`BookProof.ChapterAttentionLocality.mem_window` {d : Fin m → ℝ} {R : ℝ} {l : Fin m} : l ∈ window d R ↔ d l < R

Proved

BookProof.ChapterAttentionLocality.mem_window

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionLocality.

BookProof.ChapterAttentionLocality.mem_window {d : Fin m → ℝ} {R : ℝ} {l : Fin m} : l ∈ window d R ↔ d l < R

Formalization note: Lean 4 identifier BookProof.ChapterAttentionLocality.mem_window.

Preamble

-- Generated from ChapterAttentionLocality.lean — theorem BookProof.ChapterAttentionLocality.mem_window
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionLocality
open BookProof.ChapterAttentionLocality


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

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

Formal statement

theorem BookProof.ChapterAttentionLocality.mem_window {d : Fin m → ℝ} {R : ℝ} {l : Fin m} : l ∈ window d R ↔ d l < R := by sorry

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