A bilinear and linear bound on the unit circle

Proved

WorkbookSource.plus_44251

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

lean-workbooksource-checked

Let $x,y$ be reals such that $x^2+y^2=1.$ Prove that $x+6y+10xy\leq \frac{51}{5}.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_44251 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_44251 (x y : ℝ) (h : x ^ 2 + y ^ 2 = 1) : x + 6 * y + 10 * x * y ≤ 51 / 5   :=  by sorry

Source