`BookProof.ChapterAbelianAtomicCondensation.commutes_atomProj_iff` (T : Ell2C →L[ℂ] Ell2C) : (∀ i : ℕ, T.comp (atomProj i) = (atomProj i).comp T) ↔ ∃ d : EllInf, T = diagOp d

Proved

BookProof.ChapterAbelianAtomicCondensation.commutes_atomProj_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianAtomicCondensation.

BookProof.ChapterAbelianAtomicCondensation.commutes_atomProj_iff (T : Ell2C →L[ℂ] Ell2C) : (∀ i : ℕ, T.comp (atomProj i) = (atomProj i).comp T) ↔ ∃ d : EllInf, T = diagOp d

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

Preamble

-- Generated from ChapterAbelianAtomicCondensation.lean — theorem BookProof.ChapterAbelianAtomicCondensation.commutes_atomProj_iff
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.commutes_atomProj_iff (T : Ell2C →L[ℂ] Ell2C) :
    (∀ i : ℕ, T.comp (atomProj i) = (atomProj i).comp T) ↔ ∃ d : EllInf, T = diagOp d := by sorry

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