`BookProof.ChapterScaledDotProduct.scoreSoftmax_scaled` (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : scoreSoftmax beta (fun l => s l / Real.sqrt d) j = scoreSoftmax (beta / Real.sqrt d

Proved

BookProof.ChapterScaledDotProduct.scoreSoftmax_scaled

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScaledDotProduct.

BookProof.ChapterScaledDotProduct.scoreSoftmax_scaled (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : scoreSoftmax beta (fun l => s l / Real.sqrt d) j = scoreSoftmax (beta / Real.sqrt d) s j

Formalization note: Lean 4 identifier BookProof.ChapterScaledDotProduct.scoreSoftmax_scaled.

Preamble

-- Generated from ChapterScaledDotProduct.lean — theorem BookProof.ChapterScaledDotProduct.scoreSoftmax_scaled
import Mathlib
import Definitions.Def_ChapterScaledDotProduct
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterScaledDotProduct


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness

variable {d : ℕ}

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterScaledDotProduct.scoreSoftmax_scaled (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) :
    scoreSoftmax beta (fun l => s l / Real.sqrt d) j
      = scoreSoftmax (beta / Real.sqrt d) s j := by sorry

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