A comparison of two weighted cyclic linear ratio sums

Proved

WorkbookSource.base_21812

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

lean-workbooksource-checked

If $a,b,c$ are positive real numbers, $\sum{\frac{a}{a+2b}}\ge{\sum{\frac{a}{2a+b}}}$

Source: InternLM Lean-Workbook, record lean_workbook_21812 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_21812 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (a + 2 * b) + b / (b + 2 * c) + c / (c + 2 * a)) ≥ (a / (2 * a + b) + b / (2 * b + c) + c / (2 * c + a))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21812; Apache-2.0

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