`BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_hasSum` (h : 0 ≤ nbar) (lam : ℝ) : HasSum (fun n : ℕ => coherentOccupation lam n * thermalProb nbar n) (Real.exp (

Proved

BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_hasSum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentThermalFidelity.

BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_hasSum (h : 0 ≤ nbar) (lam : ℝ) : HasSum (fun n : ℕ => coherentOccupation lam n * thermalProb nbar n) (Real.exp (-(lam / (nbar + 1))) / (nbar + 1))

Formalization note: Lean 4 identifier BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_hasSum.

Preamble

-- Generated from ChapterCoherentThermalFidelity.lean — theorem BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_hasSum
import Definitions.Def_ChapterCoherentFidelity
import Definitions.Def_ChapterDisplacedThermalOverlap
import Mathlib
import Definitions.Def_ChapterCoherentThermalFidelity
import Definitions.Def_ChapterCoherentOccupation
import Definitions.Def_ChapterCoherentTemperature
open BookProof.ChapterCoherentOccupation
open BookProof.ChapterCoherentTemperature
open BookProof.ChapterCoherentThermalFidelity


noncomputable section


open BookProof.ChapterCoherentOccupation BookProof.ChapterCoherentTemperature
open BookProof.ChapterCoherentFidelity BookProof.ChapterDisplacedThermalOverlap
open Real

variable {nbar lam : ℝ}

Formal statement

theorem BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_hasSum (h : 0 ≤ nbar) (lam : ℝ) :
    HasSum (fun n : ℕ => coherentOccupation lam n * thermalProb nbar n)
      (Real.exp (-(lam / (nbar + 1))) / (nbar + 1)) := by sorry

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