A comparison of cyclic pairwise ratio sums

Proved

WorkbookSource.base_3151

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

lean-workbooksource-checked

If $a$ , $b$ , $c > 0$ , prove that $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq \frac{a+b}{a+b+2c}+\frac{b+c}{2a+b+c}+\frac{c+a}{a+2b+c}$

Source: InternLM Lean-Workbook, record lean_workbook_3151 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3151 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (b + c) + b / (c + a) + c / (a + b)) ≥ (a + b) / (a + b + 2 * c) + (b + c) / (2 * a + b + c) + (c + a) / (a + 2 * b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3151; Apache-2.0

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