A weighted pairwise ratio sum is at least two thirds

Proved

WorkbookSource.base_50610

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

lean-workbooksource-checked

Let $a,b,c>0$ . Prove that $\frac{a+b}{a+7b+c}+\frac{b+c}{b+7c+a}+\frac{c+a}{c+7a+b}\geq\frac{2}{3}$

Source: InternLM Lean-Workbook, record lean_workbook_50610 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_50610 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b) / (a + 7 * b + c) + (b + c) / (b + 7 * c + a) + (c + a) / (c + 7 * a + b) ≥ 2 / 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_50610; Apache-2.0

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