`BookProof.ChapterDiffuseCdfModel.measure_cdf_le` [IsProbabilityMeasure mu] [NullSingletonClass mu] {t : ℝ} (ht0 : 0 ≤ t) (ht1 : t < 1) : mu {x | cdf mu x ≤ t} = ENNReal.ofReal t

Proved

BookProof.ChapterDiffuseCdfModel.measure_cdf_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDiffuseCdfModel.

BookProof.ChapterDiffuseCdfModel.measure_cdf_le [IsProbabilityMeasure mu] [NullSingletonClass mu] {t : ℝ} (ht0 : 0 ≤ t) (ht1 : t < 1) : mu {x | cdf mu x ≤ t} = ENNReal.ofReal t

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

Preamble

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


noncomputable section

open MeasureTheory ProbabilityTheory Filter


variable (mu : Measure ℝ)

Formal statement

theorem BookProof.ChapterDiffuseCdfModel.measure_cdf_le [IsProbabilityMeasure mu] [NullSingletonClass mu] {t : ℝ} (ht0 : 0 ≤ t)
    (ht1 : t < 1) : mu {x | cdf mu x ≤ t} = ENNReal.ofReal t := by sorry

View graph