A quadratic and linear sum bound at unit product

Proved

WorkbookSource.base_38442

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

lean-workbooksource-checked

Prove that: $2(x^2+y^2+z^2)+x+y+z \geq 6 + xy + yz + xz$ given $x, y, z > 0$ and $xyz=1$ .

Source: InternLM Lean-Workbook, record lean_workbook_38442 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38442 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x * y * z = 1) : 2 * (x ^ 2 + y ^ 2 + z ^ 2) + x + y + z ≥ 6 + x * y + y * z + x * z  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_38442; Apache-2.0

View graph