Prove2Me

`BookProof.ChapterSpectralDirectSum.range_cyclicEmbedding` : LinearMap.range (cyclicEmbedding T hT xi).toLinearMap = cyclicSubspace T hT xi

Proved
BookProof.ChapterSpectralDirectSum.range_cyclicEmbedding

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSpectralDirectSum.

BookProof.ChapterSpectralDirectSum.range_cyclicEmbedding : LinearMap.range (cyclicEmbedding T hT xi).toLinearMap = cyclicSubspace T hT xi

Formalization note: Lean 4 identifier BookProof.ChapterSpectralDirectSum.range_cyclicEmbedding.

Preamble
-- Generated from ChapterSpectralDirectSum.lean — theorem BookProof.ChapterSpectralDirectSum.range_cyclicEmbedding
import Definitions.Def_ChapterAbelianGelfandModel
import Definitions.Def_ChapterSpectralMultiplication
import Definitions.Def_ChapterCyclicDecomposition
import Definitions.Def_ChapterCyclicDirectSum
import Mathlib
import Definitions.Def_ChapterSpectralDirectSum
open BookProof.ChapterSpectralDirectSum


noncomputable section

open MeasureTheory Complex


open BookProof.ChapterAbelianGelfandModel BookProof.ChapterSpectralMultiplication
open BookProof.ChapterCyclicDecomposition BookProof.ChapterCyclicDirectSum

variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]
variable (T : H →L[ℂ] H) (hT : IsStarNormal T) (xi : H)
Formal statement
theorem BookProof.ChapterSpectralDirectSum.range_cyclicEmbedding :
    LinearMap.range (cyclicEmbedding T hT xi).toLinearMap = cyclicSubspace T hT xi := by sorry

View graph