A fifth-power correction to a quadratic sum

Proved

WorkbookSource.base_3393

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

lean-workbooksource-checked

Let $a,b\ge 0$ and $a+b=1.$ Prove that $a^2+b^2\le \frac{7}{16}+a^5+b^5$

Source: InternLM Lean-Workbook, record lean_workbook_3393 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3393 (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) : a^2 + b^2 ≤ 7 / 16 + a^5 + b^5  :=  by sorry

Source