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`BookProof.ChapterEulerComplexQuat.complex_reproduces` (p : Fin n → ℝ) (hp0 : ∀ k, 0 ≤ p k) (hp1 : ∑ k, p k = 1) : ∃ v : Fin n → ℂ, (∑ k, Complex.normSq (v k) = 1) ∧ ∀ k,...

Proved
BookProof.ChapterEulerComplexQuat.complex_reproduces

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerComplexQuat.

BookProof.ChapterEulerComplexQuat.complex_reproduces (p : Fin n → ℝ) (hp0 : ∀ k, 0 ≤ p k) (hp1 : ∑ k, p k = 1) : ∃ v : Fin n → ℂ, (∑ k, Complex.normSq (v k) = 1) ∧ ∀ k, cbornProb v k = p k

Formalization note: Lean 4 identifier BookProof.ChapterEulerComplexQuat.complex_reproduces.

Preamble
-- Generated from ChapterEulerComplexQuat.lean — theorem BookProof.ChapterEulerComplexQuat.complex_reproduces
import Mathlib
import Definitions.Def_ChapterEulerComplexQuat
open BookProof.ChapterEulerComplexQuat


open scoped Quaternion BigOperators


variable {n : ℕ}
Formal statement
theorem BookProof.ChapterEulerComplexQuat.complex_reproduces (p : Fin n → ℝ) (hp0 : ∀ k, 0 ≤ p k)
    (hp1 : ∑ k, p k = 1) :
    ∃ v : Fin n → ℂ, (∑ k, Complex.normSq (v k) = 1) ∧ ∀ k, cbornProb v k = p k := by sorry

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