A fourth-power bound involving the sum of three variables

Proved

WorkbookSource.base_1961

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

lean-workbooksource-checked

If $a,b,c$ are real numbers, prove that

a^4+b^4+c^4+(a+b+c)^4 \geq 28abc(a+b+c).

Source: InternLM Lean-Workbook, record lean_workbook_1961 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1961 (a b c : ℝ) : a^4+b^4+c^4+(a+b+c)^4 ≥ 28*a*b*c*(a+b+c)  :=  by sorry

Source