`BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_const_of_const` {s : Fin m → ℝ} {c : ℝ} (hs : ∀ l, s l = c) (beta : ℝ) (j : Fin m) : scoreSoftmax beta s j = 1 / (m : ℝ)

Proved

BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_const_of_const

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxTemperatureMonotone.

BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_const_of_const {s : Fin m → ℝ} {c : ℝ} (hs : ∀ l, s l = c) (beta : ℝ) (j : Fin m) : scoreSoftmax beta s j = 1 / (m : ℝ)

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_const_of_const.

Preamble

-- Generated from ChapterSoftmaxTemperatureMonotone.lean — theorem BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_const_of_const
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSoftmaxTemperatureMonotone
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxTemperatureMonotone


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_const_of_const {s : Fin m → ℝ} {c : ℝ} (hs : ∀ l, s l = c)
    (beta : ℝ) (j : Fin m) : scoreSoftmax beta s j = 1 / (m : ℝ) := by sorry

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