Prove2Me

`BookProof.ChapterSoftmaxOrder.scoreSoftmax_denom_pos` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : 0 < ∑ l, Real.exp (beta * s l)

Proved
BookProof.ChapterSoftmaxOrder.scoreSoftmax_denom_pos

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxOrder.

BookProof.ChapterSoftmaxOrder.scoreSoftmax_denom_pos (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : 0 < ∑ l, Real.exp (beta * s l)

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxOrder.scoreSoftmax_denom_pos.

Preamble
-- Generated from ChapterSoftmaxOrder.lean — theorem BookProof.ChapterSoftmaxOrder.scoreSoftmax_denom_pos
import Definitions.Def_ChapterSoftmaxBorn
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterSoftmaxOrder
open BookProof.ChapterSoftmaxOrder


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxBorn BookProof.ChapterSoftmaxSharpness

variable {m : ℕ}
Formal statement
theorem BookProof.ChapterSoftmaxOrder.scoreSoftmax_denom_pos (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    0 < ∑ l, Real.exp (beta * s l) := by sorry

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