Prove2Me

`BookProof.ChapterAttentionStreaming.sum_scoreSoftmax_snoc_castSucc` (beta sn : ℝ) (s : Fin m → ℝ) (i : Fin m) : ∑ j : Fin m, scoreSoftmax beta (Fin.snoc s sn) j.castSucc = 1 - new

Proved
BookProof.ChapterAttentionStreaming.sum_scoreSoftmax_snoc_castSucc

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionStreaming.

BookProof.ChapterAttentionStreaming.sum_scoreSoftmax_snoc_castSucc (beta sn : ℝ) (s : Fin m → ℝ) (i : Fin m) : ∑ j : Fin m, scoreSoftmax beta (Fin.snoc s sn) j.castSucc = 1 - newWeight beta sn s

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

Preamble
-- Generated from ChapterAttentionStreaming.lean — theorem BookProof.ChapterAttentionStreaming.sum_scoreSoftmax_snoc_castSucc
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.sum_scoreSoftmax_snoc_castSucc (beta sn : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    ∑ j : Fin m, scoreSoftmax beta (Fin.snoc s sn) j.castSucc = 1 - newWeight beta sn s := by sorry

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