`BookProof.ChapterSoftmaxFluctuation.varScore_eq_sub_sq` (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : varScore beta s = (∑ l, scoreSoftmax beta s l * s l ^ 2) - meanScore beta s ^ 2

Proved

BookProof.ChapterSoftmaxFluctuation.varScore_eq_sub_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxFluctuation.

BookProof.ChapterSoftmaxFluctuation.varScore_eq_sub_sq (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) : varScore beta s = (∑ l, scoreSoftmax beta s l * s l ^ 2) - meanScore beta s ^ 2

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxFluctuation.varScore_eq_sub_sq.

Preamble

-- Generated from ChapterSoftmaxFluctuation.lean — theorem BookProof.ChapterSoftmaxFluctuation.varScore_eq_sub_sq
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSoftmaxFluctuation
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxFluctuation


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxFluctuation.varScore_eq_sub_sq (beta : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    varScore beta s = (∑ l, scoreSoftmax beta s l * s l ^ 2) - meanScore beta s ^ 2 := by sorry

View graph