apply le_trans _ chooseHalfLePowFour
case odd_prime
n : ℕ
hp : Nat.Prime (Nat.succ (2 * n))
hi : prodPrimes (Nat.succ n) ≤ 4 ^ n
⊢ ∏ p in primes (Finset.Ioc (Nat.succ n) (Nat.succ (2 * n))), p ≤ 4 ^ n
n : ℕ
hp : Nat.Prime (Nat.succ (2 * n))
hi : prodPrimes (Nat.succ n) ≤ 4 ^ n
⊢ ∏ p in primes (Finset.Ioc (Nat.succ n) (Nat.succ (2 * n))), p ≤ Nat.choose (2 * n + 1) n