lean_workbook_plus_45123

Proved

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

Let $a,b,c\geq 0$ and $\frac{a}{a+1}+\frac{3b}{b+1}+\frac{3c}{c+1}=1 .$ Prove that $abc\leq \frac{1}{120}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_45123 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a * b * c = 1) : a / (a + 1) + 3 * b / (b + 1) + 3 * c / (c + 1) = 1 → a * b * c ≤ 1 / 120   :=  by sorry

Source

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

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