A quadratic ratio sum with a symmetric correction

Proved

WorkbookSource.base_3520

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

lean-workbooksource-checked

Prove that for all positive real $a$ , $b$ and $c$ holds:

\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ca}+\frac{c^2}{2c^2+ab}+\frac{(a+b+c)^2}{ab+bc+ca}\geq 4

Source: InternLM Lean-Workbook, record lean_workbook_3520 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3520 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 / (2 * a^2 + b * c) + b^2 / (2 * b^2 + c * a) + c^2 / (2 * c^2 + a * b) + (a + b + c)^2 / (a * b + b * c + a * c)) ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3520; Apache-2.0

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