refine' div_le_div_of_le (by positivity) _
n : ℕ
⊢ ↑(centralBinom n) * Real.sqrt (↑n + 1 / 4) / 4 ^ n ≤
    ↑(centralBinom (n + 1)) * Real.sqrt (↑(n + 1) + 1 / 4) / 4 / 4 ^ n
n : ℕ
⊢ ↑(centralBinom n) * Real.sqrt (↑n + 1 / 4) ≤ ↑(centralBinom (n + 1)) * Real.sqrt (↑(n + 1) + 1 / 4) / 4