A quadratic relation bounds a sum minus product

Proved

WorkbookSource.base_815

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

lean-workbooksource-checked

Let $a,b\geq 0$ and $a^2+b^2=a+b.$ Prove that

a+ b- ab\leq \frac{9}{8}

Source: InternLM Lean-Workbook, record lean_workbook_815 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_815 (a b : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hab : a^2 + b^2 = a + b) : a + b - a * b ≤ 9 / 8  :=  by sorry

Source