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

Proved

BookProof.ChapterObservableExpectation.observableExpectation_add_left

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterObservableExpectation.

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

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

Preamble

-- Generated from ChapterObservableExpectation.lean — theorem BookProof.ChapterObservableExpectation.observableExpectation_add_left
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_left (p q : Fin m → ℝ) (v : Fin m → E) :
    observableExpectation (fun j => p j + q j) v
      = observableExpectation p v + observableExpectation q v := by sorry

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