Prove2Me

`BookProof.ChapterCoherentThermalFidelity.width_unique` (h : 0 ≤ nbar) {w : ℝ} (hw : 0 < w) (hfid : ∀ lam : ℝ, coherentThermalFidelity nbar lam = Real.exp (-(lam / w)) / w) : w = n

Proved
BookProof.ChapterCoherentThermalFidelity.width_unique

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentThermalFidelity.

BookProof.ChapterCoherentThermalFidelity.width_unique (h : 0 ≤ nbar) {w : ℝ} (hw : 0 < w) (hfid : ∀ lam : ℝ, coherentThermalFidelity nbar lam = Real.exp (-(lam / w)) / w) : w = nbar + 1

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

Preamble
-- Generated from ChapterCoherentThermalFidelity.lean — theorem BookProof.ChapterCoherentThermalFidelity.width_unique
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.width_unique (h : 0 ≤ nbar) {w : ℝ} (hw : 0 < w)
    (hfid : ∀ lam : ℝ, coherentThermalFidelity nbar lam = Real.exp (-(lam / w)) / w) :
    w = nbar + 1 := by sorry

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