A quadratic norm bound for a triple product

Proved

WorkbookSource.base_9273

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers such that $a+b+c=1$ . Prove that $2(a^2+b^2+c^2)\ge \frac{1}{9}+15abc$ .

Source: InternLM Lean-Workbook, record lean_workbook_9273 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9273 (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) ≥ 1 / 9 + 15 * a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9273; Apache-2.0

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