Lean-Workbook Plus 27783: Trigonometric identity

Proved

WorkbookRestored.plus_27783

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

lean-workbookrestored-importssource-checked

For every real $x$ , $\sin(7x)=0$ if and only if $x=k\pi/7$ for some integer $k$ .

Source: Lean-Workbook row lean_workbook_plus_27783 (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_27783 : ∀ x : ℝ, sin (7 * x) = 0 ↔ ∃ k : ℤ, x = k * π / 7   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_27783; immutable original Prove2Me node c261f4e8-123d-4481-9e3e-4b2bfb2aabef

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