Prove2Me

lean_workbook_plus_77859

Proved

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

Given the recursive relation xn+1xn+3xn−2xn+1−xn+12−2=0x_{n+1}x_n + 3x_n - 2x_{n+1} - x_{n+1}^2 - 2 = 0, derive the identity xn−2=(xn+1+2)(xn+1−xn)x_n - 2 = (x_{n+1} + 2)(x_{n+1} - x_n).

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_77859 (x : ℕ → ℝ) (n : ℕ) (h : x (n + 1) * x n + 3 * x n - 2 * x (n + 1) - x (n + 1) ^ 2 - 2 = 0) : x n - 2 = (x (n + 1) + 2) * (x (n + 1) - x n)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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