A cyclic weighted linear ratio upper bound

Proved

WorkbookSource.base_18019

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

lean-workbooksource-checked

Let $a,b,c>0$ , prove that:

\frac a{3a+b}+\frac b{3b+c}+\frac c{3c+a}\le\frac34.

Source: InternLM Lean-Workbook, record lean_workbook_18019 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_18019 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (3 * a + b) + b / (3 * b + c) + c / (3 * c + a)) ≤ 3 / 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18019; Apache-2.0

View graph