lean_workbook_plus_13005

Proved

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

Let $a,b,c>0$ and $a^4+b^3+c^2=a^3+b^2+c.$ Prove that

abc\leq1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_13005 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a^4 + b^3 + c^2 = a^3 + b^2 + c) : a * b * c ≤ 1   :=  by sorry

Source

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

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