`BookProof.ChapterAbelianAtomicCondensation.diagonal_starAlgebra_package` : Function.Injective diagOp ∧ (∀ d e : EllInf, diagOp (d * e) = (diagOp d).comp (diagOp e)) ∧ diagOp (1 :

Proved

BookProof.ChapterAbelianAtomicCondensation.diagonal_starAlgebra_package

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianAtomicCondensation.

BookProof.ChapterAbelianAtomicCondensation.diagonal_starAlgebra_package : Function.Injective diagOp ∧ (∀ d e : EllInf, diagOp (d * e) = (diagOp d).comp (diagOp e)) ∧ diagOp (1 : EllInf) = ContinuousLinearMap.id ℂ Ell2C ∧ (∀ d : EllInf, ∀ f g : Ell2C, (inner ℂ (diagOp d f) g : ℂ) = (inner ℂ f (diagOp (star d) g) : ℂ))

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

Preamble

-- Generated from ChapterAbelianAtomicCondensation.lean — theorem BookProof.ChapterAbelianAtomicCondensation.diagonal_starAlgebra_package
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.diagonal_starAlgebra_package :
    Function.Injective diagOp ∧
      (∀ d e : EllInf, diagOp (d * e) = (diagOp d).comp (diagOp e)) ∧
      diagOp (1 : EllInf) = ContinuousLinearMap.id ℂ Ell2C ∧
      (∀ d : EllInf, ∀ f g : Ell2C,
        (inner ℂ (diagOp d f) g : ℂ) = (inner ℂ f (diagOp (star d) g) : ℂ)) := by sorry

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