`BookProof.ChapterAttentionCollision.collisionProb_scoreSoftmax_pos` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : 0 < collisionProb (scoreSoftmax beta s)

Proved

BookProof.ChapterAttentionCollision.collisionProb_scoreSoftmax_pos

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionCollision.

BookProof.ChapterAttentionCollision.collisionProb_scoreSoftmax_pos (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : 0 < collisionProb (scoreSoftmax beta s)

Formalization note: Lean 4 identifier BookProof.ChapterAttentionCollision.collisionProb_scoreSoftmax_pos.

Preamble

-- Generated from ChapterAttentionCollision.lean — theorem BookProof.ChapterAttentionCollision.collisionProb_scoreSoftmax_pos
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionCollision
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionCollision


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionCollision.collisionProb_scoreSoftmax_pos (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    0 < collisionProb (scoreSoftmax beta s) := by sorry

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