`BookProof.ChapterDiffuseCdfModel.volume_Icc_inter_Iic` {t : ℝ} (ht1 : t ≤ 1) : (volume.restrict (Set.Icc (0 : ℝ) 1)) (Set.Iic t) = ENNReal.ofReal t

Proved

BookProof.ChapterDiffuseCdfModel.volume_Icc_inter_Iic

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDiffuseCdfModel.

BookProof.ChapterDiffuseCdfModel.volume_Icc_inter_Iic {t : ℝ} (ht1 : t ≤ 1) : (volume.restrict (Set.Icc (0 : ℝ) 1)) (Set.Iic t) = ENNReal.ofReal t

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

Preamble

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


noncomputable section

open MeasureTheory ProbabilityTheory Filter


variable (mu : Measure ℝ)

Formal statement

theorem BookProof.ChapterDiffuseCdfModel.volume_Icc_inter_Iic {t : ℝ} (ht1 : t ≤ 1) :
    (volume.restrict (Set.Icc (0 : ℝ) 1)) (Set.Iic t) = ENNReal.ofReal t := by sorry

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