`BookProof.ChapterAttentionOutput.headOutput_const` (beta : ℝ) (s : Fin m → ℝ) (w : E) (i : Fin m) : headOutput beta s (fun _ => w) = w

Proved

BookProof.ChapterAttentionOutput.headOutput_const

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionOutput.

BookProof.ChapterAttentionOutput.headOutput_const (beta : ℝ) (s : Fin m → ℝ) (w : E) (i : Fin m) : headOutput beta s (fun _ => w) = w

Formalization note: Lean 4 identifier BookProof.ChapterAttentionOutput.headOutput_const.

Preamble

-- Generated from ChapterAttentionOutput.lean — theorem BookProof.ChapterAttentionOutput.headOutput_const
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionOutput
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionOutput


open scoped BigOperators

open Filter Topology

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

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

Formal statement

theorem BookProof.ChapterAttentionOutput.headOutput_const (beta : ℝ) (s : Fin m → ℝ) (w : E) (i : Fin m) :
    headOutput beta s (fun _ => w) = w := by sorry

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