`BookProof.ChapterObservableOperator.observableOp_expectation` (k : Fin m → EuclideanSpace ℂ (Fin n)) (v : Fin m → ℝ) (q : EuclideanSpace ℂ (Fin n)) : expectation (observableOp k v

Proved

BookProof.ChapterObservableOperator.observableOp_expectation

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterObservableOperator.

BookProof.ChapterObservableOperator.observableOp_expectation (k : Fin m → EuclideanSpace ℂ (Fin n)) (v : Fin m → ℝ) (q : EuclideanSpace ℂ (Fin n)) : expectation (observableOp k v) q = ((BookProof.ChapterObservableExpectation.observableExpectation (bornProb k q) v : ℝ) : ℂ)

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

Preamble

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


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterObservableOperator.observableOp_expectation (k : Fin m → EuclideanSpace ℂ (Fin n)) (v : Fin m → ℝ)
    (q : EuclideanSpace ℂ (Fin n)) :
    expectation (observableOp k v) q
      = ((BookProof.ChapterObservableExpectation.observableExpectation
            (bornProb k q) v : ℝ) : ℂ) := by sorry

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