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

Proved

BookProof.ChapterObservableOperator.observableOp_expectation_real

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterObservableOperator.

BookProof.ChapterObservableOperator.observableOp_expectation_real (k : Fin m → EuclideanSpace ℂ (Fin n)) (v : Fin m → ℝ) (q : EuclideanSpace ℂ (Fin n)) : (expectation (observableOp k v) q).im = 0

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

Preamble

-- Generated from ChapterObservableOperator.lean — theorem BookProof.ChapterObservableOperator.observableOp_expectation_real
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_real (k : Fin m → EuclideanSpace ℂ (Fin n))
    (v : Fin m → ℝ) (q : EuclideanSpace ℂ (Fin n)) :
    (expectation (observableOp k v) q).im = 0 := by sorry

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