Prove2Me

`PhysMeasureBasis.selection_exists` : squareMeasure.fst ⊗ₘ squareMeasure.condKernel = squareMeasure

Proved
PhysMeasureBasis.selection_exists

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from PhysMeasureBasis.

PhysMeasureBasis.selection_exists : squareMeasure.fst ⊗ₘ squareMeasure.condKernel = squareMeasure

Formalization note: Lean 4 identifier PhysMeasureBasis.selection_exists.

Preamble
-- Generated from PhysMeasureBasis.lean — theorem PhysMeasureBasis.selection_exists
import Mathlib
import Definitions.Def_PhysMeasureBasis
import Definitions.Def_ChapterA4
open PhysMeasureBasis


open MeasureTheory Set ProbabilityTheory
open scoped ENNReal

noncomputable section
Formal statement
theorem PhysMeasureBasis.selection_exists :
    squareMeasure.fst ⊗ₘ squareMeasure.condKernel = squareMeasure := by sorry

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