`BookProof.ChapterAttentionSink.scoreSoftmax_sink_odds` (beta s0 : ℝ) (s : Fin m → ℝ) (i j : Fin m) : scoreSoftmax beta (Fin.cons s0 s) i.succ * scoreSoftmax beta s j = scoreSoftma

Proved

BookProof.ChapterAttentionSink.scoreSoftmax_sink_odds

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionSink.

BookProof.ChapterAttentionSink.scoreSoftmax_sink_odds (beta s0 : ℝ) (s : Fin m → ℝ) (i j : Fin m) : scoreSoftmax beta (Fin.cons s0 s) i.succ * scoreSoftmax beta s j = scoreSoftmax beta (Fin.cons s0 s) j.succ * scoreSoftmax beta s i

Formalization note: Lean 4 identifier BookProof.ChapterAttentionSink.scoreSoftmax_sink_odds.

Preamble

-- Generated from ChapterAttentionSink.lean — theorem BookProof.ChapterAttentionSink.scoreSoftmax_sink_odds
import Definitions.Def_ChapterObservableExpectation
import Mathlib
import Definitions.Def_ChapterAttentionSink
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionSink


open scoped BigOperators

noncomputable section


open BookProof.ChapterObservableExpectation BookProof.ChapterSoftmaxSharpness

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

Formal statement

theorem BookProof.ChapterAttentionSink.scoreSoftmax_sink_odds (beta s0 : ℝ) (s : Fin m → ℝ) (i j : Fin m) :
    scoreSoftmax beta (Fin.cons s0 s) i.succ * scoreSoftmax beta s j
      = scoreSoftmax beta (Fin.cons s0 s) j.succ * scoreSoftmax beta s i := by sorry

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