Prove2Me

`BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_eq_temperature_form` (h : 0 ≤ nbar) (lam : ℝ) : coherentThermalFidelity nbar lam = Real.exp (-(lam / (thermalTempe

Proved
BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_eq_temperature_form

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentThermalFidelity.

BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_eq_temperature_form (h : 0 ≤ nbar) (lam : ℝ) : coherentThermalFidelity nbar lam = Real.exp (-(lam / (thermalTemperature nbar + coherentWidth))) / (thermalTemperature nbar + coherentWidth)

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

Preamble
-- Generated from ChapterCoherentThermalFidelity.lean — theorem BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_eq_temperature_form
import Definitions.Def_ChapterCoherentOccupation
import Definitions.Def_ChapterCoherentFidelity
import Definitions.Def_ChapterDisplacedThermalOverlap
import Mathlib
import Definitions.Def_ChapterCoherentThermalFidelity
import Definitions.Def_ChapterCoherentTemperature
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_eq_temperature_form (h : 0 ≤ nbar) (lam : ℝ) :
    coherentThermalFidelity nbar lam
      = Real.exp (-(lam / (thermalTemperature nbar + coherentWidth)))
        / (thermalTemperature nbar + coherentWidth) := by sorry

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