A cubic correction to a quadratic bound

Proved

WorkbookSource.base_42423

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

lean-workbooksource-checked

Let $a,b,c>0$ and $a+b+c = 1$ , then

$2(a^2+b^2+c^2)\geq(a^3+b^3+c^3)+42abc-1$

Source: InternLM Lean-Workbook, record lean_workbook_42423 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_42423 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) : 2 * (a^2 + b^2 + c^2) ≥ a^3 + b^3 + c^3 + 42 * a * b * c - 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_42423; Apache-2.0

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