A weighted four-variable cyclic ratio sum is at most one

Proved

WorkbookSource.base_19564

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

lean-workbooksource-checked

For positive numbers $a$ , $b$ , $c$ and $d$ the following inequality is also true.

$\sum_{cyc}\frac{a}{2a+b+c}\leq1$

Source: InternLM Lean-Workbook, record lean_workbook_19564 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_19564 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : a / (2 * a + b + c) + b / (2 * b + c + d) + c / (2 * c + d + a) + d / (2 * d + a + b) ≤ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_19564; Apache-2.0

View graph