A difference-product bound with fixed moments

Proved

WorkbookSource.base_17570

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

lean-workbooksource-checked

Let $x, y,z$ be real numbers such that $x+y+z=1$ and $x^2+y^2+z^2=4$ . Prove that $(y-z)(x-y) \leq \frac{11}{6}$

Source: InternLM Lean-Workbook, record lean_workbook_17570 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_17570 (x y z : ℝ) (h1 : x + y + z = 1) (h2 : x ^ 2 + y ^ 2 + z ^ 2 = 4) : (y - z) * (x - y) ≤ 11 / 6  :=  by sorry

Source