Prove2Me

Lean-Workbook Plus 16252: Logarithmic inequality

Proved
WorkbookRestored.plus_16252

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

lean-workbookrestored-importssource-checked

For every real a>0a>0, cosh⁡(log⁡a)=(a2+1)/(2a)\cosh(\log a)=(a^2+1)/(2a). This formalizes part (a) of the source exercise; part (b) is a separate hyperbolic identity.

Source: Lean-Workbook row lean_workbook_plus_16252 (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_16252 (a : ℝ) (ha : a > 0) : Real.cosh (Real.log a) = (a^2 + 1) / (2 * a)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_16252; immutable original Prove2Me node c1b8f616-5daa-4947-81c5-d5d6387dc2fd

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