A two-variable fifth-power bound

Proved

WorkbookSource.base_27971

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

lean-workbooksource-checked

Let be given positive real numbers $a,b$ ,prove that $(a+b)^5\ge12ab(a^3+b^3) .$

Source: InternLM Lean-Workbook, record lean_workbook_27971 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_27971 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (a + b) ^ 5 ≥ 12 * a * b * (a ^ 3 + b ^ 3)  :=  by sorry

Source