A cyclic fourth-power comparison at unit positive sum

Proved

WorkbookSource.base_4186

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

lean-workbooksource-checked

Easy. Let $a, b, c>0, a+b+c=1$ .Prove that $a^3+b^3+c^3\ge3(a^3c+b^3a+c^3b)$

Source: InternLM Lean-Workbook, record lean_workbook_4186 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4186 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) : a^3 + b^3 + c^3 ≥ 3 * (a^3 * c + b^3 * a + c^3 * b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4186; Apache-2.0

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