lean_workbook_plus_39161

Proved

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

Let $a,b,c$ be sides of a triangle. Show that: $2(ab^2 + bc^2 + ca^2) \ge a^2b + b^2c + c^2a + 3abc$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_39161 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : 2 * (a * b^2 + b * c^2 + c * a^2) ≥ a^2 * b + b^2 * c + c^2 * a + 3 * a * b * c   :=  by sorry

Source

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

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