Prove2Me

`BookProof.ChapterSoftmaxJacobian.softmaxJacobian_symm` (beta : ℝ) (s : Fin m → ℝ) (i j : Fin m) : softmaxJacobian beta s i j = softmaxJacobian beta s j i

Proved
BookProof.ChapterSoftmaxJacobian.softmaxJacobian_symm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxJacobian.

BookProof.ChapterSoftmaxJacobian.softmaxJacobian_symm (beta : ℝ) (s : Fin m → ℝ) (i j : Fin m) : softmaxJacobian beta s i j = softmaxJacobian beta s j i

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxJacobian.softmaxJacobian_symm.

Preamble
-- Generated from ChapterSoftmaxJacobian.lean — theorem BookProof.ChapterSoftmaxJacobian.softmaxJacobian_symm
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSoftmaxJacobian
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxJacobian


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}
Formal statement
theorem BookProof.ChapterSoftmaxJacobian.softmaxJacobian_symm (beta : ℝ) (s : Fin m → ℝ) (i j : Fin m) :
    softmaxJacobian beta s i j = softmaxJacobian beta s j i := by sorry

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