`BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_vacuum_eq_fidelityC` {n : ℕ} (q k : EuclideanSpace ℂ (Fin n)) : coherentThermalFidelity 0 (‖q - k‖ ^ 2) = fidelity

Proved

BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_vacuum_eq_fidelityC

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentThermalFidelity.

BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_vacuum_eq_fidelityC {n : ℕ} (q k : EuclideanSpace ℂ (Fin n)) : coherentThermalFidelity 0 (‖q - k‖ ^ 2) = fidelityC q k

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

Preamble

-- Generated from ChapterCoherentThermalFidelity.lean — theorem BookProof.ChapterCoherentThermalFidelity.coherentThermalFidelity_vacuum_eq_fidelityC
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_eq_fidelityC {n : ℕ}
    (q k : EuclideanSpace ℂ (Fin n)) :
    coherentThermalFidelity 0 (‖q - k‖ ^ 2) = fidelityC q k := by sorry

View graph