`BookProof.ChapterSoftmaxFluctuation.meanScore_monotone` (s : Fin m → ℝ) (i : Fin m) : Monotone fun b : ℝ => meanScore b s

Proved

BookProof.ChapterSoftmaxFluctuation.meanScore_monotone

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxFluctuation.

BookProof.ChapterSoftmaxFluctuation.meanScore_monotone (s : Fin m → ℝ) (i : Fin m) : Monotone fun b : ℝ => meanScore b s

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

Preamble

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxFluctuation.meanScore_monotone (s : Fin m → ℝ) (i : Fin m) :
    Monotone fun b : ℝ => meanScore b s := by sorry

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