`BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_max_ge_of_le` {beta gamma : ℝ} (hbg : beta ≤ gamma) (s : Fin m → ℝ) (j : Fin m) (hmax : ∀ l, s l ≤ s j) : scoreSoftmax bet

Proved

BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_max_ge_of_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxTemperatureMonotone.

BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_max_ge_of_le {beta gamma : ℝ} (hbg : beta ≤ gamma) (s : Fin m → ℝ) (j : Fin m) (hmax : ∀ l, s l ≤ s j) : scoreSoftmax beta s j ≤ scoreSoftmax gamma s j

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_max_ge_of_le.

Preamble

-- Generated from ChapterSoftmaxTemperatureMonotone.lean — theorem BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_max_ge_of_le
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSoftmaxTemperatureMonotone
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxTemperatureMonotone


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_max_ge_of_le {beta gamma : ℝ} (hbg : beta ≤ gamma) (s : Fin m → ℝ)
    (j : Fin m) (hmax : ∀ l, s l ≤ s j) :
    scoreSoftmax beta s j ≤ scoreSoftmax gamma s j := by sorry

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