Prove2Me

A sixth-degree triangle-factor inequality with a difference correction

Proved
WorkbookSource.base_26965

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

lean-workbooksource-checked

Prove that (xy+xz)(xy+yz)(xz+yz)≥8(y2+z2−x2)(z2+x2−y2)(x2+y2−z2)+64(x−y)2(y−z)2(z−x)2(xy+xz)(xy+yz)(xz+yz) \geq 8\left(y^2+z^2-x^2\right)\left(z^2+x^2-y^2\right)\left(x^2+y^2-z^2\right) + 64(x-y)^2(y-z)^2(z-x)^2 for x,y,z>0x, y, z > 0.

Source: InternLM Lean-Workbook, record lean_workbook_26965 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_26965 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x * y + x * z) * (x * y + y * z) * (x * z + y * z) ≥ 8 * (y ^ 2 + z ^ 2 - x ^ 2) * (z ^ 2 + x ^ 2 - y ^ 2) * (x ^ 2 + y ^ 2 - z ^ 2) + 64 * (x - y) ^ 2 * (y - z) ^ 2 * (z - x) ^ 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_26965; Apache-2.0

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