`BookProof.ChapterCoherentDynamics.inner_phaseRotate` (theta : ℝ) (q k : EuclideanSpace ℂ (Fin n)) : (inner ℂ (phaseRotate theta q) (phaseRotate theta k) : ℂ) = inner ℂ q k

Proved

BookProof.ChapterCoherentDynamics.inner_phaseRotate

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentDynamics.

BookProof.ChapterCoherentDynamics.inner_phaseRotate (theta : ℝ) (q k : EuclideanSpace ℂ (Fin n)) : (inner ℂ (phaseRotate theta q) (phaseRotate theta k) : ℂ) = inner ℂ q k

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

Preamble

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlapComplex BookProof.ChapterCoherentFidelity

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentDynamics.inner_phaseRotate (theta : ℝ) (q k : EuclideanSpace ℂ (Fin n)) :
    (inner ℂ (phaseRotate theta q) (phaseRotate theta k) : ℂ) = inner ℂ q k := by sorry

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