A quartic symmetric inequality on the unit sphere

Proved

WorkbookSource.base_44577

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

lean-workbooksource-checked

Let $a,b,c >0$ and $a^2+b^2+c^2=1$ . Prove that $6abc(a+b+c)-2(ab+bc+ac)^2-(ab+bc+ac)+1 \geq 0$

Source: InternLM Lean-Workbook, record lean_workbook_44577 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_44577 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (h : a^2+b^2+c^2=1) : 6*a*b*c*(a+b+c)-2*(a*b+b*c+a*c)^2-(a*b+b*c+a*c)+1 ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_44577; Apache-2.0

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