`BookProof.ChapterAbelianAtomicCondensation.atomic_abelian_maximal_eq_diagonal` {A : Set (Ell2C →L[ℂ] Ell2C)} (hA : IsAtomicAbelian A) (hmax : ∀ T : Ell2C →L[ℂ] Ell2C, (∀ S ∈ A, T.

Proved

BookProof.ChapterAbelianAtomicCondensation.atomic_abelian_maximal_eq_diagonal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianAtomicCondensation.

BookProof.ChapterAbelianAtomicCondensation.atomic_abelian_maximal_eq_diagonal {A : Set (Ell2C →L[ℂ] Ell2C)} (hA : IsAtomicAbelian A) (hmax : ∀ T : Ell2C →L[ℂ] Ell2C, (∀ S ∈ A, T.comp S = S.comp T) → T ∈ A) : A = Set.range diagOp

Formalization note: Lean 4 identifier BookProof.ChapterAbelianAtomicCondensation.atomic_abelian_maximal_eq_diagonal.

Preamble

-- Generated from ChapterAbelianAtomicCondensation.lean — theorem BookProof.ChapterAbelianAtomicCondensation.atomic_abelian_maximal_eq_diagonal
import Mathlib
import Definitions.Def_ChapterAbelianAtomicCondensation
import Definitions.Def_ChapterAbelianDiagonalCountable
open BookProof.ChapterAbelianDiagonalCountable
open BookProof.ChapterAbelianAtomicCondensation


open scoped ENNReal

noncomputable section


open BookProof.ChapterAbelianDiagonalCountable

Formal statement

theorem BookProof.ChapterAbelianAtomicCondensation.atomic_abelian_maximal_eq_diagonal {A : Set (Ell2C →L[ℂ] Ell2C)}
    (hA : IsAtomicAbelian A)
    (hmax : ∀ T : Ell2C →L[ℂ] Ell2C, (∀ S ∈ A, T.comp S = S.comp T) → T ∈ A) :
    A = Set.range diagOp := by sorry

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