An asymmetric quartic lower bound

Proved

WorkbookSource.plus_26401

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

lean-workbooksource-checked

Let $a,b,c\geq 0$ . Show that $a^{4}+b^{4}+c^{4}\geq 2bc(a-b)(a-c)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_26401 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_26401 {a b c : ℝ} (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : a^4 + b^4 + c^4 ≥ 2 * b * c * (a - b) * (a - c)   :=  by sorry

Source