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lean_workbook_plus_10623

Proved

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

basically we want x>point of equality, since after the point of equality, the difference between 2x and sqrtx grow exponentially (2x is always bigger after point of equality). the 2 points of equality of x=2x \sqrt{x}=2xx​=2x are 14 \frac{1}{4}41​ and 0. so we take x>the larger of the 2, or x>14 x>\frac{1}{4}x>41​

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_10623 : ∀ x > 1/4, Real.sqrt x < 2 * x   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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