A cubic and squared-norm comparison at unit sum

Proved

WorkbookSource.base_15336

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

lean-workbooksource-checked

Let be $a,b,c>0$ such that $a+b+c=1$ . Show that : $a^3+b^3+c^3+6abc\le a^2+b^2+c^2$

Source: InternLM Lean-Workbook, record lean_workbook_15336 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15336 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) : a^3 + b^3 + c^3 + 6 * a * b * c ≤ a^2 + b^2 + c^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15336; Apache-2.0

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