`BookProof.ChapterSoftmaxOrder.scoreSoftmax_lt_iff` {beta : ℝ} (hbeta : 0 < beta) (s : Fin m → ℝ) (i j : Fin m) : scoreSoftmax beta s i < scoreSoftmax beta s j ↔ s i < s j

Proved

BookProof.ChapterSoftmaxOrder.scoreSoftmax_lt_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxOrder.

BookProof.ChapterSoftmaxOrder.scoreSoftmax_lt_iff {beta : ℝ} (hbeta : 0 < beta) (s : Fin m → ℝ) (i j : Fin m) : scoreSoftmax beta s i < scoreSoftmax beta s j ↔ s i < s j

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxOrder.scoreSoftmax_lt_iff.

Preamble

-- Generated from ChapterSoftmaxOrder.lean — theorem BookProof.ChapterSoftmaxOrder.scoreSoftmax_lt_iff
import Definitions.Def_ChapterSoftmaxBorn
import Mathlib
import Definitions.Def_ChapterSoftmaxOrder
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxOrder


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxBorn BookProof.ChapterSoftmaxSharpness

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxOrder.scoreSoftmax_lt_iff {beta : ℝ} (hbeta : 0 < beta) (s : Fin m → ℝ) (i j : Fin m) :
    scoreSoftmax beta s i < scoreSoftmax beta s j ↔ s i < s j := by sorry

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