lean_workbook_plus_9332

Proved

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

Let $a$ , $b$ and $c$ be non-negative numbers. Prove that: $8(a+b+c)^3\geq(7a-b)(7b-c)(7c-a)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9332 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 8 * (a + b + c) ^ 3 ≥ (7 * a - b) * (7 * b - c) * (7 * c - a)   :=  by sorry

Source

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

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