`BookProof.ChapterSoftmaxFluctuation.varScore_pos_of_ne` {beta : ℝ} {s : Fin m → ℝ} {a b : Fin m} (hab : s a ≠ s b) : 0 < varScore beta s

Proved

BookProof.ChapterSoftmaxFluctuation.varScore_pos_of_ne

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxFluctuation.

BookProof.ChapterSoftmaxFluctuation.varScore_pos_of_ne {beta : ℝ} {s : Fin m → ℝ} {a b : Fin m} (hab : s a ≠ s b) : 0 < varScore beta s

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

Preamble

-- Generated from ChapterSoftmaxFluctuation.lean — theorem BookProof.ChapterSoftmaxFluctuation.varScore_pos_of_ne
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.varScore_pos_of_ne {beta : ℝ} {s : Fin m → ℝ} {a b : Fin m} (hab : s a ≠ s b) :
    0 < varScore beta s := by sorry

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