A cyclic cubic-over-linear sum bounded by a squared total

Proved

WorkbookSource.base_4472

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

lean-workbooksource-checked

Let $a,b,c>0$ . Prove that $\frac{a^{2}b}{a+b}+\frac{b^{2}c}{b+c}+\frac{c^{2}a}{c+a}\leq \frac{1}{6}(a+b+c)^{2}$ .

Source: InternLM Lean-Workbook, record lean_workbook_4472 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4472 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 * b / (a + b) + b^2 * c / (b + c) + c^2 * a / (c + a)) ≤ (1 / 6) * (a + b + c)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4472; Apache-2.0

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