`BookProof.ChapterBijectionProbability.bijProb_eq_card_ratio` (n : ℕ) : bijProb n = (Fintype.card {f : Fin n → Fin n // Function.Bijective f} : ℝ) / (Fintype.card (Fin n → Fin n) :

Proved

BookProof.ChapterBijectionProbability.bijProb_eq_card_ratio

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBijectionProbability.

BookProof.ChapterBijectionProbability.bijProb_eq_card_ratio (n : ℕ) : bijProb n = (Fintype.card {f : Fin n → Fin n // Function.Bijective f} : ℝ) / (Fintype.card (Fin n → Fin n) : ℝ)

Formalization note: Lean 4 identifier BookProof.ChapterBijectionProbability.bijProb_eq_card_ratio.

Preamble

-- Generated from ChapterBijectionProbability.lean — theorem BookProof.ChapterBijectionProbability.bijProb_eq_card_ratio
import Mathlib
import Definitions.Def_ChapterBijectionProbability
open BookProof.ChapterBijectionProbability


open scoped Nat
open Filter Asymptotics

Formal statement

theorem BookProof.ChapterBijectionProbability.bijProb_eq_card_ratio (n : ℕ) :
    bijProb n =
      (Fintype.card {f : Fin n → Fin n // Function.Bijective f} : ℝ)
        / (Fintype.card (Fin n → Fin n) : ℝ) := by sorry

View graph