lean_workbook_plus_20659

Proved

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

Then it suffices to show that \n $\Leftrightarrow a^3 + b^3 + c^3 + 6abc \le 2\left( {ab\left( {a + b} \right) + bc\left( {b + c} \right) + ca\left( {c + a} \right)} \right)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_20659 {a b c : ℝ} (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a ≥ b) (hbc : b ≥ c) (hca : c ≥ a) : a^3 + b^3 + c^3 + 6 * a * b * c ≤ 2 * (a * b * (a + b) + b * c * (b + c) + c * a * (c + a))   :=  by sorry

Source

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

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