`BookProof.ChapterSpectralDirectSum.countable_orthogonalCyclicFamily` [TopologicalSpace.SeparableSpace H] {S : Set H} (hS : OrthogonalCyclicFamily T hT S) : S.Countable

Proved

BookProof.ChapterSpectralDirectSum.countable_orthogonalCyclicFamily

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSpectralDirectSum.

BookProof.ChapterSpectralDirectSum.countable_orthogonalCyclicFamily [TopologicalSpace.SeparableSpace H] {S : Set H} (hS : OrthogonalCyclicFamily T hT S) : S.Countable

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

Preamble

-- Generated from ChapterSpectralDirectSum.lean — theorem BookProof.ChapterSpectralDirectSum.countable_orthogonalCyclicFamily
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.countable_orthogonalCyclicFamily [TopologicalSpace.SeparableSpace H] {S : Set H}
    (hS : OrthogonalCyclicFamily T hT S) : S.Countable := by sorry

View graph