A comparison of the quadratic and cubic power sums

Proved

WorkbookSource.plus_10713

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

lean-workbooksource-checked

Prove that if $a,b,c \in [0, + \infty)$ then: $(a^2 + b^2 + c^2)^3 \le 3(a^3 + b^3 + c^3)^2.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_10713 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_10713 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : (a^2 + b^2 + c^2)^3 ≤ 3 * (a^3 + b^3 + c^3)^2   :=  by sorry

Source