`BookProof.ChapterSoftmaxDivergence.klDiv_scoreSoftmax_self` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : klDiv (scoreSoftmax beta s) (scoreSoftmax beta s) = 0

Proved

BookProof.ChapterSoftmaxDivergence.klDiv_scoreSoftmax_self

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxDivergence.

BookProof.ChapterSoftmaxDivergence.klDiv_scoreSoftmax_self (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : klDiv (scoreSoftmax beta s) (scoreSoftmax beta s) = 0

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxDivergence.klDiv_scoreSoftmax_self.

Preamble

-- Generated from ChapterSoftmaxDivergence.lean — theorem BookProof.ChapterSoftmaxDivergence.klDiv_scoreSoftmax_self
import Definitions.Def_ChapterAttentionEntropy
import Mathlib
import Definitions.Def_ChapterSoftmaxDivergence
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxDivergence


open scoped BigOperators

noncomputable section


open BookProof.ChapterAttentionEntropy BookProof.ChapterSoftmaxSharpness

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxDivergence.klDiv_scoreSoftmax_self (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    klDiv (scoreSoftmax beta s) (scoreSoftmax beta s) = 0 := by sorry

View graph