Prove2Me

A cubic sum bound under a quartic constraint

Proved
WorkbookSource.plus_70452

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

lean-workbooksource-checked

Prove that (a+b)2+(b+c)2+(c+a)2+12≥8(a3+b3+c3) (a + b)^2 + (b + c)^2 + (c + a)^2 + 12\geq 8(a^3 + b^3 + c^3) given (a2−ab+b2)2+(b2−bc+c2)2+(c2−ca+a2)2=3 (a^2 - ab + b^2)^2 + (b^2 - bc + c^2)^2 + (c^2 - ca + a^2)^2 = 3 .

Source: InternLM Lean-Workbook, record lean_workbook_plus_70452 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_70452 (a b c : ℝ) (h1 : (a ^ 2 - a * b + b ^ 2) ^ 2 + (b ^ 2 - b * c + c ^ 2) ^ 2 + (c ^ 2 - c * a + a ^ 2) ^ 2 = 3) : (a + b) ^ 2 + (b + c) ^ 2 + (c + a) ^ 2 + 12 ≥ 8 * (a ^ 3 + b ^ 3 + c ^ 3)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_70452; Apache-2.0

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