Prove2Me

lean_workbook_plus_75679

Proved

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

If a,b,ca,b,c are real numbers such that abc≤0abc\le 0 , then\n\n (a)   (a2+ab+b2)(b2+bc+c2)(c2+ca+a2)+(ab+bc+ca)3≥0(a) \ \ \ (a^2+ab+b^2)(b^2+bc+c^2)(c^2+ca+a^2)+(ab+bc+ca)^3\ge 0 ;\n\n (b)   (a2+ab+b2)(b2+bc+c2)(c2+ca+a2)≥3(ab+bc+ca)3(b) \ \ \ (a^2+ab+b^2)(b^2+bc+c^2)(c^2+ca+a^2)\ge 3(ab+bc+ca)^3 .

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_75679 (a b c : ℝ) (h : a * b * c ≤ 0) : (a^2 + a * b + b^2) * (b^2 + b * c + c^2) * (c^2 + c * a + a^2) + (a * b + b * c + c * a)^3 ≥ 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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