A weighted cyclic linear ratio sum is at most one quarter

Proved

WorkbookSource.base_32038

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

lean-workbooksource-checked

Prove that $\frac{a}{5a+5b+2c}+\frac{b}{5b+5c+2a}+\frac{c}{5c+5a+2b}\le \frac{1}{4}$ given $a,b,c >0$ without full expansion.

Source: InternLM Lean-Workbook, record lean_workbook_32038 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_32038 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (5 * a + 5 * b + 2 * c) + b / (5 * b + 5 * c + 2 * a) + c / (5 * c + 5 * a + 2 * b)) ≤ 1 / 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_32038; Apache-2.0

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