A cubic-sum product bound on the unit sphere

Proved

WorkbookSource.base_747

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

lean-workbooksource-checked

Let $a,b,c \in \mathbb{R}$ such that $a^2+b^2+c^2=1$ . Prove that

(a+b+c)(a^3+b^3+c^3) \leq \frac{5}{4}

Source: InternLM Lean-Workbook, record lean_workbook_747 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_747 (a b c : ℝ) (h : a^2 + b^2 + c^2 = 1) : (a + b + c) * (a^3 + b^3 + c^3) ≤ 5 / 4  :=  by sorry

Source