A cyclic quartic upper bound on the four-variable simplex

Proved

WorkbookSource.base_6731

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

lean-workbooksource-checked

Let $a$ , $b$ , $c$ , $d$ be non-negative real numbers satisfying $a+b+c+d=4$ . Prove that $a^2bc+b^2cd+c^2da+d^2ab \le 4$

Source: InternLM Lean-Workbook, record lean_workbook_6731 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6731 (a b c d : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hd : d ≥ 0) (hab : a + b + c + d = 4) : a^2 * b * c + b^2 * c * d + c^2 * d * a + d^2 * a * b ≤ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6731; Apache-2.0

View graph