lean_workbook_plus_60793

Proved

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

Prove that for positive reals $a,b,c$ with sum 2 , \n $2\ge \sum_{sym}a^2b \Longleftrightarrow (a+b+c)^3 \ge 4(\sum_{sym}a^2b)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_60793 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 2) : 2 ≥ a^2 * b + b^2 * c + c^2 * a ↔ (a + b + c)^3 ≥ 4 * (a^2 * b + b^2 * c + c^2 * a)   :=  by sorry

Source

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

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