lean_workbook_plus_18145

Proved

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

Let $a,$ $b$ are different from zero real numbers. Prove that:\n

\left(a^{2}+b^{2}\right)\left(\frac{1}{a^{2}}+\frac{1}{b^{2}}\right)+4\geq2\left(a+b\right)\left(\frac{1}{a}+\frac{1}{b}\right).

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18145 (a b : ℝ) (ha : a ≠ 0) (hb : b ≠ 0) (hab : a ≠ b) : (a^2 + b^2) * (1 / a^2 + 1 / b^2) + 4 ≥ 2 * (a + b) * (1 / a + 1 / b)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph