A strict product bound under a weighted sum

Proved

WorkbookSource.base_53135

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

lean-workbooksource-checked

Prove that for all $a,b>0$ with $a+2b=2$ , we have

\left(a^2+1\right)\left(b^2+1\right) >\frac{9}{5}

Source: InternLM Lean-Workbook, record lean_workbook_53135 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_53135 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a + 2 * b = 2) : (a^2 + 1) * (b^2 + 1) > 9 / 5  :=  by sorry

Source