Prove2Me

Three quadratic forms bound a squared mixed expression

Proved
WorkbookSource.base_43607

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

lean-workbooksource-checked

Then 3(x2+xy+y2)(y2+yz+z2)(z2+zx+x2)≥94(y+z)2(x2+(y+z)x2+yz)2. 3(x^2 + xy + y^2)(y^2 + yz + z^2)(z^2 + zx + x^2)\geq\frac {9}{4}(y + z)^2\left(x^2 + \frac {(y + z)x}{2} + yz\right)^2.

Source: InternLM Lean-Workbook, record lean_workbook_43607 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_43607 (x y z : ℝ) : 3 * (x ^ 2 + x * y + y ^ 2) * (y ^ 2 + y * z + z ^ 2) * (z ^ 2 + z * x + x ^ 2) ≥ 9 / 4 * (y + z) ^ 2 * (x ^ 2 + (y + z) * x / 2 + y * z) ^ 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_43607; Apache-2.0

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