lean_workbook_plus_60349

Disproved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Well known result: $(a+b)(b+c)(c+a)\geq \frac{8}{9}(a+b+c)(ab+bc+ca)$ and also $(ab+bc+ca)^2\geq 3abc(a+b+c)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_60349 : ∀ a b c : ℝ, (a + b) * (b + c) * (c + a) ≥ (8 / 9) * (a + b + c) * (a * b + b * c + c * a) ∧ (a * b + b * c + c * a) ^ 2 ≥ 3 * a * b * c * (a + b + c)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph