Prove2Me

A symmetric quartic inequality with coefficient eleven

Proved
WorkbookSource.base_54170

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

lean-workbooksource-checked

If x,y,zx,y,z are real numbers, then

2(xy+yz+zx)(x2+y2+z2)≤11xyz(x+y+z)+4(x4+y4+z4).2(xy+yz+zx)(x^2+y^2+z^2)\le 11xyz(x+y+z)+4(x^4+y^4+z^4).

Source: InternLM Lean-Workbook, record lean_workbook_54170 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_54170 (x y z : ℝ) : 2 * (x * y + y * z + z * x) * (x ^ 2 + y ^ 2 + z ^ 2) ≤ 11 * x * y * z * (x + y + z) + 4 * (x ^ 4 + y ^ 4 + z ^ 4)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_54170; Apache-2.0

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