A bound for a product minus its associated radical

Proved

WorkbookSource.base_9

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

lean-workbooksource-checked

$(ab+1)-\sqrt{1+a^2b^2}\leq 2$

Source: InternLM Lean-Workbook, record lean_workbook_9 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9 (a b : ℝ) : (a * b + 1) - Real.sqrt (1 + a ^ 2 * b ^ 2) ≤ 2  :=  by sorry

Source