A product of three quadratic expressions bounds a cube

Proved

WorkbookSource.base_43505

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Given $a,b,c>0$ prove that $(2(b-c)^{2}+2a^{2}+bc)(2(c-a)^{2}+2b^{2}+ca)(2(a-b)^{2}+2c^{2}+ab)\ge (a^{2}+b^{2}+c^{2})^{3}$

Source: InternLM Lean-Workbook, record lean_workbook_43505 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_43505 (a b c : ℝ) : (2 * (b - c) ^ 2 + 2 * a ^ 2 + b * c) * (2 * (c - a) ^ 2 + 2 * b ^ 2 + c * a) * (2 * (a - b) ^ 2 + 2 * c ^ 2 + a * b) ≥ (a ^ 2 + b ^ 2 + c ^ 2) ^ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_43505; Apache-2.0

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