A quartic and cubic power-sum comparison at total three

Proved

WorkbookSource.base_4616

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

lean-workbooksource-checked

Let $a, b, c$ be reals with $a + b + c = 3$ . Prove that

2(a^4 + b^4 + c^4) + 36 \geq 7(a^3 + b^3 + c^3) + 21abc.

Source: InternLM Lean-Workbook, record lean_workbook_4616 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4616 (a b c : ℝ) (h : a + b + c = 3) : 2 * (a^4 + b^4 + c^4) + 36 ≥ 7 * (a^3 + b^3 + c^3) + 21 * a * b * c  :=  by sorry

Source