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`BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_vacuum` (lam : ℝ) : coherentThermalFidelity 0 lam = Real.exp (-lam)

Proved
BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_vacuum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentThermalFidelity.

BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_vacuum (lam : ℝ) : coherentThermalFidelity 0 lam = Real.exp (-lam)

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

Preamble
-- Generated from ChapterCoherentThermalFidelity.lean — theorem BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_vacuum
import Definitions.Def_ChapterCoherentOccupation
import Definitions.Def_ChapterCoherentTemperature
import Definitions.Def_ChapterCoherentFidelity
import Definitions.Def_ChapterDisplacedThermalOverlap
import Mathlib
import Definitions.Def_ChapterCoherentThermalFidelity
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_vacuum (lam : ℝ) :
    coherentThermalFidelity 0 lam = Real.exp (-lam) := by sorry

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