lean_workbook_plus_73337

Proved

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

Prove that for non-negative reals a, b, and c, the inequality $2(a^3 + b^3 + c^3) \geq a^2(b+c) + b^2(a+c) + c^2(a+b)$ holds.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_73337 {a b c : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 2 * (a ^ 3 + b ^ 3 + c ^ 3) ≥ a ^ 2 * (b + c) + b ^ 2 * (a + c) + c ^ 2 * (a + b)   :=  by sorry

Source

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

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