`BookProof.ChapterAttentionTopK.l1dist_maskedSoftmax_le_of_isTop` (beta : ℝ) (s : Fin m → ℝ) {S T : Finset (Fin m)} (hS : IsTop (scoreSoftmax beta s) S) (hcard : T.card ≤ S.card) (

Proved

BookProof.ChapterAttentionTopK.l1dist_maskedSoftmax_le_of_isTop

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionTopK.

BookProof.ChapterAttentionTopK.l1dist_maskedSoftmax_le_of_isTop (beta : ℝ) (s : Fin m → ℝ) {S T : Finset (Fin m)} (hS : IsTop (scoreSoftmax beta s) S) (hcard : T.card ≤ S.card) (hSne : S.Nonempty) (hTne : T.Nonempty) (i : Fin m) : l1dist (maskedSoftmax beta s S) (scoreSoftmax beta s) ≤ l1dist (maskedSoftmax beta s T) (scoreSoftmax beta s)

Formalization note: Lean 4 identifier BookProof.ChapterAttentionTopK.l1dist_maskedSoftmax_le_of_isTop.

Preamble

-- Generated from ChapterAttentionTopK.lean — theorem BookProof.ChapterAttentionTopK.l1dist_maskedSoftmax_le_of_isTop
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionTopK
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterAttentionMarkov
import Definitions.Def_ChapterAttentionMasking
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionTopK


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder
open BookProof.ChapterAttentionMarkov
open BookProof.ChapterAttentionMasking

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

Formal statement

theorem BookProof.ChapterAttentionTopK.l1dist_maskedSoftmax_le_of_isTop (beta : ℝ) (s : Fin m → ℝ) {S T : Finset (Fin m)}
    (hS : IsTop (scoreSoftmax beta s) S) (hcard : T.card ≤ S.card) (hSne : S.Nonempty)
    (hTne : T.Nonempty) (i : Fin m) :
    l1dist (maskedSoftmax beta s S) (scoreSoftmax beta s)
      ≤ l1dist (maskedSoftmax beta s T) (scoreSoftmax beta s) := by sorry

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