lean_workbook_plus_61356

Proved

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

Is $8(a^3+b^3+c^3)<=9(a^2+bc)(b^2+ac)(c^2+ab)$ true for all positive reals $a, b, c$ , $abc=1$ ?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_61356 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : 8 * (a ^ 3 + b ^ 3 + c ^ 3) ≤ 9 * (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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