lean_workbook_plus_15893

Proved

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

Let $a,b,c\in \mathbb{R}$ such that $ab + bc + ca\le 0$ . Show that:\n $a^2b^2 + b^2c^2 + c^2a^2 + abc(a + b + c)\ge ab(a^2 + b^2) + bc(b^2 + c^2) + ca(c^2 + a^2)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15893 :  ∀ a b c : ℝ, a * b + b * c + c * a ≤ 0 → a^2 * b^2 + b^2 * c^2 + c^2 * a^2 + a * b * c * (a + b + c) ≥ a * b * (a^2 + b^2) + b * c * (b^2 + c^2) + c * a * (c^2 + a^2)   :=  by sorry

Source

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

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