lean_workbook_plus_12344

Proved

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

Prove the inequality $a^3+b^3+c^3\geq a^2b+b^2c+c^2a$ over $\mathbb{R_+}$ using the rearrangement inequality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12344 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a ^ 3 + b ^ 3 + c ^ 3 ≥ a ^ 2 * b + b ^ 2 * c + c ^ 2 * a   :=  by sorry

Source

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

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