A quadratic ratio with a weighted cyclic correction

Proved

WorkbookSource.base_23846

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

lean-workbooksource-checked

For $a, b, c>0$ prove that $\frac{a^2+b^2+c^2}{ab+bc+ca} + 2\sum\frac{b}{2b+a} \ge 3$

Source: InternLM Lean-Workbook, record lean_workbook_23846 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_23846 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 + c^2) / (a * b + b * c + a * c) + 2 * (b / (2 * b + a) + a / (2 * a + c) + c / (2 * c + b)) ≥ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23846; Apache-2.0

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