Prove2Me

A sixth-degree product bound involving a triple product

Proved
WorkbookSource.plus_22071

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Maybe 8(1+a+a2)(1+b+b2)(1+c+c2)≥27(1+a)(1+b)(1+c)8(1+a+a^{2})(1+b+b^{2})(1+c+c^{2})\geq 27 (1+a)(1+b)(1+c)

⇔8(x2+xy+y2)(y2+yz+z2)(z2+zx+x2)≥27(x+y)(y+z)(z+x)xyz\Leftrightarrow 8(x^{2}+xy+y^{2})(y^{2}+yz+z^{2})(z^{2}+zx+x^{2})\ge 27(x+y)(y+z)(z+x)xyz ?

Source: InternLM Lean-Workbook, record lean_workbook_plus_22071 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_22071 (x y z : ℝ) : 8 * (x ^ 2 + x * y + y ^ 2) * (y ^ 2 + y * z + z ^ 2) * (z ^ 2 + z * x + x ^ 2) ≥ 27 * (x + y) * (y + z) * (z + x) * x * y * z   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_22071; Apache-2.0

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