`BookProof.ChapterAttentionResponse.scoreValueCovariance_const` (beta : ℝ) (s : Fin m → ℝ) (w : E) (i : Fin m) : scoreValueCovariance beta s (fun _ => w) = (0 : E)

Proved

BookProof.ChapterAttentionResponse.scoreValueCovariance_const

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionResponse.

BookProof.ChapterAttentionResponse.scoreValueCovariance_const (beta : ℝ) (s : Fin m → ℝ) (w : E) (i : Fin m) : scoreValueCovariance beta s (fun _ => w) = (0 : E)

Formalization note: Lean 4 identifier BookProof.ChapterAttentionResponse.scoreValueCovariance_const.

Preamble

-- Generated from ChapterAttentionResponse.lean — theorem BookProof.ChapterAttentionResponse.scoreValueCovariance_const
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionResponse
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionResponse


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

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

Formal statement

theorem BookProof.ChapterAttentionResponse.scoreValueCovariance_const (beta : ℝ) (s : Fin m → ℝ) (w : E) (i : Fin m) :
    scoreValueCovariance beta s (fun _ => w) = (0 : E) := by sorry

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