apply Real.rpow_lt_rpow (by linarith) (twoMulLtTwoPow (by linarith))
n : ℝ
hn : 81 / 2 < n
h : 4 ^ (n / 3) ≤ (2 * n) ^ (1 + Real.sqrt (2 * n))
⊢ (2 * n) ^ ((1 + Real.sqrt (2 * n)) * 3) < (2 ^ (6 * (2 * n) ^ 6⁻¹)) ^ ((1 + Real.sqrt (2 * n)) * 3)
n : ℝ
hn : 81 / 2 < n
h : 4 ^ (n / 3) ≤ (2 * n) ^ (1 + Real.sqrt (2 * n))
⊢ 0 < (1 + Real.sqrt (2 * n)) * 3