lean_workbook_plus_54985

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that for any positive real numbers $a$ and $b$ , the following inequality holds: $a^2 + b^2 + 1 \geq a + b + ab$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_54985 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : a^2 + b^2 + 1 ≥ a + b + a * b   :=  by sorry

Source