`BookProof.ChapterAttentionStreaming.scoreSoftmax_snoc_odds` (beta sn : ℝ) (s : Fin m → ℝ) (i j : Fin m) : scoreSoftmax beta (Fin.snoc s sn) i.castSucc * scoreSoftmax beta s j = sc

Proved

BookProof.ChapterAttentionStreaming.scoreSoftmax_snoc_odds

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionStreaming.

BookProof.ChapterAttentionStreaming.scoreSoftmax_snoc_odds (beta sn : ℝ) (s : Fin m → ℝ) (i j : Fin m) : scoreSoftmax beta (Fin.snoc s sn) i.castSucc * scoreSoftmax beta s j = scoreSoftmax beta (Fin.snoc s sn) j.castSucc * scoreSoftmax beta s i

Formalization note: Lean 4 identifier BookProof.ChapterAttentionStreaming.scoreSoftmax_snoc_odds.

Preamble

-- Generated from ChapterAttentionStreaming.lean — theorem BookProof.ChapterAttentionStreaming.scoreSoftmax_snoc_odds
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionStreaming
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionStreaming


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

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

Formal statement

theorem BookProof.ChapterAttentionStreaming.scoreSoftmax_snoc_odds (beta sn : ℝ) (s : Fin m → ℝ) (i j : Fin m) :
    scoreSoftmax beta (Fin.snoc s sn) i.castSucc * scoreSoftmax beta s j
      = scoreSoftmax beta (Fin.snoc s sn) j.castSucc * scoreSoftmax beta s i := by sorry

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