`BookProof.ChapterCoherentDynamics.bornNumerC_isometry` (U : EuclideanSpace ℂ (Fin n) ≃ₗᵢ[ℂ] EuclideanSpace ℂ (Fin n)) (q k : EuclideanSpace ℂ (Fin n)) : bornNumerC (U q) (U k) = b

Proved

BookProof.ChapterCoherentDynamics.bornNumerC_isometry

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentDynamics.

BookProof.ChapterCoherentDynamics.bornNumerC_isometry (U : EuclideanSpace ℂ (Fin n) ≃ₗᵢ[ℂ] EuclideanSpace ℂ (Fin n)) (q k : EuclideanSpace ℂ (Fin n)) : bornNumerC (U q) (U k) = bornNumerC q k

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

Preamble

-- Generated from ChapterCoherentDynamics.lean — theorem BookProof.ChapterCoherentDynamics.bornNumerC_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.bornNumerC_isometry (U : EuclideanSpace ℂ (Fin n) ≃ₗᵢ[ℂ] EuclideanSpace ℂ (Fin n))
    (q k : EuclideanSpace ℂ (Fin n)) : bornNumerC (U q) (U k) = bornNumerC q k := by sorry

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