A pairwise-product bound at fixed sum three

Proved

WorkbookSource.plus_47977

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

lean-workbooksource-checked

Let $x,y,z\ge0$ and $x+y+z=3$ . Prove that: $7(xy+yz+zx)\le 18+3(xyz)^2$

Source: InternLM Lean-Workbook, record lean_workbook_plus_47977 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_47977 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) (h : x + y + z = 3) : 7 * (x * y + y * z + z * x) ≤ 18 + 3 * (x * y * z) ^ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_47977; Apache-2.0

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