`BookProof.ChapterAttentionMixture.observableExpectation_mixture` (w : Fin H → ℝ) (p : Fin H → Fin m → ℝ) (v : Fin m → E) : observableExpectation (mixture w p) v = ∑ h, w h • obser

Proved

BookProof.ChapterAttentionMixture.observableExpectation_mixture

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMixture.

BookProof.ChapterAttentionMixture.observableExpectation_mixture (w : Fin H → ℝ) (p : Fin H → Fin m → ℝ) (v : Fin m → E) : observableExpectation (mixture w p) v = ∑ h, w h • observableExpectation (p h) v

Formalization note: Lean 4 identifier BookProof.ChapterAttentionMixture.observableExpectation_mixture.

Preamble

-- Generated from ChapterAttentionMixture.lean — theorem BookProof.ChapterAttentionMixture.observableExpectation_mixture
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionMixture
import Definitions.Def_ChapterObservableExpectation
open BookProof.ChapterObservableExpectation
open BookProof.ChapterAttentionMixture


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m H : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]

Formal statement

theorem BookProof.ChapterAttentionMixture.observableExpectation_mixture (w : Fin H → ℝ) (p : Fin H → Fin m → ℝ)
    (v : Fin m → E) :
    observableExpectation (mixture w p) v = ∑ h, w h • observableExpectation (p h) v := by sorry

View graph