A cyclic quadratic-product ratio bound at fixed sum three

Proved

WorkbookSource.base_2028

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

lean-workbooksource-checked

Let $a$ , $b$ and $c$ be positive numbers such that $a+b+c=3$ . Prove that: $\frac{a^2b}{2a+b}+\frac{b^2c}{2b+c}+\frac{c^2a}{2c+a}\leq1$

Source: InternLM Lean-Workbook, record lean_workbook_2028 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2028 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a^2 * b / (2 * a + b) + b^2 * c / (2 * b + c) + c^2 * a / (2 * c + a) ≤ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2028; Apache-2.0

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