`BookProof.ChapterE.stickBreaking_surjective` {N : ℕ} (P : Fin N → ℝ) (hP0 : ∀ n, 0 ≤ P n) (hPsum : ∑ n, P n = 1) : ∃ θ : Fin N → ℝ, ∀ n, stickBreaking θ n = P n

Proved

BookProof.ChapterE.stickBreaking_surjective

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterE.

BookProof.ChapterE.stickBreaking_surjective {N : ℕ} (P : Fin N → ℝ) (hP0 : ∀ n, 0 ≤ P n) (hPsum : ∑ n, P n = 1) : ∃ θ : Fin N → ℝ, ∀ n, stickBreaking θ n = P n

Formalization note: Lean 4 identifier BookProof.ChapterE.stickBreaking_surjective.

Preamble

-- Generated from ChapterE.lean — theorem BookProof.ChapterE.stickBreaking_surjective
import Mathlib
import Definitions.Def_ChapterE
open BookProof.ChapterE


open scoped Matrix BigOperators
open Filter
open scoped Topology

Formal statement

theorem BookProof.ChapterE.stickBreaking_surjective {N : ℕ} (P : Fin N → ℝ)
    (hP0 : ∀ n, 0 ≤ P n) (hPsum : ∑ n, P n = 1) :
    ∃ θ : Fin N → ℝ, ∀ n, stickBreaking θ n = P n := by sorry

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