`BookProof.ChapterCoherentOccupation.coherentOccupation_eq` (lam : ℝ) (n : ℕ) : coherentOccupation lam n = Real.exp (-lam) * (lam ^ n / (n ! : ℝ))

Proved

BookProof.ChapterCoherentOccupation.coherentOccupation_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOccupation.

BookProof.ChapterCoherentOccupation.coherentOccupation_eq (lam : ℝ) (n : ℕ) : coherentOccupation lam n = Real.exp (-lam) * (lam ^ n / (n ! : ℝ))

Formalization note: Lean 4 identifier BookProof.ChapterCoherentOccupation.coherentOccupation_eq.

Preamble

-- Generated from ChapterCoherentOccupation.lean — theorem BookProof.ChapterCoherentOccupation.coherentOccupation_eq
import Mathlib
import Definitions.Def_ChapterCoherentOccupation
open BookProof.ChapterCoherentOccupation


noncomputable section


open Real Nat ProbabilityTheory

Formal statement

theorem BookProof.ChapterCoherentOccupation.coherentOccupation_eq (lam : ℝ) (n : ℕ) :
    coherentOccupation lam n = Real.exp (-lam) * (lam ^ n / (n ! : ℝ)) := by sorry

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