`BookProof.ChapterAttentionSparse.attendedMass_pos` (beta : ℝ) (s : Fin m → ℝ) {S : Finset (Fin m)} (hS : S.Nonempty) : 0 < attendedMass beta s S

Proved

BookProof.ChapterAttentionSparse.attendedMass_pos

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionSparse.

BookProof.ChapterAttentionSparse.attendedMass_pos (beta : ℝ) (s : Fin m → ℝ) {S : Finset (Fin m)} (hS : S.Nonempty) : 0 < attendedMass beta s S

Formalization note: Lean 4 identifier BookProof.ChapterAttentionSparse.attendedMass_pos.

Preamble

-- Generated from ChapterAttentionSparse.lean — theorem BookProof.ChapterAttentionSparse.attendedMass_pos
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionSparse
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterAttentionSparse


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

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

Formal statement

theorem BookProof.ChapterAttentionSparse.attendedMass_pos (beta : ℝ) (s : Fin m → ℝ) {S : Finset (Fin m)} (hS : S.Nonempty) :
    0 < attendedMass beta s S := by sorry

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