Prove2Me

A normalized product bound for three quadratic forms

Proved
WorkbookSource.base_15195

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

lean-workbooksource-checked

The inequality is equivalent with:

x,y,z≥0,  x+y+z=2  ⟹x,y,z\ge 0,\;x+y+z=2\;\Longrightarrow (x2+xy+y2)(y2+yz+z2)(z2+zx+x2)≤3(x^2+xy+y^2)(y^2+yz+z^2)(z^2+zx+x^2)\leq3

Source: InternLM Lean-Workbook, record lean_workbook_15195 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_15195 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) (h : x + y + z = 2) : (x^2 + x*y + y^2)*(y^2 + y*z + z^2)*(z^2 + z*x + x^2) ≤ 3  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15195; Apache-2.0

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