lean_workbook_plus_8207

Proved

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

The given expression equals: \n\n $\left (x+\frac{1}{x} \right )\left (y+\frac{1}{y} \right )+\left (x-\frac{1}{x} \right )\left (y-\frac{1}{y} \right )\ = xy+\frac{y}{x}+\frac{x}{y}+\frac{1}{xy}+xy-\frac{y}{x}-\frac{x}{y}+\frac{1}{xy}\ =2xy+\frac{2}{xy}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8207  (x y : ℝ)
  (h₀ : x ≠ 0)
  (h₁ : y ≠ 0) :
  (x + 1/x) * (y + 1/y) + (x - 1/x) * (y - 1/y) = 2 * x * y + 2 / (x * y)   :=  by sorry

Source

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

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