all_goals positivity
n : ℕ
this✝ : 0 < π
this : (Real.sqrt π)⁻¹ ≤ centralBinomialUpper n
⊢ 0 < 4 ^ n

n : ℕ
this✝ : 0 < π
this : (Real.sqrt π)⁻¹ ≤ centralBinomialUpper n
⊢ 0 < Real.sqrt (↑n + 1 / 3)

case hx
n : ℕ
this✝ : 0 < π
this : (Real.sqrt π)⁻¹ ≤ centralBinomialUpper n
⊢ 0 ≤ π
no goals