`BookProof.ChapterCoherentOccupation.coherentOccupation_energy` (lam : ℝ) : ∑' n : ℕ, ((n : ℝ) + 1 / 2) * coherentOccupation lam n = lam + 1 / 2

Proved

BookProof.ChapterCoherentOccupation.coherentOccupation_energy

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOccupation.

BookProof.ChapterCoherentOccupation.coherentOccupation_energy (lam : ℝ) : ∑' n : ℕ, ((n : ℝ) + 1 / 2) * coherentOccupation lam n = lam + 1 / 2

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

Preamble

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


noncomputable section


open Real Nat ProbabilityTheory

Formal statement

theorem BookProof.ChapterCoherentOccupation.coherentOccupation_energy (lam : ℝ) :
    ∑' n : ℕ, ((n : ℝ) + 1 / 2) * coherentOccupation lam n = lam + 1 / 2 := by sorry

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