A sixth-degree refinement involving the Vandermonde square

Proved

WorkbookSource.base_38761

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

lean-workbooksource-checked

Prove that $(x^3+y^3+z^3)^2+3( xyz )^2\geq 4( y^3z^3+z^3x^3+x^3y^3)+ [ (x-y)^2(y-z)^2(z-x)^2 ]$ for $x,y,z \in R$ .

Source: InternLM Lean-Workbook, record lean_workbook_38761 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38761 (x y z : ℝ) :
  (x^3 + y^3 + z^3)^2 + 3 * (x * y * z)^2 ≥
    4 * (y^3 * z^3 + z^3 * x^3 + x^3 * y^3) + (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_38761; Apache-2.0

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