Prove2Me

A cyclic fifth-power sum times the total bounds a squared product

Proved
WorkbookSource.base_35457

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Is this true? a,b,c∈R+a,b,c \in \mathbb{R}^+

(a+b+c)(a2b3+b2c3+c2a3)≥3(abc)2\left(a+b+c\right)\left(a^2b^3+b^2c^3+c^2a^3\right)\ge 3\left(abc\right)^2

Source: InternLM Lean-Workbook, record lean_workbook_35457 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_35457 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) * (a^2 * b^3 + b^2 * c^3 + c^2 * a^3) ≥ 3 * (a * b * c)^2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_35457; Apache-2.0

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