A quartic correction under a cubic constraint

Proved

WorkbookSource.plus_10106

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

lean-workbooksource-checked

Let $a,b >0$ and $a^3+b^3=2.$ Prove that

a +b+\frac{1}{8}(a^2-b^2)^2\le 2

Source: InternLM Lean-Workbook, record lean_workbook_plus_10106 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_10106 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a^3 + b^3 = 2) : a + b + (1 / 8) * (a^2 - b^2)^2 ≤ 2   :=  by sorry

Source