`BookProof.ChapterAttentionMixing.tendsto_l1dist_pushIter_attentionMatrix` {beta D : ℝ} (hb : 0 ≤ beta) {S : Fin m → Fin m → ℝ} {p q : Fin m → ℝ} (hp : IsProb p) (hq : IsProb q) (h

Proved

BookProof.ChapterAttentionMixing.tendsto_l1dist_pushIter_attentionMatrix

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMixing.

BookProof.ChapterAttentionMixing.tendsto_l1dist_pushIter_attentionMatrix {beta D : ℝ} (hb : 0 ≤ beta) {S : Fin m → Fin m → ℝ} {p q : Fin m → ℝ} (hp : IsProb p) (hq : IsProb q) (hD : ∀ i j l, S i l ≤ S i j + D) (i : Fin m) : Tendsto (fun n => l1dist (pushIter (attentionMatrix beta S) n p) (pushIter (attentionMatrix beta S) n q)) atTop (𝓝 0)

Formalization note: Lean 4 identifier BookProof.ChapterAttentionMixing.tendsto_l1dist_pushIter_attentionMatrix.

Preamble

-- Generated from ChapterAttentionMixing.lean — theorem BookProof.ChapterAttentionMixing.tendsto_l1dist_pushIter_attentionMatrix
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionMixing
import Definitions.Def_ChapterDutchBook
import Definitions.Def_ChapterAttentionMarkov
open BookProof.ChapterAttentionMixing


open scoped BigOperators

open Filter Topology

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder
open BookProof.ChapterAttentionMarkov

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionMixing.tendsto_l1dist_pushIter_attentionMatrix {beta D : ℝ} (hb : 0 ≤ beta)
    {S : Fin m → Fin m → ℝ} {p q : Fin m → ℝ} (hp : IsProb p) (hq : IsProb q)
    (hD : ∀ i j l, S i l ≤ S i j + D) (i : Fin m) :
    Tendsto (fun n => l1dist (pushIter (attentionMatrix beta S) n p)
      (pushIter (attentionMatrix beta S) n q)) atTop (𝓝 0) := by sorry

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