A quartic and pairwise-product bound on a sphere

Proved

WorkbookSource.base_13426

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

lean-workbooksource-checked

if real number $a$ , $b$ , $c$ satisfy $a^2+b^2+c^2=4$ prove $a^4+b^4+c^4+6(ab+bc+ca)\leq30$

Source: InternLM Lean-Workbook, record lean_workbook_13426 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_13426 (a b c : ℝ) (h : a^2 + b^2 + c^2 = 4) : a^4 + b^4 + c^4 + 6 * (a * b + b * c + c * a) ≤ 30  :=  by sorry

Source