Prove2Me

A sixth-degree difference-product bound at fixed sum

Proved
WorkbookSource.base_35217

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

lean-workbooksource-checked

Let x,y,zx,y,z are real numbers, and x+y+z=3x+y+z=3, prove that: (3−xy−yz−xz)3≥14(y−z)2(z−x)2(x−y)2(3-xy-yz-xz)^3\geq \frac{1}{4}(y-z)^2(z-x)^2(x-y)^2

Source: InternLM Lean-Workbook, record lean_workbook_35217 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_35217 (x y z : ℝ) (h : x + y + z = 3) :
  (3 - x * y - y * z - z * x) ^ 3 ≥ (1 / 4) * (y - z) ^ 2 * (z - x) ^ 2 * (x - y) ^ 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_35217; Apache-2.0

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