Prove2Me

A cubed quadratic difference sum bounds squared cyclic differences

Proved
WorkbookSource.base_21512

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

lean-workbooksource-checked

Prove the following inequality: (x2+y2+z2−xy−yz−zx)3≥274(x−y)2(y−z)2(z−x)2(x^2+y^2+z^2-xy-yz-zx)^3 \ge \frac{27}{4}(x-y)^2(y-z)^2(z-x)^2

Source: InternLM Lean-Workbook, record lean_workbook_21512 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_21512 (x y z : ℝ) :
  (x^2 + y^2 + z^2 - x * y - x * z - y * z)^3 ≥ (27 / 4) * (x - y)^2 * (y - z)^2 * (z - x)^2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21512; Apache-2.0

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