`BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_max_ge_inv_card` {beta : ℝ} (hb : 0 ≤ beta) (s : Fin m → ℝ) (j : Fin m) (hmax : ∀ l, s l ≤ s j) : 1 / (m : ℝ) ≤ scoreSoftm

Proved

BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_max_ge_inv_card

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_inv_card {beta : ℝ} (hb : 0 ≤ beta) (s : Fin m → ℝ) (j : Fin m) (hmax : ∀ l, s l ≤ s j) : 1 / (m : ℝ) ≤ scoreSoftmax beta s j

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

Preamble

-- Generated from ChapterSoftmaxTemperatureMonotone.lean — theorem BookProof.ChapterSoftmaxTemperatureMonotone.scoreSoftmax_max_ge_inv_card
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_inv_card {beta : ℝ} (hb : 0 ≤ beta) (s : Fin m → ℝ) (j : Fin m)
    (hmax : ∀ l, s l ≤ s j) : 1 / (m : ℝ) ≤ scoreSoftmax beta s j := by sorry

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