Prove2Me

`BookProof.ChapterAttentionSink.sinkWeight_lt_one` (beta s0 : ℝ) (s : Fin m → ℝ) (i : Fin m) : sinkWeight beta s0 s < 1

Proved
BookProof.ChapterAttentionSink.sinkWeight_lt_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionSink.

BookProof.ChapterAttentionSink.sinkWeight_lt_one (beta s0 : ℝ) (s : Fin m → ℝ) (i : Fin m) : sinkWeight beta s0 s < 1

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

Preamble
-- Generated from ChapterAttentionSink.lean — theorem BookProof.ChapterAttentionSink.sinkWeight_lt_one
import Definitions.Def_ChapterObservableExpectation
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterAttentionSink
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.sinkWeight_lt_one (beta s0 : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    sinkWeight beta s0 s < 1 := by sorry

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