Lean-Workbook Plus 20175: Trigonometric inequality

Proved

WorkbookRestored.plus_20175

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

lean-workbookrestored-importssource-checked

If $0\le x\le1$ and $y=\arcsin x$ , then $\cos y=\sqrt{1-x^2}$ .

Source: Lean-Workbook row lean_workbook_plus_20175 (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
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse
open Real

Formal statement

theorem WorkbookRestored.plus_20175 (x y : ℝ) (h₁ : 0 ≤ x ∧ x ≤ 1) (h₂ : y = arcsin x) : cos y = Real.sqrt (1 - x^2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_20175; immutable original Prove2Me node d330103a-4c72-4b0c-be8a-b888591eeafc

View graph