Sine and cosine at pi over four

Proved

WorkbookRestored.plus_56

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

lean-workbookrestored-importssource-checked

The two trigonometric values at $\pi/4$ agree and satisfy

\sin(\pi/4)=\cos(\pi/4)=\frac1{\sqrt2}.

Formalization Note This restores source entry lean_workbook_plus_56 from the Apache-2.0 Lean-Workbook dataset. The mathematical proposition is unchanged; targeted imports and namespace openings supply the constants missing from the original Prove2Me node 590bc002-f7b6-43bb-9b0e-587abe1258bf. This is a separate corrected node because formal statements and preambles are immutable.

Preamble

import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
import Mathlib.Tactic
open Real

Formal statement

theorem WorkbookRestored.plus_56 : sin (π / 4) = cos (π / 4) ∧ sin (π / 4) = 1 / Real.sqrt 2 ∧ cos (π / 4) = 1 / Real.sqrt 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_56; original Prove2Me theorem ID 590bc002-f7b6-43bb-9b0e-587abe1258bf; Apache-2.0.

View graph