A mixed quadratic reciprocal lower bound

Proved

WorkbookSource.base_23174

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

lean-workbooksource-checked

Let $a,b,c >0$ . Prove that $\sum \frac{1}{a^{2}+bc}\geq \frac{9}{4(ab+bc+ca)}$

Source: InternLM Lean-Workbook, record lean_workbook_23174 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_23174 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / (a ^ 2 + b * c) + 1 / (b ^ 2 + c * a) + 1 / (c ^ 2 + a * b) ≥ 9 / (4 * (a * b + b * c + c * a))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23174; Apache-2.0

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