refine' Real.le_sqrt_of_sq_le _
n : ℕ
⊢ (↑n + 1 / 2) / (↑n + 1) ≤ Real.sqrt ((↑n + 1 / 3) / (↑n + 1 + 1 / 3))

case hx
n : ℕ
⊢ 0 ≤ ↑n + 1 / 3
n : ℕ
⊢ ((↑n + 1 / 2) / (↑n + 1)) ^ 2 ≤ (↑n + 1 / 3) / (↑n + 1 + 1 / 3)

case hx
n : ℕ
⊢ 0 ≤ ↑n + 1 / 3