A cyclic mixed-product reciprocal lower bound at fixed sum three

Proved

WorkbookSource.base_6651

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

lean-workbooksource-checked

Let $a,b,c>0$ and $a+b+c=3$ . Prove that: $\frac{a}{a+2bc} +\frac{b}{b+2ac}+\frac{c}{c+2ab} \ge 1$ .

Source: InternLM Lean-Workbook, record lean_workbook_6651 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6651 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : a / (a + 2 * b * c) + b / (b + 2 * a * c) + c / (c + 2 * a * b) ≥ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6651; Apache-2.0

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