A two-variable rational inequality with a product correction

Proved

WorkbookSource.base_9970

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $x,y>0$ ,prove that: $\frac{16}{x+y}+\frac{x^2+14xy+y^2+16}{xy}\geq \frac{80}{xy+1}$

Source: InternLM Lean-Workbook, record lean_workbook_9970 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9970 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : 16 / (x + y) + (x ^ 2 + 14 * x * y + y ^ 2 + 16) / (x * y) ≥ 80 / (x * y + 1)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9970; Apache-2.0

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