A cubic sum bound with a triple-product correction

Proved

WorkbookSource.base_5250

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

lean-workbooksource-checked

Let $a,b,c\ge 0$ and $a + b + c = 1$ ,prove that $a^3 + b^3 + c^3 + 6abc\ge \frac {1}{4}$

Source: InternLM Lean-Workbook, record lean_workbook_5250 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_5250 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a + b + c = 1) : a^3 + b^3 + c^3 + 6 * a * b * c ≥ 1 / 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5250; Apache-2.0

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