`BookProof.ChapterSolovayCoordinates.tailSplitEquiv_map` (k : ℕ) : Measure.map (tailSplitEquiv k) coordinateTailMeasure = (gaussianHead k).prod coordinateTailMeasure

Proved

BookProof.ChapterSolovayCoordinates.tailSplitEquiv_map

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSolovayCoordinates.

BookProof.ChapterSolovayCoordinates.tailSplitEquiv_map (k : ℕ) : Measure.map (tailSplitEquiv k) coordinateTailMeasure = (gaussianHead k).prod coordinateTailMeasure

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

Preamble

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


open MeasureTheory ProbabilityTheory
open scoped ENNReal

noncomputable section

Formal statement

theorem BookProof.ChapterSolovayCoordinates.tailSplitEquiv_map (k : ℕ) :
    Measure.map (tailSplitEquiv k) coordinateTailMeasure =
      (gaussianHead k).prod coordinateTailMeasure := by sorry

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