Prove2Me

Lean-Workbook Plus 60494: Logarithmic inequality

Proved
WorkbookRestored.plus_60494

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

lean-workbookrestored-importssource-checked

log⁡(tan⁡(π4−a))=−log⁡(tan⁡(π4+a))\log \left ( \tan \left ( \frac{\pi}{4}-a \right ) \right ) =-\log \left ( \tan \left ( \frac{\pi}{4}+a \right ) \right ) for 0<a<π40<a<\frac{\pi}{4}

Source: Lean-Workbook row lean_workbook_plus_60494 (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.Log.Basic
open Real
Formal statement
theorem WorkbookRestored.plus_60494 (a : ℝ) (ha : 0 < a ∧ a < Real.pi / 4) : Real.log (Real.tan (Real.pi / 4 - a)) = -Real.log (Real.tan (Real.pi / 4 + a))   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_60494; immutable original Prove2Me node 95bb9098-dfbd-4098-a2ca-88ff8fcb04f7

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