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

Proved

BookProof.ChapterEulerNState.euler_reproduces

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerNState.

BookProof.ChapterEulerNState.euler_reproduces (p : ℕ → ℝ) (hp : ∀ k, 0 ≤ p k) {n : ℕ} (hn : 1 ≤ n) (hsum : ∑ j ∈ Finset.range n, p j = 1) : ∃ θ : ℕ → ℝ, ∀ k < n, bornProb θ n k = p k

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

Preamble

-- Generated from ChapterEulerNState.lean — theorem BookProof.ChapterEulerNState.euler_reproduces
import Mathlib
import Definitions.Def_ChapterEulerNState
import Definitions.Def_ChapterDoubleSlit
open BookProof.ChapterDoubleSlit
open BookProof.ChapterEulerNState


open scoped BigOperators

Formal statement

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

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