`BookProof.ChapterSolovayCoordinates.enlargeEquiv_map` (N k : ℕ) (headDist : Measure (Fin N → ℝ)) [IsProbabilityMeasure headDist] : Measure.map (enlargeEquiv N k) (coordinateStateM

Proved

BookProof.ChapterSolovayCoordinates.enlargeEquiv_map

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSolovayCoordinates.

BookProof.ChapterSolovayCoordinates.enlargeEquiv_map (N k : ℕ) (headDist : Measure (Fin N → ℝ)) [IsProbabilityMeasure headDist] : Measure.map (enlargeEquiv N k) (coordinateStateMeasure N headDist) = coordinateStateMeasure (N + k) (enlargedHeadMeasure N k headDist)

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

Preamble

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


open MeasureTheory ProbabilityTheory
open scoped ENNReal

noncomputable section

Formal statement

theorem BookProof.ChapterSolovayCoordinates.enlargeEquiv_map (N k : ℕ) (headDist : Measure (Fin N → ℝ))
    [IsProbabilityMeasure headDist] :
    Measure.map (enlargeEquiv N k) (coordinateStateMeasure N headDist) =
      coordinateStateMeasure (N + k) (enlargedHeadMeasure N k headDist) := by sorry

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