`BookProof.ChapterAbelianDiagonalCountable.vonNeumann_abelian_class_countable` : Function.Injective diagOp ∧ (∀ d e : EllInf, (diagOp d).comp (diagOp e) = (diagOp e).comp (diagOp d

Proved

BookProof.ChapterAbelianDiagonalCountable.vonNeumann_abelian_class_countable

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianDiagonalCountable.

BookProof.ChapterAbelianDiagonalCountable.vonNeumann_abelian_class_countable : Function.Injective diagOp ∧ (∀ d e : EllInf, (diagOp d).comp (diagOp e) = (diagOp e).comp (diagOp d)) ∧ (∀ T : Ell2C →L[ℂ] Ell2C, (∀ d : EllInf, T.comp (diagOp d) = (diagOp d).comp T) ↔ ∃ d : EllInf, T = diagOp d)

Formalization note: Lean 4 identifier BookProof.ChapterAbelianDiagonalCountable.vonNeumann_abelian_class_countable.

Preamble

-- Generated from ChapterAbelianDiagonalCountable.lean — theorem BookProof.ChapterAbelianDiagonalCountable.vonNeumann_abelian_class_countable
import Mathlib
import Definitions.Def_ChapterAbelianDiagonalCountable
open BookProof.ChapterAbelianDiagonalCountable


open scoped ENNReal

noncomputable section

Formal statement

theorem BookProof.ChapterAbelianDiagonalCountable.vonNeumann_abelian_class_countable :
    Function.Injective diagOp ∧
      (∀ d e : EllInf, (diagOp d).comp (diagOp e) = (diagOp e).comp (diagOp d)) ∧
      (∀ T : Ell2C →L[ℂ] Ell2C,
        (∀ d : EllInf, T.comp (diagOp d) = (diagOp d).comp T) ↔ ∃ d : EllInf, T = diagOp d) := by sorry

View graph