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Lean-Workbook Plus 33968: Trigonometric inequality

Proved
WorkbookRestored.plus_33968

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

lean-workbookrestored-importssource-checked

For each real aaa and every ε>0\varepsilon>0ε>0, there is δ>0\delta>0δ>0 such that ∣x−a∣<δ|x-a|<\delta∣x−a∣<δ implies ∣sin⁡x−sin⁡a∣<ε|\sin x-\sin a|<\varepsilon∣sinx−sina∣<ε.

Source: Lean-Workbook row lean_workbook_plus_33968 (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_33968 (a : ℝ) : ∀ ε > 0, ∃ δ > 0, ∀ x, |x - a| < δ → |sin x - sin a| < ε   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_33968; immutable original Prove2Me node 4db54880-1bd4-45ea-b4a9-1cf18646d3b6

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