A cyclic cubic and pairwise product bound at unit sum

Proved

WorkbookSource.base_20078

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

lean-workbooksource-checked

Let $x,y,z>0$ and $x+y+z=1$ . Is $xy^2+yz^2+zx^2+xy+yz+zx\leq\frac{4}{9}$ ?

Source: InternLM Lean-Workbook, record lean_workbook_20078 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_20078 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 1) : x * y ^ 2 + y * z ^ 2 + z * x ^ 2 + x * y + y * z + z * x ≤ 4 / 9  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_20078; Apache-2.0

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