`BookProof.ChapterObservableExpectation.observableExpectation_add` (p : Fin m → ℝ) (v w : Fin m → E) : observableExpectation p (fun j => v j + w j) = observableExpectation p v + ob

Proved

BookProof.ChapterObservableExpectation.observableExpectation_add

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterObservableExpectation.

BookProof.ChapterObservableExpectation.observableExpectation_add (p : Fin m → ℝ) (v w : Fin m → E) : observableExpectation p (fun j => v j + w j) = observableExpectation p v + observableExpectation p w

Formalization note: Lean 4 identifier BookProof.ChapterObservableExpectation.observableExpectation_add.

Preamble

-- Generated from ChapterObservableExpectation.lean — theorem BookProof.ChapterObservableExpectation.observableExpectation_add
import Definitions.Def_ChapterSoftmaxBorn
import Mathlib
import Definitions.Def_ChapterObservableExpectation
open BookProof.ChapterObservableExpectation


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxBorn

variable {m n : ℕ}
variable {E : Type*} [AddCommGroup E] [Module ℝ E]

Formal statement

theorem BookProof.ChapterObservableExpectation.observableExpectation_add (p : Fin m → ℝ) (v w : Fin m → E) :
    observableExpectation p (fun j => v j + w j)
      = observableExpectation p v + observableExpectation p w := by sorry

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