`BookProof.ChapterAttentionOutput.tendsto_headOutput` (s : Fin m → ℝ) (v : Fin m → E) (j : Fin m) (hmax : ∀ l, l ≠ j → s l < s j) : Tendsto (fun b : ℝ => headOutput b s v) atTop (𝓝

Proved

BookProof.ChapterAttentionOutput.tendsto_headOutput

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionOutput.

BookProof.ChapterAttentionOutput.tendsto_headOutput (s : Fin m → ℝ) (v : Fin m → E) (j : Fin m) (hmax : ∀ l, l ≠ j → s l < s j) : Tendsto (fun b : ℝ => headOutput b s v) atTop (𝓝 (v j))

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

Preamble

-- Generated from ChapterAttentionOutput.lean — theorem BookProof.ChapterAttentionOutput.tendsto_headOutput
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.tendsto_headOutput (s : Fin m → ℝ) (v : Fin m → E) (j : Fin m)
    (hmax : ∀ l, l ≠ j → s l < s j) :
    Tendsto (fun b : ℝ => headOutput b s v) atTop (𝓝 (v j)) := by sorry

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