lean_workbook_plus_19462

Proved

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

For $a, b, c$ non-negative numbers prove that:\n\n $(a^2+ab+b^2)(b^2+bc+c^2)(c^2+ca+a^2) \ge \n\n \frac{1}{3} \cdot (ab+bc+ca)^2 \cdot (2a^2+2b^2+2c^2+ab+bc+ca) \ \ ;$ \n\nThis in an improvement of Cirtoaje-Lascu inequality, from Algebraic Inequalities page 9, problem 34.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_19462 : ∀ a b c : ℝ, a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0 → (a^2 + a * b + b^2) * (b^2 + b * c + c^2) * (c^2 + c * a + a^2) ≥ 1 / 3 * (a * b + b * c + c * a)^2 * (2 * a^2 + 2 * b^2 + 2 * c^2 + a * b + b * c + c * a)   :=  by sorry

Source

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

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