n) (Nat.succ (2 * n))), p ≤ 4 ^ n * 4 ^ n