Prove2Me

A six-variable quadratic difference bound

Proved
WorkbookSource.plus_68327

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

lean-workbooksource-checked

Prove that x2+y2+z2+a2+b2+c2−a(y+z)−b(z+x)−c(x+y)≥13(a+b+c−x−y−z)2x^2+y^2+z^2+a^2+b^2+c^2-a(y+z)-b(z+x)-c(x+y) \geq \frac{1}{3}(a+b+c-x-y-z)^2 for x,y,z,a,b,c>0x,y,z,a,b,c > 0.

Source: InternLM Lean-Workbook, record lean_workbook_plus_68327 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_68327 (x y z a b c : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : x^2 + y^2 + z^2 + a^2 + b^2 + c^2 - a * (y + z) - b * (z + x) - c * (x + y) ≥ (1 / 3) * (a + b + c - x - y - z)^2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_68327; Apache-2.0

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