lean_workbook_plus_46912

Proved

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

Note that $\sqrt{2+\sqrt{2+\sqrt{2}}} < \sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}$ Denote the RHS to be $x$ . Note that $x>0$ . Then: $x = \sqrt{2+x}$ $x^2 = x+2$ $(x+1)(x-2)=0$ $x = 2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_46912  (x : ℝ)
  (h₀ : 0 < x)
  (h₁ : x = Real.sqrt (2 + x)) :
  x = 2   :=  by sorry

Source

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

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