A shifted rational product bounds a squared difference

Proved

WorkbookSource.base_12034

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

lean-workbooksource-checked

Prove that for all $a,b>0$ the following inequality holds:

4(a+b+1)+(a-b)^2\leq \frac{(a+b+1)(a+1)^2(b+1)^2}{4ab}

Source: InternLM Lean-Workbook, record lean_workbook_12034 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12034 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : 4 * (a + b + 1) + (a - b) ^ 2 ≤ (a + b + 1) * (a + 1) ^ 2 * (b + 1) ^ 2 / (4 * a * b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12034; Apache-2.0

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