`BookProof.ChapterAttentionResponse.abs_score_sub_meanScore_le` {s : Fin m → ℝ} {a b : ℝ} (ha : ∀ l, a ≤ s l) (hb : ∀ l, s l ≤ b) (beta : ℝ) (j : Fin m) : |s j - meanScore beta s|

Proved

BookProof.ChapterAttentionResponse.abs_score_sub_meanScore_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionResponse.

BookProof.ChapterAttentionResponse.abs_score_sub_meanScore_le {s : Fin m → ℝ} {a b : ℝ} (ha : ∀ l, a ≤ s l) (hb : ∀ l, s l ≤ b) (beta : ℝ) (j : Fin m) : |s j - meanScore beta s| ≤ b - a

Formalization note: Lean 4 identifier BookProof.ChapterAttentionResponse.abs_score_sub_meanScore_le.

Preamble

-- Generated from ChapterAttentionResponse.lean — theorem BookProof.ChapterAttentionResponse.abs_score_sub_meanScore_le
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionResponse
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionResponse


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder
open BookProof.ChapterSoftmaxFluctuation

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

Formal statement

theorem BookProof.ChapterAttentionResponse.abs_score_sub_meanScore_le {s : Fin m → ℝ} {a b : ℝ} (ha : ∀ l, a ≤ s l)
    (hb : ∀ l, s l ≤ b) (beta : ℝ) (j : Fin m) : |s j - meanScore beta s| ≤ b - a := by sorry

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