rw [sqrt_div (Nat.cast_nonneg _), centralBinomialUpper, div_div, mul_div_assoc',
  div_div_eq_mul_div, mul_right_comm, mul_div_mul_right]
case h
this : (Real.sqrt π)⁻¹ = (Real.sqrt π)⁻¹ / Real.sqrt 1
h : Real.sqrt 1 ≠ 0
n : ℕ
hn : 0 < n
⊢ ↑(centralBinom n) * Real.sqrt ↑n / 4 ^ n / Real.sqrt (↑n / (↑n + 1 / 3)) = centralBinomialUpper n
case h.hc
this : (Real.sqrt π)⁻¹ = (Real.sqrt π)⁻¹ / Real.sqrt 1
h : Real.sqrt 1 ≠ 0
n : ℕ
hn : 0 < n
⊢ Real.sqrt ↑n ≠ 0