`BookProof.ChapterDiffuseCdfModel.exists_cdf_eq` [IsProbabilityMeasure mu] [NullSingletonClass mu] {t : ℝ} (ht0 : 0 < t) (ht1 : t < 1) : ∃ x : ℝ, cdf mu x = t

Proved

BookProof.ChapterDiffuseCdfModel.exists_cdf_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDiffuseCdfModel.

BookProof.ChapterDiffuseCdfModel.exists_cdf_eq [IsProbabilityMeasure mu] [NullSingletonClass mu] {t : ℝ} (ht0 : 0 < t) (ht1 : t < 1) : ∃ x : ℝ, cdf mu x = t

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

Preamble

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


noncomputable section

open MeasureTheory ProbabilityTheory Filter


variable (mu : Measure ℝ)

Formal statement

theorem BookProof.ChapterDiffuseCdfModel.exists_cdf_eq [IsProbabilityMeasure mu] [NullSingletonClass mu] {t : ℝ} (ht0 : 0 < t)
    (ht1 : t < 1) : ∃ x : ℝ, cdf mu x = t := by sorry

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