`BookProof.ChapterCoherentOccupation.coherentOccupation_mean` (lam : ℝ) : ∑' n : ℕ, (n : ℝ) * coherentOccupation lam n = lam

Proved

BookProof.ChapterCoherentOccupation.coherentOccupation_mean

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOccupation.

BookProof.ChapterCoherentOccupation.coherentOccupation_mean (lam : ℝ) : ∑' n : ℕ, (n : ℝ) * coherentOccupation lam n = lam

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

Preamble

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


noncomputable section


open Real Nat ProbabilityTheory

Formal statement

theorem BookProof.ChapterCoherentOccupation.coherentOccupation_mean (lam : ℝ) :
    ∑' n : ℕ, (n : ℝ) * coherentOccupation lam n = lam := by sorry

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