A mixed quartic inequality with a constant correction

Proved

WorkbookSource.base_23481

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

lean-workbooksource-checked

Let $x,y$ and $z$ be positive real numbers. Show that $3x^2+2xy^2+xyz^2\ge 4xyz-\frac{1}{3}$

Source: InternLM Lean-Workbook, record lean_workbook_23481 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_23481 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : 3 * x ^ 2 + 2 * x * y ^ 2 + x * y * z ^ 2 ≥ 4 * x * y * z - 1 / 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23481; Apache-2.0

View graph