lean_workbook_plus_64880

Proved

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

Given $a$ , $b$ , and $c$ are positive numbers, prove that $a^{3}+b^{3}+c^{3}-3abc\geq 3|(a-b)(b-c)(c-a)|$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64880 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 + b^3 + c^3 - 3*a*b*c ≥ 3 * |(a - b) * (b - c) * (c - a)|   :=  by sorry

Source

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

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