A sixth-degree bound for a sum of cubes and a triple product

Proved

WorkbookSource.base_26818

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove $(a^2 + b^2 + c^2)^3 \ge (a^3 + b^3 + c^3 + abc)^2$

Source: InternLM Lean-Workbook, record lean_workbook_26818 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_26818 (a b c : ℝ) : (a^2 + b^2 + c^2)^3 ≥ (a^3 + b^3 + c^3 + a * b * c)^2  :=  by sorry

Source