lean_workbook_plus_11680

Proved

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

Let $a, b, c>0$ and $(a+b)(b+c)(c+a)=3(a+b+c-\frac{1}{3}).$ Prove that $abc\leq 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11680 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) (h : (a + b) * (b + c) * (c + a) = 3 * (a + b + c - 1 / 3)) : a * b * c ≤ 1   :=  by sorry

Source

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

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