lean_workbook_plus_21537

Proved

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

Prove that $a^3b^2+b^3c^2+c^3a^2\geq(a^2+b^2+c^2)abc$ for all triangle with sides $a$ , $b$ , and $c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21537 (a b c : ℝ) (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a^3 * b^2 + b^3 * c^2 + c^3 * a^2 >= (a^2 + b^2 + c^2) * a * b * c   :=  by sorry

Source

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

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