`BookProof.ChapterSoftmaxOrder.scoreSoftmax_const` (beta c : ℝ) (j : Fin m) : scoreSoftmax beta (fun _ => c) j = 1 / m

Proved

BookProof.ChapterSoftmaxOrder.scoreSoftmax_const

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxOrder.

BookProof.ChapterSoftmaxOrder.scoreSoftmax_const (beta c : ℝ) (j : Fin m) : scoreSoftmax beta (fun _ => c) j = 1 / m

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

Preamble

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxBorn BookProof.ChapterSoftmaxSharpness

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxOrder.scoreSoftmax_const (beta c : ℝ) (j : Fin m) :
    scoreSoftmax beta (fun _ => c) j = 1 / m := by sorry

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