`BookProof.ChapterSoftmaxFluctuation.partition_pos` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : 0 < partition beta s

Proved

BookProof.ChapterSoftmaxFluctuation.partition_pos

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxFluctuation.

BookProof.ChapterSoftmaxFluctuation.partition_pos (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : 0 < partition beta s

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxFluctuation.partition_pos.

Preamble

-- Generated from ChapterSoftmaxFluctuation.lean — theorem BookProof.ChapterSoftmaxFluctuation.partition_pos
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterSoftmaxFluctuation


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxFluctuation.partition_pos (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : 0 < partition beta s := by sorry

View graph