`BookProof.InverseTransform.seedSet_total_measure` (hp : ∀ i, 0 ≤ p i) (hsum : cdf p n = 1) : ∑ k ∈ Finset.range n, volume (seedSet p k) = 1

Proved

BookProof.InverseTransform.seedSet_total_measure

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterInverseTransform.

BookProof.InverseTransform.seedSet_total_measure (hp : ∀ i, 0 ≤ p i) (hsum : cdf p n = 1) : ∑ k ∈ Finset.range n, volume (seedSet p k) = 1

Formalization note: Lean 4 identifier BookProof.InverseTransform.seedSet_total_measure.

Preamble

-- Generated from ChapterInverseTransform.lean — theorem BookProof.InverseTransform.seedSet_total_measure
import Mathlib
import Definitions.Def_ChapterInverseTransform
open BookProof.InverseTransform



open MeasureTheory Set Function

variable {n : ℕ} (p : ℕ → ℝ)

Formal statement

theorem BookProof.InverseTransform.seedSet_total_measure (hp : ∀ i, 0 ≤ p i) (hsum : cdf p n = 1) :
    ∑ k ∈ Finset.range n, volume (seedSet p k) = 1 := by sorry

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