A mixed quadratic reciprocal lower bound

Proved

WorkbookSource.base_42698

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

lean-workbooksource-checked

For positives $a$ , $b$ and $c$ prove that: $\sum_{cyc}\frac{b+c}{2a^2+bc}\geq\frac{6}{a+b+c}.$

Source: InternLM Lean-Workbook, record lean_workbook_42698 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_42698 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b + c) / (2 * a ^ 2 + b * c) + (a + c) / (2 * b ^ 2 + a * c) + (a + b) / (2 * c ^ 2 + a * b) ≥ 6 / (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_42698; Apache-2.0

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