`BookProof.ChapterEntropy.invertibleProb_isEquivalent_stirling` : invertibleProb ~[atTop] (fun n : ℕ => Real.sqrt (2 * Real.pi * n) * Real.exp (-(n : ℝ)))

Proved

BookProof.ChapterEntropy.invertibleProb_isEquivalent_stirling

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEntropy.

BookProof.ChapterEntropy.invertibleProb_isEquivalent_stirling : invertibleProb ~[atTop] (fun n : ℕ => Real.sqrt (2 * Real.pi * n) * Real.exp (-(n : ℝ)))

Formalization note: Lean 4 identifier BookProof.ChapterEntropy.invertibleProb_isEquivalent_stirling.

Preamble

-- Generated from ChapterEntropy.lean — theorem BookProof.ChapterEntropy.invertibleProb_isEquivalent_stirling
import Mathlib
import Definitions.Def_ChapterEntropy
open BookProof.ChapterEntropy



open Filter Asymptotics
open scoped Topology

Formal statement

theorem BookProof.ChapterEntropy.invertibleProb_isEquivalent_stirling :
    invertibleProb ~[atTop]
      (fun n : ℕ => Real.sqrt (2 * Real.pi * n) * Real.exp (-(n : ℝ))) := by sorry

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