lean_workbook_plus_7912

Proved

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

Let $a, b$ be real numbers. Prove that

(a^2-a+1)(b^2-b+1)\geq\frac{a^2+b^2}{2}\geq\frac{a^2+ab+b^2}{3}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_7912 : ∀ a b : ℝ, (a^2 - a + 1) * (b^2 - b + 1) ≥ (a^2 + b^2) / 2 ∧ (a^2 + b^2) / 2 ≥ (a^2 + a*b + b^2) / 3   :=  by sorry

Source