`BookProof.ChapterCoherentThermalFidelity.fidelityC_width` {n : ℕ} (q k : EuclideanSpace ℂ (Fin n)) : fidelityC q k = Real.exp (-(‖q - k‖ ^ 2 / (coherentWidth + coherentWidth)))

Proved

BookProof.ChapterCoherentThermalFidelity.fidelityC_width

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentThermalFidelity.

BookProof.ChapterCoherentThermalFidelity.fidelityC_width {n : ℕ} (q k : EuclideanSpace ℂ (Fin n)) : fidelityC q k = Real.exp (-(‖q - k‖ ^ 2 / (coherentWidth + coherentWidth)))

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

Preamble

-- Generated from ChapterCoherentThermalFidelity.lean — theorem BookProof.ChapterCoherentThermalFidelity.fidelityC_width
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.fidelityC_width {n : ℕ} (q k : EuclideanSpace ℂ (Fin n)) :
    fidelityC q k = Real.exp (-(‖q - k‖ ^ 2 / (coherentWidth + coherentWidth))) := by sorry

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