Prove2Me

`BookProof.ChapterDiffuseCdfModel.map_cdf_eq_volume_Icc` [IsProbabilityMeasure mu] [NullSingletonClass mu] : Measure.map (cdf mu) mu = volume.restrict (Set.Icc (0 : ℝ) 1)

Proved
BookProof.ChapterDiffuseCdfModel.map_cdf_eq_volume_Icc

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDiffuseCdfModel.

BookProof.ChapterDiffuseCdfModel.map_cdf_eq_volume_Icc [IsProbabilityMeasure mu] [NullSingletonClass mu] : Measure.map (cdf mu) mu = volume.restrict (Set.Icc (0 : ℝ) 1)

Formalization note: Lean 4 identifier BookProof.ChapterDiffuseCdfModel.map_cdf_eq_volume_Icc.

Preamble
-- Generated from ChapterDiffuseCdfModel.lean — theorem BookProof.ChapterDiffuseCdfModel.map_cdf_eq_volume_Icc
import Mathlib
import Definitions.Def_ChapterDiffuseCdfModel
open BookProof.ChapterDiffuseCdfModel


noncomputable section

open MeasureTheory ProbabilityTheory Filter


variable (mu : Measure ℝ)
Formal statement
theorem BookProof.ChapterDiffuseCdfModel.map_cdf_eq_volume_Icc [IsProbabilityMeasure mu] [NullSingletonClass mu] :
    Measure.map (cdf mu) mu = volume.restrict (Set.Icc (0 : ℝ) 1) := by sorry

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