A pairwise-sum bound with a triple-product correction

Proved

WorkbookSource.base_21669

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

lean-workbooksource-checked

prove that: $xy+yz+zx\leq \frac{92}{81}+ \frac{2}{3}xyz$ given $x,y,z \geq 0$ and $x+y+z=2$

Source: InternLM Lean-Workbook, record lean_workbook_21669 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_21669 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) (h : x + y + z = 2) :  x * y + y * z + z * x ≤ (92 / 81 + 2 / 3 * x * y * z)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21669; Apache-2.0

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