`BookProof.ChapterCoherentDynamics.bornWeightC_isometry` (U : EuclideanSpace ℂ (Fin n) ≃ₗᵢ[ℂ] EuclideanSpace ℂ (Fin n)) (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ

Proved

BookProof.ChapterCoherentDynamics.bornWeightC_isometry

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentDynamics.

BookProof.ChapterCoherentDynamics.bornWeightC_isometry (U : EuclideanSpace ℂ (Fin n) ≃ₗᵢ[ℂ] EuclideanSpace ℂ (Fin n)) (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) : bornWeightC (U q) (fun l => U (k l)) j = bornWeightC q k j

Formalization note: Lean 4 identifier BookProof.ChapterCoherentDynamics.bornWeightC_isometry.

Preamble

-- Generated from ChapterCoherentDynamics.lean — theorem BookProof.ChapterCoherentDynamics.bornWeightC_isometry
import Definitions.Def_ChapterCoherentFidelity
import Mathlib
import Definitions.Def_ChapterCoherentDynamics
import Definitions.Def_ChapterCoherentOverlapComplex
open BookProof.ChapterCoherentOverlapComplex
open BookProof.ChapterCoherentDynamics


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlapComplex BookProof.ChapterCoherentFidelity

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentDynamics.bornWeightC_isometry (U : EuclideanSpace ℂ (Fin n) ≃ₗᵢ[ℂ] EuclideanSpace ℂ (Fin n))
    (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) :
    bornWeightC (U q) (fun l => U (k l)) j = bornWeightC q k j := by sorry

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