`BookProof.ChapterSolovayCoordinates.finiteCoordinateMarginal` (I : Finset ℕ) : Measure.map I.restrict coordinateTailMeasure = Measure.pi (fun _ : I => standardGaussian)

Proved

BookProof.ChapterSolovayCoordinates.finiteCoordinateMarginal

by leonardopedro · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSolovayCoordinates.

BookProof.ChapterSolovayCoordinates.finiteCoordinateMarginal (I : Finset ℕ) : Measure.map I.restrict coordinateTailMeasure = Measure.pi (fun _ : I => standardGaussian)

Formalization note: Lean 4 identifier BookProof.ChapterSolovayCoordinates.finiteCoordinateMarginal.

Preamble

-- Generated from ChapterSolovayCoordinates.lean — theorem BookProof.ChapterSolovayCoordinates.finiteCoordinateMarginal
import Mathlib
import Definitions.Def_ChapterSolovayCoordinates
open BookProof.ChapterSolovayCoordinates


open MeasureTheory ProbabilityTheory
open scoped ENNReal

noncomputable section

Formal statement

theorem BookProof.ChapterSolovayCoordinates.finiteCoordinateMarginal (I : Finset ℕ) :
    Measure.map I.restrict coordinateTailMeasure =
      Measure.pi (fun _ : I => standardGaussian) := by sorry

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