lean_workbook_plus_47000

Proved

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

Let $a, b, c$ be positive real numbers. Prove that \n $a^3b^4 + b^3c^4 + c^3a^4 \hspace{0.25cm} \geq \hspace{0.25cm} 2(abc)(ab+bc+ca)^2 - 5(abc)^2 (a+b+c)$ \n

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_47000 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 * b^4 + b^3 * c^4 + c^3 * a^4 >= 2 * a * b * c * (a * b + b * c + c * a)^2 - 5 * (a * b * c)^2 * (a + b + c)   :=  by sorry

Source

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

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