Prove2Me

`BookProof.ChapterAttentionRetrieval.scoreSoftmax_le_exp_neg_margin` {beta delta : ℝ} (hb : 0 ≤ beta) (s : Fin m → ℝ) {j l : Fin m} (h : s l + delta ≤ s j) : scoreSoftmax beta s l

Proved
BookProof.ChapterAttentionRetrieval.scoreSoftmax_le_exp_neg_margin

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionRetrieval.

BookProof.ChapterAttentionRetrieval.scoreSoftmax_le_exp_neg_margin {beta delta : ℝ} (hb : 0 ≤ beta) (s : Fin m → ℝ) {j l : Fin m} (h : s l + delta ≤ s j) : scoreSoftmax beta s l ≤ Real.exp (-(beta * delta))

Formalization note: Lean 4 identifier BookProof.ChapterAttentionRetrieval.scoreSoftmax_le_exp_neg_margin.

Preamble
-- Generated from ChapterAttentionRetrieval.lean — theorem BookProof.ChapterAttentionRetrieval.scoreSoftmax_le_exp_neg_margin
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionRetrieval
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionRetrieval


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m n : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
Formal statement
theorem BookProof.ChapterAttentionRetrieval.scoreSoftmax_le_exp_neg_margin {beta delta : ℝ} (hb : 0 ≤ beta) (s : Fin m → ℝ)
    {j l : Fin m} (h : s l + delta ≤ s j) :
    scoreSoftmax beta s l ≤ Real.exp (-(beta * delta)) := by sorry

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