lean_workbook_plus_6824

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that for four positive real numbers $a,b,c,d$ the following inequality holds and find all equality cases: \n

a^3 +b^3 +c^3 +d^3 \geq a^2 b +b^2 c+ c^2 d +d^2 a.

\n\nAM-GM is nicer and there should also be some factorization, but Muirhead with $[3,0,0]\succeq [2,1,0]$ kills it.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6824 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : a^3 + b^3 + c^3 + d^3 ≥ a^2 * b + b^2 * c + c^2 * d + d^2 * a   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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