`BookProof.ChapterCyclicDecomposition.cyclicSubspace_le_orthogonal` {M : Submodule ℂ H} (hM : Invariant T hT M) {v : H} (hv : v ∈ Mᗮ) : cyclicSubspace T hT v ≤ Mᗮ

Proved

BookProof.ChapterCyclicDecomposition.cyclicSubspace_le_orthogonal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCyclicDecomposition.

BookProof.ChapterCyclicDecomposition.cyclicSubspace_le_orthogonal {M : Submodule ℂ H} (hM : Invariant T hT M) {v : H} (hv : v ∈ Mᗮ) : cyclicSubspace T hT v ≤ Mᗮ

Formalization note: Lean 4 identifier BookProof.ChapterCyclicDecomposition.cyclicSubspace_le_orthogonal.

Preamble

-- Generated from ChapterCyclicDecomposition.lean — theorem BookProof.ChapterCyclicDecomposition.cyclicSubspace_le_orthogonal
import Definitions.Def_ChapterSpectralMultiplication
import Mathlib
import Definitions.Def_ChapterCyclicDecomposition
open BookProof.ChapterCyclicDecomposition


noncomputable section

open MeasureTheory Complex


open BookProof.ChapterSpectralMultiplication

variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]
variable (T : H →L[ℂ] H) (hT : IsStarNormal T)

Formal statement

theorem BookProof.ChapterCyclicDecomposition.cyclicSubspace_le_orthogonal {M : Submodule ℂ H} (hM : Invariant T hT M) {v : H}
    (hv : v ∈ Mᗮ) : cyclicSubspace T hT v ≤ Mᗮ := by sorry

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