A quartic correction to a two-variable sum bound

Proved

WorkbookSource.base_30311

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

lean-workbooksource-checked

Let $a$ and $b$ be positive real numbers such that $a^2+b^2=2$ . Prove that $a +b+\frac{1}{16}(a^2-b^2)^2\le 2$ .

Source: InternLM Lean-Workbook, record lean_workbook_30311 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_30311 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a^2 + b^2 = 2) : a + b + (1 / 16) * (a^2 - b^2)^2 ≤ 2  :=  by sorry

Source