`BookProof.ChapterE2.exists_angles_realize` (n : ℕ) (p : Fin n → ℝ) (hp : ∀ i, 0 ≤ p i) (hsum : ∑ i, p i = 1) : ∃ θ : ℕ → ℝ, ∀ i : Fin n, bornProb θ n i = p i

Proved

BookProof.ChapterE2.exists_angles_realize

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterE2.

BookProof.ChapterE2.exists_angles_realize (n : ℕ) (p : Fin n → ℝ) (hp : ∀ i, 0 ≤ p i) (hsum : ∑ i, p i = 1) : ∃ θ : ℕ → ℝ, ∀ i : Fin n, bornProb θ n i = p i

Formalization note: Lean 4 identifier BookProof.ChapterE2.exists_angles_realize.

Preamble

-- Generated from ChapterE2.lean — theorem BookProof.ChapterE2.exists_angles_realize
import Mathlib
import Definitions.Def_ChapterE2
import Definitions.Def_ChapterDoubleSlit
open BookProof.ChapterDoubleSlit
open BookProof.ChapterE2


open scoped BigOperators
open Finset

Formal statement

theorem BookProof.ChapterE2.exists_angles_realize (n : ℕ) (p : Fin n → ℝ)
    (hp : ∀ i, 0 ≤ p i) (hsum : ∑ i, p i = 1) :
    ∃ θ : ℕ → ℝ, ∀ i : Fin n, bornProb θ n i = p i := by sorry

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