`BookProof.ChapterEntropy.invertibleProb_eq` (n : ℕ) : invertibleProb n = (Nat.factorial n : ℝ) / (n ^ n : ℝ)

Proved

BookProof.ChapterEntropy.invertibleProb_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEntropy.

BookProof.ChapterEntropy.invertibleProb_eq (n : ℕ) : invertibleProb n = (Nat.factorial n : ℝ) / (n ^ n : ℝ)

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

Preamble

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



open Filter Asymptotics
open scoped Topology

Formal statement

theorem BookProof.ChapterEntropy.invertibleProb_eq (n : ℕ) :
    invertibleProb n = (Nat.factorial n : ℝ) / (n ^ n : ℝ) := by sorry

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