`BookProof.ChapterAbelianClassificationList.restrict_atomSet_pure_inc` (mu : Measure α) [IsFiniteMeasure mu] : (mu.restrict (atomSet mu)) (atomSet (mu.restrict (atomSet mu)))ᶜ = 0

Proved

BookProof.ChapterAbelianClassificationList.restrict_atomSet_pure_inc

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianClassificationList.

BookProof.ChapterAbelianClassificationList.restrict_atomSet_pure_inc (mu : Measure α) [IsFiniteMeasure mu] : (mu.restrict (atomSet mu)) (atomSet (mu.restrict (atomSet mu)))ᶜ = 0

Formalization note: Lean 4 identifier BookProof.ChapterAbelianClassificationList.restrict_atomSet_pure_inc.

Replaces the unuploadable node BookProof_ChapterAbelianClassificationList_restrict_atomSet_pure, whose statement name is already declared inside its published definition bundle; the _inc suffix publishes the same statement as its own node.

Preamble

-- Generated from ChapterAbelianClassificationList.lean — theorem BookProof.ChapterAbelianClassificationList.restrict_atomSet_pure_inc
import Definitions.Def_ChapterMeasureAtomicDiffuse
import Definitions.Def_ChapterAtomicDiagonalModel
import Definitions.Def_ChapterDiffuseUnitaryModel
import Definitions.Def_ChapterLinftyMultiplication
import Definitions.Def_ChapterLpRestrictSplit
import Definitions.Def_ChapterLpScaleMeasure
import Mathlib
import Definitions.Def_ChapterAbelianClassificationList
open BookProof.ChapterAbelianClassificationList


noncomputable section

open MeasureTheory ProbabilityTheory


open BookProof.ChapterMeasureAtomicDiffuse BookProof.ChapterAtomicDiagonalModel
open BookProof.ChapterDiffuseUnitaryModel BookProof.ChapterLinftyMultiplication
open BookProof.ChapterLpRestrictSplit BookProof.ChapterLpScaleMeasure

variable {α : Type*} [MeasurableSpace α] [MeasurableSingletonClass α]

Formal statement

theorem BookProof.ChapterAbelianClassificationList.restrict_atomSet_pure_inc (mu : Measure α) [IsFiniteMeasure mu] :
    (mu.restrict (atomSet mu)) (atomSet (mu.restrict (atomSet mu)))ᶜ = 0 := by sorry

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