A linear-bilinear bound on a circle

Proved

WorkbookSource.base_15779

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

lean-workbooksource-checked

Let $a,b>0$ and $a^2+b^2=5.$ Prove that

ab+a+5b\leq 13

Source: InternLM Lean-Workbook, record lean_workbook_15779 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15779 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a^2 + b^2 = 5) : a * b + a + 5 * b ≤ 13  :=  by sorry

Source