lean_workbook_plus_15755

Proved

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

Let $a,b,c>0$ and $a+b^2+c^2=1$ . Prove that \n

abc(a+1)(b+1)(c+1)\leq \frac{27}{64}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15755 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (hab : a + b^2 + c^2 = 1) :  a * b * c * (a + 1) * (b + 1) * (c + 1) ≤ 27 / 64   :=  by sorry

Source

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

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