The cube of a sum of squares bounds a squared sum of cubes

Proved

WorkbookSource.base_37794

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

lean-workbooksource-checked

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

Source: InternLM Lean-Workbook, record lean_workbook_37794 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_37794 (a b c : ℝ) : (a^2+b^2+c^2)^3 ≥ (a^3+b^3+c^3)^2  :=  by sorry

Source