`BookProof.ChapterObservableOperator.bornProb_sum_one` (b : OrthonormalBasis (Fin m) ℂ (EuclideanSpace ℂ (Fin n))) (q : EuclideanSpace ℂ (Fin n)) (hq : ‖q‖ = 1) : ∑ j, bornProb (fu

Proved

BookProof.ChapterObservableOperator.bornProb_sum_one

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

Prove the following Lean 4 theorem from ChapterObservableOperator.

BookProof.ChapterObservableOperator.bornProb_sum_one (b : OrthonormalBasis (Fin m) ℂ (EuclideanSpace ℂ (Fin n))) (q : EuclideanSpace ℂ (Fin n)) (hq : ‖q‖ = 1) : ∑ j, bornProb (fun j => b j) q j = 1

Formalization note: Lean 4 identifier BookProof.ChapterObservableOperator.bornProb_sum_one.

Preamble

-- Generated from ChapterObservableOperator.lean — theorem BookProof.ChapterObservableOperator.bornProb_sum_one
import Mathlib
import Definitions.Def_ChapterObservableOperator
import Definitions.Def_ChapterDoubleSlit
open BookProof.ChapterDoubleSlit
open BookProof.ChapterObservableOperator


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterObservableOperator.bornProb_sum_one (b : OrthonormalBasis (Fin m) ℂ (EuclideanSpace ℂ (Fin n)))
    (q : EuclideanSpace ℂ (Fin n)) (hq : ‖q‖ = 1) :
    ∑ j, bornProb (fun j => b j) q j = 1 := by sorry

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