A normalized quartic bound with a triple-product correction

Proved

WorkbookSource.base_8251

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

lean-workbooksource-checked

Let $x,y,z\geq 0,x+y+z=1$ ,prove that: $21xyz+1\geq 16(xy+xz+yz)^2$

Source: InternLM Lean-Workbook, record lean_workbook_8251 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_8251 (x y z : ℝ) (hx : x + y + z = 1) (hx0 : 0 ≤ x) (hy0 : 0 ≤ y) (hz0 : 0 ≤ z) : 21 * x * y * z + 1 ≥ 16 * (x * y + x * z + y * z)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8251; Apache-2.0

View graph