Prove2Me

Lean-Workbook Plus 67003: Comparing reflected square-root distances

Proved
WorkbookRestored.plus_67003

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For 0≤x≤π/20\le x\le\pi/2, 1+(π−x)2−1+x2≥0\sqrt{1+(\pi-x)^2}-\sqrt{1+x^2}\ge0.

Source: Lean-Workbook row lean_workbook_plus_67003 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
open Real
Formal statement
theorem WorkbookRestored.plus_67003 (x : ℝ) (hx : 0 ≤ x ∧ x ≤ π/2) : 0 ≤ Real.sqrt (1 + (π - x) ^ 2) - Real.sqrt (1 + x ^ 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_67003; immutable original Prove2Me node a3978486-7726-4f8a-986b-f8dda2fee828

View graph