`BookProof.ChapterEulerNState.exists_theta_tailProd` (p : ℕ → ℝ) (hp : ∀ k, 0 ≤ p k) {n : ℕ} (hsum : ∑ j ∈ Finset.range n, p j = 1) : ∃ θ : ℕ → ℝ, ∀ m ≤ n, tailProd...

Proved

BookProof.ChapterEulerNState.exists_theta_tailProd

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerNState.

BookProof.ChapterEulerNState.exists_theta_tailProd (p : ℕ → ℝ) (hp : ∀ k, 0 ≤ p k) {n : ℕ} (hsum : ∑ j ∈ Finset.range n, p j = 1) : ∃ θ : ℕ → ℝ, ∀ m ≤ n, tailProd θ m = tailSum p n m

Formalization note: Lean 4 identifier BookProof.ChapterEulerNState.exists_theta_tailProd.

Preamble

-- Generated from ChapterEulerNState.lean — theorem BookProof.ChapterEulerNState.exists_theta_tailProd
import Mathlib
import Definitions.Def_ChapterEulerNState
open BookProof.ChapterEulerNState


open scoped BigOperators

Formal statement

theorem BookProof.ChapterEulerNState.exists_theta_tailProd (p : ℕ → ℝ) (hp : ∀ k, 0 ≤ p k) {n : ℕ}
    (hsum : ∑ j ∈ Finset.range n, p j = 1) :
    ∃ θ : ℕ → ℝ, ∀ m ≤ n, tailProd θ m = tailSum p n m := by sorry

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